BIOLOGY J 1 - TEXT-BOOKS OF PHYSICAL CHEMISTRY EDITED BY SIR WILLIAM RAMSAY, K.C.B., F.R.S. STOICHIOMETRY TEXT-BOOKS OF PHYSICAL CHEMISTRY EDITED BY SIR WILLIAM RAMSAY, K.C.B., F.R.S. STOICHIOMETRY. By SYDNEY YOUNG, D.Sc., F.R.S., Professor of Chemistry in the University of Dublin. With 88 Figures in the Text. Together with an INTRODUCTION TO THE STUDY OF PHYSICAL CHEMISTRY by Sir WM. RAMSAY, K.C.B., F.R.S. Crown 8vo, 7*. 6rf. Also to be had separately. AN INTRODUCTION TO THE STUDY OF PHYSICAL CHEM- ISTRY. Being a General Introduction to the Series. By Sir WILLIAM RAMSAY, K.C.B., F.R.S. Crown 8vo, is. net. CHEMICAL STATICS AND DYNAMICS, including the Theories of Chemical Change, Catalysis, and Explosions. By J. W. MELLOR, D.Sc. (N.Z.), B.Sc. CVict.). Crown 8vo, 7*. f>d. THE PHASE RULE AND ITS APPLICATIONS. By ALEXANDER FINDLAY, M.A., Ph.D., D.Sc., Lecturer on Physical Chemistry, University of Birmingham. With 134 Figures in the Text. Crown 8vo, 5$. SPECTROSCOPY. By E. C. C. BALY, F.I.C., Lecturer on Spectroscopy, University College, London. With 16.3 Illustrations. Crown 8vo, IQS. 6d. THERMOCHEMISTRY. By JULIUS THOMSEN, Emeritus Professor of Chemistry in the University of Copenhagen. Translated by KATHARINE A. BURKE, B.Sc. (.Lond.), Assistant in the Department of Chemistry, University College, London. Crown 8vo, gs. ELECTROCHEMISTRY. Part I. General Theory. By R. A. LEHFELDT, D.Sc., Professor of Physics at the East London Technical College. Including a Chapter on the Relation of Chemical Constitution to Conductivity. By T. S. MOORE, B.A., B.Sc., Lecturer in the University of Birmingham. Crown 8vo, 5$. ELECTROCHEMISTRY. Part II. Applications to Electrolysis, Primary and Secondary Batteries, etc. By N. M. C. WILSMORE, M.A., D.Sc. [In preparation. STEREOCHEMISTRY. By A. W. STEWART, D.Sc. With 87 Illustrations. Crown 8vo, ior. 6d. RELATIONS BETWEEN CHEMICAL CONSTITU- TION AND PHYSICAL PROPERTIES. By SAMUEL SMILES. D.Sc. [In preparation. THERMODYNAMICS. By F. G. DONNAN, M.A., Ph.D. [In preparation. ACTINOCHEMISTRY. By C. E. K. MEES, D.Sc., and S. E. SHEPPARD, D.Sc. [in preparation. PRACTICAL SPECTROSCOPY, with Tables of Wave- Lengths. By J. H. POLLOK, D.Sc. [In preparation. LONGMANS, GREEN, AND CO. LONDON, NEW YORK, BOMBAY, AND CALCUTTA STOICHIOMETRY BY SYDNEY YOUNG, D.Sc., F.R.S. PROFESSOR OF CHEMISTRY IN THE UNIVERSITY OF DUBLIN WITH EIGHTY-EIGHT FIGURES IN THE TEXT TOGETHER WITH AN INTRODUCTION TO THE STUDY OF PHYSICAL CHEMISTRY BY SIR WILLIAM RAMSAY, K.C.B., F.R.S. Editor of the Series LONGMANS, GREEN, AND CO 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, AND CALCUTTA 1908 All rig Jits reserved BIOLOGY LIBRARY BIOLOGY PREFACE THE determination of the relative atomic weights, of hydrogen and oxygen is attended by great expeximehtar'dffficulties, and, in arriving at a final decision as to*' the value to be adopted, chemists have placed even greater reliance on physico-chemical investigations of the properties of the gases than on the purely chemical determination of the equivalent of oxygen. It was also in consequence of the determination of the specific gravities of nitrogen and oxygen by Lord Rayleigh and by Leduc that doubt was first felt as to the accuracy of the value found by Stas for the atomic weight of nitrogen, and it is chiefly owing to further investigations of the physical properties of these gases, and of other gaseous compounds of nitrogen, that the lower value has been definitely adopted. I have therefore thought it best, after describing the laws of chemical combination, to give a detailed account of the properties of gases before proceeding to a discussion of the methods of determining atomic weights. The importance of the generalizations of Van der Waals regarding corresponding temperatures, pressures, and volumes is now so fully recognized that no apology is, I think, neces- sary for the amount of space devoted to this subject, and to a description of the methods of determining the critical constants. It seems almost unnecessary to express my indebtedness V 167738 vi PREFACE to Ostwald's great " Lehrbuch der allgemeinen Chemie." I have also derived much valuable assistance from Nernst's " Theoretische Chemie," and from D. Berthelot's memoir " Sur les Thermometres a Gaz." The original papers to which reference is made in the footnotes have, in the great majority of cases, been consulted. S. YOUNG. TRINITY COLLEGE, DUBLIN, October, 1907. CONTENTS PAGE INTRODUCTION TO THE STUDY OF PHYSICAL CHEMISTRY, by Sir WILLIAM RAMSAY, K.C.B., F.R.S. xiii This Introduction was originally prefixed to Dr. Findlay s ''Phase Rule," which was the first volume of the Series issued. It belongs properly, however, to this volume, and is therefore included here. CHAPTER I. FUNDAMENTAL LAWS OF CHEMICAL COMBINATION .... i Elements and Compounds, i. The Conservation of Matter, i. Definition of an Element, 2. Law of Definite Proportions, 5. Law of Multiple Proportions, 5. Law of Equivalent Weights, 6. The Atomic Theory, 8. Ancient Atomic Hypotheses, 8. Dalton's Atomic Theory, 8. CHAPTER II. GENERAL PROPERTIES OF GASES n The Solid, Liquid, and Gaseous States of Matter, n. Boyle's Law, 12. Gay Lussac's Law, 13. Perfect Gases, 18. Deviations from Boyle's and Gay Lussac's Laws, 18. Behaviour of Gases under High Pressures, 18; under very Low Pressures, 28, Coefficients of Expansion and of Pressure, 35. CHAPTER III. PROPERTIES OF GASES (continued] 40 The Densities of Gases and Vapours, 40. Gay Lussac's Law of Volumes, 46. Avogadro's Hypothesis, 47. Molecular Weights, 48. Value of R for Perfect Gases, 50. Specific Heats of Gases, 5 1 . Ratio of the Two Specific Heats, 54. viii CONTENTS CHAPTER IV. PAGE DETERMINATION OF ATOMIC WEIGHTS 56 Relation between Atomic Weight and Equivalent, or Quantivalence, 56. Law of Dulong and Petit, 65. Mitscherlich's Law of Isomorphism, 65. CHAPTER V. ACCURATE DETERMINATION OF ATOMIC WEIGHTS .... 68 Experimental Errors, 68. Oxygen and Hydrogen, 70. Silver, 79. Chlorine, 83. Bromine and Iodine, 84. Potassium, 84. Sulphur, 84. Sodium and Lithium, 85. Nitrogen, 85. General Remarks, 86. CHAPTER VI. THE PERIODIC LAW 91 Physical Properties of the Elements Atomic Volumes, 91. Electro-chemical Character, 97. Other Physical Properties, 100. Valency, 100. Utility of the Periodic Table, 112. CHAPTER VII. THE DISSOCIATION OF GASES AND VAPOURS 114 Deville's Experiments, 114. Abnormal Vapour Densities, 115. Ammonium Chloride, 115. Phosphorus Pentachloride, 117. Hydrogen Iodide, 118. Iodine, 119. Nitrogen Peroxide and Acetic Acid, 120. CHAPTER VIII. THE PROPERTIES OF LIQUIDS 122 Liquefaction, 122. Vapour Pressure, 124. Boiling Point, 136. Surface Tension, 144. Heat of Vaporization, 146. Correction of Boiling Point to Normal Pressure, 157. CHAPTER IX. THE PROPERTIES OF LIQUIDS (continued} 159 The Densities and Specific Volumes of Liquids, 159 ; of Saturated Vapours, 164. Law of Cailletet and Mathias, 165. The Critical Point, 170. The Critical Temperature, 170; Pressure, 177; Volume, 178. Relation between Critical Temperature and Boiling Point, 181. Thorpe and Rlicker's Relation, 183. CONTENTS ix CHAPTER X. PAGE THE KINETIC THEORY OF GASES l %$ Historical, 185. Boyle's Law, 186. Avogadro's Hypothesis, 187. Ratio of Specific Heats, 188. Mean Free Path, 189. Dissociation of Gases, 190. Calculation of Percentage Number of Molecules dissociated, 193. CHAPTER XL THE KINETIC THEORY OF GASES (continued) 199 GASES UNDER HIGH PRESSURES: Theory of Van der Waals, 199. Equation of State, 201 ; for Constant Volume, 203. Theoretical Pressure-volume Diagram, 204. Isochors, 208. Calculation of Critical Constants, 213. The Reduced Equation of State, 215. The Generalizations of Van der Waals regarding corresponding Temperatures, Pressures, and Volumes, 216. Deductions from the Generalizations, 223. Graphical Representation of the Generalizations, 225. Characteristic States of Matter, 229. Modifications of the Generalizations, 236. CHAPTER XII. PROPERTIES OF SOLIDS 239 General Properties, 239. Melting Point, 239. Vapour Pressure, 242. Triple Point, 242. Volatilizing Point, 243. Crystalline Form, 245. Specific Heat and Atomic Heat, 247. CHAPTER XIII. MIXTURES 251 MIXED GASES : Diffusion, 25 1 . Dalton's Law of Partial Pressures, 253. Leduc's Modification, 253. MIXED LIQUIDS : Molecular Attractions, 255. Density and Specific Volume, 256. Specific Heat, 257. Specific Refractive Power, 258. VAPORIZATION OF MIXED LIQUIDS : Non-miscible Liquids Vapour Pressures, 260. Boiling Points, 260. Composition of Vapour, 261. In- finitely Miscible and Closely Related Liquids Vapour Pressures, 262. Boiling Points, 263. Composition of Liquid and Vapour Phases, 266. Infinitely Miscible Liquids not closely related Vapour Pressures, 268. Boiling Points, 271. Composition of Liquid and Vapour Phases, 274. Distillation of Mixtures, 277. Critical Constants of Mixed Liquids, 282. Relation between Composition and Critical Temperature or Critical Pressure, 289. x CONTENTS CHAPTER XIV. PAGE SOLUBILITY AND MISCIBILITY 292 Solubility of Gases in Liquids, 292. Miscibility of Liquids and Critical Solution Point, 293. Solubility of Solids in Liquids, 296. Solidification of Liquid Mixtures, 298. Absorption of Gases by Solids, 302. CHAPTER XV. PROPERTIES OF DILUTE SOLUTIONS 304 Freezing Points, 304. Vapour Pressures, 306. Boiling Points, 310. Diffusion of Liquids and Osmosis, 313. Osmotic Pressure, 316. Laws of Osmotic Pressure, 320. CHAPTER XVI. DISSOLUTION AND VAPORIZATION 328 Comparison of Osmotic Pressure and Vapour Pressure, 328. Specific Solution Volume and Critical Solution Temperature, 329. Application of Law of Cailletet and Mathias, 334. CHAPTER XVII. THE DETERMINATION OF MOLECULAR WEIGHTS 337 From Chemical Considerations, 337. Molecular Weights of Gases and Vapours, 339 ; of Liquids, 346. Calculation of Molecular Weight from Density of Liquid and Critical Temperature and Pressure, 351. The Gaseous and Liquid States of Matter, 352. Molecular Association, 355. Molecular Weights of Dissolved Substances : from Osmotic Pressure, 359 ; from Depression of Freezing Point, 360 ; from Lowering of Vapour Pressure, 360 ; from Rise of Boiling Point, 361 ; from Diminution in Solubility, 361. Dissociation, Molecular Association, and Electrolytic Dis- sociation, 361. Theory of Electrolytic Dissociation, 363. NAME INDEX 371 SUBJECT INDEX 37 SYMBOLS observed or real pressure of gas or vapour. osmotic pressure, calculated pressure (for perfect gas), critical pressure, reduced pressure. Centigrade temperature, absolute temperature. . critical temperature (Centigrade or absolute).- reduced (absolute) temperature. observed volume (z/ L = volume of liquid, v\ of vapour), volume of a gram (specific volume), molecular volume = M X v. critical volume, reduced volume. s = observed density or specific gravity = - S = calculated ,, ,, ,, (for perfect gas) d observed vapour density (density of O 2 = 16 at same tempera- ture and pressure). D = calculated vapour density = m = mass or weight (in grams). M = mass or weight (in gram-molecules = ) M - molecular weight. L = heat of vaporization. L' = heat effusion. L" heat of volatilization (of solid). H = specific heat. e = increase of internal energy per unit rise of temperature E = molecular rise of boiling point. E' = molecular depression of freezing point. UNIVERSITY Of INTRODUCTION TO THE STUDY OF PHYSICAL CHEMISTRY BY SIR WILLIAM RAMSAY, K.C.B., F.R.S. To define exactly the provinces of the Sciences of Physics and Chemistry is not easy. The definition that the object of Chemistry is the study of the changes which matter undergoes during the formation and decomposition of compounds, while that of Physics has reference to changes which affect matter independently of its composition, hardly meets the case. It is true that it is possible to deduce certain laws relating to the properties of matter, which are valid irrespective of the chemical composition of the matter ; but such laws deal with the beha- viour of matter in motion, or acted on by gravitational or other forces -which apply only to matter in bulk. For example, Newton's law of " gravitation " that two masses approach each other as if impelled by a force which varies directly as their masses, and inversely as the square of the distance which separates them takes no cognizance of the nature of the matter which attracts : the law is not affected by the chemical composition of the acting bodies. Similarly, the laws dealing with inertia are true, whatever the nature of the matter to which these laws apply. But when phenomena relating to change of volume by pressure, to the surface phenomena of liquids, to electricity, to heat, light, and other forms of wave-motion, are considered, the laws deduced from them contain specific xiv INTRODUCTION TO THE constants, so that their numerical application can be made only when these specific constants are known. Thus although the same differential equation governs the flow of heat in all kinds of matter, it contains a specific constant, viz. the " con- ductivity ; " and as this varies for different kinds of matter, the chemical nature of the substance becomes a factor in the problem. The birth of physical chemistry may be said to date from the recognition of this fundamental idea ; where the laws or generalizations regarding properties of matter depend not merely on the masses or rates of motion of the objects con- sidered, but also on their composition and chemical nature, their consideration falls under the heading " Physical Chemistry." It was not until the middle of the nineteenth century that this began to be recognized ; although many facts had been discovered, and many laws deduced before that date, physical chemistry was not differentiated from physics, on the one hand, and chemistry on the other, until the dependence of certain physical phenomena on the chemical composition of the objects under consideration had become obvious. The attempts of the ancients to interpret the facts around them led to little of value. For long mankind was contented to observe certain phenomena, and to utilize them for industrial purposes, if they were found suitable. Yet in all ages " philo- sophers," or lovers of wisdom, as they liked to call themselves, have endeavoured to " explain " certain observed facts. This word " explain " is frequently used without any very definite view of its signification. It may be defined as "to state the unknown in terms of the known," and this process was facili- tated by grouping observed facts into similars and dissimilars. The " properties of matter," for example, were " explained " by the Greeks and their predecessors by the theory that all matter partook of the nature of fire, air, earth, and water the so-called " elements " in greater or less proportion. But this STUDY OF PHYSICAL CHEMISTRY xv hypothesis, which, so long as only the solidity, fluidity or gaseous nature of matter was in question, appeared reasonable, failed to throw light on the changes which matter undergoes during combustion. And in the seventeenth century, Boyle, in his Sceptical Chymist^ pointed out that it was impossible to explain the existence of the numerous chemical substances known in his day, or the transformations which they may be made to undergo, by this ancient hypothesis. The word " element " was otherwise defined by Boyle as the constituent of a compound body; and he denied that the properties of matter could be modified by assimilating the qualities of fire, air, earth, and water. In the light of this revolution of thought it became of importance to determine which of the numerous forms of matter were to be regarded as elementary and which as com- pound, or composed of two or more elements in a state of combination ; and also to produce such compounds by causing the appropriate elements to combine with each other. The progress of science was, however, retarded by the existence of certain preconceived notions, which had first to be disproved before advance was possible. The first of these was the failure to recognize the material nature of air, and to differ- entiate between one gas and another. Although Boyle himself discovered the most important law, which goes by his name, and which deals with the compressibility of air, and although the fact that air possesses weight had been foreshadowed by Jean Rey, physician to the court of France, and by Torricelli, the inventor of the barometer, it was not until experiments were made by Black, in 1752, on carbonic acid that it was distinctly recognized that gases may differ in kind, and that each possesses its own particular density. The investigations of Scheele, ' Priestley, and Cavendish in the succeeding years showed that many kinds of gas exist; and in the following century Faraday, by liquefying ammonia, chlorine, and other b xvi INTRODUCTION TO THE gases, proved that a gas is merely a vapour at a high tem- perature; and Andrews, by his investigation on the critical temperature of carbon dioxide, showed that above that tempe- rature that gas cannot be liquefied by compression alone. Towards the end of the nineteenth century, Pictet and Cailletet succeeded in liquefying oxygen ; Wroblewski, Olszewski, Kam- merlingh Onnes, and Dewar prepared liquid oxygen and air on a fairly large scale ; and the more recently invented machines of Hampson and Linde have much facilitated the process of liquefaction. Olszewski was the first to liquefy hydrogen in minute quantity; and on a larger scale, Dewar and, later, Travers have succeeded in preparing liquid hydrogen in bulk. The only gas which has as yet resisted liquefaction is helium. The second fallacy was an inverted notion of the pheno- mena of combustion. It had long been held, probably since the eighth century, that the property of burning which many substances possess was due to the sulphur which it was supposed that they contained. At that date, what were later called " hypostatical (or underlying) principles " were added to the four elements, as capable of modifying the nature of matter. These were : salt, which conferred fixity in the fire ; mercury, which conferred volatility and metallic lustre ; and sulphur, which carried with it combustibility. This idea was somewhat modified by Becher, who conceived all combustible matter to contain a terra pinguis^ or fatty earth. His pupil, Stahl, having observed that it was possible to confer combusti- bility on many substances which had lost that power on having been burned, by calcining them in absence of air with bodies such as charcoal, wood, coal, flour, etc., which themselves possessed the property of burning, extended, about the year 1690, the use of the idea of "sulphur," or terra pinguis, and at the same time changed its name to " phlogiston." We see here the conception of the substantial nature of flame, which will be alluded to later on. This phlogiston was not merely a STUDY OF PHYSICAL CHEMISTRY xvii principle which was lost during combustion ; it was at the same time possible to transfer it from a body rich in it to one containing little or none. From this point of view, metals were regarded as substances rich in phlogiston ; when they were calcined in the air, the remaining " calces " were looked upon as metals from which phlogiston had escaped, but by heating such " calces " with charcoal or other substances rich in phlogiston, that principle was transferred to the " calces," and metals were reproduced. The metals were therefore con- sidered to be compounds of their calces with phlogiston. Other substances, such as phosphorus or sulphur, when burned, gave acid liquids, to which it was not so easy to add phlogiston ; but even they could be phlogisticated ; and sulphur and phos- phorus were regarded as compounds of sulphuric and phosphoric acids with phlogiston. The discovery of oxygen in 1774 by Priestley and by Scheele, and the explanation of its functions by Lavoisier during the ten following years, revolutionized the method of regarding combustion. It was then recognized that combustion is union with oxygen ; that an earth, or " calx," is a compound of a metal with oxygen ; that when a metal becomes tarnished and converted into an earthy powder, it is being oxidized; that the resulting oxide, when heated to redness out of contact with air with charcoal or carbon, or with compounds such as coal, flour, and wood, of which carbon is a constituent, gives up its oxygen to the carbon, forming an oxide of carbon, carbonic oxide, on the one hand, or carbonic " acid-" on the other, while the metal is reproduced in its "reguline" or metallic condition; and that the true elements are metals, carbon, phosphorus, sulphur, and similar bodies, and not the products of their oxidation. The third mistaken notion was the material nature of heat. The fact that flames were actually seen issuing from burning bodies early led to the view that they were material objects ; xviii INTRODUCTION TO THE and fire was therefore regarded as one of the "elements;' Even after the overthrow of the ancient notions of combustion, it was believed that, although devoid of weight, heat was a substance. The earlier treatises often began with " the three imponderables " heat, light, and electricity. Under the name of " caloric " this view was long held regarding heat. Towards the end of the eighteenth century Count Rumford had noticed, at Munich, that an apparently inexhaustible supply of heat could be generated by the boring of cannon, and that if bored under water the rise of temperature was such that the water could be kept in a state of ebullition. He argued, therefore, that the heat was not previously in combination with the iron of the cannon, or of the drill, but that it was produced by friction. At a later date Davy succeeded in melting two pieces of ice by rubbing them together. That bodies possess a certain capacity for, or power of holding, heat was discovered by Leslie and Black, who investi- gated the specific heats of many different substances. Black also made experiments on the quantity of heat absorbed by different substances when they melt or evaporate, and intro- duced the conception of "latent" heat, i.e. heat which is possessed by a body, but which is insensible to a thermometer. The first table of capacities for heat was published by Kirwan in 1780 : though Crawford had published the result of attempts to determine the specific heats of gases in 1779. In 1 80 1 Dalton published in the memoirs of the Man- chester Literary and Philosophical Society r , 5, p. 515, an account of experiments which proved that while the compression of gases was attended by an evolution of heat, their expansion rendered them colder; and Leslie attempted to introduce quantitative measurement. In 1807 Gay-Lussac applied the temperature changes resulting from the compression of gases to the measurement of their specific heats; and in 1816 Laplace had differentiated between the specific heat of a gas STUDY OF PHYSICAL CHEMISTRY xbc at constant volume and under constant pressure, and had applied his results to Newton's equation relating to the velocity of sound. The explanation was first given, however, by Julius Robert Mayer. While former investigators held the idea that the phenomena were to be explained by the view that on compressing a gas caloric escaped, as water does when a sponge is squeezed, and on allowing it to expand the heat enters and again fills the pores of the gaseous matter, Mayer regarded the heat produced as the equivalent of the work expended on the gas. From the known alteration of temperature which a gas undergoes on expanding and the resulting heat which it absorbs on the one hand, and from the work which the gas can do during expansion on the other, he attempted to calculate the equivalence of heat and work. Almost at the same Bate J. P. Joule made quantitative experiments, in which he measured the rise of temperature of a known weight of water when it was set in violent agitation by a stirring apparatus driven by a descending weight. The doctrine of the existence of heat as a subtle form of matter thus gradually became extinct ; and heat is now regarded when it is asso- ciated with matter as a state of motion of the particles of matter, atomic or molecular ; and when " radiant " i.e. during the condition of transit from one body to another (in which state the name "heat" is perhaps inapplicable) as a state of strain in an imaginary medium, the ether, the strain being passed from place to place in the form of waves. It was not until these misconceptions the immaterial nature of gases, the inverted notion of combustion, and the material nature of heat had been removed, that progress in physical chemistry became possible. But even with their removal the way was not clear, for it was necessary that a working hypothesis regarding the nature of matter should first have been formed. This was primarily due to John Dalton, a Manchester schoolmaster. xx INTRODUCTION TO THE It had been noticed by Wenzel, by Richter, by Wollaston, and by Cavendish towards the close of the eighteenth century that the same compounds contain the same constituents in the same proportions, or, as it is expressed, "possess constant composition." Wollaston, indeed, had added to this the further fact that when the vegetable acid, oxalic acid, is combined with potash it forms two compounds, in one of which the acid is contained in twice as great amount relatively to the potash as in the other. The names monoxalate and binoxalate of potash were applied to these compounds to indicate the respective proportions of the ingredients. Dalton conceived the happy idea that by applying the ancient Greek conception of atoms to such facts, the relative weights of the atoms could be determined. Illustrating his views with the two compounds of carbon and hydrogen, marsh gas, and olefiant gas, and with the two oxides of carbon, carbonic oxide and carbonic " acid," he regarded the former as a compound of one atom of carbon and two of hydrogen, and the latter as a compound of one atom of carbon and one of hydrogen, and similarly for the two oxides of carbon. Knowing the relative weights in which these elements enter into combination, he deduced what he supposed were the relative weights of the atoms. Dalton's work was first expounded by Thomas Thomson, Professor at Glasgow, in his System of Chemistry, published in 1805, and subsequently in Dalton's own System of Chemical Philosophy, the three volumes of which were published in 1808, in 1810, and in 1827. The determination of these "constants of Nature," the atomic weights, was at once followed out by many chemists, Thomson among the first. Chief among the chemists who pursued this branch of work was Jacob Berzelius, a Swede, who devoted his long life (1779-1848) to the preparation of compounds, and to the determination of their composition, or, as it is still termed, the determination of the " atomic weights " STUDY OF PHYSICAL CHEMISTRY xxi more correctly equivalents of the elements of which they are composed. It is to him that we owe most of our analytical methods, for prior to his time there were few, if any, accurate analyses. Although Lavoisier had devised a method for the analysis of compounds of carbon, viz. by burning the organic compounds in an atmosphere of oxygen contained in a bell-jar over mercury, and measuring the volume of carbon dioxide produced, as well as that of the residual oxygen, Berzelius achieved the same result more exactly and more expeditiously by heating the substance, mixed with potassium chlorate and sodium chloride, and thus estimating the hydrogen as well as the carbon. This process was perfected by Liebig. Berzelius, however, was able to show that compounds of carbon, like those of other elements, are instances of combination in constant and multiple proportions. In 1815 two papers were published in the Annals of Philosophy by Dr. Prout, which have had much influence on the progress of chemistry. They dealt with the figures which were being obtained by Thomson, Berzelius, and others, at that time supposed to represent the " atomic weights " of the elements. Prout's hypothesis, based on only a few numbers, was that the atomic weights were multiples of that of hydrogen, taken as unity. There was much discussion regarding this assertion at the time, but as it was contradicted by Berzelius's numbers, the balance of opinion was against it. But about the year 1840 Dumas discovered an error in the number (12*12) liven by Berzelius as the atomic weight of carbon ; and with his collaborator, Stas, he undertook the redetermination of the atomic weights of the commoner elements for example, carbon, oxygen, chlorine, and calcium. This line of research was subsequently pursued alone by Stas, whose name will always be remembered for the precision and accuracy of his experiments. At first Stas inclined to the view that Prout's hypothesis was a just one ; but it was completely disproved by xx ii INTRODUCTION TO THE his own subsequent work, as well as by that of numerous other observers. It is, nevertheless, curious that a much larger proportion of the atomic weights approximate to whole numbers than would be foretold by the doctrine of chances ; and perhaps the last has not been heard of Prout's hypothesis, although in its original crude form it is no longer _ worthy of credence. To Dalton th2 smallest portions of matter, whether consist- ing of single atoms, as that of oxygen, O, or of compounds, such as water, to which he ascribed the composition HO, were alike regarded as atoms. This view, however, conflicted with experimental data arrived at by Gay-Lussac in the year 1808. In conjunction with Humboldt, Gay-Lussac had redis- covered about three years before what had previously been established by Cavendish, namely, that, as nearly as possible, two volumes of hydrogen combine with one volume of oxygen to form water, the gases having been measured at the same temperature and pressure. Humboldt suggested to Gay-Lussac that it would be well to investigate whether similar simple relations obtain between the volumes of other gaseous sub- stances when they combine with each other. This turned out to be the case ; it appeared that almost exactly two volumes of carbonic oxide combine with one volume of oxygen to form two volumes of carbonic acid gas ; that equal volumes of hydrogen and chlorine unite to form hydrochloric acid gas; that two volumes of ammonia consist of one volume of nitrogen in union with three volumes of hydrogen, and so on. From such facts Gay-Lussac was led to make the statement that the weights of equal volumes of gases, whether simple or compound, and therefore their densities, are proportional to their empirically found combining or atomic weights, or to rational multiples of the latter. Gay-Lussac regarded this discovery of his to be a support for the atomic theory, but it did not accord with many of the then received atomic weights. STUDY OF PHYSICAL CHEMISTRY xxiii The assumption that equal volumes of gases contain equal numbers of particles, or, as they were termed by him, molecules integranteS) was made in 1811 by Avogadro, Professor of Physics at Turin. This theory, which has proved of the utmost im- portance to the sciences of both chemistry and physics, had no doubt occurred to Gay-Lussac, but had been rejected by him for the following reasons : A certain volume of hydrogen, say i cubic centimeter, may be supposed to contain the same number of particles (atoms) as an equal volume of chlorine. Now, these two gases unite in equal volumes. The deduction appears so far quite legitimate that i atom of hydrogen has combined with i atom of chlorine. But the resulting gas occupies 2 cubic centimeters, and must therefore contain the same number of particles of hydrogen chloride, the compound of the two elements, as i cubic centimeter originally contained of hydrogen or of chlorine. Thus we have 2 cubic centimeters containing, of uncombined gases, twice as many particles as is contained in that volume after combination. Avogadro's hypothesis solved the difficulty. By premising two different orders of particles, now termed atoms and molecules, the solu- tion was plain. According to him, each particle, or molecule, of hydrogen is a complex ; it contains 2 atoms ; the same is the case with chlorine. When these gases combine, or rather react, to form hydrogen chloride, the phenomenon is one of a change of partners ; the molecule, the double atom, of hydrogen splits ; the same is the case with the molecule of chlorine ; and each liberated atom of hydrogen unites with one of chlorine, forming a compound, hydrogen chloride, which equally consists of a molecule, or double atom. Thus 2 cubic centimeters of hydrogen chloride consist of a definite number of molecules, equal in number to those contained in i cubic centimeter of hydrogen plus those contained in i cubic centimeter of chlorine. The case is precisely similar if other gaseous compounds be considered. xxiv INTRODUCTION TO THE Berzelius was at first inclined to accept the theory, and indeed went so far as to change many of his atomic weights to make them fit it. But later he somewhat withdrew from his position, for it appeared to him hazardous to extend to liquids and solids a theory which could be held only of gases. Avo- gadro's suggestion accordingly rested in abeyance until 1858, when Cannizzaro, Professor of Chemistry in Rome, published an essay in which all the arguments in favour of the hypothesis were collected and stated in a masterly manner. Although as early as 1811 a distinction had been drawn between the two classes of particles, atoms, or single particles of elements, and molecules, or congeries of atoms, which may either be of one kind, in which case the molecule is one of an element, or of different kinds, in which case the molecule is one of a compound, yet, as we have seen, the theory was not accepted by chemists and physicists until after 1858. Inasmuch as physical chemistry rests on the molecular hypothesis of matter, researches before that date referred merely to the physical properties of matter, and just conclu- sions could not be drawn from them. It is necessary, in many very important researches, to pay attention to data considered with reference to equal numbers of molecules, instead of to equal masses of substance ; and relations really simple remained undiscovered until the molecular hypothesis was generally adopted. Yet many interesting observations were made before the middle of the eighteenth century, of great value in themselves, although their true bearing was not evident until the molecular hypothesis of matter had been established. For example, Boyle's law (1662) relating to the compressi- bility of air was found to apply with more or less accuracy to the compressibility of other gases ; and Gay-Lussac's or Dalton's law (1808) dealing with the expansion of gases with tempera- ture, also holds approximately for all gases. The progress of STUDY OF PHYSICAL CHEMISTRY xxv science, however, has always been characterized by the dis- covery of approximate relations ; the divergence from exactness has generally at first been attributed to the imperfection of the observations ; and with improvements in apparatus, and with introduction of extreme conditions, these " laws " have always been discovered to be only approximately applicable ; to render them more in accordance with fact, modifications have had to be introduced which lessen the deviations ; but all that can be said of any so-called " laws " is that at the best they represent the results of measurement as accurately as the methods of experiment allow. It is seldom the case that the causes of divergence can be fully discovered. Yet in some instances it is possible to surmise that the cause is known, even although the phenomena are too complicated to be solved numerically. The moon pursues an approximately elliptical course round the earth, due to her own proper motion and to the attraction of the earth j yet the path is influenced by the attraction of the sun, and in a lesser degree by that of the planets, and in a still smaller by that of the fixed stars. Owing to the number and complexity of these various attractions, it is impossible to do more than approxi- mate numerically to the actual path of the moon's orbit; yet as many of these attractions are almost inconceivably minute, their effect may be disregarded. In such an instance the law of attraction is a simple one ; but with molecules, instead of masses, the laws of attraction have still to be discovered. Applying this conception to Boyle's and Gay-Lussac's laws, it was soon discovered that they held only with approximation ; and in 1829 Dulong and Arago, and later Pouillet, Regnault, and Natterer, investigated the variation of the product of pressure and volume, which, according to Boyle's law, should remain constant so long as temperature is stationary. . The investigation from a practical point of view was continued by Amagat, Mathias, Ramsay and Young, and others ; and from xxvi INTRODUCTION TO THE the theoretical side by van der Waals, Clausius, and many others. It is clear that Boyle's law can be valid only under one of two suppositions either that the molecules of a gas themselves occupy no space, or that the molecules themselves are equally compressible with the gas. The last supposition has not re- commended itself; it has been generally assumed that mole- cules are analogous to solid spheres, or solid particles of some definite form ; and that as a great increase of pressure causes only a small decrease in the volume of a solid, so a " solid " molecule must be regarded as practically incompressible. That the compressibility of a gas must necessarily be less than that calculable from Boyle's law was predicted by Daniel Bernoulli (1738) ; but he did not recognize that another influence may be at work, tending to reduce the distance between the molecules, namely, their mutual attraction. The two conceptions were first introduced by van der Waals. But the simple formula devised by him does not accurately represent facts, and we are still ignorant of even approximately exact laws relating to the compressibility of gases, and their expansion on rise of tem- perature. But certain gases, on rise of temperature, did not show even the approximate regularity in expansion demanded by Gay-Lussac's law. Bineau, who had determined the density of many vapours at relatively high temperatures, discovered that ammonium chloride, cyanide, hydrosulphide and carbonate as well as phosphoric chloride, and chloride and bromide of phosphonium possessed a vapour density only half as great as that implied by their formulae. The explanation was given by Cannizzaro, Kopp, and Kekule. They pointed out that these substances decompose when heated into simpler constituents ammonium chloride, for example, into ammonia and hydrogen chloride and that, on cooling, the original substance is re- produced. To this decomposition Deville gave the name STUDY OF PHYSICAL CHEMISTRY xxvii "dissociation." Wiirtz, in 1865, traced the gradual dissociation and re-formation of amylene hydrobromide, and other instances followed ; from that date the justice of the theory of reversible decomposition by heat, or dissociation, of certain substances was established. It was for long believed that molecules exercise a repulsive action on one another, and tend to part company on account of this repelling force. And it was known that if forces of any kind suffer displacement in the direction of their action without external work being done, heat is evolved. It would follow, therefore, that if a gas were to expand without doing work, its temperature should rise. Joule and Thomson (Lord Kelvin) showed, however, that on free expansion, most gases, instead of rising in temperature, undergo a small decrease. Hence there must be a small attractive, and not a large repulsive force between their particles. Waterston, in 1845, attributed the pressure of a gas to the impacts of its molecules on the walls of the containing vessel, and on the manometer ; while the temperature of the gas was conditioned by the rate of the motion of its particles. His work, however, remained unnoticed until attention was directed to it by Lord Rayleigh ; and Kronig in 1856, and Clausius in 1857, following Joule in 1851, deduced from these hypo- theses the "kinetic theory of gases," by means of which, considering molecules as hard, smooth, elastic spheres, a mechanical explanation of Boyle's and Gay-Lussac's laws and of Avogadro's hypothesis was given. By introducing numerical data for pressure and volume, the actual average velocity of a molecule of any gas could be calculated ; and the measure- ments of Thomas Graham, published in 1833, of the rate of passage of gases through porous septa, and through narrow openings, were shown to approximate closely to numbers cal- culated on the basis of the relative average velocities of the molecules of different gases. It was also possible to calculate xxviii INTRODUCTION TO THE the " free path," or average distance which a molecule traverses before collisions with other molecules ; and also from measure- ments of the friction of gases in passing through capillary tubes, the relative diameters of the gaseous molecules, and consequently their volumes. The attraction between the molecules of any gas decreases rapidly with rise of temperature ; and with hydrogen gas, the boiling-point of which is about 20-5 absolute, or 252-5 C., there is no sensible attraction at ordinary temperatures. Hence deviations from Boyle's law, in this case, by increase of pressure, are ascribable solely to the space occupied by the molecules relatively to that which they inhabit. It is therefore easy to calculate the actual volume of the " solid " molecules in any given volume of hydrogen gas ; it appears to be somewhat less than yoW tn P art f tne space inhabited by hydrogen mole- cules at ordinary temperature and pressure. Knowing this, the actual diameter of a hydrogen molecule may be estimated as about i '6 X io" 8 centimeter; or, otherwise expressed, there are present in i cubic centimeter of hydrogen 5 X io 19 mole- cules ; or, again, the thousandth part of that volume, or i cubic millimeter of hydrogen gas contains about 50,000 million million molecules. The corresponding numbers for other gases can be calculated similarly from their relative diameters. It has already been mentioned that Julius Mayer and Joule regarded heat as a form of energy (a word introduced by Rankine), and that Joule measured the equivalence between heat and work ; and also that Clausius attributed the heat con- tained in gases, at least, to the state of motion of their mole- cules. The " First " and the " Second Law of Thermodynamics " stand in close connection with these conceptions. The first law is that as heat and work are numerically interchange- able, and are both forms of energy, energy is indestructible and uncreateable. A loss of energy is only apparent ; it is not really lost, but only appears in another form. The second is that STUDY OF PHYSICAL CHEMISTRY xxix heat cannot of its own accord pass from a colder to a warmer body ; or in Thomson's (Lord Kelvin's) words : It is impossible by means of any lifeless material contrivance to pro diice mechanical action from a given mass of matter by cooling it below the tempe- rature of the coldest surrounding objects. Still another method of expressing the same truth is A thermodynamic perpetual motion is impossible ; the perpetual motion being derived from a machine in which there is, it is true, neither creation nor destruction of energy, but a cyclical production of useful external work at the expense of a heat reservoir of constant temperature, or other source of " equilibrated " energy. These two laws have been productive of the greatest advances in physics and in chemistry ; they may now be regarded as the fundamental bases of both sciences. The first law is involved in the determination of the ratio between the specific heat of gases at constant volume and at constant pressure. From this ratio a very important deduction has been drawn regarding the molecular complexity of gases, viz. that while certain gases, such as mercury-vapour and the gases of the argon group, con- sist of molecules of the simplest possible nature, that is, of single atoms, other gases, such as hydrogen, oxygen, nitrogen, and chlorine, consist of molecules composed each of two atoms. The conclusion as regards the last-mentioned gases had been arrived at from chemical considerations; but the proof was wanting, until corroborated by means of these physical aids. The subject has been fully worked out from the theoretical side by O. E. Meyer and by Boltzmann, whose work on the kinetic theory is also of great value. Early researches of a physico-chemical nature were made in 1819 by Dulong, Director of the Ecole Poly technique at Paris, in conjunction with Petit, Professor of Physics there. These led to the discovery that equal amounts of heat are required to raise equally the temperature of solid and liquid elements, pro- vided quantities are taken proportional to their atomic weight ; xxx INTRODUCTION TO THE in other words, equal numbers of atoms of elements have equal capacity for heat. By this means, an approximate estimate of the atomic weight of an element may be arrived at ; and this, taken in conjunction with the exact determination of the equivalent of the element, may be made to yield a knowledge of the exact atomic weight. It would follow from this that as equal volumes of mercury gas and the gases of the argon group contain the same number of atoms (for the molecule is in their case identical with the atom), equal volumes should possess equal capacity for heat. If the molecular weight, or what is the same for these gases, the atomic weight, be ex- pressed in grams, the specific heat at constant volume for such weights is 3 ; i.e. to raise the temperature of 4 grams of helium, 20 grams of neon, 40 grams of argon, 8r6 grams of krypton, 128 grams of xenon, or 200 grams of mercury- vapour through i, provided the gas is not allowed to expand, requires as much heat as could raise 3 grams of water from 18 to 19 C. And if the gas be allowed to expand, work will be done owing to the displacement of the atmosphere, so that other two heat units or calories are equivalent to that work ; the specific heat "at constant pressure" is therefore 5, and the ratio between the two is as 3 : 5, or as i : if . It is found that for gases with diatomic molecules, such as O 2 , N 2 , H 2 , etc., while the specific heat for equal atomic weights is 5 for constant volume, that for constant pressure is 7 ; the ratio between the two is as 5 : 7, or as i : i '4. Gases with more complicated molecules have higher specific heats; but the ratio between the atomic heat at con- stant volume and constant pressure is a smaller one, and does not display the same regularity as that between the atomic heats of monatomic and diatomic gases. . These relations are realizable by aid of the kinetic theory of gases, which postulates that the motion of the molecules is equivalent to their temperature. With monatomic molecules this motion is almost entirely translatory ; with diatomic or STUDY OF PHYSICAL CHEMISTRY xxxi polyatomic molecules, on the other hand, there is not merely translatory motion from place to place in the containing vessel, but also there must be atomic motion within the molecule. The atomic motion is represented by the absorption of a certain amount of heat, when the temperature of the compound gas is raised. This view is due to Naumann (1876). The specific heats of equal number of atoms of solids, on the other hand, if the atomic weights be expressed in grams, approximate to the number 6, nearly twice as great as that for monatomic gases at constant volume. It may be conjectured that the heat is partially accounted for by over- coming the restraint to which the molecules are subject in the solid state ; and as the atomic heats are approximately equal, it may be argued that the molecules of all solid elements are subject to approximately equal restraint. As certain elements, namely, carbon, silicon, boron, and beryllium, are characterized by specially low atomic heats at ordinary temperature, it might be argued that their atoms are less restrained in their motion than those of the other solid elements. Yet, as Weber showed, at high temperatures their atomic heats become more normal j and it is difficult to see why a rise of temperature should increase any restraint due to natural attraction of atoms in the molecule. In compounds, too, as shown by Neumann (1831), Regnault (1840), Joule (1844), and Kopp (1864), the specific heats of equal numbers of molecules is approximately constant, though to some elements it would appear that exceptionally low atomic heats must be ascribed. Altogether the theory of the specific heats of solids and liquids is in an unsatisfactory state, and further investigations are much needed. We have here an instance, however, of the necessity of taking into consideration the chemical constants of the sub- stances investigated, i.e. atomic and molecular weights, in order to secure even approximate regularity. For the specific heats of elements and compounds present no regularity, unless they xxxii INTRODUCTION TO THE be referred to atomic or molecular weights. Hence the deter- mination of specific heats has been undertaken mainly by chemists ; and the data obtained are among the earliest examples of physico-chemical constants. The relations discovered by Gay-Lussac between the volumes of gases and their combining proportions stimulated others to investigate the question whether similar relations could not be found for liquids and solids. The first successful attempts were made by Hermann Kopp in 1842. The number of cubic centimeters of liquid at its boiling point, obtainable by condensing that volume of gas which contains the molecular weight of the liquid expressed in grams, was termed by Kopp the " specific volume." But it has since been found preferable to retain this term for the reciprocal of the density, i.e. for the volume occupied by one gram of the substance ; and to substitute the term " molecular volume " for the constant suggested by Kopp. Working with carbon compounds, it was easy, by subtraction, to ascertain the difference in molecular volume for compounds differing by CH 2 , i.e. the difference between consecutive compounds in a homologous series, and so to arrive at values for individual elements. It was then possible to calculate the molecular volumes of compounds by adding together the atomic volumes of the elements which they contained. The investigation was continued by Ramsay, Thorpe, Lessen, Schiff, and others ; and it transpired that, as a rule, elements in compounds retain the atomic volumes which they possess in the free state ; that the constitution of a compound has an appreciable influence on its molecular volume ; and that certain elements are capable of assuming different volumes, according to the manner in which they are com- bined. ! Properties which, like molecular weights and molecular volumes, can be numerically valued as the sum of the values of similar terms for elements, are on Ostwald's suggestion STUDY OF PHYSICAL CHEMISTRY termed " additive." Those which are influenced by constitu- tion, as to some extent molecular volumes, are termed " con- stitutive ; " and those which, like gaseous pressures, depend wholly on the number, and not on the nature of the molecules, are termed " colligative." It was soon discovered that other properties of matter could be treated so as to exhibit their " additive " nature ; among these are : the molecular refractive index, or the relative retardation which different compounds and elements offer to the passage of light (Gladstone and Dale, 1858; Landolt, 1864; L. Lorenz and H. Lorentz, 1880; Briihl, 1880); the dispersion of light, or the relative angle which passage through a prism separates rays of known wave- length (Gladstone and Dale, Kanonnikoff) ; the molecular rotation of the plane of polarized light by its passage through transparent chemical compounds in a magnetic field (Perkin) ; and molecular coefficients of viscosity (Thorpe and Rodger). It is, however, also possible to treat such data partly from a " colligative," partly from a " constitutive " point of view ; and attempts in this direction, more or less successful, have been made by Schroder and by I. Traube. The latter has been able to apply his method also to molecular volumes in solution in various solvents. The surface energy of liquids has been shown by Eotvos (1886), and by Ramsay and Shields (1890), to have a simple relation to their molecular weights. At and above the critical point of a liquid it no longer possesses a surface, for liquid and gas are one. As the temperature falls below the critical point, however, the surface energy increases ; and the rate of increase for equal numbers of molecules on a liquid surface, is approximately equal for all normal liquids. This affords a means of determining the molecular complexity of compounds and elements in the liquid state, for it is a colligative property. Other methods have yielded evidence corroborative of the quan- titative results deduced from measurements of surface tension ; xxxiv INTRODUCTION TO THE for example, the ratio between the density of a substance at its critical point and its normal gaseous density (Young), the rate of variation of its vapour pressure with increase of tem- perature, and similar properties. The distinguishing characteristic of chemical compounds is their constant composition. But it is often difficult to decide whether or not a particular substance has or has not definite composition. Substances which do not exhibit constancy in this respect are termed "mixtures," and such mixtures some- times consist of compounds mixed with excess of one or other constituent. The investigation of the nature of mixtures, accordingly, has long been regarded as the legitimate sphere of the chemist. The first definite law regarding mixtures was discovered by Dr. Henry in 1803; it refers to solution of sparingly soluble gases in water. It is : The amount of gas absorbed or dissolved by a given amount of liquid is proportional to the pressure of the gas. As, however, the volume of the gas is inversely pro- portional to the pressure, it follows that a given quantity of liquid always dissolves the same volume of gas, whatever the pressure, temperature, of course, being maintained constant. A convenient way of stating the same fact is to use the word " con- centration " to signify the quantity of substance in unit volume ; it then follows that the concentration of the gas in the space occupied solely by gas is proportional to the concentration of the solution of the gas in the liquid, for by doubling the pressure the concentration of the gas is doubled, for twice the weight is contained in unit volume ; and as the amount in solution is also doubled, its concentration is increased in the same proportion. Henry's discovery was extended in 1807 by Dalton to the case of gaseous mixtures. His law is: If a liquid is exposed to a mixture of gases , the amount of each gas dissolved is proportional to its partial pressure \ and to its solubility. The solubility of gases in liquids generally decreases on STUDY OF PHYSICAL CHEMISTRY xxxv rise of temperature; but as the critical point of the liquid is approached, other phenomena intervene, which have been investigated largely by Kammerlingh Onnes and his pupils in the physical laboratory at Leiden, in Holland. The behaviour of mixtures of liquids on distillation has also been investigated by Konovalow (1881); and his work has been greatly extended by Young. In certain cases, if the liquids are immiscible, the vapour pressure at any given tem- perature is the sum of the vapour pressures of the constituents of the mixture ; if the liquids are miscible, the vapour pressure of the mixture is less than the sum of the pressure of each ; and it may be less than that of either. In certain cases the boiling point of such a mixture remains constant, under constant pressure ; and as constancy of boiling point has been regarded as a sign of definite chemical composition, it has been argued that the mixture was a true chemical compound. But this view is incorrect. Alteration of pressure, as was shown by Roscoe and Dittmar in 1860, alters the composition of the mixture, and the conclusion as to constancy of chemical composition is disproved. Many researches have been made on the solubility of solids in liquids. As a rule, the higher the temperature the more soluble the solid is. But for each temperature there exists a maximum of solubility ; the solution is then said to be " saturated." Certain substances, however, such as slaked lime, decrease in solubility with rise of temperature ; and this has been shown to be due to the fact that as the temperature rises the soluble compound (in the case mentioned above, calcium hydroxide, Ca(OH) 2 ) loses water, and is converted gradually into an insoluble, or a much less soluble substance (CaO). The laws relating to the mutual solubility of two or more salts in each other's solutions will be alluded to later. The state of saturation may be reached in one of two ways : the solution may either be saturated at a high temperature, xxxvi INTRODUCTION TO THE and allowed to cool to the required temperature, or the solvent may be shaken up with the powdered solid until it is saturated. In each case the same end-point results ; a state of equilibrium is reached. Yet Ostwald has shown that if the solid is finely divided, it is more soluble than if in coarse lumps. The rate of diffusion of liquids was carefully investigated by Thomas Graham (1851). It has already been mentioned that Graham's results as regards the relative rates of diffusion of gases are in accord with the rates of motion of their molecules. The diffusion of liquids into each other is also due to molecular motion. And as gaseous pressure is attributed to the collision of the molecules of the gas with the walls of the containing vessel, so the molecules of liquid, by virtue of their motion, must also generate pressure. But in a mixture of liquids a method for the measurement of the pressure of one of them is not easy to devise. The account of an experiment carried out by Ramsay for gases will render the method clear. A vessel constructed of the metal palladium, at a high tem- perature, allows hydrogen to pass through its walls, but is impervious to nitrogen and other gases. If such a vessel be filled with nitrogen, and heated to a constant high temperature under a definite pressure, say that of the atmosphere ; and if a current of hydrogen be passed over its exterior, the hydrogen will enter, while the nitrogen cannot escape through the metal walls. The pressure in the interior will rise, owing to the entry of the hydrogen, until the total pressure in the interior of the vessel will equal the atmospheric pressure of the original nitrogen, plus the pressure of the hydrogen which has entered ; and if the hydrogen on the exterior is at atmospheric pressure, the total pressure registered will be two atmospheres. The increase of pressure may be regarded as due to the nitrogen, since the hydrogen, being able to pass in each direction through the palladium, will balance its external arid internal pressures. STUDY OF PHYSICAL CHEMISTRY xxxvii The palladium may be termed a " semi-permeable " septum, since it is permeable to one substance, and not the other. By a similar device the pressure of substances dissolved in liquids may be measured. In this case the pressure of the dissolved substance is termed its "osmotic" pressure; it is that which tends to spread the dissolved substance through the solution by diffusion, from a place of greater to a place of less concentration ; it is due to the motion of the molecules of the dissolved substance. It had been long known that a bladder filled with alcohol and placed in water would swell, and might even burst, owing to the entry of the water through the animal membrane. This entry was ascribed by F. Perrot (1815) to the tendency of miscible liquids to " wander " through each other, until they were uniformly distributed throughout the mixture. This pheno- menon, however, had more direct interest for botanists than for physicists, inasmuch as it appeared to be related to the ascent of sap in plant-stems ; and it was first qualitatively in- vestigated by M. Traube (1867), who, after attempting the preparation of artificial diaphragms of tannate of gelatine, and of ferrocyanide of copper, found that these membranes were permeable to some substances and not to others. Quantitative measurements were made by W. Pfefter (1877), who obtained his best results with ferrocyanide of copper diaphragms ; and van't Hoff showed, in 1885, that the quotient obtained by dividing the pressure by the concentration is constant at equal temperatures a law comparable with Boyle's law for the compressibility of gases, for concentration may be regarded as the reciprocal of volume. Van't Hoff also showed that the increase of osmotic pressure with increase of temperature followed Gay-Lussac's law, and again confirmed the analogy between gases and substances in dilute solution. De Vries and Tammann amplified the work of Pfeffer (1888) by de- termining at what degree of dilution various solutions exercised xxxviii INTRODUCTION TO THE equal osmotic pressure; and van't Hoff pointed out that for certain substances, such as sugar, salicin, etc., the quantities of dissolved substances were then present in proportion to their molecular weights. Moreover, he went a step further, and showed that the osmotic pressure exercised by a solution of cane-sugar at a definite temperature and at a definite concentration (i.e. with a definite weight of cane-sugar con- tained in unit volume of the solution) was the same as the pressure which would be exercised at the same temperature by a gas containing a number of molecules per unit volume equal to that of the cane-sugar. The osmotic pressures of dissolved salts, however, do not exhibit the same simplicity. The reason for this divergence was first pointed out by van't Hoff, and will be referred to later. The fact that solutions of compounds in pure solvents raise the boiling point of the solvent had been known for long; it was investigated in 1822 by Faraday, and later (1824) by Griffiths, and (1835) by Legrand. They, and Wiillner (1856-1858), investigated chiefly the behaviour of salts; and Ostwald (1884) pointed out that if the rise in boiling point of the solution be referred, not, as these authors had done, to the relative weights of dissolved substance, but to their relative molecular weights, equal numbers of molecules of different salts, dissolved in the same weight of solvent, produce an approxi- mately equal rise in the temperature at which the solution boils. But it was not until Raoult (1886) had extended the researches to solutions of carbon compounds other than salts, that regu- larity was introduced. It then transpired that equal numbers of dissolved molecules produce an equal rise in the boiling point of the solution ; or, stated in another manner, the pre- sence of equal numbers of molecules of two substances in equal quantities of the same solvent reduces the vapour pressure of the solutions to an equal extent. The connection between these STUDY OF PHYSICAL CHEMISTRY xxxix phenomena and between similar relations dealing with the depression in the freezing point of a solvent produced by the pressure of dissolved substances was shown by van't Hoff in 1887; and the thermodynamic explanation was given by him, and in a different form also by Arrhenius in 1888. Arrhenius, too, propounded a theory to account for the irregular behaviour of salts as regards their osmotic pressure, and the rise in boiling point and depression in freezing point of solutions containing them, which they exhibit. It is that when dissolved, salts dissociate into two or more constituents, each of which produces an effect as if it constituted a separate molecule; and that these constituents are identical with the ions, or carriers of electricity, when the salts are subjected to the influence of an electric current. Many arguments in favour of this hypothesis were collected and published by van't Hoff in 1887; others are to be found in the volume-relations, the colour, the optical, the magnetic, and other properties of salts. The connection between the osmotic pressure of dissolved substances and the rise of boiling point or depression of freezing point which their solutions exhibit can be shown only by the aid of thermodynamics. But one consideration will make it plain that such a connection must exist. The osmotic pressure of a dissolved substance evidently depends on its concentration in the solution ; if the concentration be increased, the osmotic pressure will be increased proportionally. This could be achieved by applying an external pressure to the solution, so that solvent would be expelled through the semi-permeable membrane, just as the pressure of a gas can be increased by diminishing its volume by application of external pressure. Now, the amount of work done in diminishing the volume of the solution is the same, whether the solvent be removed by pressing it through the diaphragm, or by freezing it out, or by removing it by evaporation; and thus the relation between xl INTRODUCTION TO THE osmotic pressure and the depression of vapour pressure 01 freezing point can be established. There is, indeed, a fourth method of altering concentration, and that is by shaking the solution with some other liquid which does not mix with the original solvent, but which dissolves the substance, and so removes it partially from the original solvent ; and here, again, similar thermodynamic considerations can be introduced. The relationship between the volumes, expansions, optical properties, and other properties of solids have been to some extent worked out. Many approximate numerical relations, based on the molecular weights of the solids, have been eluci- dated ; but, as a rule, the results have not been so useful as those with gases and liquids. Allusion has already been made to the equality of the atomic heats of the solid elements, dis- covered by Dulong and Petit ; and to the extension of Dulong and Petit's law to compounds by Neumann in 1831. Reg- nault, Kopp, and Joule have contributed to our knowledge of such relations ; the ease with which very low temperatures can now be obtained leads to the hope that in the near future this knowledge may be considerably increased, and that some philo- sophical basis may be found for the irregularities which have hitherto been discovered. That almost every change in a chemical system is accom- panied by a gain or loss of energy is evident, if heat be regarded as a form of energy, for heat is almost always evolved or absorbed during the formation or decomposition of every chemical compound. The total energy in any substance eludes measurement; but the difference in energy-content between any one state and any other can be determined. The province of thermal chemistry is the measurement of such differences of energy in the form of heat. The first important theoretical advance in this direction was due to Hess (1840), in his postulate that the total evolution STUDY OF PHYSICAL CHEMISTRY xli of foot during any chemical process is the same whether the process takes place in one or in several stages. Actual determinations of the heat evolved during combustion of various substances, and of the heat-changes which take place on solution, were made by Andrews (1841 and subsequent years) and by Graham (1843) ; and Favre and Silbermann greatly added to our knowledge of facts of this nature (1852-1853). The most remarkable series of researches on the heat-changes which accompany chemical action are due to Julius Thomsen of Copenhagen, and to Mar- cellin Berthelot of Paris ; the former published his first treatise in 1853, and the latter in 1865, and they have continued their investigations almost to the present day (1903). Each of these authors enounced a principle, which has subsequently turned out to be incorrect, viz. that those chemical reactions take place which are accompanied by an evolution of heat. But this incorrect hypothesis led to the production of an enormous mass of experimental work. The evolution of heat during the formation of numerous compounds from their elements, the heat-changes occurring during the conversion of one compound into another, the heats of combustion of com- pounds of carbon and other elements, that evolved during the neutralization of bases by acids and during the progress of allotropic and isomeric change, have, in many cases, been measured, and many interesting conclusions have been arrived at. One of the most interesting is the fact that on neutralizing a dilute solution of a monobasic acid by a monoacid base, nearly the same amount of heat is evolved in most cases ; and the tracing of this fact to its cause that such an action is accompanied by only one chemical change, the combination of the hydroxyl ion, OH', of the base with the hydrogen ion, H', of the acid. The metallic and acid ions remain, for the most part, unaffected by mixing their solutions. When combination occurs, or where the acid or the base, in solution, exists not wholly in the state of ions, the regularity no longer holds. xlii INTRODUCTION TO THE Other interesting results have been arrived at in the case of explosive bodies, which are always endothermic, i.e. are formed with absorption of heat ; while stable bodies are generally pro- duced with heat evolution. With rise of temperature, sub- stances formed with evolution of heat become more unstable ; and the converse is also true, that endothermic substances become more stable on rise of temperature. On the whole, however, little of theoretical importance has been deduced from the very numerous data of thermal chemistry. It is true that F. W. Clarke has recently published the outlines of an attractive theory, which makes it possible to calculate the heats of formation of many compounds from simple considerations ; but the accuracy of Clarke's deduction has been disputed by Julius Thomsen. The first application of electricity to chemistry dates from the time of Priestley (1772) ; he proved that the effect of pass- ing electric sparks through air was to produce an acid substance, which he supposed to be carbonic acid ; but in 1775 Caven- dish carried out a marvellously careful set of experiments, and showed that the acids actually produced were nitrous and nitric. Not long afterwards van Marum (1785) and van Trostwyk and Deimann (1789) showed that hydrogen and oxygen result from the action of powerful sparks on water. Shortly after (1791) Galvani discovered that a feeble current of electricity caused the muscles of a frog's leg to contract, and Volta invented his " pile." .With such a " pile," Nicholson and Carlisle "decomposed water" (1800), and found that from the wire attached to the zinc disc oxygen was evolved, while from the other wire bubbles of hydrogen escaped. At the same time the water round the former became acid, and round the latter alkaline. That acid and alkali could be pro- duced by the decomposition of " pure " water was a puzzle to many; and it was not until Humphry Davy showed in 1800 that STUDY OF PHYSICAL CHEMISTRY xliii the alkalinity and acidity were due to the electrolysis of minute traces of salt, dissolved out of the vessel in which the water was contained, and that pure water in vessels of gold or platinum was a practical non-conductor, and gave rise by its decom- position to no alkali or acid, that the anomaly was explained. Davy also evolved a theory by means of which he en- deavoured to connect electrical with chemical phenomena. Starting from the known fact that acids or bases in contact with metals acquire an electrical charge, he argued that the same must be the case with atoms j that in entering into chemical combination they acquire electrical charges of different sign, and cohere, owing to the same reason which causes electrical attraction of oppositely electrified bodies. According as the charge is greater or less, the chemical attraction is powerful or feeble. Davy found the difference of chemical potential to increase with rise of temperature, and drew the not unnatural conclusion that this increase runs parallel to the increase of chemical affinity, which causes combination more readily at a high than at a low temperature. Indeed, Davy did not regard these as two different phenomena, one the cause, the other the effect, but he regarded them as essentially the same. Decomposition by an electric current he believed to be a reversal of the phenomena of combination. In giving the atoms of the decomposing compound opposite charges to those which they had acquired by their combination, the atoms were restored to their previously neutral state ; the positive atoms or groups were attracted to the negative pole ; their positive charges were neutralized by a corresponding negative charge from the pole, and the atom or group was liberated in the free state. Davy's views made no lasting impression, for they were shortly afterwards superseded by those of Jacob Berzelius (1806). Berzelius held the view that all chemical compounds consisted of a combination of two opposite constituents. To this view he was led by the observation that an electric current xliv INTRODUCTION TO THE apparently decomposed salts into an acid portion and a basic portion, each of which goes respectively to the negative or to the positive pole ; combustible substances, alkalies or alkaline earths, collect at the positive pole, while oxygen, acids, and in general oxidized substances go to the negative pole. He also believed that the decomposition of mixtures or of compounds was in compound proportion to their chemical affinity and to their surface of contact, and that the absolute amount of the decomposition was proportional to the quantity of electricity, and that this varied with the surface of contact between the metal and the conducting liquid ; it was also supposed by him to be proportional to the conductivity of the solution. The course of the reactions occurring during decomposition was believed to be influenced by the affinity of the components for the material of the wires, by the mutual affinity of the constituents, and by the cohesion of the resulting compounds. To justify these suppositions he made the hypothesis that each atom contains electric charges of different amounts; and in general both a positive and a negative electric charge, one at each pole. His theory differed from that of Davy essentially in this, that while Davy believed that the atoms acquired their charges only by contact with each other, Berzelius imagined the atoms to be endowed from the start with electrical charges. But although any atom contained both a positive and negative charge, they were not necessarily equal in amount ; hence some atoms were essentially negative, whilst others were essentially positive. During combination, the oppositely electrified atoms attracted each other, and by equalizing their charges, more or less, heat and light were the accompaniments of the partial or complete restoration of the electrical neutrality. Berzelius himself acknowledged, however, that the neutralization of the electric charges removed the cause of the persistence of the compound, if chemical affinity were considered to be due to electric attraction. But Berzelius made use of his "binary" STUDY OF PHYSICAL CHEMISTRY xlv theory more as a means of classification than for the purpose of explaining chemical or electrical phenomena ; and owing to that advantage it persisted for long. The next advance in the subject was due to Michael Faraday (1831-1838). His first statement was: The amount of a substance decomposed by an electric current is proportional to the amount of electricity which passes through it. This was soon after followed by the important law which goes by his name : If the same current passes through several electrolytes^ the amounts of the diffei'ent substances separated from the compound are proportional to the chemical equivalents of tJie substances separated. The same amount of electricity, he showed, always liberated the same amount of explosive mixture of oxygen and hydrogen from dilute sulphuric or hydrochloric acid, whatever the " strength " of the current, the size of the electrodes, the dilution of the liquid, or the temperature. It was Faraday who introduced the term electrolysis to signify the process of separation of the constituents of a com- pound body by means of an electric current ; the conductor, of which the components undergo such separation, he called the electrolyte; the moving parts were termed by him ions (or "movers"), and those which go towards the anode he called the anionS) and similarly, the ions which move towards the kathode were termed by him the kations (ana = up ; kata = down ; hodos = a way). Faraday was careful to point out that the passage of a current through an electrolyte, and the separation of the ions at the electrodes, although they are concurrent, are yet abso- lutely distinct phenomena. While Davy's view that the products of electrolysis are the metal or hydrogen, on the one hand, and the non-metal, or electro-negative group, on the other, had been overshadowed by Berzelius's contention, that one product is an acid, and the other a base, the question was not settled until Daniel], xlvi INTRODUCTION TO THE Professor at King's College, London (1839), showed that if a current be passed through " water " (dilute acid) as well as through a solution of sodium sulphate, the same amount of hydrogen is collected in each case; but in the latter, an equivalent of "soda" (sodium hydroxide) is also set free. Hence the current would appear to be doing double work in the solution of sodium sulphate; not merely liberating the correct amount of hydrogen, but also liberating the soda. He pointed out the obvious explanation : that the primary product of the electrolysis of the sodium sulphate is sodium, and that the hydrogen is really produced by the' action of that metal on the water, at the moment of its liberation. Early in the days of electro-chemistry (1805) a hypothesis was brought forward by Grothuss to explain a phenomenon which had been pointed out by Davy, namely, that the element liberated at one pole has not been driven bodily from the opposite pole to the one at which it is liberated. As a striking proof of this, he caused the current by which " water " was electrolysed to pass through his own body ; and it was incon- ceivable that the same atom of oxygen, for example, could have passed from the negative to the positive pole through his organism. Grothuss imagined the atoms to be already charged. The atoms of oxygen and hydrogen in the water molecules gave up their charges to their respective poles, and escaped ; the neighbouring atoms changed partners, those at the end of the chain combining with the atoms left without partners. But Clausius (1857) disproved Grothuss's theory, which had main- tained its ground for over half a century. He pointed out that if a certain " force " is required to effect decomposition, no decomposition should take place until that force has come into operation ; as a matter of fact, however, the smallest conceiv- able electric " force " is sufficient to effect decomposition of an electrolyte. He therefore imagined that in any electrolytic solution some of the atoms are continually changing partners, STUDY OF PHYSICAL CHEMISTRY xlvii and that they move under the influence of the current at the instant when they are unattached, that is, while the exchange is taking place. This hypothesis had previously been put forward by Williamson, with the view of explaining all chemical action ; some molecules, he supposed, were always undergoing decomposition ; their constituent atoms, or groups, however, did not necessarily reunite, but were ready to unite with those of other molecules which also had undergone decomposition. The relative rate of motion of the ions was first measured by Hittorf. Although it had been noticed by Faraday (1834), and by Daniell and Miller (1845), that during the electrolysis of a salt the salt became more concentrated in the neighbour- hood of one pole, and more dilute round the other, it was not until 1853 that the true explanation was found by Hittorf in the fact that the two ions do not move at an equal rate. If they do, there is no such alteration of concentration. But in the more numerous cases, where their rate of motion is different, the salt concentrates round the pole to which the more rapidly moving ion is travelling. Hittorf also pointed out that compounds, solutions of which are good conductors of electricity, are precisely those bodies which are most susceptible of chemical reaction. In later years this dictum has proved one of great importance. Accurate measurements of the rate of passage of charged ions through their solutions were first made by Kohlrausch in 1869, with this remarkable result: that the ions move independently of one another. Hence the electrical conduc- tivity of any salt may be arrived at by the sum of the rates of transport of its ions. Further progress was made in 1887 by Arrhenius, who showed that, on sufficient dilution, all salts arrive at a maximum conductivity, of the same order of magnitude ; and he deduced from this that, with increasing dilution, a larger and larger number of molecules become ionised, i.e. resolved into ions. d xlviii INTRODUCTION TO THE Indeed, many salts, in fairly concentrated solution, are already largely split into ions ; while acids, on the other hand, even at very small concentration, are to some extent in the non-ionised form. The reactivity of a salt, he contended, was due to the actual number of ions present in unit volume. And van't Hoff showed the proportionality between the relative number of ions, thus determined electrically, and the osmotic pressure which they exert, as well as their influence in raising the boil- ing point and depressing the vapour pressure or the freezing point of the solutions which contain them. The connection between the amount of energy expended electrically in the cell of a battery, and the heat evolved when the reaction between the constituents of the cell proceeds with- out production of a current, or with a closed circuit, was first calculated and experimentally proved by Joule and Thomson (Lord Kelvin), the latter of whom summed up the results of the investigation in the proposition : The intensity of an electro- chemical apparatiis is, in absolute measure, eq2ial to the mechanical equivalent of as much of the chemical action as occurs by means oj a current of unit strength^ in unit time. But experiments by Boscha, Raoult, and others did not always succeed in cor- roborating the truth of this assertion. The anomaly was explained by Helmholtz, as well as by Willard Gibbs (1878) in his great work. The discrepancy was caused by the neglect to take into account the temperature-coefficient of the electro- motive power of the particular cell employed. If this is small, as, for example, in a Daniell's cell, in which zinc is replaced by copper, the agreement with Joule and Thomson's statement is a close one ; but if it is large, as in many other instances, the necessary correction must be introduced in order that experiment and theory give the same result. The further development of electro-chemistry belongs to the present day, and will be thoroughly considered in the volume devoted to that subject. STUDY OF PHYSICAL CHEMISTRY xlix The connection of chemical action with light is a subject which has attracted much attention, owing to its connection with the practical aspect of photography on the one hand, and with astronomy on the other, in the form of spectroscopy. But even yet few general conclusions have been drawn. The fact that silver-salts are alterable by light was observed as early as 1727 by Schultze; and Scheele, the discoverer of oxygen, observed that this action is due chiefly to the violet part of the spectrum (1777). Senebier made quantitative experiments in 1784; and Daubeny, in 1836, made similar quantitative experiments on the influence of different colours of the spectrum on the absorption of carbon by plants. It was for long believed that three distinct varieties of waves were emitted by luminous bodies; waves of light, of heat, and of chemical action ; but it appears that all waves may have all three effects, and that the wave-length of those waves which produce the maximum of chemical action depends on the kind of chemical action which results from them. Thus, while the maximum effect on plant-life is produced by light of such a wave-length that it has also nearly the greatest luminosity, the maximum effect in decomposing silver bromide is caused by vibrations in the ultra-violet part of the spectrum ; and heat effects are produced by vibrations iri the infra-red. It has been pointed out by Mayer that while, generally speaking, the effect of ether waves in promoting chemical action is merely that of causing it to start, so that energy is lost, the action on living plants is of an opposite character, for by its influence energy is stored. The action in the first case is one resembling catalysis, and merely increases the rate at which chemical action proceeds while in the second, the radiant energy from the sun is stored by means of the plant as chemical energy. Many attempts, more or less successful, have been made to measure, by the chemical changes produced, the intensity of 1 INTRODUCTION TO THE the radiations which produce these changes ; the best known are the researches of Bunsen and Roscoe (1851-1862), and Draper (1857). Many more recent researches have, however, been made. The development of spectroscopy has of recent years been very rapid, so far as relates to the measurement of the spectra of different substances. Although the refraction of light was first explained by Newton, and investigated in the early half of the eighteenth century by Brewster, rapid progress was made when Kirchhoff discovered, in 1860, that all substances emit rays of light of the same wave-length as those which they absorb. The introduction of the spectroscope as a means of analysis by Bunsen and Kirchhoff drew attention to the advantage of the study of spectroscopy, and established many important laws. The fact that gases made luminous by an electric current of high potential could be made to emit different kinds of spectra, according to the nature of the discharge, was the discovery of Pliicker and Hittorf (1865) ; and the fact that each compound, if it can only stand the tem- perature at which it emits luminous rays, has its own special spectrum was first announced by Mitscherlich in 1869. The first theoretical discussion of spectra is due to Maxwell (1875); ne pointed out that harmonic relations should be found between the wave-length of the lines of the spectra of any substance. Mascart, Stoney (1871), and Lecoq de Bois- baudran (1889) have shown that such " harmonic relations" exist in some cases ; and other authors have sought to establish such relations; the most successful is due to Balmer, whose formula has yielded excellent results in the hands of Rydberg, Runge and Paschen, Kayser, Lorenz, Zeeman, and others. There is, however, a vast unexplored field in spectroscopy ; for although the visible waves, as well as those in the ultra- violet part of the spectrum, have been investigated in many instances, the infra-red waves have been hardly looked for. STUDY OF PHYSICAL CHEMISTRY li Langley, indeed, has measured the lines in the infra-red part of the solar-spectrum by means of his " bolometer," an instru- ment capable of detecting very minute differences of tempera- ture ; but this instrument has been little applied to the spectra emitted by gases or by hot solids. Speculations regarding the reason of chemical combination date from the earliest times. The word " affinity," or " chemical affinity," calls us back to the time of Hippocrates, whose view was that " like draws to like ; " that substances which combine must have something in common, like wine and water, silver and gold. As solution and mixture passed in those days for combination, there was some reason for his dictum. Empe- docles, the first atomist, held a different view, founded on imaginary hates and loves between the atoms. In the Middle Ages, even quainter ideas are to be met with ; that the particles of the acid solvents are sharp, like needles or spears, and that they transfix and support the particles of dissolved metal; that sweet liquids are sweet, because of the rounded form of their ultimate particles; and that they therefore have not a similar solvent action. With Newton a new view arose. He himself did not believe that affinity was due to an attraction identical with that of gravitation ; but leant to the view that the force varied inversely with some higher power of the distance than the square. But Buffon, the French naturalist, in spite of Newton's well-considered thought, supposed that the form of the objects attracting the ultimate particles could^ make it possible that the laws of the inverse square held for chemical attraction; and his views were widely disseminated and accepted. - Davy's and Berzelius's electro-chemical theories have already been alluded to, and need not be further discussed here. Attempts to arrange qualitatively the order of affinity of the elements for each other were frequently made in the eighteenth lii INTRODUCTION TO THE century. As early as 1718, Geoffrey arranged in order various chemical substances (for elements in the modern sense of the word were even then not recognized) in the order of what he supposed to be their affinity for each other. For instance, under " metallic substances " we find the order iron, copper, lead, mercury, silver, as regards their affinity for nitric acid ; and for vitriolic acid the order was sulphurous or oily principle, fixed alkali, volatile alkali, absorbent earth (i.e. calcium carbonate), iron, copper, silver, and so on. The idea which guided him he expressed thus : " Whenever two substances, which have some inclination to combine, are combined with each other, and a third is presented to them which has more affinity to one of the two than the other, that other is expelled." The same idea was fully elaborated by Torbjorn Bergmann in 1783. He distinguished between various kinds of attraction : for example, particles of the same kind were held together by attractio aggre- gationis ; compounds remained compounds by virtue of attractio compositionis, which might be of two kinds, according as they had been prepared in solution (attractio solutionis) or by fusion (attractio fusionis). Simple expulsion of one constituent out of a compound by the action of another was due to attractio simplex electiva; while exchange between the constituents of two compounds was caused by attractio duplex. Attempts not merely to determine the order, but also the relative amount of such affinities, were made by De Morveau (1793) ; he attempted to ascertain the relative affinities of metals for mercury by measuring the weights required to separate plates of a number of metals of the same size from a surface of mercury, and concluded that as adhesion and affinity must be fundamentally the same, he was measuring relative affinity. He 'also gave six laws of affinity: that only liquids act; that affinity takes place only between the smallest particles of substance ; that the affinity between any two substances is partly conditioned by the relative amount of each ; that chemical affinity acts only STUDY OF PHYSICAL CHEMISTRY liil if it can overcome cohesion ; that compounds differ entirely in properties from their constituents ; and that affinity is greatly influenced by temperature. We have here a statement that the relative amounts of substance present influence their behaviour as regards a third. This law was originally stated by Wenzel in 1777, in this form : The affinities of bodies for a common solvent are inversely as their rates of solution in that solvent ; also, that the strength of chemical action is proportional to the concen- tration of the acting material. Count Berthollet, independently of Wenzel, enunciated the same doctrine in 1799, and stated clearly that it was impossible, as Bergmann had attempted, to arrange substances in a definite order of chemical affinity, but that the affinity was deeply affected by the relative amounts of substances present. He succeeded in reversing the actions which had hitherto been supposed to decide the order of chemical affinity : for example, he decomposed barium sulphate by boiling potash ; potassium sulphate by boiling milk of lime j calcium oxalate by nitric acid, and so on. Although in each case only a partial decomposition was attained, yet that decomposition occurred at all was regarded by him as a proof that a large quantity of a reagent could reverse the order of chemical affinity. He regarded these reversed actions to be due to the small surface of the precipitate, compared with the large and constantly renewed surface of the acting liquid ; so that when a liquid acts on a solid, the activity of the liquid is conditioned not by its total amount, but by the degree of its concentration ; and similarly for gases. For when a gas is liberated by any reaction, it removes itself, and can no longer act on the dis- solved substances; hence a comparatively small quantity of reagent is capable of liberating a large quantity of gas. The elasticity of the gas may be regarded as a force acting in opposition to the affinities of liquids. Combination may be either helped or hindered by a rise of temperature ; helped, if liv INTRODUCTION TO THE the rise of temperature so diminishes the cohesion of the acting substances as to increase chemical action; hindered, if one of the substances changes its state by the rise of temperature and removes itself from the sphere of action. The action of solvents is in reality the overcoming of cohesion, so that the affinities of the dissolved substances can manifest themselves. It is thus evident that Berthollet's ideas on the measurement of chemical affinity differed in important respects from those of his predecessors. According to him, at least one of the reacting substances must separate, in order that a reaction shall take place; the state of equilibrium is thus destroyed, and the reaction proceeds until so much of one or other substance separates as to restore the balance. But Berthollet was misled into making the false statement that -the composition of compounds may vary within limits, and that the proportion of the constituents of each compound depends on the relative proportion in which the constituents are present during the process of its formation. Proust, a countryman of Berthollet's, refuted Berthollet's statement by direct experiment, and showed that the supposed compounds on which Berthollet based his contention were not really definite compounds, but mixtures. The definite and invariable composition of chemical compounds, as has been already stated, was fixed by Dalton and by Berzelius. While, then, it is true that the relative amount of a com- pound formed during any reaction is conditioned by the proportions of the reacting substances present, it does not follow that the composition of the compound itself is thus affected ; nor is it true, as Berthollet fancied, that the relative affinities of acids are to be gauged by the relative amounts required to saturate a given base. While Gay-Lussac saw this error, he defended Berthollet's main contention, and maintained that the partition of acids with a base sufficient to saturate only one of them was affected by the relative amounts of the acids STUDY OF PHYSICAL CHEMISTRY lv present. But the difference between altering the relative amount of a compound formed and altering the composition of the compound is a fundamental one. Berthollet's work, Essai de Statique Chimique, was conse- quently soon forgotten; and it was not until 1835 that the question was revived by Persoz, Professor at Strassburg,"who attempted to give a table analogous to Bergmann's of the relative affinity of oxides for acids. And Berthollet's views were resuscitated for analytical purposes by Rose in 1842, and later, in 1853, by Bunsen. Bunsen exploded a mixture of hydrogen and carbon monoxide with an amount of oxygen insufficient for both, and concluded that instead of a gradual progression in the proportions of water vapour and carbon dioxide pro- duced, the ratio remained definite until a certain excess of oxygen was present, and that it then altered suddenly ; so that there was always a definite molecular proportion between the amounts of the two products of oxidation. Similar results were obtained by his assistant Debus, in precipitating carbonates of calcium and barium by the action of carbon dioxide or their hydroxides. But these experiments were subsequently proved to be erroneous. The law of " mass-action," although foreshadowed by re- searches of Biot (1835) was first stated in precise terms by Wilhelmy in 1850. In order to examine the state of equi- librium in any system, it is clear that the conditions must not be changed : for example, the solution must not be concen- trated by evaporation ; nor must other substances be added ; nor must the temperature be altered ; nor must the solvent be changed, as, for example, by the addition of alcohol to an aqueous solution ; hence some physical property must be made use of, which shall reveal the result of the change which has taken place, without disturbing equilibrium. For this purpose Wilhelmy made use of the rotation of the plane of polarized light caused by cane-sugar, and by its products Ivi INTRODUCTION TO THE of decomposition on treatment with an acid, dextrose and levu- lose. In this way the rate of change could be measured with out the introduction of any foreign substance. This law and its consequences will be fully considered in the volume on chemical dynamics. In 1855, J. H. Gladstone made use of the colours of solutions of reacting substances and their products to investigate the position of equilibrium, and in one instance he employed the rotation of polarized light ; and to him belongs the credit of pointing out that after this manner tables of relative affinity could be constructed. Berthelot and Pe'an de St. Gilles, in 1862 and 1863, in investigating the action of acids on alcohols, which is attended with the. formation of esters, did much to elucidate the nature of chemical action. They showed that the action is a gradual one j that it is never complete, but that the amount of ester formed tends towards a limiting value ; and that this limit is the same, whether it be reached by the action of acid on alcohol, or of water on ester. They also showed that the rate of action, but not the limit, was greatly increased by rise of temperature, and that pressure has little influence on the process. Their conclusion agreed with that of Wilhelmy, that the quantity of ester formed at any moment is proportional to the product of the acting masses, and inversely proportional to the volume they occupy. About this date (1857) Deville began to publish his results of experiments on dissociation, which have already been alluded to. He drew an analogy between the temperature of dissociation of a compound and the boiling point of a liquid ; or, to be more precise, the pressure exercised by a gaseous constituent of the dissociating body at a given temperature, and the pressure exerted by the vapour of a liquid at a given temperature. With rise of temperature, vapour pressure increases ; and similarly with rise of temperature the pressure due to dissociation increases. Curiously enough, however, Deville was against the theory of mass-action; and yet his STUDY OF PHYSICAL CHEMISTRY Ivii experiments furnish one of the most striking proofs of the justice of that doctrine. The first attempt to determine the value of chemical affinity by help of the then recently developed ideas of thermo- dynamics is due to Julius Thomsen, of Copenhagen (1854). Defining "affinity" as that force which holds together the constituents of a compound, he believed that it was possible to measure the amount of that force by measuring the heat evolved in a reaction by which the body was formed, which would be equivalent to the heat required to decompose the body that is, he thought it possible to measure a force in terms of an energy. He also believed that all chemical changes which take place spontaneously, or after being started, are necessarily accom- panied by an evolution of heat. It is true that he was acquainted with changes, such as the solution of salts in water, which were attended by absorption, and not evolution of heat; but he attempted to explain away such cases by premising that it was only purely chemical actions which were attended by evolution of heat. In 1867, Berthelot independently announced the same principle ; and a somewhat heated discussion between Thomsen and Berthelot took place in 1873, as to claims of priority and as to the exact nature of the statement involved, which need not be further pursued, inasmuch as the matter in dispute was a false statement. But the question had been solved by Waage, former Pro- fessor of Chemistry, and Guldberg, Professor of Mathematics, at Christiania, who published, in 1865, a pamphlet termed Etudes sur les Affinites chimiques. The fundamental idea of this work was the law of mass-action : that the chemical action is propor- tional to the quantities of substances acting; the last being deter- mined by the amounts in unit volume. If two substances act on each other, the action is proportional to the relative amount of each, and will be zero if the amounts of acting bodies is zero, Iviii INTRODUCTION TO THE and therefore it is proportional to the product of the two. Further, the action will depend on the nature of the substances, on the temperature, and on other circumstances ; these influ- ences can be expressed by a factor, hence the " force " of the chemical affinity can be represented by the expression kpq, if k is the factor, and p and q are the acting masses. But this action is balanced by forces acting in opposition to the forma- tion of the new system, which tend to restore the primary con- dition of the substances. If the substances formed by the original reaction are p' and q\ and the new factor k', equilibrium will be established when kpq = k'p'tf. Although it is not pos- sible to calculate the actual amount of the " chemical forces," it is possible to calculate their ratio, by knowing the position of equilibrium, when the reaction has gone as far as it will, under a given set of conditions. The actual result of such calcu- lations is, however, to give the relative velocities of chemical reactions; and van't Hoff, in 1877, pointed out that it is suffi- cient to confine attention to such velocities, and not to ascribe the velocities to an impelling force, and thereby to introduce mechanical ideas which are unnecessary for the purpose. Guldberg and Waage proved their thesis by many experimental researches; while in 1869 Julius Thomsen had shown that the problem can be solved by thermochemical measurements. Ostwald, in 1876, made quantitative measurements of volume- changes during reactions, which also afforded data for the proof of the law. Horstmann was the first to apply thermodynamics to chemical processes (1869), treating first the problems of dis- sociation. The similarity* between dissociation and vapour pressure makes it possible to treat the former in the same manner as the latter, because both classes of reaction are reversible. Berthelot's and Thomsen's law, implying that that change necessarily takes place which is accompanied by a dis- sipation of energy ', was replaced by another : that of all possible STUDY OF PHYSICAL CHEMISTRY li x systems that one is most stable in which the entropy is at its maximum. The consideration of this doctrine will be found in the volume on Thermodynamics. This principle was later announced by Lord Rayleigh. The most remarkable advance in this direction, however, is due to Willard Gibbs (1874-1878). It is hardly too much to say that all subsequent advances are merely applications and variations of Gibbs's fundamental considerations. In his epoch-making work, Gibbs treats of the chemical potential of a substance, of coexisting phases of matter, of cases of mixture of ideal gases as regards their equilibrium with liquids and solvents, or with solids, of surface-tension, and of electric action between bodies. In van't HofFs Etudes de dynamique chimique (1884), numerous instances are adduced of the application of the laws of chemical dynamics, and the influence of temperature was especially studied. And after Arrhenius of Stockholm had brought out his theory of the independent existence of ions in solutions (1884), van't Hoff in 1887, as has already been narrated, drew deductions from measurements of osmotic pressure by de Vries and by Pfeffer, of the depression of vapour pressure and of rise of boiling point of solvents caused by dissolved substance, and of lowering of freezing points investigated by Raoult, and of Arrhenius's determinations of electric conductivity, and welded all these ideas into a homo- geneous whole. Physical Chemistry deals, as we have seen, with the nature of the changes which take place when substances interact ; its province, however, also includes the structure of compounds. It is evident that while it is possible to represent the composition of compounds by formulae, and the changes which they undergo by equations, the symbolic representation must be incomplete unless the distribution of the atoms in space of three dimen- sions is portrayed. The first advance in this direction was made by Louis Pasteur in 1861. He found that crystals of 1x INTRODUCTION TO THE dextro-rotatory, or right-handed, tartaric acid (a solution of which in water has the remarkable property of rotating the plane of a beam of polarized light to the right) possessed small facets, developed only on one corner of the crystal. Neutral tartaric acid, or racemic acid, which in solution is without action on polarized light, possessed no such facet on its crystals ; but on crystallizing a certain double salt of racemic acid containing ammonium and sodium, two kinds of crystals were deposited, some with facets developed on the upper right- hand corner, and some on the corresponding corner of the left hand ; the former, in solution, rotated the plane of polarized light to the right; the latter, to the left. From these obser- vations Pasteur drew the inference that the existence of two varieties of tartaric acid must be due to the different arrange- ment in space of their atoms of carbon, hydrogen, and oxygen. In 1874 LeBel and van't Hoff simultaneously devised a theory to " explain " (i.e. to depict by means of a mechanical model) such compounds. It is based on the fundamental conception that each tetravalent carbon atom forms the middle point of a tetrahedron, whilst the elements or groups in com- bination with the carbon atoms are situated at each corner of the tetrahedron. Only when all four combined atoms or groups are different, is it possible for isomerism to occur ; the difference is similar to that which distinguishes the left from the right hand. Two or more of such tetrahedra may be linked together, by union of their carbon atoms; and Wislicenus pointed out that the isomerism of such substances as maleic and fumaric acids may be explained on the assumption that two of the carbon atoms in each of these acids is " doubly bound." Many compounds are known in which such structural differences are not permanent ; a compound and its isomeride may continually change, the one into the other; and the amount of each present in a solution may depend on the temperature, the extent of dilution, the presence of other STUDY OF PHYSICAL CHEMISTRY Ixi bodies, etc., so that a state of equilibrium ensues. This phenomenon is termed " tautomerism." Such conceptions have been extended to compounds of nitrogen (LeBel), sulphur (Smiles and Pope), tin (Pope), silicon (Kipping), and of cobalt, chromium, and the platinum metals (Werner). It has also been found possible to guess the probable structure of many, if not of all compounds. Such conceptions form the subject of the volume entitled Stereochemistry. In the volumes of this series the main divisions of the great subject of physical chemistry will be covered, while each in itself will be as complete a treatise as possible without over- lapping. The divisions are Stoichiometry^ or the various methods employed to determine atomic and molecular weights, and the classification of compounds (Professor Sydney Young, D.Sc., F.R.S.) ; the Relations between Chemical Constitution and Physical Properties (Samuel Smiles, D.Sc.) ; Chemical Statics and Dynamics (J. W. Mellor, D.Sc.); The Phase Rule (Alexander Findlay, D.Sc.) ; Thermodynamics (F. G. Donnan, M.A., Ph.D.); Spectroscopy (E. C. C. Baly, F.I.C.); Practical Spcctroscopy with tables of wave-lengths (F. A. Pollok, B.Sc.) ; Thermochemistry (Prof. Julius Thomsen, translated by Miss Burke, B.Sc.) ; Actinochemhtry (C. E. K. Mees, D.Sc., and S. E. Sheppard, D.Sc.); Electrochemistry (Part I., R. A. Lehfeldt, D.Sc.; Part II., N. M. C. Wilsmore, M.A., D.Sc.); and Stereochemistry (A. W. Stewart, D.Sc.). In each of these volumes the subject is brought up to the date of the latest discovery; and although it is, of course, impossible to avoid compilation, original papers are the chief sources of information, and copious references are introduced. It is hoped by issuing a series of volumes, instead of a single comprehensive treatise, to keep abreast of the vast subject of physical chemistry; for as the edition of each volume is exhausted, it will be possible for each author to bring his subject up to date. STOICHIOMETRY CHAPTER I FUNDAMENTAL LAWS OF CHEMICAL COMBINATION Elements and Compounds. All chemical substances are divided into two great classes elements and compounds. The term "element" was employed by the ancient philosophers and alchemists, but rather in the sense of a principle or property than of a definite chemical substance, and it is to Robert Boyle (1627-1691) that we are indebted for the first precise scientific definition of the elements as substances which are themselves not capable of further separation, but which can be obtained from a combined body, and out of which the compound can again be prepared. Since the time of Boyle this definition has been universally accepted, and those substances have been classed as elements which up to the present time have resisted all attempts to decompose them. Compounds, on the other hand, may be formed by the union of elements, and may be decomposed by the action on them of other chemical substances or by heat or electricity. The Conservation of Matter. It is believed that the total amount of matter in the universe remains unaltered, whatever changes may occur in its distribution. It has long been believed, also, that the total amount of each element is equally unalterable, although if the element is able to combine with others, the amount existing in the free state or in any particular state of combination may vary considerably from time to time. No direct experimental proof of the law or doctrine of the I B 2 STOICHIOMETRY Conservation of Matter is possible,, but all quantitative analyses are based on the assumption that when a chemical change occurs, there is no alteration in the total mass of the reacting substances. It is, indeed, possible to put this matter to the test of experiment by allowing a chemical reaction to take place in a sealed glass tube. A very minute alteration could be detected by weighing the tube on a very delicate balance before and after the chemical change had occurred. This subject has been very carefully investigated by H. Landolt, 1 and also by Heydweiller 2 and others. In most cases the minute differences observed were within the limits of experimental error, but a slight loss (maximum 0*199 nigrm. in Landolt's experiments, and 0*217 mgrm. in Heydweiller' s) was noted with certain reactions. No gain of anything like this magnitude was observed by either experimenter ; in fact, the gains were always within the limits of experimental error. The slight loss in the case of certain reactions has not been explained, but Landolt points out that glass is not absolutely impermeable to all gases ; for example, Bunsen has shown that carbon dioxide passes slowly through it. Again, when ferrous sulphate reacts with silver salts, giving metallic silver and ferric salts, there is a measurable loss in weight so long as the materials are contained in plain glass vessels, yet if the inner walls of the vessel are protected by a layer of solid paraffin, the loss becomes almost inappreciable. The only conclusion which can be drawn from the experi- ments is that no unassailable evidence against the absolute truth of the doctrine of the conservation of matter has yet been obtained, and that if any changes in the quantity of matter do occur, they are too minute to be measured except by the most refined and careful observations. Definition Df an Element. The extension of the doctrine of the conservation of matter to that of the conservation of each element is justifiable so long as the definition of an element already given is strictly applied. The suggestion has been made from time to time that the bodies which are now 1 Zeitschr. phys. C/iem., 55, 589 (1906). 2 DrudJs Ann., 5, 394 (1901). LAWS OF CHEMICAL COMBINATION 3 classed as elements have in the first place been formed by the condensation of one or of a very few primordial forms of matter ; but even if this were proved to be the case, the definition would remain valid until some means of recon- verting the "elements" into the primordial substances, or of producing a simpler from a more complex "element," had been discovered. If decomposition or disintegration of any of the substances now classed as elementary should be found to occur, it would be necessary either to remove these substances from the list of elements or to modify the definition so as to bring it into harmony with the facts, and at the same time to limit the law of conservation to matter as a whole. There can be no doubt that the bodies now termed elements form a class apart from those which are termed compounds, and it is probable that, as a matter of convenience, the term " elementary " will still be employed even if disintegration should be found to be a phenomenon of frequent occurrence. Although no means have yet been discovered whereby decomposition of the " elements " may be brought about at will, 1 yet strong evidence of the very slow spontaneous disintegration of a few of them has recently been obtained. It was observed in 1896, by Becquerel, that uranium salts possess the property of emitting rays which are able to pass through thin plates of metal and other opaque substances, and to act on a photographic plate. The study of the radio- activity of uranium compounds led to the discovery of the element radium by M. and Mme. Curie in 1898. The compounds of this element were found to emit rays of three distinct kinds, and also a gaseous emanation, which is itself intensely radio-active. An immense number of researches have been carried out on this subject, for an account of which reference may be made to Rutherford's " Radio-activity " (1905). It will be sufficient to mention that Rutherford and Soddy advanced the theory that the atoms of radio-active substances are undergoing spontaneous disintegration, with formation of a series of radio-active substances which differ in 1 But sec footnote 2, p. 4. 4 STOICHIOMETRY chemical properties from the parent substances and from each other, and that the radiations to which reference has been made accompany the breaking up of the atoms. The emanation from radium is a gaseous substance which can be transferred from one vessel to another; its products are luminous and strongly radio-active, and, like radium itself, it undergoes slow disintegration, one of the products formed, as shown by Ramsay and Soddy, 1 being the monatomic gas helium. 2 The metals uranium, thorium, and actinium are all radio- active, and all undergo very slow disintegration, and it is con- sidered probable by Rutherford that radium is derived in this way, not directly, but after intermediate stages, from uranium. The changes undergone by radium are accompanied by the liberation of a relatively enormous amount of energy ; it is found, for example, that the temperature of a mass of a radium salt (the metal has not yet been separated) is always higher than that of the surrounding matter, yet the diminution in weight is so small that it has not yet been detected by the most sensitive balance, although the gaseous emanation has been collected and its volume measured. It is safe, indeed, to assert that, had it not been for the great activity of the rays emitted by radio-active substances, radium would not have been discovered, and the disintegration of the atoms would not have been demonstrated. It has not been found possible to hasten or to retard the disintegration of any of the radio- active substances; the process goes on spontaneously,, and each substance has its own definite and measurable rate of disintegration. In the case of radium, at any rate, the radiation is quite unaffected by alteration of temperature 3 or pressure. 4 1 Proc. Roy. Soc., 73, 346 (1904). 2 Ramsay has recently stated (Nature, 76, 269 (1907) ), that in presence of water, the gas formed by the disintegration of radium emanation is not helium, but neon, and that in presence of a solution of copper sulphate it is argon. The copper (either as sulphate or nitrate) appears at the same time to suffer disintegration to a minute extent, the residue after removal of the copper showing the spectrum of the allied metal lithium faintly. 3 Becquerel, Compt. rend., 133, 199 (1901) ; Curie, Soc. de Physique, March 2, 1900; Rutherford, Radio-activity, 2nd edit., p. 210. 4 Schuster, Nature, 76, 269 (1907) ; Eve and Adams, same reference. LAWS OF CHEMICAL COMBINATION 5 If, then,, an element be denned as a substance which can- not, by any means known to us, be decomposed at will into simpler forms of matter, it will be correct to classify, not only the metals uranium and thorium, but also the radio-active gaseous emanation as elements. In the light of Ramsay's recent observation of the disintegration of copper, however, it appears probable that the definition will require modification. The Law of Definite Proportions. In the latter half of the eighteenth century, Wenzel (1740-1793) showed that, in the formation of any given salt, the acid and the base combine together in definite proportions. Berthollet, 1 however, con- sidered that in the chemical union of two substances, the composition of the product would vary with that of the original mixture, unless any exceptional circumstances, such as precipitation or escape of gas, stood in the way of this mass action. Proust, on the other hand, held the view that the composition of a chemical compound is perfectly definite, and by careful experiments, carried out from 1799 to 1807, he was able to prove the correctness of his conclusions. The truth of the law of definite proportions has since been confirmed by innumerable experiments. The Law of Multiple Proportions. It had long been known that certain metals could form more than one oxide or sulphide, but while Berthollet considered that such a metal could unite with any quantity of oxygen within certain limits, forming an indefinite number of oxides, Proust held that the number of oxides was limited, and that the composition of each was invariable. He showed, for example, that tin forms two oxides with the percentage composition I. II. Tin 88-15 78-81 Oxygen 11-85 21-19 100*00 100*00 John Dalton (1766-1844) pointed out that if, in such a case, the amount of one element is taken as constant, the 1 Essai de Statique Chimique^ 1803. 6 STOICHIOMETRY quantities of the other bear a very simple ratio to each other. Thus, in the case considered, taking 7*44 as the constant weight of tin, the composition of the two oxides would be I. II. Tin . , 7-44 7-44 Oxygen roo 2*00 As a result of his experiments on the compounds of carbon with oxygen and with hydrogen, and of nitrogen with oxygen, Dalton was able to formulate the law of multiple proportions, which may be stated as follows : If one element forms with another several combinations, the weights of the second element which unite with a constant weight of the first vary in the different compounds according to very simple numerical proportions. Thus carbon forms two gaseous compounds with oxygen, and taking the constant weight of carbon as 0*75, the weights of oxygen are i and 2. Again, phosphorus and chlorine form two compounds which have the composition I. II. Phosphorus . . . 0*2915 0-2915 Chlorine . . . . ro i'6 But i : i'6 :: 3 : 5, or the weights of chlorine that unite with 0*8745 P art by weight of phosphorus are 3 and 5. The Law of Equivalent Weights. Wenzel observed that when two neutral salts, AB and CD, react together to form two new salts, AD and BC, one of which is insoluble, the solution remains neutral; he concluded, therefore, that if solutions of the two salts are mixed in such proportions that the quantity of the component D is just sufficient to unite completely with A, there must be exactly the requisite amount of C present to combine with the whole of B, because any excess of B or C would cause the solution to become either alkaline or acid. Later, Richter (1762-1807) made quantitative, but not very accurate, determinations of the relative quantities of LAWS OF CHEMICAL COMBINATION 7 various acids and bases which react to form salts. He found, for example, that 1000 parts by weight of sulphuric acid would saturate 859 parts of soda or 1605 of potash, and that 859 parts of soda would neutralize 1405 of nitric acid. But 1405 parts of nitric acid neutralize 1605 of potash, so that 859 parts of soda, 1605 of potash, 1000 of sulphuric acid, and 1405 of nitric acid, may be regarded as equivalent quantities. Again, it has been shown that if a given substance A forms compounds with other substances B, C, D, ;/Z A parts by weight of A uniting with m B parts of B, m c of C, and m D of D respec- tively, and if B, C, and D form compounds with each other, the weights of C and D which unite with m B parts of B are either /// and m D respectively, or simple multiples or sub- multiples of these amounts. For example, i gram 1 of hydrogen unites with 35*5 grams of chlorine to form hydrogen chloride, with 23 of sodium to form sodium hydride, with 8 of oxygen to form water, and also with 1 6 of oxygen to form hydrogen peroxide. And it is found that 23 grams of sodium combine with 35^5 of chlorine to form common salt, with 8 of oxygen to form sodium oxide, and also with 1 6 of oxygen to form sodium peroxide ; lastly, chlorine and oxygen form two compounds containing, for each 35*5 parts of chlorine, 8 and 32 parts respectively of oxygen. Thus the quantities of oxygen which unite with i part by weight of hydrogen, with 23 parts of sodium, or with 35*5 of chlorine, are either 8, 1 6, or 32 parts, all them simple multiples of 8. Wollaston proposed the term "equivalent" to denote the amount of an element that unites with or displaces one part by weight of hydrogen, and the Law of Equivalent Weights may be stated as follows : When two or more elements unite to form a compound^ the weights of these elements are proportional to their equivalents or to simple multiples of them. 1 More exactly rooS gram. STOICHIOMETR Y THE ATOMIC THEORY. Ancient Atomic Theory. The idea that matter is not infinitely divisible, but that it is composed of minute indivisible particles or atoms, is a very old one. It is to be found in the works of Leucippus and Democritus, written twenty-four centuries ago, and was more fully developed by Lucretius. The views of these philosophers were, however, purely specula- tive, and were not in any way founded on observation or experiment. The chief conclusions arrived at by Lucretius may be shortly stated as follows : l 1. Atoms have different shapes; but the number of shapes is finite, and there is an infinite number of atoms of each shape. 2. Nothing whose nature is apparent to sense consists of one kind of atom only. 3. The atoms move through space at a greater speed than does sunlight. Dalton's Atomic Theory. At the beginning of the nine- teenth century, John Dalton brought forward the great theory which forms the basis of modern chemistry. The new atomic theory, unlike those of the ancient philosophers, was based on facts ascertained by experiment, and was concerned, not with the shapes or relative sizes of atoms, but solely with their relative weights. It may be of interest to compare the views of Dalton with those of Lucretius. A single verbal alteration the substitu- tion of weights for shapes is all that is required in the first statement of Lucretius, which thus becomes 1. Atoms have different weights ; but the number of weights is finite, and there is (practically) an infinite number of atoms of each weight. In conformity with Boyle's definition of an element, Dalton considered that 2. Chemical elements consist of one kind of atom only. 3. Dalton himself did not take into consideration the motions of the atoms, but we now know that the smallest 1 Tait, "Recent Advances in Physical Science" 1876. LAWS OF CHEMICAL COMBINATION 9 particles or molecules of a gas move with velocity many thousand times smaller than that of light (vide p. 187). Dalton made determinations of the composition of a number of compounds, but his results were not very accurate. He stated that i part by weight of hydrogen united with 5*5 parts of oxygen to form water, and he assumed, as the simplest possible case, that, in the formation of the smallest particle of water, one atom of hydrogen combines with one atom of oxygen. Dalton employed the term "atom" to denote the smallest particle, not only of an element, but also of a com- pound, and he spoke of a binary, ternary, or quaternary atom according to the number of elementary atoms composing it. Now if, on the one hand i part by weight of hydrogen combines with 5*5 parts of oxygen, and, on the other hand i atom of hydrogen combines with i atom of oxygen to form a binary atom of water, it follows that, taking the weight of an atom of hydrogen as unity, that of the atom of oxygen must be 5^5. In this way Dalton calculated the atomic weights of a number of elements. Wollaston objected to the use of the term " atomic weight," on the ground that there was no justification for the assumption that the smallest particle of water contained an equal number of atoms of the component elements ; and, in order to avoid all theoretical considerations, he proposed to substitute the term " equivalent weight " or " equivalent," as defined on p. 7, for atomic weight. He did not believe that it would ever be possible to ascertain the relative number of atoms of two or more elements which unite together to form the smallest particle of a compound, and he therefore considered that the atomic weights of the elements could never be determined. It is true that, when Dalton brought forward the atomic theory, no facts were known which threw any light on the chemical formulae of compounds, and it was therefore doubtful whether the equivalent of any given element or a multiple or sub multiple of the equivalent should be taken as the atomic weight. Wollaston's objection was so far justified, but he was io STOICHIOMETRV t mistaken in supposing that the problem could never be solved. In order to find the atomic weight of an element, it is usual (a) to make an accurate determination of its equivalent by analytical methods ; (b) to ascertain the relation between the equivalent and the atomic weight. It is not, however, essential that the equivalent should be determined, and, indeed, in the case of helium, neon, argon, krypton, and xenon, which appear to be incapable of entering into combination, such a determination would obviously be impossible. In order to find the atomic weights of these elements a knowledge of the properties of gases is requisite. CHAPTER II THE PROPERTIES OF GASES The Solid, Liquid, and Gaseous States of Matter. Matter exists in three forms or states of aggregation, the solid, the liquid, and the gaseous, which may be readily distinguished from each other by the following characteristic properties : A solid substance retains its shape unless acted upon by some external force. The amount of force required depends on the nature of the solid whether soft or hard and on its original shape. Thus, a piece of lead is more easily bent than a similar piece of iron, and a strip of tinfoil more easily than a thicker strip of sheet tin. If the force applied is not too great, the solid recovers its original shape when freed from its action, and is said to be elastic as regards shape. The volume of a solid at constant temperature can only be very slightly altered even by exposure to enormous pressure. In other words, a solid is almost incompressible. The shape of a liquid, on the other hand, is very easily altered, as, for example, when water or alcohol is poured from one vessel into another. Under ordinary conditions a sub- stance in the liquid state is only slightly compressible, more so, however, than when solid, 1 Not only is the shape of a gas more easily altered than that of a liquid, but when placed in any vessel, the gas has the property of completely filling and therefore of taking the shape of that vessel. Moreover, the volume of a gas is readily changed by altering the pressure to which it is exposed, unless that pressure is already very high. 1 Near the critical point a liquid is even more compressible than a gas at the ordinary temperature and pressure (p. 178). II 12 STOICHIOMETRY Gases and liquids have no elasticity as regards shape, but at constant temperature they recover their original volume when, after compression, the added pressure is removed. In other words, gases and liquids are perfectly elastic as regards volume. The volume of a gas is affected by change of temperature to a much greater extent than that of a liquid or solid, and the volume of a liquid more than that of a solid. The gaseous state of matter is also distinguished from the liquid or solid state by the much greater simplicity of the relations between temperature, pressure, and volume ; and, in studying these relations, it is therefore convenient to consider the behaviour of gases first. Boyle's Law. The influence of pressure on the volume of air was first studied by Robert Boyle in 1662, and, later, by Mariotte in 1679. Boyle determined the relation between the volume and pressure of a given mass of air at constant temperature between 4 and ^ atmos., and found that the volume varied inversely as the pressure. The same law has been found to hold for other gases, and it may be stated generally that, under moderate or low pres- sures and at sufficiently high temperatures, the volume of a gas at constant temperature varies inversely as the pressure. This statement is known as Boyle's law; it may be expressed by the equation v _/ i/~/ or pv = p'v' = const, at constant temperature. The density of a gas, s, may be defined as the mass of i cubic centimetre of it, and its specific volume, v, as the volume of i gram. Hence v = - s and p = cs at constant temperature where c is a constant j or the density of a gas at constant temperature is directly proportional to the pressure. THE PROPERTIES OF GASES 13 The relation between the pressure and volume of a gas at constant temperature may be represented graphically by measuring the pressures as ordinates and the volumes as abscissae, as in Fig. i. At any given temperature, say f lt let the distance ao be proportional to the pressure / of the gas, and co to the volume v which it occupies under that pressure ; from a and c draw the straight lines ab and cb perpendicular to the axes ox and oy respectively. Then the point b measures the volume v of the gas under the pressure / and at the tempera- ture /j. Similarly, the point V measures the volume v' of the gas under pressure /' at the same temperature, and so for any other points on the curve passing through b and b'. The curve is termed an isotherm^ or line of constant temperature ; its form is that of a rectangular hyperbola, the rectangles abco (=pv) and db'c'o ( = p'v') being equal. At higher temperatures, 4, 4, the relations between pressure and volume are represented by curves of similar form, but lying to the right of and above the first isotherm. Gay Lussac's Law. The expansion of air under constant pressure was first investigated by Dalton and by Gay Lussac, 14 STOICHIOMETRY but Dalton's results were not sufficiently accurate to enable him to draw a correct conclusion from them. Gay Lussac showed that the volume of a gas increases by -^ of its volume, measured at o C., for each rise of i C., or v t = z/ (i + a/), where a, the coefficient of expansion, = ^ or o'oc^y. 1 But the measurement of temperature is by no means so simple as that of pressure. It is customary to take the melting point of pure ice under atmospheric pressure and the boiling point of pure water under a barometric pressure of 760 mm. of mercury as standard temperatures ; and on the Centi- grade scale the melting point of ice is called zero, and the interval of temperature between the two points is divided into 100 parts or degrees, which should be of equal value. But changes of temperature are most conveniently indicated by the expansion or contraction of liquids, gases, or occasionally solids, and for ordinary and very many scientific purposes the mercurial thermometer is employed. The position of the mercury in such a thermometer, however, depends not only on the expansion of the mercury, but also to a much smaller extent on that of the glass. Now, two mercurial thermometers, made of different kinds of glass, which gave correct readings at o C. and at 100 C. would not register exactly the same temperature at, say, the boiling point of ethyl alcohol, 78*3 C., because the coefficients of expansion would not be quite the same for the two kinds of glass. Similarly, two thermometers, containing liquids of sufficiently high boiling point, say mercury and bromonaphthalene, although both correct at o and 100, would give slightly different read- ings at intermediate temperatures. The coefficient of expansion of air is more than 20 times as great as that of mercury, and about 145 times that of glass, and an air thermometer is therefore not only much more delicate than a mercurial one, but the alteration in the volume of the glass vessel containing the air is of relatively small importance. Moreover, many gases have almost exactly 1 Charles appears to have been the first to discover that the co- efficient of expansion is nearly the same for the more commonly occurring gases. THE PROPERTIES OF GASES 15 the same coefficient of expansion under ordinary or low pressures, and it is reasonable, therefore, to assume that the relation between the temperature and the volume of a gas is a very simple one. Using a mercurial thermometer, it is found that the co- efficient a remains very nearly constant between o and 100, and it is assumed that the slight variation is due to the errors in the thermometric scale, and that the true coefficient is really constant. Suppose, then, that a quantity of air or other gas were enclosed in a perfectly cylindrical tube by an air-tight and frictionless piston, and that the volume of air, as indicated by the piston, were to be marked on the tube, firstly, with the air thermometer immersed in melting ice ; and, secondly, in the steam from water boiling under a pressure of 760 mm. We should thus obtain the two fixed points o C. and 100 C. on the thermometer. By dividing the linear distance between the two fixed points into 100 equal parts we should mark out 100 equal volumes, since the tube is cylindrical, and it is assumed that, making the small correction for the expansion of the glass, each of these divisions is exactly one degree. 1 If, now, divisions of the same length were to be marked from the zero point to the bottom of the tube, there would be found to be 273 of them; or the volume corresponding to a single division would be ^ of the total volume at o C. If we call each division a degree, there will be 273 degrees on the thermometric scale below o C., and the temperature 273 is called the absolute zero on the Centigrade scale. A more rational method of expressing temperature is to start from the absolute zero instead of the arbitrary zero of the Centigrade scale. On this absolute scale of temperature the melting point of ice will be 273, and the boiling point of water under normal pressure will be 373 ; and, generally, the absolute 1 D. Berthelot (" Sur les Thermometres a Gaz," pp. 80-99; Travatix et Mem. du Bur. Int. de P. et Mes.) has shown that the maximum error between o and 100 at 760 mm. pressure is for the air or nitrogen thermometer, o'Oi8 ; for the hydrogen thermometer, 0*001; for CO 2> i6 5 TO 1C H 10 ME TR Y temperature is obtained by adding 273 to the Centigrade temperature, orT = /'-|-273. Thus v t = z> (i + at) In words, the volume of a gas under constant pressure varies directly as the absolute temperature. 1 P4 The relation between volume and absolute temperature is shown graphically in Fig. 2. The straight lines of equal pressure, or isobars, radiate from the zero of temperature (absolute) and volume. Similarly, if the volume is kept constant while temperature and pressure vary, it is found that the pressure varies directly 1 The absolute scale of temperature, as derived from the air thermo- meter, agrees almost exactly with the ther mod ynamical scale, which is independent of the nature of the body considered. THE PROPERTIES OF GASES 17 as the absolute temperature, or p ~ ^T at constant volume. This relation is shown graphically in Fig. 3. The straight lines of equal volume (or density) isochors or isometrics radiate from the zero of pressure and absolute temperature. V4 Va Va Vi T FIG. 3. Combining the laws of Boyle and Gay Lussac, when both pressure and temperature vary, we have the equation py = / O z/ (i -f- <*/) 273 = RT where R is a constant depending on the units of pressure, temperature, and mass, and on the nature and mass of the gas. If the volume v of a quantity of gas has been measured at a (Centigrade) temperature ^ and under a pressure p l} it may be required to know what the volume z> 2 would be at another temperature 4 and under the pressure / 2 . Converting the Centigrade temps. ^ and / 2 into T x and T 2 respectively, the ratio between the two volumes is given by the equation rp , or v = v l x~ x :r AI A i8 STOICHIOMETRY Thus 100 c.c. of air measured at 10 C. and under a pressure of 740 mm. would become at 20 and under the pressure 800 mm. 273 2O 740 z; 2 = 100 X - LS - - X P- = 273 + 10 800 c.c. Perfect Gases. A gas which followed the laws of Boyle and Gay Lussac exactly would be called a perfect gas, but the most careful experiments have shown that, under ordinary conditions of temperature and pressure, even the gases which are most difficult to condense, such as hydrogen, oxygen, and nitrogen, show slight deviations from these laws ; and that the deviations are more marked in the case of gases which are more easily condensed. Deviations from Boyle's and Gay Lussac's Laws. As regards Boyle's law, for example, Lord Rayleigh, 1 taking the value of pv as unity when the pressure is i atmos., finds the following values of p'v' when the pressure is reduced to 0^5 atmos. 1, 327. 2 " Relation des Experiences," 1847. * Journ. pr. Ghent., 56, 127 (1852). 4 Compt. rend., 70, 1131 (1870) ; 83, 1211 (1877); 84, 83 (1877); 88, 6 1 and 411 (1879). 5 " Memoires sur 1'e'lasticite et la dilatabilite des fluides jusqu'aux trs hautes pressions," Ann. Chim. Phys., Series VI., vol. 29, 1893. 20 STOICHIOMETR Y manometer could be taken to pieces and a glass tube inserted at the top, so that readings at various heights could be taken. The compression pumps contained mercury and glycerine, and were connected with the manometer and the glass volume tube, which consisted of a wide cylinder fused to a graduated and calibrated capillary tube of about i mm. A B internal and 10 mm. external diameter, and 500 mm. in length. Three different tubes were employed, so that the volume of gas should always be large enough to allow of accurate results being obtained. The compressibility of air (or of hydrogen, nitrogen, or any other gas) having been deter- mined by this method up to a pressure of 430 atmos., an air or gas manometer could after- wards be employed for the measurement of pressures up to that limit. For higher pres- sures it was necessary to employ some mechanical method of measurement, and Amagat modified the apparatus originally devised by Gally-Cazalat on the principle of the hydraulic press in such a manner that accurate results could be obtained by means of it. The apparatus was provided with a series of pistons ranging from 12 cm. to 5*527 mm. in diameter, the ratio of the lower pressure measured by a column of mercury to that on the compressed gas being equal to the ratio of the cross-sections of the two pistons in use. In this way pressures up to 3000 atmos. could be calculated from readings on a mercury column not exceeding 5*2 metres in height. A preliminary comparison with air and nitrogen manometers up to 430 atmos. showed good agreement. Up to 430 atmos. it was possible to compress the gases or liquids in thick-walled capillary glass tubes with no compensating external pressure beyond that of the atmosphere. For higher pressures, however, it was necessary to enclose the volume tubes in a CL O 5OO IOOO PRESSURE IN ATMOSPHERES. FIG. 6. temperatures up to a little over 30 (crit. t.= 31*35) each isothermal consists of three distinct parts : starting from the lowest pressures there is (a) a curved line sloping downwards, (b) a straight line passing vertically downwards, (c) a nearly straight line sloping upwards. The vertical straight line (/ = constant) shows what occurs during the liquefaction of the gas, and this part of the diagram will be considered in Chapter VIII. THE PROPERTIES OF GASES 23 Above 31*35 the isothermals show continuous curvature, and it will be observed that as the temperature rises, the depression in the isothermals becomes less marked, though it is still quite obvious, especially in Fig. 6, at 258. Minimum Values of pv. For each isothermal on the diagrams there is a minimum value of pv, and the broken line (Figs. 6 and 7) passes through these minima. It will be seen that as the temperature rises the pressure corresponding to the minimum pv increases gradually,, reaches a maximum, and then falls. The behaviour of ethylene is very similar to that 2-O 100 200 PRESSURE IN ATMOSPHERES. FIG. 7. of carbon dioxide at the same temperatures, but the experi- ments were made only up to 198, and the maximum pressure was not quite reached. With oxygen, however, a gas which is much more difficult to condense, the maximum has been passed at o, as will be seen from the table below. 2 4 STOICHIOMETR Y C0 2 C 2 H 4 2 T P Minimum. PV / Minimum. pv P Minimum. pv o 34'5 0-0740 42 OT570 175 0-9120 15 30 76 0-2185 87 0-3900 165 0-9910 60 H3 0-4830 125 0*6245 100 2IO 0-8140 161 O'922O 100 i '3750 137 245 1-0850 185 I 'l66o 198 255 I-4920 188 i '5340 258 218 i-Sioo Although in the case of hydrogen at o there is no mini- mum pv, the whole isothermal sloping upwards as a nearly straight line, the isothermals at lower temperatures show minima, which become more pronounced as the temperature falls. Thus, Witkowski l has determined the isothermals for hydrogen from +100 C. to - 212 C., and Kamerlingh Onnes and Braak 2 have made very accurate measurements between 104 C. and 217 C. The following data are taken from their paper : Temperature. Minimum pv. P. -182-75 0-32630 33'3 6 -I95-20 0-27338 47-69 204-62 0-22935 52-10 -212-73 0-18780 53'63 -2I7-32 0-16335 5i'57 The minimum values of pv, plotted against the correspond- ing pressures, fall on a parabola, the summit of which gives the maximum pressure. This was found to be 5373 atmos., the temperature being 209-6 C., and the value of pv 0*20394 (pv at o C. and i atmos. = i). The earlier results obtained 1 Acad. Set. Cracovie Bull., 6, 305 (1905). 3 Comm. Phys. Lab. Leiden, No. 97, 1907. THE PROPERTIES OF GASES 25. by Witkowski agree fairly well with those of Onnes and Braak. Again, for air, Witkowski 1 has shown that the pressures corresponding to the minimum values of pv reach a maximum at -75, the pressure at this temperature being 124 atmos. It appears, from what has been stated, that there must be a particular temperature for each gas at which the depression in the isothermal just disappears, so that the isothermal is horizontal through a considerable range of pressure. At this temperature the gas follows Boyle's law exactly up to a fairly high pressure, and behaves to this extent like a perfect gas. It may also be said that each isothermal is practically horizontal for a short distance just as it reaches and passes the minimum /z>, and that the gases behave like perfect gases, so far as Boyle's law is concerned, under these conditions also. The isothermals at very high pressures approximate in form to straight lines, nearly parallel to each other. There is, however, slight curvature, as shown by the values of * v ~~ * v . P - P given in the table below for hydrogen and oxygen at o. Pressures. Hydrogen. Oxygen. 500-1000 atmos. 0'000732 0'OOII58 1000-1500 ,, 690 1106 1500-2000 ,, 638 1054 2000-2500 ,, 612 1015 2500-3000 ,, 579 0971 As regards the influence of temperature, the values of p fr pv are distinctly higher at 100 than at o for CO. 2 and QH 4 at pressures from 200 to 1000 atmos., and for nitrogen and air there seems to be a slight rise with rise of temperature, but with hydrogen the values at o, 100, and 200 show no decided variation. Coefficient of Dilatation under Constant Pressure, . v at' 1 A cad. des Sci. de Cracovie, 1891. 26 STOICHIOMETRY Amagat tabulates the values of - . (= a), where v is the 1) L^t volume at the lower of the two temperatures in each case, not the initial volume at o C. The values of a for CO 2 and C 2 H 4 at each temperature rise at first with rise of pressure, reaching a maximum, and then falling again. The higher the temperature the higher is the pressure at which the maximum occurs. Thus, in the table for CO 2 from 40 to 50 the maximum (0*07566) occurs at 90 atmos.; from 90 to 100 the maximum (0-01247) is at 150 atmos. ; and from 198 to 258 the maximum (0*00364) is at 300 atmospheres. The fall in value of a with further rise of pressure for a given temperature interval continues, with O 2 , H 2 , N 2 , and air, up to 3000 atmos. As regard the variation of a with temperature at constant pressure, it is found that the values increase to a maximum and then fall. The higher the pressure the higher is the temperature at which the maximum occurs, but at high pressures the rise is less marked than at low ones. In the tables for CO 2 and C 2 H 4 the maximum is not reached at pressures above 400 and 300 atmos. respectively, but the results obtained with oxygen, hydrogen, nitrogen, and air indicate that it would be attained at higher temperatures. These maxima do not differ greatly from those observed at constant temperature with rise of pressure. Amagat states that at any pressure and at sufficiently high temperatures becomes constant as in the case of perfect gases, but the volume is not directly proportional to the absolute temperature, but to the absolute temperature diminished by a constant, or v = cT a. The constant a diminishes as the pressure falls, and becomes zero at low pressures, when v - cT at constant pressure, and the gas follows Gay Lussac's law. Pressure Coefficients at Constant Volume. Amagat con- siders the two coefficients, /3 = ^ ~- and B = -^. For the. THE PROPERTIES OF GASES 27 first he adopts the old name, " coefficient of dilatation at con- stant volume " ; the second, which is simply the differential of pressure with regard to temperature, he calls the coefficient of pressure. It will be better, however, to employ the terms "coefficient of increase of pressure " for /3, and " differential of pressure " for B. Considering a series of constant volumes, the coefficient /3, for a given temperature, increases with diminution of volume to a maximum and then falls. The maximum is most pro- nounced at low temperatures. The differential B increases rapidly as the volume diminishes. At any constant volume the differential B remains nearly constant ; the slight variations tend to disappear at sufficiently high temperatures, and even at all temperatures under suffi- ciently high pressures. Thus, at constant volume the pressure is nearly proportional to the absolute temperature minus a constant, or / = cT a. The constant a diminishes as the volume increases, and is zero for perfect gases. This law, which was found by Ramsay and Young and by Bams to apply, approximately at any rate, to liquids as well as gases, and which also follows from the equation of state of Van der Waals (p. 201), will be considered more fully in Chapter XI. The compressibilities of CO 2 , SO 2 , C 2 H 4 , and NH :5 were compared with those of nitrogen by Roth, 1 but the pressures to which the gases were subjected were not high enough to show the minimum values of pv at constant temperature. Very important investigations on the properties of gases have been and are being carried out by Kamerlingh Onnes and his co-workers at Leiden. Schalkwijk, 2 has determined the values of pv for hydrogen at 20 very accurately from 20 to 60 atmos., and gives the formula /z'ao = ro7258 + o'ooo6-67 and this was v + v found to be the case within the limits of experimental error down to exceedingly low pressures. It was not found possible to determine the compressi- bilities of other gases (O 2 , N. 2 , CO 2 ) by means of the apparatus, but by a modification of the method the coefficients of expansion at constant pressure were determined at a series of low pressures. Ramsay and Baly found that the results with oxygen were erratic when the pressure was about 075 mm. Battelli l employing both glass and iron vessels, found that hydrogen followed Boyle's law down to a pressure of 0*02 mm. But he observed a deviation with air at pressures between 2 and 5 mm., and with oxygen a break at about 07 mm. Carbon dioxide was found to be more compressible than is required by Boyle's law, but Battelli attributes this deviation to absorp- tion by the walls of the vessels. Thiesen 2 pointed out that Bohr's and Battelli's results do not really agree, and he himself observed no break with oxygen at low pressures. After filling one of his balloons with glass wool, some peculiarities were observed with oxygen, but Thiesen saw no reason for assuming any anomaly at 07 mm. 1 N. Cimento, 1, 5 and 81 (1901) ; and Phys. Zeitschr., 3, 17 (1901). 2 Ann. d. Physik., 6, 2, 280 (1901). STOICHIOMETRY M Rayleigh 1 devised a manometer suitable for very low pressures, which were ascertained with very great accuracy by tilting the forked manometer (Fig. 9) until the fine pointers one in each arm just touched the surface of the mercury at B, B. The tube A was connected by flexible tubing with a reservoir of mercury, and the manometer was set at first with the pointers touching the mercury when both limbs were com- pletely exhausted. The angle through which the manometer was tilted was measured by the angle of rotation of the mirror M, which was fixed to the platform N, resting on the three points L (shown in plan below). The mirror, stand, and manometer were rigidly attached to a board, which could be rotated on a horizontal axis parallel to the face of the mirror, lying ap- proximately in the mirror surface and at about the middle of the height of the operative part. Between 1*5 mm. and o'oi mm. hydrogen, nitrogen, and oxygen were found to follow Boyle's law within the limits of experimental error. The mean error in pressure from that re- quired to make/z/ equal to the mean value in any series was usually less than 0*00 1 mm., and the + and errors were generally well distributed. In the following year Rayleigh,' 2 employing a quite different form of manometer, determined the relation between the values of pv at 75 and 150 mm. for five gases. Calling the larger volume and the smaller pressure v l and/! respectively, p-p-^ = B . p$) v The values of B observed were as follows : FIG. 9. 1 Phil. Trans. 196, 205 (1901). 2 PhiL Trans., 198, 417 (1902). THE PROPERTIES OF GASES 33 IB. Air o'99997 H. 2 0*99997 O.j I'OO024 Argon 1*00021 N 2 O 1*00066 The results with oxygen were not so satisfactory as with the other gases, the individual values varying from 1-00005 to i '00044. It is? therefore, quite possible that the mean value may be a little too high. Referring back to the values of B for hydrogen, nitrogen, oxygen, and air (p. 18) for the pressures \ atmos. and i atmos, the conclusion to be drawn from the whole of Lord Rayleigh's results, and from those of Regnault, Amagat, Leduc and Sacerdote/ Jaquerod and Sheuer, 2 and others, is that the values of B approach and finally reach unity as the pressure falls, those for hydrogen rising and for the other gases falling. For the pressure range 75 to 150 mm., the differences from unity are quite negligible in the case of hydrogen, air, and presumably nitrogen. There is probably still a slight difference with oxygen, but this disappears at still lower pressures. In the case of nitrous oxide, B has still a fairly high value between 75 and 150 mm. It is easy to understand how, by the introduction of moderate experimental errors or other disturbing factors, a simple physical relation may be transformed into an apparently complex one, but it is in the highest degree improbable that the transformation of a really complex relation into an apparently simple one could be thus brought about. Again, the fact that so many observers have obtained practically concordant results with hydrogen, but very dis- cordant results with oxygen, seems to prove that there is some cause of disturbance other than ordinary experimental error, peculiar to the latter gas, but no satisfactory explanation of the anomalies observed by Bohr, Battelli, and Ramsay and Baly has yet been suggested. 1 Compt. rend., 125, 297 (1897). 2 Compt. rend., 140, 1384 (1905). 34 STOICHIOMETRY The general results obtained with gases under moderate or low pressures may be stated as follows : 1. Comparing different gases at the same temperature, say o, and through the same range of pressures, say from 0*5 to i atmos., / changes from a relatively large negative value to a small positive value as we pass from the more easily to the less easily condensable gases. 2. Comparing any one gas at a series of temperatures and through the same range of pressure, changes (or would be found to change if the experiments could be carried out) from a relatively large negative value to a small positive value as the temperature rises. Few data are actually available for any one gas, but it may be noted that for nitrogen at 0, = 0*000571 per metre of mercury; at about 52 ^ ' = o'oooooo, and at 100 the value is + 0^000347 . Thus for a moderate range of pressure nitrogen follows Boyle's law accurately at about 52, but not at o or 100. 3. For the less easily condensable gases, such as hydrogen and nitrogen, * ' at any constant temperature above, say, o remains constant or nearly so from zero pressure to 3 or 4 atmos., but for the more easily condensable gases, such as carbon dioxide, there is distinct variation. 1 4. If is constant and small for a gas between, say, o and 3 or 4 atmos., the value of ^ between these limits of pressure will be practically constant for a given value of 8p whatever the actual pressures, and will approach more and more closely to unity as fy becomes smaller. The fact, therefore, that Rayleigh found no measurable variation in the value of pv between 1*5 mm. and o'oi mm. in the case of hydrogen, nitrogen, and oxygen need not be taken to prove 1 D. Berthelot, " Sur les Thermometres a Gaz," p. 7. THE PROPERTIES OF GASES 35 that . = o between those limits of pressure, but that its value remained very small. In other words, Rayleigh's results do not prove that these gases follow Boyle's law absolutely at very low pressures, but that the deviations are too small to be detected even in experiments of such remarkable accuracy. Coefficients of Expansion and of Pressure. In the equation v t = z/ (i + at) at constant pressure a is the coefficient of expansion; and in the equation p t = pj^i + j3t) at constant volume ft is the coefficient of increase of pressure. The values given on the following page have been obtained for various gases, p being the constant pressure at which a was determined, and / the initial pressure in the determination of ft. Gay Lussac was of opinion that all gases had the same coefficients of expansion (a) under constant pressure ; that they all followed Boyle's law ; that they therefore all had the same coefficients of increase of pressure (ft) at constant volume ; and, lastly, that a = ft. Regnault showed that no real gas is perfect^ but he con- cluded that the coefficients for different gases become more and more nearly equal as the pressure falls, and that the state- ment that the coefficients are equal may be taken as correct only for very low pressures. D. Berthelot 1 points out, as already stated, that for the gases formerly called permanent the values of ~- on any isotherm at about the ordinary temperature are small, and may be regarded without sensible error as constant up to pressures of 3 or 4 atmos. In other words, up to pressure's of 3 or 4 atmos. the isotherms may be regarded as straight lines. Berthelot shows that the coefficients of expansion and 1 Loc. dt. STOICHIOMETR Y Gas. Observer. P a(o-ioo) .P 0(o -100) Hydrogen Regnault I almos. 0*003661 I atmos. 0-003668 55 Chappuis i metre 0-00366004 i metre 0-00366254 ,, K. Onnes I 0-0036627 and Bondin 53 Richards i atmos. 0-0036609 and Marks 5 J Travers and 700 mm. 0-00366255 Jaquerod 55 5 j 5 55 0-0036627 Helium 3 J 700 ,, 0-00366255 jj j j 5oo 55 0-0036628 Nitrogen Regnault I atmos. 0-003668 5 1 Chappuis i metre 0-00367313 i metre 0-0036744 53 53 i -387 metre 0-00367750 793-5 mm. 0-0036718 5 ? j> 530-8 0-0036683 Air Regnault i atmos. 0-003671 i atmos. 0*003665 Oxygen Makower mean values 663-38 0-0036738 and Noble tt j j 353-99 0-0036698 Carbon monoxide Regnault i atmos. 0-003669 i atmos. 0*003667 Carbon dioxide ij 5 > 0-003710 ) 9 0-003688 ii Richards 0-0037282 and Marks Sulphur dioxide Nitrous oxide Regnault 91 11 II 0-003903 0-003719 I atmos. > 0-003845 0-003676 0(0 -1067) Nitrogen Jaquerod 240 0-0036643 and Perrot Air | 230 0*0036643 Oxygen 9 180-230 0-0036652 Carbon monoxide > 230 0*0036648 Carbon dioxide 9 240 0-0036756 If 170 0*0036713 of increase of pressure, a and /?, may be conveniently studied by consideration of the pvp diagram. In Fig. 10, let A A' and BB'B" be two isotherms relating to temperatures /\ and 4 respectively. From the point O' (OO f = /) draw a straight line parallel to the axis of ordinates cutting the isotherms in A' and B'. From O to A' draw a straight line, and produce it to cut the second isothermal in B". Then the lines AA' and BB" repre- sent isotherms, O'B' an isobar, and OB" an isochor, or line of equal volume. THE PROPERTIES OF GASES 37 The angular coefficient of the isotherm AA', or the co- efficient of deviation from Boyle's law at /, is d(pv) O'A'- OA dp OO' The coefficient of expansion, a, under constant pressure between the temperatures ^ + / 2 is v'-v i A'B' 4 - A X O The coefficient of increase of pressure, /?, at constant volume is i A'B" / 2 - A X OA' When the pressure (or density) decreases indefinitely, a and (3 tend towards a common limit, which may be termed y, the coefficient of expansion (or increase of pressure) charac- teristic of the perfect gaseous state 7 = i AB - A X OA 38 STOICHIOMETRY In order to calculate y, any three out of the four following constants must be known : the angular coefficients of the two isotherms ; a, giving the point A' and B' ; and ft, giving A' and B". The values of y, have been calculated by D. Berthelot for nitrogen and hydrogen from the determination of Chappuis. 1 Thus for nitrogen Chappuis finds (1) ato, = -0-000571 (2) between o and 100 for p = i metre, iooa = 0*367313 (3) between o and 100 for p = i metre, looft = 0*367440 d(pv) Hence at 100 , = +0-000347 and looy = 0*366185 From determinations by Chappuis between o and 100 of a for p = 1386-8 mm. and of ft for / = 793*5 mm. and 532*9 mm. respectively, three independent values of y may be calculated. They are- Mean of all. looy = 0-366185, 0*366184, 0*366177 0-366182. For the above determinations vessels of platinum-indium or of hard glass were employed. Experiments with a porcelain vessel gave variable and evidently untrustworthy results. In the case of hydrogen the data are less complete and the calculated values of y less concordant. It is quite possible that a vessel of platinum-iridium may be unsuitable for hydrogen even at 100, and the only determination of a was made in a vessel of this alloy. Only the third determination of ft was carried out in a vessel of hard glass. The three values of looy calculated by Berthelot for hydrogen are 0*366248, 0*366206, and 0-366169 respectively, of which he regards the 1 Travaux ft Memoires du Bureau international des Poids et Mesures. THE PROPERTIES OF GASES 39 last as the most correct. The mean of the five values, four for nitrogen and the last for hydrogen, would give y = 0*00366180 and - = 273*090 [The mean of all seven values would be y = 0-00366193 and - = 273-080.] CHAPTER III GENERAL PROPERTIES OF GASES (continued) The Densities of Gases and Vapours. The weight of a given body is proportional to its mass and to the force of gravity acting on it. The attractive force varies slightly with the latitude and with the height above the sea-level, but in one locality weight is simply proportional to mass, and the terms are frequently employed as synonymous. The density, s, of a substance may be denned as the weight (or mass) of unit volume of that substance. The gram is taken as the unit of weight, the cubic centimetre as the unit, of volume. The specific gravity of a substance may be defined as its weight in terms of that of the same volume of some standard substance under specified conditions of temperature, and, if necessary, pressure. In the case of liquids and solids, sometimes of gases also, it is customary and most convenient to take water at 4 C. as the standard substance, because the unit of weight, the gram, was originally defined to be the weight of i cubic centimetre of water at 4 C., that is, at its point of maximum density, and in practice the unit of volume is taken to be that occupied by i gram of water at 4. That being the case, the density of a substance is numerically equal to its specific gravity. The specific volume, v, is the reciprocal of the density or specific gravity, and may be defined as the volume occupied by i gram of a substance. Of course, as the volume of a substance depends on the temperature and pressure, these should be mentioned in stating 40 THE PROPERTIES OF GASES 41 its specific volume or density, but as the volume of a solid or liquid under ordinary conditions is not appreciably affected by moderate changes of pressure, the temperature only need usually be mentioned. 1 Gases, under ordinary conditions, are so much lighter than liquids or solids that it is frequently convenient to state the weight of a litre instead of that of a cubic centimetre, and for many purposes it is useful to compare the specific gravity of a gas with that of another standard gas under the same con- ditions of temperature and pressure. When a substance is liquid or solid under ordinary con- ditions, but can be vaporized by raising the temperature or reducing the pressure, and when the specific gravity of its vapour is compared with that of a standard gas at the same temperature and pressure, the ratio so obtained is always termed by chemists the vapour density of the substance. There is thus some ambiguity in the use of the terms " density " and " specific gravity," but confusion is hardly likely to arise, because the magnitude of the value stated is a sufficient indication of what is meant. At one time it was customary to express the specific gravity of a gas, and the vapour density of a liquid or solid, in terms of that of air taken as unity, but air is a mixture, and its composi- tion is not absolutely constant. Many chemists preferred to take hydrogen as the standard gas, because the atomic weight of hydrogen was taken as unity. Within recent years, however, it has been thought better to take 16 as the atomic weight of oxygen, so that the recognized unit is ^e f tne atomic weight of oxygen, and not the atomic weight of hydrogen, which differs slightly from it. Following this change, many experimenters have recently 1 Some chemists take water at o as the standard, others take water at the same temperature as that of the substance investigated ; it is therefore I r advisable to state the temperature of the water thus Sp. gr. at -%, or at 4 -5-, or at - -Q. It is, of course, only in the first of these cases that the specific gravity is numerically equal to the density. 42 STOICHIOMETRY taken 16 as the specific gravity of oxygen, making this gas the standard. The accurate determination of the density of a gas is a very difficult matter, for the gas must be contained in a vessel of large capacity and of relatively great weight. An error in weighing may therefore be negligible as regards the total weight of globe and gas, but of great importance as regards that of the gas itself. Again, owing to the buoyancy of the air, the apparent weight of a large globe is greatly affected by changes in atmo- spheric pressure. The surface of glass, also, is slightly hygro- scopic, and the apparent weight of a glass globe therefore depends to a slight extent on the hygrometric state of the air. Regnault was the first to avoid some of these difficulties by employing as a counterpoise a second globe of as nearly as possible the same weight and capacity as that required for the gas. Regnault, however, overlooked the fact, pointed out later by Rayleigh, that since glass is slightly elastic, the capacity of a globe is affected by changes of pressure, being slightly less when exhausted than when filled with gas. The weight of air displaced when the vessel is exhausted is therefore slightly less than when it is full, and the apparent weight of the exhausted globe is therefore a little too great. Regnault's actual globes of 10 litres capacity have been broken, but Crafts has estimated the correction as 3 mgrm. In making the determinations, the utmost care must be taken to exhaust the globe completely before weighing it, and in order to avoid the introduction of impurities, it is advisable to exhaust the globe two or three times after admission of small quantities of the gas under examination. The globe is then filled with the gas at a known temperature and pressure, and is again weighed. The following are some of the best determinations of the weight of a litre of a few gases at o and 760 mm. at the latitude of Paris : THE PROPERTIES OF GASES 43 Rayleigh. Morley. Leduc. Oxygen . . . Hydrogen . . Nitrogen . . . 1-42905 0-08998 l 1-2507 I -4290 0-08987 I-2503 I -4288 0-08982 Determination of Vapour Densities. Various methods have been devised for the determination of the vapour density of a substance which is liquid (or solid) at the ordinary temperature. The three which have been most frequently employed are those of Dumas, Hofmann, and V. Meyer. Dumas' Method. Dumas employed a glass bulb with the neck drawn out to a fine tube. The bulb was first weighed full of air at a known temperature and pressure, and by subtracting the calculated weight of air, that of the empty bulb was ascertained. A quantity of the liquid was introduced by warming the bulb and holding the open end of the tube under the liquid. The bulb was then heated in a suitable bath to a temperature 20 or more above the boiling-point of the liquid, when brisk ebullition took place, and the air in the bulb was expelled by the vapour. When the escape of vapour ceased, the fine tube was sealed near the end, and the bulb was thus filled with the vapour at the temperature of the bath and under atmospheric pressure. After cooling, the bulb with the little tube that was drawn off was weighed again, and the weight of vapour thus ascertained. Finally, the capacity of the bulb was determined by breaking the end of the tube under recently boiled water and weighing the bulb full of water. The vapour density is equal to the weight of vapour divided by that of the same volume of the standard gas at the temperature of the bath and under the atmospheric pressure. The chief advantage of Dumas' method is the simplicity of the apparatus required, but it is not suitable for substances which can only be obtained in small quantity, because a con- siderable amount of liquid must be evaporated in order to ensure complete expulsion of air from the bulb. Hofmann 's Method. This is an improvement on a method 1 This value is admittedly a little too high. 44 STOICHIOMETRY devised by Gay Lussac. The apparatus consists of a eudio- meter tube graduated in millimetres and calibrated, or graduated in cubic centimetres; a mercury trough; and a vapour-jacketing tube similar to B (Fig. u). The eudiometer is filled with mercury, and if an accurate result is required, the mercury should be boiled in the tube to remove all air and the film of condensed gas adhering to the glass. The tube is then inverted in the trough of mercury. The substance is weighed in a small bulb, which is usually loosely stoppered or may be drawn out to a fine capillary tube, and the little bulb is passed up into the eudiometer, great care being taken to avoid loss of material or introduction of air. The bulb rises past the mercury, and the substance evaporates into the vacuous space either at once or when the eudiometer is heated by the jacket- ing vapour. The amount of substance required is very small, and the weight is determined directly. The temperature is that of the jacketing vapour ; the volume is read on the eudio- meter, but in exact work must be corrected for the expansion of glass ; the pressure is the difference between the corrected heights of the barometer and of the column of mercury in the eudiometer. The corrections for pressure are, unfortunately, somewhat uncertain. In the first place, the heights of the two columns of mercury must be corrected to o C., but while the upper part of the mercury in the eudiometer is at the temperature of the vapour, the lower part is at or about the temperature of the room, and it is impossible without a special appliance, such as the integrating thermometer of Ramsay and Steele, 1 to estimate with accuracy the temperature of the intermediate portion ; in the second place, if the temperature is high the vapour pressure of mercury cannot be neglected, but the diffusion of mercury vapour is a slow process, and unless consider- able time is allowed, the maximum pressure may not be attained. On the other hand, readings may be taken at different temperatures, and by replacing the open mercury trough by a closed cylindrical glass vessel, A (Fig. n), connected with a pump and pressure gauge, the external pressure may be altered, 2 Zeit.phys. Chem., 44. 348 (1903). THE PROPERTIES OF GASES 45 and a series of determinations may be made at different pressures and volumes. 1 Victor Meyer's Method. This method is the most con- venient for ordinary purposes, and is the one which is most frequently employed. The long tube A (Fig. 12), which may be of glass, porcelain, platinum, or perhaps quartz, is carefully dried, and a little dry sand or fine asbestos is placed in it as a protection against fracture when the bulb con- taining the substance is To PUMP AND GAUGE.**- - =* FIG. ii. FIG. 12. introduced. The tube is closed above by a cork, and is heated below in a suitable bath, B, or in a furnace to a temperature 1 Ramsay and Young, Phil. Trans., 178, 57 (1887) ; Young, Proc. Phys. Soc. t 13, 658 (1895) 4 6 S TOICHIOME TR Y which must be well above the boiling point of the substance under investigation, the expanded air being allowed to escape in bubbles through the water in the trough C. The graduated tube D, previously rilled with water and inserted in the trough, is then placed in position over the delivery tube, and the bulb containing a weighed quantity of the substance is introduced. This may be done by moving the cork, dropping in the tube, and replacing the cork at once ; or the little bulb may be supported at the top of the tube while the cylindrical bulb is being heated, and may afterwards be released and allowed to fall by a mechanical arrangement without removing the cork. Rapid evaporation takes place, and the vapour expels its own volume of hot air, which is finally collected at the tem- perature of the room in the graduated tube. As the air is collected over water it becomes saturated with moisture. If b is the barometric pressure, p' the vapour pressure of water at the temperature of the room, and /" the pressure of the column of water in the graduated tube reduced to millimetres of mercury, the true pressure of the dry air = b p' p" p. If the heated vapour itself could be cooled to the temperature of the room without condensing, and if its coefficient of ex- pansion were the same as that of air, its volume under a pressure / would be the same as that of the cooled air. Calling the weight of substance m t the temperature of the room /, and the volume of air collected v t it may be stated that m gram of the substance would occupy as vapour v c.c. at f and under pressure p. The vapour density may therefore be calculated without knowing the temperature of the bath or furnace. The method can be employed up to temperatures which are limited only by the melting or softening of the material of the vapour-density tube. Numerous modifications of these methods have been devised for special purposes. Gay Lussac's Law of Volumes. Cavendish in 1781 dis- covered that hydrogen and oxygen combine together to form water in the exact, or almost exact, ratio of 2 volumes of hydrogen to i volume of oxygen. Gay Lussac and Humboldt confirmed the correctness of this ratio in 1805, and Gay Lussac THE PROPERTIES OF GASES 47 afterwards determined the volumetric composition of several compounds ; he published in 1809 the generalization known as Gay Lussac's " Law of Volumes," which may be stated as follows : IVhen two or more gaseous substances combine together to form a compound^ the volumes of the combining gases bear a simple ratio to each other and also to that of the compound when it is also a gas. Thus, for example, i volume of nitrogen combines with 3 volumes of hydrogen to form 2 volumes of ammonia gas. Gay Lussac also showed how the density of the gaseous compound could be calculated from the densities of the compound gases, and in some cases he found that there was a fair agreement between the calculated and observed densities. It is clear, however, that, since under ordinary conditions of temperature and pressure no known substance behaves as a perfect gas, the law of volumes cannot in general be regarded as strictly true, neither can the observed and calculated densities of the gaseous compounds be expected to show exact agreement. But from what has been stated (p. 37), it may be concluded that the law would be found strictly applicable to gases under exceedingly low pressures, at any rate at sufficiently high temperatures. According to Gay Lussac and Humboldt, the volumes of hydrogen and oxygen which unite to form water are in the ratio of 2:1, but the very accurate experiments of Morley * show that at o and 760 mm. the true ratio is 2-00268, a value which agrees very closely with that obtained by Scott, 2*00285 (corrected to o and 760 mm.). But the value of pv for hydrogen decreases, while that of oxygen increases, with fall of pressure, and at zero pressure the ratio would be 2-0027 X IT g* vo SA which would be very close indeed to 2. Avogadro's Hypothesis. Shortly before the enunciation of 1 A mer. Jour. Set., 1891. 48 STOICHIOMETRY the law of volumes Dalton had brought forward his atomic theory, according to which a simple ratio exists between the number of atoms of different elements which unite together to form a compound, and Gay Lussac attempted unsuccessfully to bring the atomic theory into harmony with the law of volumes by assuming that the densities of gases are proportional to their atomic weights. Bernoulli, in 1740, had attributed the pressure exerted by a gas to the impact of the rapidly moving particles against the walls of the containing vessel. Avogadro, in iSn, 1 and, independently but somewhat later, Ampere brought forward the hypothesis that equal volumes of different gases, measured at the same temperature and pressure, contain the same number of these particles, which Avogadro termed molecules.' 2 ' Molecular Weights. If this hypothesis is true, the densities of different gases at the same temperature and pressure must be proportional to the masses of the molecules or the molecular weights (p. 60). But just as it is only at exceedingly low pressures that Gay Lussac's law of volumes can be said to be strictly true, so it is only at such pressures that Avogadro's hypothesis can be strictly applicable to real gases. If, however, the densities of two gases under ordinary atmospheric pressure and the values of , are known, it is easy to calculate what their densities would be if they behaved as perfect gases. Thus the density of oxygen compared with that of hydrogen at o C. and i atmos. pressure was found by Morley to be 15*90. The corrected value would, however, be where/! = i atmos. and/ = zero pressure ; 1 Journal de Physique, 73, 58 (1811). 2 The bearing of Avogadro's hypothesis on the determination of atomic w eights will be considered later. THE PROPERTIES OF GASES 49 i d(pv) where a = /z -X^T at o = 2(1 - B), where B=yJ*- = I -B< where B'=g A A, A being i atmos., \ atmos., and zero pressure respectively. The values of B for a few gases are given on p. 18, under the heading p'v'. The corresponding value of a are as follows : Oxygen .......... 0*00094 Hydrogen .......... + 0*00053 Nitrogen .......... 0*00056 Carbon monoxide ....... 0*00081 Carbon dioxide ........ 0*00668 Nitrous oxide ........ 0*00747 For carbon dioxide Chappuis finds the value a = 0*00665 ; and for hydrogen and nitrogen, from determinations of com- pressibility between i and 2 atmos., a = -\- 0*00057 and 0*00043 respectively. From determinations at pressures between 400 and 800 mm. Jaquerod and Scheuer obtain the following values of a : Hydrogen .......... + 0*00052 Oxygen .......... 0*00097 Nitric oxide ......... o'ooii7 Taking Lord Rayleigh's values of a for oxygen and hydrogen, the corrected density of oxygen is I O'OOOQ4 - i 4- 0*00053 The molecular weight of oxygen is therefore 3176 if that of hydrogen is taken as 2 ; it is, however, more convenient to state the molecular weights of gases and vapours in terms of that of oxygen, which is taken as 32. E 50 STOICHIOMETRY On this basis, the molecular weight of hydrogen is iffc- Adopting Lord Rayleigh's values for oxygen and nitrogen, the molecular weight of the latter gas is 0-96737 i - 0-00056 *00094 32 x - - - X - ^- = 28-016 rio^r; i o*c D. Berthelot has calculated the following values from the data obtained by Leduc and Sacerdote : Molecular weights. Hydrogen 2*0145 Nitrogen 28*013 The agreement with Lord Rayleigh's values is very satis- factory. Value of R for Perfect Gases. It is now possible to calculate the value of R in the equation for perfect gases. PV = RT If unit mass, say i gram, of gas be taken in each case, the value of R will depend on the molecular weight as well as on the units of pressure and volume, but if one gram-molecule (the molecular weight in grams) of each gas be taken, R will be constant for any given units of pressure and volume, for it is now known that 32 grams of oxygen, 2*0145 grams of hydrogen, or 28*015 grams of nitrogen would each occupy 22*41 litres at o C. and under normal atmospheric pressure if they behaved as perfect gases. Taking the millimetre of mercury as the unit of pressure, and the cubic centimetre as the unit of volume, the equation will be, for any perfect gas THE PROPERTIES OF GASES 51 or with the litre and the atmosphere as units of volume and pressure, respectively, the equation becomes 273 According to D. Berthelot (loc. cit.), the constant is given with greater accuracy by taking the volume of a gram-molecule of gas as 22*412 litres, and the absolute zero of temperature as 273-09 C. The value of R for the two systems of units would then become 62,372 and 0^08207 respectively. Specific Heats of Gases. The specific heat of a substance is the amount of heat required to raise the temperature of unit mass (usually i gram) of it through i C. The unit of heat is called a calorie, and is taken to be the amount of heat required to raise the temperature of i gram of water through i C., either from o to i or from 15 to I6 . 1 If the volume of gas is kept constant when the temperature is raised, the pressure increases, and heat is required to increase the kinetic energy of rectilinear motion of the molecules and also the energy of vibration or oscillation, if any, of the mole- cules. If, on the other hand, the pressure is kept constant, the gas expands, and work must also be done against the external pressure. The heat required to raise the temperature of i gram of the gas through i C. in the first case is called the specific heat at constant volume, c a and in the second case, the specific heat at constant pressure, c p . If the increase in molecular or internal energy is the same in both cases, and if heat is not required to produce any other changes, the difference between the two specific heats, c p t vt is the amount of heat equivalent to the external work done in expansion against pressure. In other words, if the energy of a gas at a given temperature is independent of the volume, the 1 If the specific heat of water at 15 is taken as unity, the value at o = 1*00664 ; it falls gradually with rise of temperature to 20, at which point the value is 0-99947 ; it then rises again slowly, becoming equal to unity just below 25 (Bartoli and Stracciati, Beibldtter, 15. 761 (1891); confirming Rowland's work). 52 STOICHIOMETRY heat equivalent to the work done in expansion is equal to fp - t,- Early experiments by Gay Lussac, and more accurate determinations by Joule, seemed to indicate that when air was allowed to expand into a vacuum, and therefore without developing mechanical power, no change of temperature occurred. But it is evident that if there is a force of attraction between the molecules of a gas, this force will diminish as the distance between the molecules increases, and therefore, when the gas expands, some work must be done in overcoming this attraction, and there must always be a slight cooling on expansion due to this cause. Again, work may be measured as the product of pressure and volume, pv, and it has been shown that for the ordinary gases at constant temperature the product pv is not quite constant. For example, in the case of air at o C. the value of pv increases as the pressure falls, and hence there should be cooling on expansion; but with hydrogen at o the product pv diminishes with fall of pressure, and there should therefore be a slight heating on expansion. The actual heat change produced in any case should be the algebraic sum of the changes due to the two causes. Experiments by Joule and Thomson, in which gases were forced through a porous plug, showed a decided cooling effect in the case of air and carbon dioxide even at 100, but with hydrogen a small heating effect was observed both at 7 and at 90. Thus, with hydrogen, the heating effect due to the change in value of pv was greater than the cooling effect due to molecular attraction. The statement that the internal energy of a gas at constant temperature is independent of the volume is, in fact, only true for perfect gases ; hence it is only for perfect gases that the difference between the specific heats at constant pressure c. p and constant value c v is strictly a measure of the external work done in expansion. The term molecular heat may be conveniently applied to the product of the specific heat into the molecular weight of any substance, and it may be proved that for a perfect gas the THE PROPERTIES' OF GASES 53 difference between the molecular heat at constant pressure Q, and that at constant volume C is equal to the gas constant R expressed in calories. For if we raise the temperature of one gram-molecule of gas from T to (T -f i) at constant pressure, the volume increases from V to V x - . But V x (T + i) = V T ' Therefore C p - C v And the external work is equal to the product of the pressure PV into the increase of volume = -- = R. = R. [i litre atmosphere = 24*17 calories, and R = 0*08207 litre atmos. = 1*984 calorie; therefore C^ C v = 1*984 calorie, or, roughly, C p C v = 2 calories.] For the methods of determining the specific heats of gases reference may be made to Preston's " Theory of Heat." Most experimenters have determined the specific heats at constant pressure, but Joly l has obtained accurate values for the specific heat at constant volume by means of the steam calorimeter, and has shown that for air and carbon dioxide the specific heat in- creases with the density, while for hydrogen it appears to dimmish. The specific heats of gases at very high temperatures have been studied chiefly by Mallard and Le Chatelier, by Vieille and by Berthelot. It is found that the specific heat in all cases increases as the temperature rises, and Le Chatelier 2 con- cludes that the molecular heats of all gases may be expressed approximately by the formula C p = 6*5 + #T, where a is a constant which increases with the complexity of the molecule. a H 2 , N 2 , O 2 , CO . . . . o-ooio NH 3 0-0071 CO 2 0-0084 N 2 O 0-0089 C 2 H 4 0-0137 CHC1 3 0*0305 C 2 H 5 Br 0*0324 C 3 H 6 O 0-0403 C 6 H 4 0*0510 CH 3 COOC 2 H 5 .... 0-0674 (C 2 H 5 ) 2 0-0738 1 Proc. Roy. Soc. t 41, 352 (1886). Zeitschr. physik. Chem., 1, 456 (1887). 54 STOICHIOMETRY Ratio of the Two Specific Heats. This ratio, ~ = y, which is of great importance in chemical theory, may be cal culated from the velocity of sound in a gas by the formula of Laplace where/ is the pressure, s the density, and u the velocity. The value of y for air, calculated in this way, was found to be 1*408. The ratio may also be determined by the method of Clement and Desormes, based on the adiabatic equation pv* = const. Air at a pressure/!, slightly lower than that of the atmosphere / , is enclosed in a large globe, provided with a very wide stopcock and a narrow pressure gauge. The stop- cock is opened for a moment, so that air rushes in until the pressure rises to / , and at the same time the temperature, owing to compression of the air, rises slightly. The stopcock is at once closed and the temperature allowed to fall again, when the final pressure p% is measured. r r , log A -log A Inen y = , ; - log A- log A By this method Rontgen 1 obtained the value 1*405 3 for dry air. Lastly, if the velocities of sound in two gases are compared at the same temperature and pressure, and if the value of y for one of them is known, that of the other may be calculated. For ?/! = \7y, x - and 2 = \/y a X 7 Si V S% / 2 " ~ \/^~ 2 an d 7i ~ 7s ~ * ~\ The method of Kundt has chiefly been employed for this purpose. A glass rod, AB (Fig. 13), is sealed at its middle point 1 Pogg. Ann., 148, 580 (1873). THE PROPERTIES OF GASES. 55 or fitted by a cork to the wide tube DC. The end of the rod at A is enlarged and flattened so that it nearly closes the tube. A small quantity of a light powder lycopodium, cork-dust, or precipitated silica is placed in the tube between D and A, and, by tapping the tube, is made to lie evenly along it. The tube may be filled with any gas by means of the side tubes E and F. When the rod is made to vibrate longitudinally by drawing a piece of cotton-wool moistened with alcohol firmly along it from C to B, the vibrations are communicated to the gas in the tube, and the fine powder tends to gather into little D G A C B ~~~ FIG. 13. heaps along the tube. The piston G is moved backwards or forwards until the best position is found. The powder indicates the position of nodes and inter-nodes and the distance / between two heaps measures the half wave-length of sound in the gas. The velocity is equal to the product of the wave- length into the number of vibrations in unit time, and since the rod AB always gives the same note, the velocities of sound in two different gases may be compared by placing them suc- cessively in the tube and measuring the distances /j and / 2 between the heaps. These distances are proportional to the velocities u and //. 2 , therefore = * * J * or, if the densities are stated in terms of that of a standard gas, taken as unity 71 - 7a X - If the second gas is air, y. 2 = 1*405. The experimental results and their bearing on chemical theory are considered in Chapter X., p. 188. CHAPTER IV DETERMINATION OF ATOMIC WEIGHTS Relation between Atomic Weight and Equivalent, or Quanti- valence. It has been stated (p. 10), that, in order to find the atomic weight of an element, it is usual (a) to determine its equivalent with the greatest possible accuracy, and (b) to ascertain the relation between the equivalent and the atomic weight. The equivalent was first defined as the weight of an element that combines with or displaces i part by weight of hydrogen. The atomic weight of hydrogen was also taken as unity. The best determinations indicate that 7 '94 parts of oxygen unite with i part of hydrogen to form water, and the equivalent of oxygen is therefore 7*94 if that of hydrogen = i. But the equivalents of a great number of elements are ascertained by direct comparison with that of oxygen, very few with that of hydrogen, and it is therefore convenient to adopt the even value 8 as the equivalent of oxygen, and to define the equiva- lent of any other element as the weight of it that combines with or displaces 8 parts by weight of oxygen or the equivalent weight of some other element. In the case of hydrogen this weight would be 1*0075. It is convenient to adopt the same value for the atomic weight as for the equivalent of hydrogen, and it may therefore be stated that the atomic weight of hydrogen, according to the most exact determinations yet made, is 1*0075. But the experimental difficulties attending the determination of the exact ratio between the equivalents of hydrogen and oxygen are very great, and for the present the International 56 DETERMINATION OF ATOMIC WEIGHTS 57 Committee appointed to consider the question of atomic weights do not consider themselves justified in going beyond the third place of decimals, and they adopt the value 1*008 for the atomic weight of hydrogen. With regard to oxygen, the even value, 8, being adopted as the equivalent, it remains to be ascertained whether 8 or, if not, what multiple or submultiple of 8 is to be taken as the atomic weight of that element. In considering the ratio between the atomic weight and the equivalent of any element, the accuracy of the experimental determination of the equivalent is not a matter of importance, and, for the purposes of this discussion, it will be sufficient to adopt the whole numbers i and 8 for the equivalents of hydrogen and oxygen respectively. The ratio of atomic weight to equivalent for any element having been ascertained, the equivalent now determined with the greatest possible accuracy must be multiplied by this ratio, in order to obtain the " exact " atomic weight. Consider the case of an element, A, which forms a compound with a second element, B, the equivalent of which is known. The equivalent of A can then be calculated if the com- position of the compound has been accurately determined. For example, the percentage composition of the native oxide of tin is Tin 78-81 Oxygen 21-19 lOO'OO ,_Q.Q_ v, O The equivalent of tin is therefore ; = 2975. If the ratio of the number of atoms of A to that of B in the smallest particle of the compound is a simple one, then the atomic weight of each element must bear a simple ratio to its equivalent. The simplest case is that in which both the elements A and B and also the compound A^B, are gaseous or can be easily vaporized. Take, for example, the compound water, which 58 STOICHIOMETRY is formed by the combination of i part by weight of hydrogen with 8 parts by weight of oxygen (approximately). In order to calculate the ratio between the atomic weights of hydrogen and oxygen the quantivalence of oxygen must be determined. To do this, it is necessary to ascertain the number of atoms of each element in the smallest particle of water in other words, to find the values of x and y in the formula for water, HA- It is found experimentally that 2 volumes of hydrogen unite with i volume of oxygen to form two volumes of steam (approximately), if the constant temperature and pressure are such that the steam does not condense to liquid water. Again, Dalton assumed that i atom of hydrogen unites with i atom of oxygen to form i binary atom of water. The numerical relations are very simple in both cases, but there is a want of agreement between them. Gay Lussac attempted to bring the atomic composition into agreement with the volumetric composition by assuming that, at the same temperature and pressure, the densities of gases, both simple and compound, are proportional to their empirically found combining weights or to simple multiples of them, but there were difficulties which he failed to explain. Avogadro, in 1811, brought forward the hypothesis that equal volumes of all gases, measured at the same temperature and pressure, contain the same number of smallest particles or molecules. He saw, however, that the volumetric composition of gases could not be explained if it were assumed that the molecules of elementary gases were identical with the atoms ; for, if that were so, it would follow that 2 atoms of hydrogen unite with one atom of oxygen to form two complex atoms of steam. This, however, would involve the subdivision of the atom of oxygen, which, by definition of the term " atom," is impossible. To overcome this difficulty, Avogadro introduced the notion of two kinds of molecule, the molecule integrant*, or smallest particle of an element or compound that exists in the free (gaseous) state, and the molecule elementaire, i.e. the atom or smallest particle of an element capable of entering into DETERMINATION OF ATOMIC WEIGHTS 59 combination. [The terms " molecule " and " atom " are now employed instead of integrant molecule and elementary mole- cule.] The molecule of a gaseous element need not, according to Avogadro, be identical with the atom, but may consist of two or more atoms united together. Assuming that the molecules of hydrogen and oxygen are diatomic, it would follow from the volumetric composition that 2 diatomic molecules of hydrogen unite with i diatomic molecule of oxygen to form 2 molecules of steam, each consist- ing of two atoms of hydrogen and one atom of oxygen. The equation representing the synthesis of water would therefore be written 2H 2 + O, = 2H 2 O It might, however, equally well be assumed that the mole- cules of hydrogen and of oxygen are tetratomic, or, generally, that they each contain an even number of atoms, the equation being written 2H. 2x -j- O,, = 2H 2 /), where x and y are any whole numbers. The simplest assumption is, no doubt, the most probable ; but, granting the correctness of Avogadro's hypothesis, the only points actually proved are that the number of atoms of hydrogen in the molecule of water is the same as in the mole- cule of gaseous hydrogen, and that the number of atoms of oxygen in the molecule of water is half as great as in the molecule of gaseous oxygen. In order to find the values of x and y in the equation it is necessary to ascertain the actual number of atoms of hydrogen and oxygen either (a) in the molecule of water, or (b) in the molecules of hydrogen and oxygen respectively. (a) By the action of the metal sodium on water, hydrogen is expelled, and a compound, sodium hydroxide, is formed which, for a given weight of oxygen, contains exactly half as much hydrogen as water does. There are many other ways in which 60 STOICHIOMETRY the hydrogen in water may be replaced by other elements or groups of elements, and it is always found that either the whole or exactly one half of the hydrogen is so replaced. It may therefore be concluded that there are two atoms of hydrogen and two only in the molecule of water. (b) The density of a gas, or the vapour density of a substance which is liquid or solid under ordinary conditions, is denned as the weight of it compared with that of the same volume of a standard gas, measured at the same temperature and pressure. As already stated (p. 41), it is found best for accurate work to take oxygen as the standard gas and to call its density 1 6 ; but for the present purpose the slight error introduced by taking the density of hydrogen as unity is of no importance. Calling the gas or vapour A, and hydrogen H, the density d^ of A is equal to weight of A weight of same volume of H at same temperature and pressure But the weight of a gas is equal to the number of its molecules, N, multiplied by the weight of a single molecule (the molecular weight) M. Therefore , = But by Avogadro's hypothesis N A = N H , therefore , M A ^ = MH and M H = -~r "A If, then, the values of M A and d^ can be determined, that of M H may be calculated. The density of methane, compared with that of hydrogen, is 8 (approximately), and it is found that in 8 parts by weight of methane there are 6 parts of carbon and 2 of hydrogen. It is found that the hydrogen in methane can be replaced in 4 DETERMINATION OF ATOMIC WEIGHTS 61 and only 4 equal stages by chlorine, the compounds known as methyl chloride, methylene chloride, chloroform, and carbon tetrachloride, respectively, being formed. Thus i, f, f, or | of the hydrogen may be replaced by chlorine, and it is found that one or other of these fractional amounts of hydrogen may also be replaced in methane by other elements, or by groups of elements. The most probable explanation is that the molecule of methane contains 4 atoms of hydrogen. Taking the atomic weight of hydrogen as unity, the weight of hydrogen in the molecule of methane must be 4, that of carbon - = 12, and the molecular weight of methane 4 + 12 = 16. But The vapour density of acetic acid is variable at low temperatures, but at high temperatures and under moderate or low pressures it has the constant value 30. In 30 parts by weight of acetic acid there are found to be 12 parts of carbon, 2 of hydrogen, and 16 of oxygen. When acetic acid reacts with metallic oxides, hydroxides, or carbonates, one-fourth of the hydrogen is always replaced by the metal, and when the acid is treated with chlorine |, f , or f of the hydrogen is replaced by that element ; it may there- fore be concluded that there are 4 atoms of hydrogen in the molecule of acetic acid, and 4 parts by weight of hydrogen in the molecular weight of the acid. Therefore the molecular weight, M A = - -- = 60. But The vapour density of metallic mercury is 100, and it may be proved by the methods which will be considered later that its atomic weight is 200. The velocity of sound in mercury vapour was determined by Kundt and Warburg, and the ratio of the specific heat at constant pressure to that at constant volume was found to be 62 6" TOICHIOME TR Y 1-66. From this it follows (p. 188) that there is no increase of internal energy of oscillation or vibration of the parts of the molecule with rise of temperature, but only of the kinetic energy of rectilinear motion of the molecules as a whole ; in other words, it follows that the molecules are monatomic. Therefore the molecular weight is equal to the atomic weight, or M A = 200 ; and M H = ^ = fgg = 2 By these different methods it is proved that the molecular weight of hydrogen = 2, and since the atomic weight = i, there must be 2 atoms in the molecule. Therefore in the equation it follows that x = i. The replacement of oxygen in water or other compounds by hydrogen, chlorine, or other elements or groups of elements cannot be effected so easily as that of hydrogen, but the atomic weight of oxygen and, indirectly, the value of y may be ascertained in a different manner. The value of M H in the equation M A having now been definitely established, that of M A may be calculated for any gas or vapour if d^ has been determined ; for M A = = 204 approximately. Mercury forms two series of salts, and the two equivalents, found by the accurate analysis of the mercurous and mercuric compounds, are 200 and 100 respectively. Mercury is therefore monovalent and divalent respectively in these compounds, and the atomic weight = 200 x i = 100 x 2 = 2 oo accurately. Mitscherlich's Law of Isomorphism. This law is based on observations of the crystalline form, and the behaviour on crystallization of analogous chemical substances. Mitscherlich 2 examined first the arsenates and phosphates of sodium, potas- sium, and ammonium, and by comparing the corresponding phosphates and arsenates of the same metal the number of molecules of water of crystallization being the same for any two substances compared he made out the following points : 1 Aim. Chim. Phys., ii. 10, 395 (1819). 2 Ibid., 14, 172 (1820) ; 19, 350 (1821) ; 24, 264 (1823). 66 STOICHIOMETRY (1) The form of the crystals, as shown by the measure- ment of their angles, is the same. (2) Each crystal deposited from a mixed solution contains both substances, and is of the same form as crystals obtained from a solution of either pure substance. (3) A crystal of one substance, placed in a saturated solution of the other, continues to grow by superposition of the second substance, the form of the crystal remaining unaltered. Substances which have the same crystalline form and are capable of forming either mixed or superposed crystals, in the manner described, are said to be isomorphous. It may be stated that, as a general rule, isomorphous sub- stances have analogous chemical constitution; thus, if the chemical formula of one substance is known, and another substance is found to be isomorphous with it, it may be con- cluded that, in all probability, the formula of the second substance is analogous to that of the first. The equivalent of gallium, taking that of oxygen as 8, is 23*3; its atomic weight is therefore 23-3, 46*6, 70, 93*3, . . . according as the formula of the oxide is Ga 2 O, GaO, Ga 2 O 3 , GaO 2 . . . The oxide is basic, and the sulphate forms with potassium sulphate a double salt, which, like the alums, separates from its aqueous solution in regular octahedra. Moreover, gallium potassium sulphate can form mixed crystals with other alums, and is therefore isomorphous with them. Since the formula of ordinary alum is K 2 SO 4 ,Al 2 (SO 4 )o,- 24H 2 O, it follows that that of gallium alum is K 2 SO 4 ,Ga 2 (SO 4 ) 3r 24H 2 O ; hence the formula of the sulphate must be Ga 2 (SO 4 ) 3 , and this would be derived from the oxide Ga 2 O 3 just as A1 2 (SO 4 ) 3 is obtained from A1 2 O 3 . Gallium is therefore trivalent, and its atomic weight is 23*3 X 3 = 70. By these different methods it may be decided whether the equivalent itself or what multiple (or possibly sub-multiple) of it must be taken for the atomic weight. Further light on the question is frequently thrown by the periodic arrangement of the elements, which is described and discussed in Chapter VI. As already mentioned, the gaseous elements helium, neon, argon, krypton, and xenon (and to these the gaseous emanation DETERMINATION OF ATOMIC WEIGHTS 67 from radium may perhaps be added) appear to be incapable of entering into combination with each other or with other elements ; they have, therefore, no equivalents, or may be said to have zero valency. The densities of these gases, however, and hence their molecular weights, have been determined, and it has been found by Ramsay and Travers, 1 by determining the velocity of sound in them, that the ratio of the specific heat at constant pressure to that at constant volume is in each case about 1*6. It is, therefore, concluded that their molecules, like those of mercury, are monatomic, and that their atomic weights are identical with their molecular weights. 1 Proc. Roy. Soc., 67, 329 (1901). CHAPTER V DETERMINATION OF ATOMIC WEIGHTS (continued) ACCURATE DETERMINATION OF ATOMIC WEIGHTS Experimental Errors. Before describing the actual deter- minations of the atomic weights of some of the elements, it will be well to consider shortly the nature of the experimental errors that are met with. No observer, however expert, can hope to attain absolute accuracy in any measurement, however simple. Suppose, for example, that the determination is that of the mass expressed in grams of a certain piece of metal, and that a number of trials are made with the same balance and the same set of weights. The values found will probably agree in every case to the fourth place of decimals, possibly to the fifth, but pro- bably not to the sixth ; the limit of accuracy depending partly on the expertness of the observer, partly on the sensibility of the balance, and partly on the actual mass of the piece of metal, for the sensibility of a balance diminishes as the load on it is increased. It is usual to take the arithmetical mean of the individual values as the final result, and an estimate of the accuracy of the determinations is afforded by the smallness of the probable error ^ which is calculated by the formula / s = o*o74e;\/ T r '^ V n(n i) where n is the number of observations in the series, and s the sum of the squares of the variations of the individual values from the mean. One of the weights, however, might be faulty, and yet a large error, due to this cause, would not be 68 DETERMINATION OF ATOMIC WEIGHTS 69 eliminated or even diminished by increasing the number of observations, since the same weights would be employed in each case. Errors of this kind are termed constant errors^ and are frequently difficult to deal with. In this particular case the best plan would be to make a very careful comparison of the weights used with a set of standard weights ; but the probable existence of the constant error might at any rate be discovered by making a number of determinations with a second set of weights. It is improbable that the two sets of weights should be faulty to the same extent, and if the second result did not differ from the first by an amount greater than the calculated probable error, the final mean might be accepted with much greater confidence than either singly. On the other hand, if there was a marked difference between the two results, the existence of a constant error in either one or the other would be demonstrated. In all scientific work constant errors of the kind just described should be excluded as far as possible by a pre- liminary careful examination, calibration, etc., of the apparatus to be employed. Again, it must be remembered that if a body is weighed in air it will appear to be lighter than in a vacuum by the weight of air displaced, and in accurate work the correction from apparent to true weight should always be made, otherwise a (practically) constant error will be introduced. In the determination of atomic weights constant errors may readily occur owing to the incompleteness of a chemical change, the occurrence of a subsidiary and perhaps unnoticed reaction, the partial solubility of a precipitate, the slight vola- tility of a solid, the occlusion of a gas in a solid, and so on ; and it is always advisable to determine a given atomic weight by two or more quite different methods in which the same constant error is unlikely to occur. Owing to the possible existence of constant errors, it does not always follow that, of two results, the one with the smaller probable error is to be preferred to the other. For example, in 1891, E. W. Morley made a series of wonderfully concordant determinations of the relative volumes of H and O which unite 70 STOICHIOMETRY together to form water. The measurements were made with the utmost care, and the method was varied to the extent that in some observations hydrogen and in others oxygen was in excess. The mean result was 2 '0002 3 0*000015. Morley, however, was led to suspect the existence of a constant error, and he afterwards redetermined the ratio of the volumes from the specific gravity of the mixed gases evolved by the electrolysis of acidified water. The mean result obtained was 2*00274 o '00005, and although the probable error was considerably greater, he adopted the second value in preference to the first, and, in fact, rejected the first altogether. When several series of determinations have been made by the same method, or by different methods which are all believed to be free from constant errors, the probabh error of the mean of each series must be taken into account in calculating the final mean. This is done by means of the following formula : ABC ~Ji 12 "T" ~~9, M = where A, B, C . . . are the individual means, and a, ft, c . . . their respective probable errors. The probable error of the final mean is given by the formula e = t /i , i . i V 0*00094 and +0*00053 for oxygen and hydrogen respectively, the corrected density, and therefore the atomic weight, of oxygen is 15-88. The correction of the observed to normal densities may be 78 STOICHIOMETRY made by a different method depending on the modified equation of state. It has been stated that the equation PV = RT is not strictly applicable to real gases, the deviations under high pressures being very great. Van der Waals (Chapter XI.) has proposed the modified equation (p + )( _ ,) = RT where a and b are constants depending on the nature of the substance. From this equation _ i/ 27^ i\ ~ iV " 8 X B) where , TT, and 6 are the reduced volume, pressure, and temperature respectively (p. 215). But D. Berthelot * has shown that much better results are given by the equation and if the critical volume, pressure, and temperature of a gas are known, this equation may be conveniently employed. D. Berthelot shows that the corrected densities obtained by this method agree extremely well with those given by the method described on p. 48. It will be seen that the best determinations of the atomic weight of oxygen, taking that of hydrogen as unity, lead to the value 0=- 15-88 Hence, if the atomic weight of oxygen is taken as 16, that ydrogen = = I' 15 55 have adopted the value of hydrogen = = I'ooyq. The International Commission 15 55 H = 1-008 1 Compt. rend., 144, 194 (1907) ; " Sur les Thermometres a Gaz," p. 49 (1903). DETERMINATION OF ATOMIC WEIGHTS 79 Silver. For details of the determinations of the atomic weights of the elements, larger works such as Ostwald's " Lehrbuch der Allgemeinen Chemie," F. W. Clarke's " Re- calculation of the Atomic Weights," [" Constants of Nature," Smithsonian Institution], or Meyer and Seubert's "Die Atomgewichte der Elemente," must be consulted. It is impossible here to describe more than a few typical examples. Among the most accurate atomic weight determinations that have ever been made are those of Stas 1 (1813-1891), and they have been rightly regarded as models by all later chemists. Not only was Stas an exceedingly skilful and careful manipu- lator, as shown by the very low probable error in nearly every series of his experiments, but he fully realized the importance of avoiding constant errors ; for he took the utmost care in purifying the materials used in the determinations of the atomic weight of each element, he employed as many different methods as possible, and, wherever practicable, he introduced minor variations in the conditions of experiment or in the materials employed. Stas's determination of the atomic weight of silver has always been regarded as a masterpiece of accurate experimental work, and no better example can be chosen. Stas employed no fewer than five different methods, depending on reactions represented by the following equations: I. (a) 2KC1O 3 = 2KC1 + 3 according to Ostwald Ag = 107-9376 0-0037 In three cases the individual value differs from the mean by an amount smaller than the probable error calculated for the individual and even for the mean atomic weight ; in the other two cases the difference is only very slightly greater than the probable error of the individual value. It appears hardly possible, therefore, that there can be any constant error of appreciable magnitude in any of the five series. The data afforded by the very numerous experiments carried out by Stas may be treated in different ways, and slight variations in the calculated atomic weight of silver are thus possible. The values calculated by several chemists are given below, including that adopted by Stas himself. Stas, 107*930 Ostwald, 107-9376 (from the experiments of Stas only). Thomsen, 107-9299 ( ). Meyer and Seubert, 107-9296 ( ,, ,, ). Clarke, 107-924 (from all sources). Van der Plaats, 107-9244 ( ). In the table compiled by the International Commission, the value 107'93 is adopted. From the foregoing data the atomic weights of several other elements may be calculated. Chlorine. By heating silver chlorate, the ratio AgCl : O was found to be 143-3940 0*0097, and if Ag = 107*9376 0-0037, it follows that + o"oio6 Again, from the synthesis of silver chloride Ag : Cl = 107-9376 : 35-4524 0-0040 84 STOICHIOME TR Y Combining the two values, Cl = 35'45 2 9 0-0037 Bromine and Iodine. For bromine and iodine the cor- responding ratios are available; in both cases the ratio depending on the direct synthesis of the silver halide has by far the lower probable error. The values calculated by Ostwald are Br = 79*9628 0*0032 I = 126*8640 0*0035 Potassium. The results obtained by heating potassium chlorate lead to the ratio KC1 : O = 74*5902 : 16 therefore, subtracting the atomic weight of chlorine, K = 39' 1 373 0*0058 Again, KC1 : Ag"= 74'5 88 4 : 107-9376 /. K = 39*1355 0*0037 and together K = 39' 1 3 61 0*0032 Sulphur. From the analysis of silver sulphate Ag 2 SO 4 : Ag 2 = 311-9428 : 2 x 107-9376 and subtracting the values of 2Ag + 40 S = 32*0676 0*0151 Again, from the synthesis of silver sulphide S = 32*0622 0*0044 As the final result S = 32*0626 0-0042 DETERMINATION OF ATOMIC WEIGHTS 85 Sodium and Lithium. As the atomic weights of these elements may be used in calculating that of nitrogen, the results obtained by Stas may be given. From the ratio NaCl : Ag NaCl = 58-5104 0-0019 and Na = 23*0575 0*0041 Similarly for lithium LiCl = 42*4832 + 0*0018 and Li = 7*0303 + 0*0042 Nitrogen. Potassium nitrate was prepared from the chloride by treatment with excess of nitric acid, and it was found that KC1 : KNO 3 = 74*5884 : 101-1729 Subtracting the values of K and 36 N = 14*0368 0*0055 From the corresponding sodium salts NaCl : NaNO 3 = 58*5104 : 85*1064 .'. N = 14*0489 0*0052 and from the lithium salts LiCl : LiNO 3 = 42-4832 : 69*0761 and N = 14*0458 0*0053 Lastly, by the preparation of silver nitrate from metallic silver Ag : AgNO 3 = 107-9376 : 169*9709 and subtracting the values for Ag and 30 N = 14*0333 0*0061 86 STOICHIOMETR Y Combining the four values N = 14*0410 0*0037 General Remarks. If, in place of the value for silver cal- culated by Ostwald, one of the lower values given on p. 83 had been employed, the atomic weights of the halogens would have been higher, but those of the other elements considered would in most cases have been somewhat lower. Again, when the results obtained by other experimenters who employed similar methods are included in the calculations, small differ- ences are produced, but the accuracy of Stas's work is so great that, when the probable errors are taken into account, the final values differ very slightly indeed from those of Stas. In the following table are given (a) The atomic weights calculated by Stas himself from his results. [O = 16 in all cases.] (b) Those calculated by Ostwald from Stas's results. (c) Those calculated by Clarke from all sources. (d) The values taken from the International Table for 1905. Element. Atomic weights. 00 t CO oo Silver . 107-930 107-9376 107-92 107-93 Chlorine 35*457 35*4529 35-45 35*45 Bromine 79-952 79-9628 79*95 79-96 Iodine . 126*850 126-8640 126-85 126-97 Potassium 39-142 39-1361 39-11 39-I5 Sodium . 23*045 23*0575 23-05 23-05 Lithium 7-022 70303 7-03 7-03 Nitrogen 14-055 14-0410 14-04 14-04 It will be seen that the values adopted in 1905 are nearly identical with those derived from Stas's determinations, and it is only quite recently that any doubt has been felt whether the accuracy of some of these values may not have been somewhat overestimated. It is to be noticed that the atomic weights of all the other elements are referred, directly or indirectly, to that of silver. DETERMINATION OF ATOMIC WEIGHTS 87 But the ratio Ag : O cannot be directly determined, owing to the impossibility of preparing the oxide of silver in a pure state. Each value for the atomic weight of silver is therefore affected by the errors in two ratios, and at least one additional ratio must be found in order to calculate the atomic weight of any one of the other elements. There are, therefore, three separate errors involved in each of these values. It may happen that the errors partially compensate each other, but, on the other hand, it is always possible that they may be in the same direction; and although the experimental work of Stas must always be regarded as magnificently accurate, it is possible that, by employing more direct methods with some- thing like the same accuracy, still better results may be obtained. The methods of determining the specific gravities of gases, their compressibilities, and their coefficients of expansion and of increase of pressure, have been so greatly improved that these constants may now be employed in the calculation of atomic weights. The specific gravities of nitrogen and oxygen found by Lord Rayleigh 1 in 1894, and by Leduc 2 in 1898, showed good agreement, but indicated that, unless the deviations from Boyle's law were considerable, the results were not in accord- ance with the accepted atomic weights of the two elements. Lord Rayleigh 3 afterwards, as a result of his researches on the compressibilities of gases under low pressures, showed how the theoretical densities and the atomic weights could be calculated from the observed densities, and gave as the atomic weight of nitrogen 14*009. The theoretical researches of D. Berthelot have already been discussed, and it need only be stated that in 1898 he deduced the following molecular weights from the data obtained by Leduc and Sacerdote, Rayleigh, and Morley N 2 = 28*013 ; N 2 O = 44*000 1 Proc. Roy. Soc., 55, 340 (1894). 2 Reckerches sur les Gas, Paris, 1898 ; Compt. rend., 125, 299 (1897). 3 Proc. Roy. Soc., 73, 153 (1904). 88 STOICHIOMETRY D. Berthelot has recently 1 discussed the results obtained by various experimenters since that date, and from Rayleigh's determinations he finds N 2 = 28-016 ; N. 2 O = 43'999 while from other data he calculates the following values : NH 3 = 17*015 (Jaquerod and Sheuer) NH 3 = 1 7 '02 1 (Perman and Davies) NO' = 30*003 (Gray) The mean atomic weight of nitrogen deduced from these molecular weights would be i4'oon. The question has been very fully considered by Guye, 2 who discusses the relative accuracy of the physico-chemical and the old gravimetric methods, and concludes that the evidence is in favour of the former, and that the atomic weight of nitrogen is probably a little lower than 14*01. He also gives the results of gravimetric and volumetric determinations of the com- position of nitrous oxide, from which he deduces the atomic weights, N = 14*007 and 14-015 respectively. The analysis of nitric oxide has also been carried out by Gray, 3 with the result N = 14*010 while from the densities of nitrogen and nitric oxide, Gray has obtained the values 1 4-008 and 14-006 respectively. The last result has been confirmed by Guye and Davila. Lastly, Guye contends that the alteration of the atomic weight of nitrogen from 14*04 to, say, 14*01 involves corre- sponding alterations in the atomic weights of silver and of most of the other elements, and he gives as the most probable value for silver Ag = 107-89 1 Compt. rend., 144, 269 (1907). 2 So<^ ehim. de Paris ; June, 190";. 3 Trans. Ghent. Soc., 87, 1601 (1905). DETERMINATION OF ATOMIC WEIGHTS 89 Confirmatory evidence has been obtained in the case of chlorine, the atomic weight of which appears to be somewhat higher than that given by Stas, for it has been found by Dixon and Edgar, 1 that 1*0076 gram of hydrogen combines with 35-463 grams of chlorine. Richards and Wells also find the value Cl = 35*473 ; and from the density of hydrogen chloride, determined by Jaquerod and Scheuer, together with the com- pressibility, measured by Leduc and Sacerdote, D. Berthelot deduces the molecular weight 36*482, which would give the atomic weight, Cl = 35*474. A. Scott 3 has titrated ammonium chloride and ammonium bromide against silver, and has obtained lower values than Stas. Taking the atomic weight of silver as 107*93, the follow- ing molecular weights were obtained : Stas. Scott. NH 4 C1 53-532 53'5i6 NH 4 Br 9 8 '3 2 97*995 If Cl = 35*457 an d Br = 79*952, the values for N from Scott's results are 14*029 and 14*010 respectively; but if Cl = 35-473 (Richards and Wells), then, from NH 4 C1, N = 14-013. The suggested alterations in the atomic weights of silver and bromine would bring the calculated atomic weight of nitrogen in both cases below 14*000, and Gray 4 points out that many of the discrepancies, which have been found to exist on recalculating the atomic weights of some of the elements, would not be removed by adopting the lower value for silver, and that, on the other hand, fresh difficulties would thereby be created. He considers, however, that the atomic weight of chlorine should be raised from 35*457 to 35*473; and it may be pointed out that the latter value, obtained by 1 Proc. Roy. Soc., 76A, 250 (1905). 2 "A Revision of the Atomic Weights of Sodium and Chlorine." Carnegie Institution, 1905. 3 Proc. Chem Soc., 21, 309 (1905). 4 Trans. Chem. Soc., 89, 1173 (1906). 90 STOICHIOMETRY Richards and Wells from the ratio Ag : AgCl is based on the value 107*93 f r silver. In the International Table for 1907 the value N = 14*01 has been adopted, but the commissioners have not felt justified in making any other alterations until further evidence of then- necessity has been obtained. CHAPTER VI THE PERIODIC LAW CERTAIN simple relations have long been known to exist between the atomic weights of nearly related elements, such, for example, as the fact that the atomic weight of bromine is approximately equal to the mean of those of chlorine and iodine; but it was not until 1864 that attention was called by Newlands to the existence of a general relation between the properties of the elements and their atomic weights. Newlands pointed out that if the elements are arranged in the order of the atomic weights a system of octaves is obtained, the first and last of any eight consecutive elements possessing similar properties thus chlorine resembles fluorine, sulphur is closely related to oxygen, and so on. To this generalization Newlands gave the name of the law of " octaves." At that time, however, there was much difference of opinion regarding the atomic weights of many of the elements, and the views of Newlands were not accepted. A similar generalization was subsequently arrived at by Mendele'eff and by Lothar Meyer, and the question was studied by Carnelley and others. The generalization, commonly known as the " periodic law," may be expressed by the statement that the properties of the elements are periodic functions of their atomic weights. PHYSICAL PROPERTIES OF THE ELEMENTS. Atomic Volumes. Lothar Meyer paid special attention to the physical properties of the elements, notably their specific gravities in the solid state ; but he pointed out that the periodicity is seen more clearly by considering, instead of the 9 2 5 TOICHIOME TR Y specific gravities or specific volumes, the products of the specific volumes into the atomic weights, or the atomic volumes. at. wt. Atomic volume = sp. vol. X at. wt. = sp. gr. In the following table are given the specific gravities and atomic volumes of the elements in the solid state so far as they are known, and in a few cases the same constant for the elements in the liquid state at the ordinary boiling-point or at some other temperature. The constants for the liquid state are enclosed in brackets. For the solid state the specific gravities would be somewhat higher and the atomic volumes lower. The atomic weights are taken from the International Table for 1907. Element. Symbol. Atomic weight. Specific gravity. Atomic volume. Hydrogen . . . H I '008 0-09 II Helium . . . He 4'0 Lithium . . . Li 7"3 o"594 11-8 Beryllium . . Be 9'I 1-85 4-92 Boron .... B iro 2-68 4-11 Carbon . . . C I2'0 1'57-3'S 7-6-3-4 Nitrogen . . . N 14-01 (0-89) ' (I5-7) Oxygen . . . O 16-0 (I-I2) 1 (I4'3) Fluorine . . . F 19*0 (I-I4) l (16-7) Neon .... Ne 20 Sodium . . . Na 23*05 G'974 237 Magnesium . . Mg 24-36 1-743 14-0 Aluminium . . Al 27-1 2-67 10-2 Silicon .... Si 28-4 2'49 II'4 Phosphorus . Sulphur . . . P S 3 ro 32*06 1-83-2-34 1-96-2-05 l6- 9 -I3-3 16-4-15-6 Chlorine . . . Cl 35 '45 (I-6) 1 (22-2) Argon .... Ar 39'9 (I'M)" (33-o) Potassium . . . K 39^5 0-865 45'3 Calcium . . Ca 40*1 1-578 25-4 Scandium . . . Sc 44-1 3'8 11-6 Titanium . . Ti 48-1 3'5 I3-7 Vanadium . . . V 51-2 5'5 9'3 Chromium . . Cr 52-1 6-9 7-6 Manganese Mn 55'o 7'4 7'4 Iron .... Fe 55'9 7'9 7-1 Nickel .... Ni 587 8'3 7'i Cobalt .... Co 59'o 8-9 6-6 Copper . . Cu 63-6 8-9 7'i Zinc .... Zn 65'4 6-9 9'5 1 Liquid at boiling-point. THE PERIODIC LAW 93 Element. Symbol. Atomic weight. Specific gravity. Atomic volume. GalMum . . . Ga 70 47 14-9 Germanium . Ge 72'5 5'5 13-2 Arsenic . . . As 75'0 47-57 16-0-13-2 Selenium . . . Se 79'2 4'5-4 ! 8 17-6-16-5 Bromine . . . Br 79-96 (3-19) l 25'I Krypton . . . Kr 81-8 (2'i5) 2 38"! Rubidium . . . Rb SB'S 1-52 56-0 Strontium . . . Sr 87-6 2'5 35'i Yttrium . . . Y 89-0 Zirconium . . Zr 90*6 4'i5 21-8 Niobium . Nb 94 7-06 i3'3 Molybdenum . . Mo 96-0 8-6 1 1 '2 Ruthenium . . Ru 1017 I2'I 8-4 Rhodium . . . Rh 103-0 12' I 8'5 Palladium . . Pd 106-5 1 1 "5 9'3 Silver .... Ag 107-93 10-47 10-3 Cadmium . Cd II2'4 8-65 13-0 Indium . . . In "5 7-42 I5'5 Tin Sn 119-0 7-2 16-5 Antimony . . . Sb I20'2 6-8 17-7 Tellurium . . . Te 127-6 6-2 20 '6 Iodine .... Xenon .... I Xe I26-97 128 4'95 (3'5) 2 25-6 36-6 Caesium . . . Cs I32-9 1-88 70-7 Barium . . . Ba !37'4 375 36-7 Lanthanum . . La 138-9 6-16 22-5 Cerium Ce 140-25 6-73 20-8 Praseodymium . Pr 140-5 Neodymium . . Nd 143-6 Samarium . Sm !5o-3 Europium . . . Eu !52 Gadolinium . . Gd 156 Terbium . . . Tb 159-2 Erbium . . . Er 166-0 Thulium . . . Tu 171 Ytterbium . . Yb 173-0 Tantalum . Ta 10-8 16-8 Tungsten . . . Osmium . , . W Os 184 191 19-1 22-5 9-6 8'5 Iridium . . . Ir 193-0 22-4 8-6 Platinum . . Pt 194-8 21-5 9-1 Gold .... Au 197-2 19-26 10-2 Mercury . . Hg 2OO'O 14-2 14-1 Thallium . . . Tl 204-1 11-8 i7'3 Lead .... Pb 206-9 11-37 18-2 Bismuth . . . Bi 208-0 974 21-4 Radium . . . Ra 225 Thorium . . . Th 232-5 U'2 20-8 Uranium . . . U 238-5 18-7 12-8 Liquid at o C. " Liquid at boiling-point. 94 STOICHIOMETRY ? O O CV1 li] o UJ - y j- o 00 ? 1 4) X > .---"*' 3 m o 4 HX> 4f * : d m & 3_ "- u o- d V) s "^ : ^. DOOOOOOOr 3 is M. ! $ V ( b) i Vl INTERMEDIATE Pr.Nd,Sm,Eu,Gd,lb,Er.Tu,Yb VIb Vil (y) THE OXIDES. The oxides may be divided into three classes: (a) basic' oxides, such as lime, which unite with acids to form salts with elimination of water, thus CaO + 2HC1 = CaCla + H a 6 (b} acid-forming oxides, which unite with water to form acids ; for example - SO 3 + H 2 O = H 2 SO 4 (c) other oxides, including suboxides and peroxides. Of these, the suboxides are generally reducing agents, while the per- oxides act as oxidizing agents. Many of the elements form more than one oxide, one of them, manganese, as many as six. When such a series is formed, it is found that the oxides tend to become less basic or THE PERIODIC LAW 105 more acidic as the amount of oxygen increases, and several elements form both basic and acid-forming oxides. Thus, of the six oxides of manganese, two, MnO and Mn 2 O 3 , are basic ; two others, MnO 3 and Mn 2 O 7 , are acid forming; and one, MnO 2 , is classed as a peroxide, although, as it gives a very unstable tetrachloride when treated with cold hydrochloric acid, it might also be called a feebly basic oxide. Manganese thus forms at least four groups of compounds, and the following are typical members of them : Manganous sulphate, MnSO 4 , derived from MnO Manganic sulphate, Mn 2 (S0 4 ) ; j, ,, Mn a O 3 Potassium manganate, K 2 MnO 4 , MnO 3 Potassium permanganate, KMnO 4 , Mn. 2 O 7 Manganese is found, in fact, to show relationship to one group of elements in the manganous compounds, to another in the manganic compounds, and so on. The oxides of the elements are tabulated on p. 106, according to Lothar Meyer's arrangement (slightly modified), the formulae for the basic oxides being printed in German characters, the acid- forming oxides in italics, and the other oxides in ordinary type. Some oxides have both basic and acid-forming properties, and in such cases the symbol for oxygen is printed in one type, and that for the associated element in the other. Referring to this table, comparing it with the atomic volume diagram (Fig. 14) and the periodic table on p. IO4, 1 and considering first the alkali metals, it is found that their charac- teristic oxides have the general formula M 2 O ; the oxides combine readily with water, forming soluble and strongly alkaline hydroxides, thus, M 2 O + H 2 O = 2MOH. There are also peroxides known. Descending the atomic volume curves to the right, the elements (neglecting argon) which follow the alkali metals are 1 The student is strongly advised to make copies of the two tables and the atomic volume diagram. The general relationships between the elements can best be grasped by constant reference to them, and the study of inorganic chemistry is thus greatly facilitated. io6 STOICHIOMETR V 00 -* 4 )_^ I I io8 STOICHIOMETRY beryllium, magnesium, calcium, strontium, barium, and to these may be added radium. Their characteristic oxides have the general formula MO ; they are strongly basic, especially those of calcium, strontium, and barium, these elements being frequently known as the alkaline earth metals. The oxides are, however, less basic than those of the corresponding alkali metals, their affinity for water is less pronounced, and the hydroxides, M(OH) 2 , are less soluble. Peroxides are also known. Following the calcium group are the elements B, Al, Sc, Y, La. Their oxides have the general formula M 2 O 3 ; that of boron is acid-forming; aluminium oxide is both basic and feebly acid-forming; the others are basic, but not nearly so strongly as the corresponding oxides of the metals of the previous group. Next in order we have the elements C, Si, Ti, Zr, Ce, and it is probable that thorium also belongs to this group. The general formula of the characteristic oxides is MO 2 . The first four of these oxides are acid-forming; the last two are basic. Starting again from the alkali metals (excluding lithium and also the inert gases) and descending the curves to the left, the first elements met with are the halogens, F, Cl, Br, I. 1 These elements have little affinity for oxygen ; indeed, the only stable oxide known is iodine pentoxide. It may be remarked, however, that the most stable oxyacid of chlorine is perchloric acid, HC1O 4 , which may be regarded as a derivative of the unknown anhydride C1 2 O 7 , thus C1 2 O 7 + H 2 O = 2HC1O 4 . Similarly the anhydride of periodic acid would have the formula I 2 O 7 . It may therefore be permissible to take M 2 O 7 as the general formula of the characteristic, or, at any rate, of the highest oxides of the group ; and it will be noted that fluorine is the seventh element from lithium, and chlorine the seventh from sodium, in ascending order of atomic weights. After the halogens come the elements of the oxygen group, O, S, Se, Te. The characteristic compounds of this group are 1 Tellurium has a slightly higher atomic weight, but a lower atomic volume than iodine. THE PERIODIC LAW 109 the acids H 2 SO 4 , H._,SeO 4 , H. 2 TeO 4 , of which the corresponding anhydrides, SO 3 and TeO 3 , are known. We may therefore take the general formula for the oxides as MO 3 . The nitrogen group of elements, N, P, As, and Sb, comes next, and bismuth, on account of its close chemical relationship to the others, may also be included. Each of these elements forms several oxides, the highest of which is the pentoxide M 2 O 5 . With the exception of Bi 2 O 5 , the pentoxides are acid- forming. All the elements from lithium to fluorine and from sodium to chlorine are thus accounted for, but there remain the heavy metals between Ti and As, Zr and Sb, Ce and Bi respectively, and lastly the single metal uranium. Descending the curves to the right, titanium is followed by vanadium and zirconium by niobium ; after cerium come the series of rare metals from praseodymium to ytterbium, and then the element tantalum. The three elements vanadium, niobium, and tantalum, in their chemical properties, show close relationship to nitrogen and phosphorus ; thus the pentoxides V 2 O 5 , Nb. 2 O 5 , and Ta. 2 O 5 are acid-forming. Vanadium, however, is somewhat more metallic in character than arsenic, although it has a lower atomic weight. The eight elements N, P, V As, Nb, Sb, Ta, Bi may then be classed together in one large group, which may be subdivided into the two smaller groups, N, P, As, Sb, Bi, and V, Nb, Ta. Following the vanadium elements, we have Cr, Mo, and W, and to these may be added uranium. In their physical properties these elements differ completely from oxygen and sulphur ; they are hard, lustrous metals of very high melting point, whereas sulphur and oxygen are typical non-metals. In a low state of oxidation their compounds show no resemblance to those of the elements of the sulphur group ; but, on the other hand, they form oxides of the general formula MO 3 , and some of these oxides unite with water to form acids, the others with alkalis to form salts, corresponding to sulphuric acid and the sulphates respectively. The trioxides may therefore, like sulphur tri- oxide, be classed as acid-forming oxides. It is to be noted, also, that all these elements form oxychlorides of the general 1 10 STOICHIOMETR Y formula MO. 2 C1 2 . It appears, then, that in their highest state of oxidation, the elements Cr, Mo, W, and U are chemically related to the sulphur elements, and the eight elements form one large group consisting of two sub-groups, O, S, Se,Te and Cr, Mo, W, U. The next element to chromium is manganese, a hard metal of high melting point. As already stated, manganese forms two basic oxides, MnO and Mn 2 O 3 , and these oxides and the compounds derived from them closely resemble the corre- sponding chromium compounds. The oxide MnO 3 , an acid- forming oxide, also resembles CrO 3> but the highest oxide, Mn 2 O 7 , unites with water to form permanganic acid, which is closely analogous to perchloric acid. In its highest state of oxidation, then, manganese, the seventh element from potas- sium, is related to the halogens. No other metal resembling both manganese and the halogens is known. The three metals, iron, nickel, and cobalt, which follow manganese, are closely allied to each other; they are similar in appearance, hardness, malleability and fusibility, and they all possess magnetic properties ; they also exhibit close analogies, in many of their compounds. In many respects they resemble manganese, and iron shows some relationship to chromium also. The lowest oxides have the general formula MO, and the corresponding sulphates of Mn, Fe, Ni and Co form iso- morphous double sulphates of the form M 2 'SO 4 ,M"SO 4 ,6H 2 O, in which M' may be potassium, rubidium, caesium, or the group NH 4 . All three metals form sesquioxides ; of these Fe 2 O 3 is basic, and the sulphate, like the corresponding sul- phates of manganese and chromium, forms a double salt with potassium sulphate, crystallizing with twenty-four molecules of water. These double sulphates are isomorphous with ordinary alum, and are termed chrome alum, manganese alum, and iron alum respectively. Lastly, iron forms salts known as ferrates, such as K 2 FeO 4 which are analogous to the manganates and chromates. In the next long series of elements from rubidium to iodine there is a similar triplet consisting of ruthenium, rhodium, and palladium, and in the broken series from caesium to bismuth, a THE PERIODIC LAW in third triplet, osmium, iridium, and platinum. These six metals are characterized by their high specific gravity, their infusibility and their chemical inactivity; they are not attacked by any single acid, but are converted into tetrachlorides by the action of aqua regia, and the tetrachlorides unite with potassium chloride to form double chlorides of the form K 2 M IV C1 6 . It is noteworthy that ruthenium and osmium form easily fusible tetroxides, and that OsO 4 is volatile without decomposition These are the only known cases of octavalency. Following the three triplets are the metals copper, silver, and gold. These metals show relationships, on the one hand to the triplets which they follow, and on the other hand to the alkali metals. They are heavy metals of high melting point, not acted on by water, and not easily attacked by acids, gold being only dissolved by aqua regia. But silver is monovalent, and copper and gold form monochlorides in addition to the higher compounds ; the oxide of silver is slightly soluble in water, giving an alkaline solution, and many of the silver salts are isomorphous with those of potassium. The next in order are the metals zinc, cadmium, and mercury, and these elements show double relationship, on the one hand to copper, silver, and gold, and on the other hand to the alkaline earth metals. They are usually divalent, but mercury behaves as a monad in the mercurous compounds, These metals are more electro-positive than the corresponding elements of the copper group, less so than the alkaline earth metals. Many zinc and cadmium salts are isomorphous with those of magnesium, and some with those of manganese, iron nickel, and cobalt. This is notably the case with the double sulphates isomorphous with ferrous ammonium sulphate, (NH 4 ). 2 SO 4 ,K 2 SO 4 ,6H 2 O. In this salt the ferrous iron may be replaced by Cr, Mn, Ni, Co, Cu, Mg, Zn, and Cd. In the following groups are the metals gallium, indium, and thallium, which show the closest relationship to the elements of the aluminium group in both their physical and chemical properties. They are triads, but, in addition to the sesqui- oxides, indium and thallium form monoxides. It is noteworthy that thallous chloride shows close analogy to the chlorides of H2 6* TOICHIOME TR Y the alkali metals, and that thallous oxide, T1. 2 O, unites with water, forming a soluble and strongly alkaline hydroxide, T1OH. Gallium and indium can replace aluminium in alum ; thallium cannot do so, but it can replace potassium in the same compound. There are lastly the tetrad metals, germanium, tin, and lead, which are very closely allied to the elements of the carbon group. Utility of the Periodic Table. In Mendele'efs table, p. 103, the symbols for scandium, gallium, and germanium are placed in brackets. These elements were unknown when the Russian chemist brought forward his periodic law, but he left blank spaces where they occur in order to bring the succeeding elements into their appropriate groups. Moreover, he predicted that these elements would eventually be discovered, and he gave a very full account of their chemical and physical properties, based on a consideration of those of the elements near them in the table. The elements, when discovered, were found to possess the properties described by Mendeleeff. The existence of other unknown elements has similarly been predicted. For example, it was from a consideration of the position of argon and helium in the periodic table that Ramsay suspected the existence of similar inert gases, and these were afterwards discovered by Ramsay and Travers. One may also anticipate the ultimate discovery of a metal resembling manganese and showing some relationship to the halogens, with an atomic weight between those of molybdenum and ruthenium. The periodic table has been of great value in calling attention to doubtful atomic weights ; thus beryllium was regarded by many chemists as a triad, and, its equivalent being 4^5, it was believed by them to have the atomic weight 13*5. But there would be no place for a triad element with this atomic weight in the table, whereas if the metal were divalent its atomic weight would be 9, and it would fall naturally between lithium and boron. The question was finally decided by Nilsson and Pettersson, who obtained the value 40 for the vapour density of the chloride. The mole- THE PERIODIC LAW 113 cular weight is therefore 80, and this agrees with the formula Bed., (9 + 71 = 80), but not BeCl 3 (13-5 + 106-5 = I20 )- It must, however, be admitted that potassium and argon, and tellurium and iodine, respectively, can only be brought into their proper groups by reversing the order of the well-deter- mined atomic weights. CHAPTER VII THE DISSOCIATION OF GASES AND VAPOURS THE earliest experiments on the dissociation or reversible decomposition by heat of compounds which are stable at ordinary temperatures were made by Deville in I858. 1 Deville studied chiefly the commoner gaseous compounds which require a very high temperature to bring about their decomposition. Recognizing the fact that if left in contact with each other the constituents would recombine, partially at any rate, on cooling, he devised various methods of separating the gases at the high temperature. For example, Deville 2 was able to demonstrate the dissociation of water vapour at temperatures from 1100 to 1300 C. by passing the steam through a porous tube placed in a wider porcelain tube through which a current of carbon dioxide was passed. The tubes were heated in a furnace, and measurable quantities of hydrogen and oxygen were found in the carbon dioxide, although the vapour density of water appeared to be normal at 1157. When electric sparks are passed through a gas, the temperature in the immediate neighbourhood of the sparks is exceedingly high, but the temperature gradient is very steep, and as recombination of the products of dissociation can only take place within definite limits of temperature, it may easily happen that they may cool below the lower limit before they have an opportunity of recombining. Thus it is well known that ammonia gas may be decomposed by the passage of sparks through it, but it is found that the decomposition is 1 Comptrend., 45, 821 (1857). 2 Ibid., 56, 195 (1863). 114 DISSOCIATION OF GASES AND VAPOURS 115 never quite complete, and it was noticed by Morren, 1 and, later, by other observers, that when sparks are passed through a mixture of nitrogen and hydrogen a very small amount of ammonia is formed. Moreover, by placing some acid over the mercury in the eudiometer tube which contained the mixed gases, the ammonia was absorbed, or by cooling the tube in liquid air it was condensed, 2 and it was thus found possible to bring about the combination of a considerable amount of nitrogen and hydrogen. In all probability the diatomic mole- cules of nitrogen and hydrogen are dissociated at the high temperature of the sparks, and, on cooling, the atoms recom- bine for the most part to form gaseous nitrogen and hydrogen, but also to a small extent to form ammonia. When the molecules of ammonia reach the high-temperature region they are at once decomposed again, and a state of equilibrium is soon reached in which the number of molecules of ammonia formed and decomposed in unit time is equal. But if some of the ammonia is absorbed or condensed, the amount left falls below that required for equilibrium, and a fresh quantity must be formed to take the place of that removed. Thus the amount of ammonia formed in unit time exceeds that decomposed, and a large quantity of the mixed gases may be slowly caused to combine. Deville imitated the conditions of the spark by employing a glazed porcelain or metal inner tube and passing a current of cold water through it, and was thus able to demonstrate the dissociation of carbon monoxide into carbon dioxide and carbon. A further improvement was effected by making a narrow slit in the inner tube and diminishing the internal pressure, so that gas from the outer tube passed slowly into the water. In this way the dissociation of sulphur dioxide, hydrogen chloride, and carbon dioxide was clearly demonstrated. Abnormal Vapour Densities. According to the rule that the molecular weight of a substance is numerically equal to twice its vapour density (compared with that of oxygen taken as 1 6), the vapour density of ammonium chloride should be 1 Compt. rend., 52, 527 (i 86 1). 2 Briner and Mettler, Compt. rend., March, 1907. n6 5 TOICHIOME TR Y either I 4~r'4"r35 4 _ tne molecules of gas are simple, or n x 27*7 if they are complex, n being the number of simple NH 4 C1 molecules united together. Deville and Troost, 1 how- ever^ determined the vapour density of ammonium chloride at 350 and at 1040, and obtained the values 14-6 and 14*45. Deville considered that the vapour of ammonium chloride did not follow the ordinary laws relating to gases, but Pebal 2 showed that when a piece of the salt is placed in a tube on one side of a plug of asbestos (Fig. 15) and heated strongly, an excess of ammonia passes through the asbestos, leaving excess of hydrogen chloride on the other side. The separation Was shown by passing air through the tubes and over moistened litmus paper. The vapour from the ammonium chloride must therefore have contained free ammonia and free hydrochloric acid ; in other words, dissociation must have occurred. Deville considered that dis- sociation was caused by contact of the heated vapour with the asbestos, but Than 3 showed that FIG. 15. the same result was obtained when a porous diaphragm of ammonium chloride was employed in place of the asbestos. Deville 4 brought about the admixture of ammonia gas and hydrogen chloride in a vessel heated by the vapour of boiling mercury, and observed that an air thermometer placed by the side of the other vessel indicated a rise of temperature ; but Than 5 showed that when the two gases were mixed together at 350, no contraction or expansion took place. The discrepancy between the two last-named results may 1 Annalen, 123, 199 (1862). 2 Ibid., 123, 199 (1862). 3 Ibid., 131, 138 (1864). 4 Compt. rend., 56, 729 (1863). * Annalen, 131, 129 (1864). DISSOCIATION OF GASES AND VAPOURS 117 perhaps be explained by the fact that the pressure in Than's experiment was lower than in Deville's, and that dissociation is complete at the lower pressure, but not quite at the higher. At any rate, such a discrepancy might well be observed at 280, for at this temperature the vapour density of ammonium chloride was found by Ramsay and Young 1 to be 13*3 under a pressure of 88*4 mm., but 15*2 under a pressure of 135 mm. The vapour density of tertiary amyl bromide, formed by the combination of amylene with hydrogen bromide, was found by Wurtz 2 to be normal up to about 60 above its boiling point under atmospheric pressure ; the density then diminished with rise of temperature, slowly at first, then more rapidly, and finally more slowly again until it became constant at half the original value. Phosphorus pentachloride has been the subject of much controversy and of many experiments. Cahours 3 observed that the vapour density of this substance diminishes with rise of temperature, becoming constant, however, above 300, with a value half as great as that calculated for the formula PC1 5 . Deville 4 called attention to the fact that the vapour has the peculiar colour of chlorine, and that the depth of colour increases as the temperature rises. He pointed out that the phenomena could be best explained by the assumption that the pentachloride undergoes dissociation into the trichloride and chlorine. The correctness of the explanation was confirmed by Wanklyn and Robinson, 5 who, by the simple arrangement shown in Fig. 16, effected a partial separation of the com- ponents of phosphorus pentachloride and also of sulphuric acid without the aid of a porous diaphragm. Sulphuric acid or phosphorus pentachloride was heated in the bulb A, and a current of air was passed through B. The residue in A was found to contain an excess of SO 3 and of PC1 3 respectively. 1 Phil. Trans., 177, pt. i., 99 (1886). 2 Compt. rend., 60, 728 (1865). 3 Ann. Chim. Phys. (3), 20, 373 (1847). 4 Compt. rend., 62, 1158 (1866). 5 Annalen, 127, 110(1873). S TOICHIOME TR Y Wurtz l also made the important discovery that in presence of an excess of phosphorus trichloride the pentachloride is more stable, and by deter- mining the vapour densi- ties of mixtures of the two B j chlorides in known pro- portions he was able to showthat the dissociation of the pentachloride could be entirely prevented by em- FlG l6 ploying a sufficiently large excess of the trichloride. The dissociation of hydrogen iodide and the combination of hydrogen and iodine have been very thoroughly studied by Lemoine (" Etudes sur les equilibres chimiques," p. 72 (1881)), who showed that under any given conditions of temperature and pressure the final state of equilibrium x 10 I tc u. u. O 1 IOO 2OO 3OO HOURS FIG. 17. is the same, whether the change that takes place is the partial combination of equivalent quantities of hydrogen and iodine, or the partial dissociation of hydrogen iodide (Fig. 17). Lemoine observed that the rate of change is much greater 1 Compt. rend., 76, 601 (1873). DISSOCIATION OF CASES AND VAPOURS 119 at high than at low temperatures ; thus, starting with hydrogen and iodine, he found that at 440 equilibrium was attained in about an hour, at 350 after several days, and at 260 only after several months. The rate of combination was also in- creased by raising the pressure. More rapid combination was also brought about by the presence of spongy platinum, but in this case the amount of combination when equilibrium was established was not increased. The influence of temperature and of pressure on the amount of dissociation or combination was carefully studied, and it was found the experiments being always continued until equilibrium was finally attained that the amount of disso- ciation was increased, or the amount of combination diminished, (a) by rise of temperature under constant pressure, (fr) by diminution of pressure at constant temperature. Similar results have more recently been obtained by Bodenstein. 1 Lastly, it ^vas found by Lemoine that the stability of hydrogen iodide is increased by the pressure of an excess of either component. Thus at 440 and under a pressure of o'g atmos., the follow- ing results were obtained : Ratio of combined Composition of mixture. to total iodine. 1 equivalent H + i equivalent I .... 0*74 2 equivalents H + i I .... 0*84 3 H + i I .... 0-87 4 H + i 1 .... 0-88 The effect of alteration of temperature and of pressure on the vapour density of iodine has been thoroughly investigated by Meier and Crafts, 2 who give their results in the form of a diagram (Fig. 18). It will be seen that at constant pressure the vapour density remains constant at 8*8 (air = i) up to about 700, then diminishes, slowly at first, afterwards more rapidly, and finally slowly until, at the lowest pressure at any rate, it again becomes 1 Ber. % 26, 2603 (1893) '> Zeit. phys. Chem., 22, i (1897). 2 Compt. rend., 92, 39 (1881). 120 STOICHIOME TR Y constant at 4/4. At constant temperature (between, say, 700 and 1500) the vapour density is diminished by lowering the pressure. These results are precisely such as are obtained with a substance which undergoes dissociation, and as the higher density corresponds to the formula I 2 and the lower density to the formula I, it is assumed that the changes are represented by the equation I 2 fr I + I. 1600 TEMPERATURE $ iy 8 8 Jh 8 8765 VAPOUR DENSITY (AiR=l) FIG. 18. Similar results have been obtained by Deville and Troost l and by E. and L. Natanson 2 with nitrogen peroxide, and by Ramsay and Young 3 with acetic acid, and in all probability 1 Compt. rend.,, 237 (1867). 2 Wied. Ann., 27, 606 (1886). 3 Trans. Chem. Soc., 49, 790 (1886). DISSOCIATION OF GASES AND VAPOURS 121 dissociation takes place in these cases in accordance with the equations (C 2 H 4 2 ) 2 $2C 2 H 4 2 The dissociation of iodine, nitrogen peroxide, and acetic acid differs from that of hydrogen iodide in two respects : (i) the final state of equilibrium is reached with great rapidity ; (2) the products of dissociation are alike, thus I + I, NO 2 + NO 2 , whereas with hydrogen iodide they are different, H 2 + I 2 . For this reason it is, of course, impossible to have an excess of either component. In the case of nitrogen peroxide the change of density is accompanied by a change of colour. Thus, at a low tem- perature, say 20 C., nitrogen peroxide is colourless, or nearly so ; at o C. the colour is yellow, and as the temperature rises it changes to orange, orange-red, and finally red-brown, reaching its greatest intensity at 140, the temperature at which the change from N 2 O 4 to 2NO 2 is complete. If the tempe- rature is raised still higher the intensity of the colour again diminishes, slowly at first, then rapidly, and at last slowly again, and at about 600 the gas is quite colourless. On cooling, the colour reappears, and becomes most intense again at 140. This further change has been investigated by Richardson, 1 who showed that the NO 2 molecules are dissociated into molecules of nitric oxide and oxygen, thus In this case two molecules of the peroxide give three molecules of the mixed gases, and the densities are in the ratio of 3 : 2. 1 Tran. Chem. Soc., 51, 397 (1887). CHAPTER VIII THE PROPERTIES OF LIQUIDS Liquefaction. The relations between the temperature, pressure, and volume of carbon dioxide were first carefully studied by Andrews, 1 who illustrated his results by means of the diagram which is reproduced in Fig. 19, pressures being measured as ordinates, and volumes as abscissae. Consider first the gas under the conditions of temperature, pressure, and volume represented by A. When the volume is diminished by compression at the constant temperature 13*1, the pressure rises steadily until it reaches a definite value, indicated, together with the corresponding volume, by the point B. It then ceases to rise, but the volume continues to diminish, and liquefaction gradually takes place. The volume of vapour diminishes rapidly, while that of the liquid formed by its con- densation increases slowly, until the whole of the vapour is converted into liquid. The change of volume is indicated by the horizontal line BC, the pressure being constant. After- wards, as shown by the line CD, the pressure increases rapidly, while the volume of liquid diminishes very slowly. At 2 1 '5 the changes are similar to those at 13*1, but the constant pressure under which liquefaction occurs is higher, the volume of gas is smaller when liquefaction begins, and the volume of liquid is greater when it is complete. The liquid is also more compressible. At 31*1 the curve is continuous, and is not quite horizontal in any part of its course. At this temperature no separation of liquid is seen to occur. At 32-5 the flattening of the curve 1 Phil. Trans,, 1869, pt. ii. p. 575. 122 THE PROPERTIES OF LIQUIDS 123 it is is less marked; it is still noticeable at 3 5 '5, but at 48' i' too slight to be seen in the diagram. Andrews showed that above a certain temperature, which he called the critical temperature, ordinary liquefaction cannot 50 occur. Under low pressures the carbon dioxide is certainly gaseous; under very high pressures it possesses some of the properties of a liquid, but the passage from the one state to the other, if it can be said to occur at all, is continuous. He gives this temperature as 30*92. 124 STOICHIOMETRY The dotted lines in the upper left-hand side of the diagram show what the position of the isothermals for 48-1, 31 -i, and 13*1 respectively would be if the behaviour of carbon dioxide, as regards Boyle's and Gay Lussac's laws, were similar to that of air. Vapour Pressure. Below 30-92 there is, for any given temperature /, a definite pressure/ the vapour pressure under which liquefaction of carbon dioxide occurs ; a definite volume ?'v the volume of saturated vapour at which liquefaction commences ; and a definite volume V L that of the condensed liquid at which it is complete. If at the same temperature, /, starting with compressed liquid, the process is reversed, evaporation begins when the pressure falls to /, the volume of liquid being z> L , and is complete when the volume is # v . In Fig. 7, p. 23, where the values of pv observed by Amagat are plotted against the pressures, the process of liquefaction is also illustrated, the vertical portions of the isothermals at and below 30 indicating constancy of pressure with change of pv between definite limits. In the "Andrews" diagram it will be noticed that the 13*1 isothermal between B and C is not perfectly horizontal, but that it slopes very gently upwards and is rounded off at C, and these peculiarities are even more noticeable at 21-5. The cor- responding portions of the isothermals (o to 30) in Amagat's diagram are made perfectly vertical, and in Fig. 20, in which the volumes of a gram of isopentane are mapped against the pressures, the experimental observations being represented by small circles, it will be seen that there is no sign whatever of a rise of pressure during the process of liquefaction, The gradual change in the form of the isothermals is also more fully shown than in Andrews's diagram for carbon dioxide. Andrews explained this slight rise and final rounding off of the isothermals by the fact that he was unable to remove the last traces of air from his carbon dioxide. During the process of liquefaction the greater part of this air remained undissolved, the pressure rising slowly owing to its gradual compression, and it was only by raising the pressure considerably that the last bubble of air could be got into solution. Amagat succeeded THE PROPERTIES OF LIQUIDS 125 in obtaining practically pure carbon dioxide, and the rise of pressure during condensation was in his case negligible. 14 16 20 cc 8 12 VOLUMES Or A CRAM. FIG. 20. The critical point of pure carbon dioxide, as observed by Amagat, is 31-35. The vapour pressures of carbon dioxide and the volumes 126 STOICHIOMETR Y of saturated vapour and liquid observed by Amagat at a few temperatures are given below. Volumes of a gram of Temperature. Vapour pressure in atmospheres. Liquid. Saturated vapour. 34'3 1-094 10-4 IO 44'2 1-168 7'5 2 20 56'3 1-305 5-26 30 707 1-672 2-99 31'25 72-8 2'012 2-37 It will be seen that the vapour pressure of carbon dioxide increases more and more rapidly with rise of temperature, and a similar dependence of vapour pressure on temperature is observed with all liquids. At a given temperature, however, the vapour pressures of different substances may differ widely, as will be seen from the following table. Vapour pressure at o in mm. Carbon dioxide 26070*0 SO 2 1165-0 Ethyl ether 184-9 Water 4-6 Mercury o'ooo2 It has been stated that Andrews explained the rise of pressure which he observed during the condensation of carbon dioxide by the presence of a very small amount of air in the gas. He stated his belief that if the carbon dioxide had been quite pure, no such rise of pressure would have been observed. The opinion expressed by Andrews has generally been accepted as correct, but within recent years some experimenters, notably Battelli, have observed a similar rise of pressure during the condensation of vapours, and have refused to admit that the rise could be due to the presence of air or other impurity, or to experimental error. They believe, on the contrary, that the vapour pressure depends on the relative volumes of liquid and vapour. THE PROPERTIES OF LIQUIDS 127 It has been shown, however, 1 that it is only when great care is taken to ensure absence of air or other impurities, and when other errors are very carefully avoided, that trustworthy results can be obtained. The various sources of error are discussed, and it is shown that their influence is greater (a) at high tempe- ratures than at low ones, and (b) during condensation than during evaporation. Under the best conditions the vapour pressure was found to be quite independent of the volume. For example, in 152 determinations of the vapour pressures of various hydrocarbons at temperatures up to 180, instead of a fall in pressure being observed during partial evaporation of the liquid, there was an apparent rise of 0*001 per cent., due, no doubt, to slight errors of experiment. In 493 determina- tions of the vapour pressures of twenty-one different stable sub- stances at all temperatures (up to 310 in one case), the mean fall in pressure during partial evaporation was only 0^037 per cent., which is quite within the limits of probable experimental error. Moreover, if Battelli's contention were correct, it would, of course, make no difference in what manner the alteration in the relative volumes of vapour and liquid was brought about, whether by condensation, by evaporation, or by removal of part of the liquid or vapour. For example, imagine a barometer tube of the form shown in Fig. 21. Let there be a short column of a pure liquid over the mercury, but below the stopcock, the whole space above the mercury containing nothing but the pure liquid and its vapour ; and let the temperature be kept constant by means of a suitable bath. Let the height of the mercury be first read with the stopcock open, when the volume of vapour is very large relatively to that of the liquid. Then let the stopcock be closed, so as to shut off the bulb. The volume of vapour will now be relatively small, and, according ZT to Battelli, the vapour pressure should therefore be higher. A depression of the mercury should in that case be 1 Young, /ourn. de Chim. phys., 4, 425 (1906). 128 STOICHIOMETRY observed. Thus by alternately opening and shutting the stop- cock, the mercury would alternately rise and fall, and work might be done; moreover, this work would bear no relation to the energy, if any, expended in opening and shutting the stopcock. It may safely be stated that such a result would not be obtained, and that the vapour pressure of a pure substance at constant temperature is independent of the relative volumes of liquid and vapour. All pure stable substances behave alike in so far that the vapour pressure increases more and more rapidly with rise of PRESSURE. FIG. 22. temperature. .If the pressures are plotted against the tempera- tures, a curve like that in Fig. 2 2 is obtained. The upper limit of this curve is the critical point ; the lower limit would be the freezing-point of the liquid if this, like the melting point of a solid, were a fixed point ; in practice, however, most substances may remain liquid several degrees, some substances many degrees, below their freezing points if carefully cooled, and the vapour pressures of liquids in this unstable or metastable condition may be determined. Many attempts have been made to discover a general rela- tion between temperature and vapour pressure. The formulae which have been proposed are discussed in the volume on Thermodynamics, and it will be sufficient here to point out THE PROPERTIES OF LIQUIDS 129 lhat, for purposes of calculation and interpolation, it is fre- quently convenient to employ an empirical formula such as that suggested by Biot log/ = a + M + cfi The constants a, b, and V c is the critical volume. That is to say, at the critical temperature the value of ~ is exactly twice what it would be for the substance as a perfect gas occupying the same volume. Determination of Vapour Pressure. The vapour pressures of a liquid at temperatures below its ordinary boiling point may be determined by placing a little of the liquid iA a baro- meter tube so that it rests on the surface of the mercury (Fig. 23). Some of the liquid at once evaporates, and the pressure exerted by the vapour causes the mercury to fall a certain distance which depends on the temperature and on the liquid introduced. If a second barometer tube be placed in the same trough of mercury, the difference between the heights of the two columns of mercury each of them corrected to o C. is proportional to the vapour pressure, and it is usual to express this pressure directly in millimetres or centimetres of mercury. To obtain an accurate result it is obvious that the liquid must be pure, and also that air must not be introduced with it. But it is probable that all liquids are capable of dissolving a small amount of air, and this dissolved air can only be removed by boiling. Also in filling a barometer tube the mercury must be boiled, so as to remove not only the dissolved gas, but also that adhering to the walls of the tube. For the determination of vapour pressure, a tube of the form shown in the diagrams (Figs. 23 and 24) may be employed. It is first placed with the open end upwards, and nearly filled with mercury, and it is then connected with an air-pump and exhausted. The mercury is then heated with a Bunsen burner until it boils freely, beginning at the bottom of the tube so as THE PROPERTIES OF LIQUIDS to drive bubbles of gas gradually up the tube. After this process is complete, the tube is disconnected from the pump, and about a cubic centimetre of the pure liquid is introduced. The tube is again exhausted, and the liquid is boiled gently for some time to expel all dissolved air, and, while still boiling, mercury is admitted, the tube being placed in such a position that the liquid rises into the closed end of the tube near the junction. Disconnecting from the pump, the tube, the open end of which is closed by a finger, is inverted in such a manner that the liquid flows past the mercury to the other end, and the tube is then placed in the trough of mercury, and the finger removed. If air has been satisfactorily removed, the liquid should remain adhering to the top of FIG. 23. FIG. 24. the tube and to the mercury until the tube has been heated or vigorously tapped. The tube may conveniently be heated to a constant known temperature by means of the jacketing apparatus shown in Figs. 23 and n. By reducing the pressure in the jacketing apparatus the temperature of the vapour may be lowered, and 1 3 2 STOICHIOMETR Y thus a series of readings of vapour pressure at different tem- peratures may be taken with a single liquid in the bulb. For the determination of vapour pressure at temperatures higher than the ordinary boiling-point, an apparatus similar in FIG. 25. principle to that employed by Andrews in his researches on carbon dioxide is the most suitable. The apparatus, which may also be employed for the deter- mination of the specific volumes of liquids and saturated vapours, and of the compressibilities of liquids, vapours, or gases, is shown in Fig. 25. In consists of a long wrought-iron THE PROPERTIES OF LIQUIDS 133 or steel tube, with three shorter tubes at right angles to it. The long tube is securely fixed in a horizontal position, the branches being vertical. One end of the horizontal tube is closed, the other end is fitted with a thick steel ring, A, and perforated screw, B, through both of which passes a steel plunger, C. The space between the ring and the screw serves as a stuffing box to prevent leakage. It may be filled with the wick of a common tallow candle from which most of the outer part of the tallow has been removed, and which may be wound round the plunger before the screw is inserted. The other extremity of the plunger is cut as a screw, and passes through the nut D, which is rigidly fixed to the same stand as the iron tube. The screw can be turned by means of the circular handle E, and the capacity of the iron vessel thus increased or diminished. Each of the vertical branches, like the horizontal tube, is provided with a steel ring and perforated screw, and through each screw and ring passes a thick-walled glass tube of about i'5 mm. internal diameter, kept in position by an enlargement, which presses against a leather washer fitting the bottom of the screw. Each stuffing box contains, instead of a candle-wick, a well-greased, perforated, cylindrical indiarubber stopper, which rests on a greased leather washer fitting the upper side of the steel ring. The glass tubes are closed above, but open below; they are all graduated in millimetres and carefully calibrated ; two of them serve as air manometers. The internal diameter of one of them, F, which serves for the measurement of moderate pressures, is the same throughout ; that of the lower end of the other, G, which is intended for high pressures, is much greater, so that this tube is provided with a reservoir of relatively great capacity. The third or " experimental " tube contains the liquid under in- vestigation, and is usually similar to the simpler manometer. The iron apparatus is filled with pure mercury when the plunger is drawn out as far as possible, and the manometers, containing dry air free from carbon dioxide, are then inserted. The manometers are kept at a known and nearly constant temperature by a current of cold water. If the total capacity, # , of a manometer were known, and 134 STOICHIOMETR Y also the absolute temperature T and pressure A f tne a ^ r when the manometer was inserted in the iron apparatus, the pressure corresponding to any reading of the volume and temperature of air correcting for the deviations from Boyle's law would be given by the formula pV A^o T = "TV or / = --- X 1 v T = c V But in practice it is better to ascertain the constant must be corrected (i) for the difference in level of the mercury in the experimental tube and manometer, (2) for the pressure of the column of unvaporized liquid, (3) for the expansion of the heated column of mercury, (4) if necessary, for capillarity, (5) for the deviation of air (in the manometer) from Boyle's law, as determined by Amagat. No correction for the vapour pressure of mercury should be applied, because evaporation through a long column of liquid is an exceedingly slow process. If, when the volume is reduced, the last bubble of vapour cannot be condensed without noticeable rise of pressure, it may safely be concluded that air has not been completely removed. In that case the results must be rejected, and 136 STOICHIOMETRY the experimental tube taken down, emptied, cleaned, dried, and refilled, and the determinations repeated. More accurate results are obtained by taking readings at a series of increasing than of diminishing volumes. For substances, such as carbon tetrachloride, which attack mercury at high temperatures, the experimental tube may be modified in such a manner that the mercury is not heated. 1 The method of calculation is, however, more troublesome. The Boiling Point of a Pure Liquid. Consider a sealed tube containing a pure liquid and its vapour, but no air or other gas. If the whole tube is at a temperature /, the vapour of the liquid will exert a definite pressure /. If the tube be heated to a higher temperature, /', evaporation will take place until the vapour pressure has risen to/', that corresponding to the new temperature. If air were present in the tube, evaporation would take place more slowly, because time would be required for the vapour to diffuse through the air, but eventually the partial pressures of the vapour would be/ and/' respectively at the two temperatures, while the total gaseous pressure in the tube would be greater on account of the air. Consider next an open long-necked flask containing a pure liquid heated below by a flame. The temperature will rise and evaporation will take place, so that the partial pressure of the vapour in the flask will increase, while that of the air will diminish, the total pressure remaining equal to that of the atmosphere. Some of the vapour, coming in contact with the cool walls of the vessel, will give up heat and be condensed again, and thus the walls will be warmed. As the temperature continues to rise evaporation will increase, until at last the liquid will boil and vapour will be evolved with great rapidity. In a vessel of this form the vapour from the boiling liquid will drive the air before it, diffusion being too slow to enable air from outside to enter the flask, and the upper surface of the liquid will eventually be in contact with its vapour only. When the liquid boils, the pressure of the vapour in the flask is equal to that of the atmosphere outside, but the term " boil- ing point " is somewhat ambiguous, for it is not the temperature 1 Young, Trans. Chem. Soc., 59, 911 (1891). THE PROPERTIES OF LIQUIDS 13? reached by the liquid when ebullition takes place, nor that of the freely boiling liquid. In order that a bubble may be formed at the bottom of the liquid, where the heat is applied, it is clear that in addition to the pressure of the vapour in the flask, that of the column of liquid must be overcome. Also the cohesion of the liquid and its adhesion to the walls of the vessel must be overcome, and if the vessel be clean and smooth, and the liquid free from dissolved air, a bubble may not form until the temperature has risen very considerably in other words, until the liquid has become considerably superheated. When a bubble is at last formed it may expand with explosive rapidity, and there will be a sudden burst of vapour ; at the same time the temperature will suddenly fall towards the point at which it would remain stationary if ebullition were to take place regularly and freely. Failing the formation of fresh bubbles, the temperature will rise again until explosive ebullition again takes place. The liquid in this state is said to boil with bumping. Clearly, then, its temperature does not depend on the pressure only, but also on the facility with which bubbles are formed. The vapour which escapes from a superheated liquid may itself be superheated at first, but as it rises and gives up heat to the walls of the vessel, its temperature falls until condensa- tion begins to take place. Now, the temperature of condensa- tion except in special circumstances and in absence of liquid, is found to depend only on the pressure, and to be identical with what in the language of science is termed the boiling point. In practice, therefore, the boiling point is measured, not by placing a thermometer in the liquid, but in the vapour well above it. When, however, the liquid bumps violently, the rush of superheated vapour may be so great that the temperature does not fall to the condensing point before reaching the thermometer, and the temperature is then observed to fluctuate more or less violently. In order to prevent a liquid from bumping, bits of platinum wire, small tetrahedra of silver or platinum, or small pieces of porous material, such as fragments of pumice stone or of a broken clay pipe, may be placed in the liquid, or a very slow 138 STOICHIOMETRY current of air may be passed into it through a capillary tube. If, however, the latter method is adopted, an error is necessarily introduced, for the true boiling point of a liquid depends on the pressure of its vapour, and not necessarily on the total gaseous pressure to which it is exposed. If an indifferent gas that is to say, a gas which has no chemical action on the liquid is present, the total pressure remains the same, but the pressure of the vapour is reduced, and the boiling point must therefore be lower. That this is really the case may easily be proved by a simple experiment. An air-bath, provided with a regulator for admission of air and with two holes for the insertion of thermometers, is heated to about 200., the temperature being registered by a thermometer. The second thermometer is fitted with a grooved cork, so that when placed in the bath a passage may be left for escape of air or steam ; its bulb is well covered with cotton-wool, and is immersed in boiling water. The thermometer is transferred as rapidly as possible from the boiling water to the heated bath, when the temperature is seen to fall very quickly from about 100 to 60 or 70. If the air regulator be now closed the temperature will slowly rise, but will fall again when air is again admitted. Finally, if steam be passed rapidly into the bath the temperature will rise to nearly 100, but will fall again if the current of steam be stopped. From these changes it is clear that the tempera- ture of the water on the cotton-wool does not depend on that of the bath, nor on the atmospheric pressure, but on the relative amount of aqueous vapour in the air in contact with the water that is to say, on the partial pressure of the steam. In the case of the wet and dry bulb hygrometer, the reason why the temperature of the wet bulb usually falls below that of the dry bulb, is that the boiling point of water under a pressure equal to the partial pressure of the moisture in the air is lower than the actual temperature of the air as registered by the dry bulb. This is usually expressed by saying that the air is not saturated with moisture. When a drop of water is placed on a red-hot piece of platinium foil and assumes the spheroidal state, its temperature THE PROPERTIES OF LIQUIDS 139 is found not to rise to 100, and the reason for this may be that the drop of water is not surrounded by pure steam, but by a mixture of steam and air. Again, if a large flat dish, such as a frying-pan, be nearly filled with water and strongly heated from below, it is not easy to make the water boil, because air from the sides readily mixes with the steam, and so reduces its partial pressure con- siderably below the atmospheric pressure. From what has been stated, it is evident that the " boiling point " of a liquid can under no conditions be the temperature at which the liquid "boils," or is in a state of ebullition, be- cause a bubble must be formed below the surface, and, even if ebullition takes place with perfect freedom, the pressure on the vapour in the bubble must be greater than that of the atmo- sphere. On the other hand, the boiling point of a liquid may be determined by reading its temperature, when the conditions are such that the liquid cannot boil in the ordinary sense of the word. The necessary conditions are that the liquid shall have a perfectly free surface for evaporation, and that the heat shall be applied from outside the surface. A method based on these considerations, and devised by Ramsay and Young, 1 is specially suitable for the determination of boiling points under greatly reduced pressures, and it is under very low pressures that bumping is most liable to occur when a liquid is boiled in the ordinary way. The apparatus (Fig. 27)- consists of a wide vertical glass tube, A, closed below, to which a side tube, B, is fused near the top. The side tube is connected with a bulb, C, which may be cooled by water or a freezing mixture, and from the bulb passes a second tube, D, which is connected with an air-pump and gauge to measure the internal pressure. A small tube, closed by an indiarubber tube and clip, E, serves to admit air into the apparatus. The vertical tube is closed above by an indiarubber stopper perforated with two holes, through one of which passes a thermometer, F, and through the other a glass tube provided with a stopcock and reservoir, G, above. The bulb of the thermometer is covered with cotton-wool, and the 1 Phil. Trans., 175, 37 (1884). 140 STOICHIOMETR 1 lower extremity of the glass tube is drawn out and bent round so that the narrow end just touches the cotton-wool. The liquid to be investigated is placed in the reservoir, and the apparatus is exhausted. A little liquid is then admitted FIG. 27. so as to moisten the cotton-wool. The condensing bulb is then cooled, and the vertical tube is heated by means of a water or oil bath, which should always be kept at a temperature at least 20 higher than that registered by the thermometer. The liquid on the cotton-wool evaporates rapidly and dis- places the air in the lower part of the vertical tube, so that the remaining liquid is soon surrounded by vapour quite free from air. Under these conditions the liquid soon reaches its true THE PROPERTIES OF LIQUIDS 141 boiling point, but it cannot become superheated since evapora- tion takes place with perfect freedom, and, of course, ebullition is impossible. The temperature and pressure are read, and a small quantity of air is then admitted to raise the pressure, when the temperature rises at once, and soon becomes constant again at the boiling point under the higher pressure. Or, of course, the pressure may be reduced by pumping, when the temperature falls. Fresh quantities of liquid are added from time to time in small quantities from the reservoir. A large number of readings can thus be taken in an hour or two, and the reduction of pressure can be carried to any desired extent. For pressures above about 500 mm. the boiling points- are best determined in the ordinary way, the thermometer being placed in the vapour and not in the liquid. This method was employed by Regnault for the determination of boiling points under very high pressures, closed iron vessels being substituted for the ordinary glass apparatus. Errors due to bumping or to superheating of the vapour when the quantity of liquid is very small may be almost completely obviated by covering the bulb of the thermometer with a very little cotton-wool, so as to keep it always moist. The whole of the mercury not only in the bulb, but also in the stem of the thermometer, should be heated by the vapour so as to avoid the somewhat uncertain correction for the cool portion. Definition of the Term ''Boiling Point." The scientific term boiling point may be defined as the highest temperature attainable by a liquid under a given pressure of its own vapour, when evaporating with a perfectly free surface, and when the heat reaches the surface from without. If the boiling points of a pure liquid are determined under a series of pressures and the temperatures are plotted against the pressures, a curve is obtained which is identical with the vapour-pressure curve for the same substance. In other words, the vapour pressures or boiling points of a liquid may be determined either by the statical methods described under the heading "Vapour pressures," or by the dynamical methods described under the heading " Boiling point." That the vapour pressure of a pure liquid at a given temperature is equal to the 142 STOICHIOMETRY pressure under which the liquid boils at that temperature (or, more correctly, under which the vapour from the boiling liquid has that temperature) may readily be demonstrated by means of the apparatus (Fig. 23) employed for the determination of vapour pressures. If some of the same liquid be placed in the barometer tube and in the bulb of the jacketing apparatus, it will be found that when the liquid is boiling under any pressure, the heated barometer and the gauge correcting, of course, for the difference in temperature of the mercury columns register the same pressure. Relations between the Boiling Points of Different Sub- stances. When the boiling points of certain closely related substances such as chlorobenzene and bromobenzene, ethyl bromide and ethyl iodide, or methyl acetate and ethyl acetate are compared together under equal pressures/ the following simple relation is found to hold good. If T A and T B are the boiling- points, on the absolute scale of temperature, of the two substances under a pressure /, and T A ' and T B ' their boiling- points under another pressure /' T ' T -,= = constant AB J-B This relation, expressed in the form / = ;--{- qt, where t and f are the boiling points (on the Centigrade scale) of two liquids under the same pressure, and r and q are constants, had been brought forward by Diihring 2 as applicable to all liquids. In ordinary cases, however, the actual relation is less simple, and may be expressed by the equation R' = R + c (t 1 -t) where R is the ratio of the absolute temperatures of the two substances corresponding to any vapour pressure, the same for both ; R' is the ratio at any other pressure, again the same for 1 Ramsay and Young, Phil. Mag., (5) 20, 515 (1885) ; 21, 33, 22, 37 (1886). 2 "Neue Grundgesetze zur rationellen Physik und Chemie," p. 70. Leipzig, 1878. THE PROPERTIES OF LIQUIDS 143 both ; c is a constant ; and /' and / are the temperatures of one of the substances corresponding to the two vapour pressures. If the values of R' are plotted against the temperature differ- ences, t' t, a straight line is therefore obtained (Ramsay and Young, loc. tit.). Strictly speaking, the equation should be expressed in the form T ' T, T, ' - T A ) and Porter l has shown that this relation can be derived from Bertrand's vapour-pressure formula 'T - <*' if n has the same value for different substances. But since c is very small, the equation may usually be written T ' T been employed without sensible error, the value of c being, of course, different in the two cases; and it is in this form that it has most frequently (Fig. 28). The constant c = o for the closely related substances re- ferred to above; in the com- parison of ten esters the highest value of c was found to be 0*000048, but for widely dif- ferent substances it may be higher, for example, 0*000141 for methyl acetate and ben- zene, and 0*0006845 for sul- phur and carbon bisulphide. FIG. 28. 1 Phil. Mag. y June, 1907, p. 724. H4 STOICHIOMETRY The formula is applicable from the lowest pressures to the critical point, and is of considerable utility in two respects : (1) If the boiling points of a pure substance are known through a wide range of pressure, those of a second substance may be ascertained for any pressure between the same limits if the constant 536*5 at 100, and 464^3 at 200. The chief error to be guarded against is the loss or gain of heat by the calorimeter, which may be caused by radiation, convection, or conduction while the experiment is proceeding. i. Every object in a room is constantly losing heat by radiation, and gaining heat by absorbing that radiated from surrounding objects. A calorimeter should therefore be con- structed in such a manner as to reduce this interchange of heat to a minimum, and it should not be in contact with a good conductor. Bearing in mind that a brightly polished metallic surface radiates and absorbs heat badly, that air is a bad conductor, although convection currents take place freely in it, and that glass and ebonite are bad conductors, the principle on which the apparatus in general use is based may be readily under- stood. A known quantity of water is placed in the calorimeter A, Fig. 30, made of brightly polished silver. The outer metallic vessel B contains water or other badly conducting material, such as felt or cot- ton-wool. Contact between the metallic walls of the two vessels is prevented by the conical buttons of ebonite C,C, and conduction from one wall to the other must be exceed- ingly slow through air or ebonite. The calorimeter also perfectly shielded from is FIG. 30. draughts, and the temperature changes are so slow that convection currents are hardly appreciable. 150 STOICHIOMETRY A still better form of calorimeter is, however, afforded by the silvered vacuum vessels devised by Dewar for the storage of liquid air. In these, conduction between the inner and outer vessel can only take place through the glass connecting them at the top, convection currents are entirely absent, and radiation is reduced to a minimum. The vacuum vessel may be further protected by wrapping felt or cotton-wool round it, or placing it in an outer vessel, as in the case of the ordinary calorimeter (B, Fig. 30). Under the best conditions, however, some interchange of heat takes place, and there must be some loss of heat by evaporation of water from the calorimeter. The rate of change of temperature must therefore be mea- sured before and after the experiment, and from the data so obtained the change of temperature during the actual experi- ment, due to other causes than the condensation of vapour, can be estimated. The liquid under investigation is heated in a flask or boiler near the calorimeter, the vapour being conveyed to the con- denser by a tube which slopes upwards, so that any liquid formed in it by condensation may return to the boiler. The connecting tube should be protected by non-conducting material, or may be heated externally by vapour from the boiler. The calorimeter must obviously be protected by a screen from the heat radiated from the boiler, but it is impossible entirely to prevent the transference of heat from the hot con- necting tube to the calorimeter by conduction. The amount of heat thus gained should be estimated, if possible, by a blank experiment. The water in the calorimeter must be thoroughly stirred, for two reasons : firstly, warm water is lighter than cold, and tends to rise to the surface ; secondly, water is a very bad conductor of heat. Not only the water itself, but the calorimeter, the stirrer, the thermometer, and the condenser, and the receptacle for the liquid formed by condensation receive heat, and the weight of water which has the same capacity for heat as these various parts of the apparatus must be estimated once for all, and is termed the water equivalent of the calorimeter. THE PROPERTIES OF LIQUIDS 151 Calling the actual weight of water m' t the water equivalent ;//', the observed initial and final temperatures of the water /i and / 2 , the final temperature after all corrections 4', and the mean specific heat of water between ^ and 4 H', the amount of heat received by the calorimeter is (m' + /")H'W ~ A) The vapour, on reaching the calorimeter, condenses, and the temperature of the liquid formed by condensation falls from the condensing point / to the final temperature / 2 - Call- ing the weight of vapour condensed ;;/, and the mean specific heat of the liquid between / and / a H, the heat given up to the calorimeter is ;;/L + mH(t 4). Therefore niL = (m 1 + 0z")H'(/ 2 ' - A) - mH(t - 4) A separate determination of the specific heat of the liquid is required. In Regnault's experiments the condensed liquid was not retained in a receptacle in the calorimeter, but was collected in a separate vessel placed below it. The final temperature of the liquid was therefore A at the beginning of the experiment, but / 2 at the end. The mean final temperature may be taken as = t mt and the expression mH(t 4) becomes mH(t t m ). The apparatus employed by Regnault is cumbrous, and can only be employed for liquids which are obtainable in large quantities. Berthelot' 1 employed as ^boiler a glass pear-shaped flask (A, Fig. 31) with a wide vertical delivery tube passing centrally through the bottom of the flask. The liquid was heated by a ring-shaped burner, B. Very much smaller quantities of liquid could be used, and the duration of the experiment was reduced to from 2 to 4 minutes, exclusive of the time required to determine the radiation correction. Berthelot obtained the value 536*2 for the heat of vaporization of water at 100. 1 Compt. rend., 85, 647 (1877) \Journ. de Phys., 6, 337 (1877). 152 STOICHIOMETR Y Many determinations by the ordinary method have been made by Andrews, 1 Brix, 2 Favre and Silbermann, 3 Louguinine, 4 and others. Various other methods or modifications of those described have been devised. Among the more important are the following : i. The substance is distilled from a vessel placed in the calorimeter itself, the heat being supplied by the water or ice in the calorimeter. This method, which is only suitable for volatile substances, has been employed by Regnault, also by Chappuis, 5 Mathias, 6 Jahn, 7 Griffiths and Marshall, 8 and others. Mathias made an important investigation of the heats of vaporization of carbon dioxide, and of sulphur dioxide and nitrous oxide. He kept the temperature of his calorimeter constant, and at the same time measured the heat absorbed by carefully adding concentrated sulphuric acid. Griffiths and Marshall, who made an exceedingly care- ful determination of the heat of vaporiza- FIG. 31. tion of benzene, obtained the same results by passing a measured current of electricity through a coil of platinum wire in the calorimeter. An electrically heated platinum wire has been used as a source of heat in the still by Ramsay and Marshall, 9 Kahlenberg, 10 (5), Quarterly Journ. Chem. Soc., 1, 27 (1847). Fogg. Ann., 55, 341 (1842). Compt. rend., 39, 729 (1854) ; Ann. Chim. Phys. (3), 37 (1853) ; ibid. 1, 225 (1874). Ann. Chim. Phys. (7), 7, 251 (1896). Ibid., (6), 15, 498 (1888). Ibid. (6), 21, 69 (1890) ; and Journ. dc Phys., Nov., 1905. Zeit.phys. Chem., 11, 788 (1893). Phil. Mag., 41, i (1896). Ibid., 41, 38 (1896). Journ. Phys. Chem., 5, 215, and 284 (1901). THE PROPERTIES OF LIQUIDS 153 Shearer, 1 J. C. Brown, 2 Estreicher, 3 and others. Ramsay and Marshall and Brown kept the liquids at their boiling points by heating them with a jacket of their own vapour. Ramsay and Marshall's method was a comparative one, pure benzene being taken as the standard substance. The other experimenters calculated the heat directly or indirectly from the current. A quite different method was employed by Dewar, 4 and by Behn, 5 for liquefied gases. They dropped pieces of metal of known weight and specific heat into the liquid, and measured the volume of gas evolved. Lastly, Joly's steam calorimeter has been employed with good results by Wirtz. 6 The experiments of Mathias on the heats of vaporization of carbon dioxide are of great interest, for they extended from 6t>5 to 3i'i6, or almost to the critical temperature. The carbon dioxide contained 0/75 per cent, of air, which would cause the critical temperature to be rather lower than the true value 3 1 '35. The formula deduced by Mathias from his results, L 2 = 118-485(31 - /) - 0-4707(31 - /) 2 , gives L = o at 31. The experiments may be taken to prove that the heat of vaporization does really become zero at the critical point. J. E. Mills 7 has calculated the heats of vaporization of a large number of substances, chiefly those investigated by Young, over a wide range of temperature, generally from o to the critical point, by means of the formula and has shown that the formula =- ^r= = constant (//) 1 Phys. Rev., 17, 469 (1903)- 2 Trans. Chem. Soc., 83, 987 (1903). 3 Zdt.phys. Chem., 49, 597 (1904). 4 Chem. News, 71, 192 (1895). 5 Drude's Ann., 1, 270 (1900). 6 Wied. Ann., 40, 438 (1890). 1 Journ. Phys. Chem., 6, 209 (1902) ; 8, 383 and 593 (1904) ; 9, 402 (1905) ; 10, I (1906). 154 STOICHIOMETRY (where L is the heat of vaporization, E x is the heat equivalent to the external work, and therefore L E x is the internal heat of vaporisation; S L and s v are the densities of liquid and saturated vapour respectively) holds, with a few doubtful exceptions, for all the stable substances at all temperatures. Thirty-one substances were examined; of these, water, three alcohols, and acetic acid are known to behave abnor- mally in many respects, and the accuracy of the measure- ments of three others is not altogether satisfactory. The remaining twenty-three substances, excluding determinations within 10 of the critical temperature, afforded 378 values of p.' ; of these 349 were within two per cent, of the mean values of /*' adopted, and only 3 showed divergences greater than five per cent. The 29 divergences greater than two per cent, occurred where the measurements were likely to be lea'st accurate. T TT The formula -77=- ^j=- was based on the assumptions V S L VJy that 1. The molecules are evenly distributed. 2. The number of molecules does not change during vaporization. 3. No energy is spent in intra-molecular work ; in other words, the molecules are stable. 4. The attraction does not vary with the temperature. 5. The molecular attraction varies inversely as the square of the distance. Mills concludes that if the first four assumptions are valid the fifth must be accepted, and that the law of molecular attraction is similar to that of gravitation as far as the variation of the force with the distance is concerned. The Law of Despretz. It was pointed out by Despretz, 1 that the ratio - is approximately the same for different v v V L substances at their boiling points under the sa.me pressure. 1 Ann. Chim. Phys. t 24, 323 (1823). THE PROPERTIES OF LIQUIDS 155 But under atmospheric pressure V L is very small relatively to v v , and may be neglected. The statement may therefore be made that is approximately a constant. v v 2 2 '4 T But the volume v v = -^r- . litres under atmospheric pressure (where M is the molecular weight). T ' VV = 'M therefore, from the law of Despretz ML -7p- = constant. This law was discovered independently by Pictet in 1876 (reference unknown), Ramsay in I877, 1 an d by Trout on in i884, 2 and is generally known as Trouton's law. It has been the subject of numerous investigations, and the conclusion generally stated is that it is not true for widely different sub- stances, but that it generally holds for the members of any group of closely related bodies. The following are a few values of -7=- : ML T Hydrocarbons . . . . 20 to 21 Esters .... about 21 P, PC1 3 , C0 2 , H 2 S, CS 2 . . 2 1 -2 to 2 1 -4 S, SiQ 4 , Hg . . . . 21-6 to 22 Br 2 , HI 23 NH 3 ... 23-6 Water and alcohols about "* 26 From the equation - = - . -^ it follows that if 1 Philosoph. Soc. of Glasgow. 2 Phil. Mag., 18, 54. 156 STOICHIOMETRY = constant for different substances at their boiling V v - V points under equal pressures, -~ T must also be constant. The dp values of -,- T were calculated by Young in 1884 for a number of substances at a series of equal pressures, and the conclusions are given in the Brit. Ass. Rep.) 1885. The whole subject was discussed by Ramsay and Young in 1885 and I886. 1 It is pointed out (i) that closely related substances have in many cases the same value of ,- ' T, (e.g. chlorobenzene and bromobenzene, or ethyl chloride and ethyl bromide) ; (2) that the values for substances which are not closely related, other than those which dissociate when heated, or which contain a hydroxyl group, show differences amounting generally to less than 10 per cent., but in extreme cases reach- ing even 15 per cent. (e.g. carbon disulphide and aniline); (3) that if the comparison for any two such substances is made at a series of pressures extending over a wide range, the ratio of the values of -?- T is practically independent of the pressure; (4) that if one of the two substances undergoes dissociation (e.g. nitrogen peroxide) or contains a hydroxyl group (e.g. water or an alcohol or fatty acid), the values of ,-. T may differ by more than 60 per cent. (e.g. ammonium carbamate and carbon disulphide) ; (5) that in such cases the dp ratio of the values of ~ ' T may not remain constant at different pressures. These points are illustrated in the following table, which dp contains the values of -~- T at a few of the pressures at which the comparisons were made : 1 Phil. Mag. (5), 20, 515 ; 21, 135. THE PROPERTIES OF LIQUIDS 157 VALUES OF x T. Pressure in mm. cs, C 2 H 6 C1. C 2 H & Br. Ether. Aniline. Ethyl alcohol. N 2 4 . Ammo- nium carbamate. <50 676 _ 715 _ 750 853 _ 1087 100 1,280 1.3 6 4 1.304 1481 1,642 1331 2102 2OO 2,373 2,528 2,438 2,531 2788 3.155 3030 3938 300 3,430 3,536 3,513 3.595 4014 4,541 4304 5870 500 5,417 5.5 2 o 5,654 5,6l2 6231 7.197 6939 I OOO IO, IOO 10,290 10,371 io,5>3 13,827 2OOO 18,470 19,141 18,848 19.787 25,179 5000 41,130 41,702 41,306 43.3H ,~ 56,460 _ They are more clearly seen by taking the value for carbon disulphide as unity at each pressure. REDUCED VALUES OF -*- x T, TAKING THAT FOR CS 2 AS UNITY AT EACH PRESSURE. Ammo- Pressure in mm. CS 2 . C 2 H r ,Cl. C 2 H 5 Br. Ether. Aniline. Ethyl alcohol. N 2 4 . nium carbamate. 5 ooo 058 _ "IIO 262 _ 1-609 IOO ooo 066 019 !57 283 1-043 I-643 200 ooo 1-065 027 066 i75 3 2 9 1-277 1-659 300 'OOO I '03 1 024 49 165 324 1-255 I-7II 500 '000 1-019 044 036 150 329 I-28I IOOO ooo 1*019 027 '041 369 2OOO ooo 1-037 '02 1 072 364 5000 ooo I -014 004 053 '373 Mean of all values \ I '000 1-032 1-032 1-049 1-152 I-336 1*219 1-667 The values of ~- were mostly determined graphically by drawing tangents to the vapour-pressure curves, and individual errors as high as two per cent, are not improbable. The probable errors in the mean value are of course very much smaller. Correction of Boiling Point to Normal Pressure. It is frequently required to compare the boiling points of different substances, either that of a liquid under investigation with 158 S TO 1C H 10 ME TR Y the known boiling point of the pure substance in order to identify it, or to obtain information as to its purity ; or it may be desired to compare the boiling points of a series of homologous or isomeric compounds. A satisfactory comparison can only be made if the pressure is the same in all cases, and, as it is usually most convenient to determine the boiling point under the actual atmospheric pressure, the temperature must be corrected for the difference between the actual and the normal pressure of 760 mm. The temperature correction, A/, to be added to the observed boiling point, /, the barometric pressure being /, i dt i where c = -r- X ^ dp 1 For ordinary substances the mean value of c is about 0*00012. It is, however, considerably higher for some of the liquefied gases; for example, about 0-000145 for oxygen and nitrogen. On the other hand, it is much lower, about 0*00010, for the alcohols and water. The values of c for a large number of substances are given in Young's "Fractional Distillation," p. 15 ; also Trans. Chem. Soc.^ 81, 777 (1902). A smaller list had previously been published by Crafts. 1 1 Berichte, 20, 709 (1887). CHAPTER IX THE PROPERTIES OF LIQUIDS (continued) The Densities and Specific Volumes of Liquids. If the density of a liquid is merely required to be known at o or at about the ordinary temperature, it may be determined by means of the specific-gravity bottle or the Sprengel tube, preferably of the modified form devised by Perkin. 1 The capacity of the vessel at o is deduced from the weight of water it contains at that temperature. With the ordinary specific-gravity bottle the actual determinations must be made at a temperature higher than that of the room, and corrections must be made for the expansion of water and glass. The Perkin- Sprengel tube (Fig. 32) has the great advantage that it may be filled at o and afterwards weighed at a higher temperature. The tube must contain liquid at o from the end A to the etched mark B, any excess being removed by tilting the tube and touching A with a piece of filter- paper. When the tube is replaced in a vertical position some of the liquid flows back into the little bulb, and when expansion takes place with rise of tem- perature small with water, which contracts up to 4, but con- siderable with some substances the liquid passes into the bulb. FIG. 32. 1 Trans. Chem. Soc., 45, 444 (1884). 159 160 STOICHIOMETRY The determination is first made with water to find the capacity of the tube, and afterwards with the liquid under investigation, either at o or with the tube immersed in water of known temperature. Diffusion of vapour through the narrow tubes is so slow that no appreciable loss even of volatile liquids occurs during the determination. The specific-gravity tube may be suspended from the balance beam by the looped platinum wire C. All weighings must be corrected for the buoyancy of the air. The density, s, = -, where ;// is the corrected weight of liquid, and v is the capacity of the vessel from A to B at the temperature of experiment. If the densities are required at a series of temperatures not extending above the boiling point of the liquid under atmo- spheric pressure, a cylindrical bulb sealed to a long graduated tube of narrow bore is usually employed. The bulb and tube are calibrated, and the freshly distilled liquid is run in until it fills the bulb and part of the tube. The liquid is weighed, and readings of the volume are taken at different temperatures. Accurate determinations of the specific volumes and expansions of liquids up to their boiling points have been made by Kopp, Pierre, Thorpe, Elsasser, Gartenmeister, Zander, and others. For temperatures above the boiling point an apparatus such as that of Andrews must be employed, on account of the increased pressure. The volume of a liquid at a given temperature and under a pressure equal to the vapour pressure is termed the orthobaric volume. 1 At temperatures below the ordinary boiling point the compressibility is so slight that the determinations may be made without sensible error under atmo- spheric pressure. Above the boiling point the pressure should be made as nearly as possible equal to the vapour pressure. No difficulty is experienced until the temperature reaches about 0*85 of the critical temperature (calculated on the absolute scale), because a small alteration in pressure has no sensible effect on the volume. At higher temperatures the liquid becomes so compressible that it is necessary to make the 1 Ramsay and Young, Phil. Trans., 177, pt. i., 135 (1886). THE PROPERTIES OF LIQUIDS 161 pressure exactly equal to the vapour pressure. To do this, however, is difficult, because at these relatively very high temperatures ebullition takes place very easily even when the liquid is quite free from air. If, when the vapour is all con- densed, the pressure is reduced even slightly below the vapour pressure, ebullition at once takes place, and the pressure must be raised again to condense the vapour formed. If, on the other hand, the pressure is even slightly too high, the observed volume of liquid will be appreciably less than the orthobaric volume. In order to obtain the greatest possible accuracy, it is best to adopt a method which has been employed with some differ- ences in detail by Mathias, 1 Amagat, 2 and Young and Thomas. 3 Starting with the vapour completely condensed, the volume is increased until a little vapour has been formed ; when the temperature is quite constant, readings of the volumes of liquid and saturated vapour are taken. The volume is again in- creased, and after the temperature has become constant the volumes of liquid and vapour are again read. The process is continued so as to obtain four or more readings of the two volumes. Each time that the total volume is increased some of the liquid evaporates, so that the volume of liquid diminishes and that of the saturated vapour increases. Calling the first and third volumes of liquid V L ' and z/ L "' and the corresponding volumes of saturated vapour ?V an( i v \" } the ratio R of the specific volume of saturated vapour to that of liquid is given by the equation _ Vv" ~ v v _ v* V - v v" ~ ' ' ~ " In this way two independent values of R are obtained, and the mean may be taken as correct. The volume of liquid, if all the vapour were condensed, would be Ann. de Toulouse, 1891. 2 Compt. rend., 114, 1093 (1892). 3 Trans. Chem. Soc., 63, 1199 (1893). M 162 STOICHIOMETRY so that there are four independent values of the orthobaric volume of liquid. Finally, if m is the weight of sub- f\ stance in the tube, the orthobaric volume of a gram of liquid = V L = m The volume of a gram of saturated vapour, v v , may be calculated from the same data, for v v = Rv L . If the two values of R and the four values of V L , respectively, are not concordant, evidence is afforded either that the liquid contains air or some other impurity, or that there is some other source of error which requires investigation. If, on the other hand, the vapour pressure has been found to be independent of the relative volumes of liquid and of vapour, and concordant values of R and of V L have been obtained, there is strong evidence that the liquid is pure, and that the various details of the experiment method of heating and of reading the volumes, calibration of the tubes, and so on are satisfactory. There are many liquids which attack mercury either at all temperatures or when heated, and the specific volumes of such substances cannot be deter- mined by the method just described. The difficulty has been overcome by Young 1 by the employment of a graduated and calibrated sealed tube (Fig. 33), containing only the pure liquid and its vapour. When the temperature of such a tube is raised, the volume of liquids tends, on the one hand, to increase owing to expansion, but, on the other hand, to diminish owing to evaporation into the space above. Let m be the weight of substance (liquid and vapour) in the tube, V L the observed volume of liquid, and z> v that of the saturated vapour of the temperature /. If the weight of substance had been i gram, and the capacity of the tube 1 Trans. Chew. Soc., 59, 37, 126, 929 (1891) ; Proc. Phys. FIG. 33. soc., 18,617(1895). THE PROPERTIES OF LIQUIDS 163 , the volumes of liquid and saturated vapour would have been and respectively, say V L and v v . Let R be the ratio of the specific volume of saturated vapour to that of liquid, and V L the true volume of a gram of liquid at /; then r R = V L - V L but neither R nor V L are known. Let a second tube, similar to the first, but containing a relatively smaller amount ;// of substance, be heated to the same temperature, t. Calling the observed volumes of liquid and saturated vapour v and z> v ', the reduced volumes for i gram of substance and a tube of capacity , - would be v ' v ' L , and - v , respectively, say V L ' and v v '. m m From the second determination R. V L - V L ' V v = Vy' ' V L - V L ~ V L - V L ' V L V V ' V L 'VV andVL = --, Vy - R can then be calculated, and the volume of a gram of saturated vapour = Rv L . The method of constructing and filling the tube is described in the Trans. Chem. Soc., 59, 37 (1891), also a method of heating by which the volumes of liquid and saturated vapour may be determined with a single tube. The calculation in that case is different, and the experimental difficulties are much greater. The simplified method of heating the tube is described in the Proc. Phys. Soc., 13, 617 (1895); also Zeit. -bhysik. Chem., 29, 193 (1899). At low temperatures the orthobaric volumes of a gram of liquid increase slowly with rise of temperature, but at higher 1 64 STOICHIOMETRY temperatures the rate of increase becomes greater, and it is very great near the critical point. For purposes of calculation the formula v, = v (i -f- at -f- bt' 1 -j- ^ . . .) is usually em- ployed, the number of terms depending partly on the range of temperature and partly on the accuracy required (v = the volume at the lowest temperature, / , and t = t 4). At low or moderate temperatures the relation between density and temperature may, according to MendeleerT, 1 be expressed by the simple formula s t = s (i - kt) This equation is discussed on p. 170. Expressed as volumes, the equation is or v, = v (i -f kt + 2 / 2 + #V 3 . . .) Volumes of Saturated Vapour. The methods of deter- mining the volumes of saturated vapour by means of the modified Andrews apparatus and by the sealed-tube method have already been described. It is much more difficult to obtain accurate determinations of the volume of saturated vapour than of liquid, and when both have been determined with the Andrews apparatus, it is frequently advisable to employ the sealed-tube method for the saturated vapours only. In this case only one tube is required for a given range of temperature, for in the equation R - Vv -vT^V,, the values of V L obtained with the Andrews apparatus may be taken as correct. There are thus two partially independent values of the specific volume of saturated vapour at each temperature. In order to calculate R by either method, it is necessary to measure a relatively large volume of saturated vapour and a relatively small volume of liquid. Moreover, the determi- nation of the volume of liquid involves two readings. The 1 Ann. Chim. Phys. (6), 2, 271 (1884). THE PROPERTIES OF LIQUIDS 165 lower the temperature the greater is the value of R and the smaller the difference between the two volumes of liquid ; the greater, therefore, is the influence of errors of reading. With the Andrews apparatus the method can only be employed at temperatures above about 0*85 of the critical temperature (absolute scale), but the sealed-tube method can be made available for lower temperatures by greatly increasing the internal diameter of the middle portion of the tube, so as to greatly increase the volume of saturated vapour, while keeping the extremities of the tube narrow where the volume of liquid is read (Fig. 34). If the volumes of a gram of liquid and saturated vapour are plotted against the temperature, a closed curve is obtained, as ACB, Fig. 35, where the observed results for normal pentane are given. The summit of the curve C indicates the critical temperature and the critical volume. Law of Cailletet and Mathias. When the den- sities of liquid and saturated vapour are plotted against the temperatures, the closed curve takes the form ACB, in Fig. 36. It was pointed out by Cailletet and Mathias l that the means of the densities of any substance in the state of liquid and saturated vapour, when plotted against the temperature, fall on a straight line (DC, Fig. 36). The law of Cailletet and Mathias was confirmed by Amagat in the case of carbon dioxide within the limits of experimental error, and has been fully dis- cussed by Young. 2 In the case of normal pentane the law was found to hold with perfect accuracy from o to the critical temperature 197*2, as will be seen from the diagram and from the table on p. 166, where the observed 1 Compt. renJ., 102, 1202 (1886) ; 104, 1563 (1887). 2 Phil. Mag., 50, 291 (1900). FiG. 34. 1 66 STOICHIOMETR Y mean densities are compared with those calculated from the equation s t = s + at where j = 0-3231, a = 0-00046, and / = t C. Tempera- ture. *v s v . Mean. Calculated. A X 10*. 0-6454 0-0008 0-3231 0-3231 O 30 0-6165 0-0025 0-3095 0*3093 2 50 0-5957 0*0046 0-3001 0-3001 O 70 Q'5739 0*0079 0*2909 0-2909 9 0-5503 0*0129 0-28l6 0-2817 + I 1 10 0-5248 0-0203 0-2725 0-2725 O 130 0-4957 0*0310 0*2634 0-2633 I 150 0-4604 0*0476 0*2540 0-2541 + I 170 0*4162 0-0735 0*2448 0-2449 + 1 1 80 0-3867 0*0935 0-2401 0*2403 + 2 190 0-3445 0-1269 0-2357 0-2357 195 0-3065 0*1609 0*2337 0-2334 - 3 197 0*2640 0*2005 02323 0*2325 + 2 197-1 0-2560 0-2090 0-2326 0*2324 2 197-15 0-2472 0-2168 0-2320 0*2324 + 4 ORTHO BARIC 12 16 2O VOLUMES OF A GRAM FIG. 35. With other substances, however, excepting perhaps normal hexane, there was found to be very slight curvature of the THE PROPERTIES OF LIQUIDS [67 diameter, so slight in most cases that until the whole of the data were carefully examined it was attributed to error of experiment. For ordinary purposes of calculation over a moderate range of temperature the formula s t = SQ -f- a/ may, in fact, be employed, but when great accuracy is required, or when extrapolation is necessary, the formula s t = S G + a/ + /3/ 2 must be used. The experimental data are then reproduced with great exactitude, except in the case of the alcohols, which show marked deviation from the simple law. At the upper extremity of the diameter, where it intersects the closed curve, the densities of liquid and saturated vapour I90 C I7 C Q. I I50< 130 O 2 O3 O4- O5 DENSITY FIG. 36. are equal ; the temperature is the critical temperature, and the density may therefore be termed the critical density ; its reci- procal is the critical volume of a gram. If determinations of the two kinds of density have been made at a series of high temperatures, extending to within 10 or 20 of the critical temperature, a straight line drawn to pass as evenly as possible through the points representing the mean densities would give the critical density with very fair accuracy, but if the curvature is at all marked the same straight line i68 STOICHIOMETRY would not give the true mean densities at low temperatures, as will be seen from Fig. 370, in which the mean densities for normal octane are given. Conversely, a straight line drawn through the points representing the mean densities at low temperatures would not give the true critical density (Fig. 37^). In either case the formula s t = S Q + at + /3/ 2 would have to be used, and the extrapolation should not be carried too far. The lower limit of the diameter would be the freezing point of the substance, if it were not possible to cool a liquid below that temperature without solidification taking place. This process is, however, possible to some extent with all substances, and may be carried very far with some, as, for example, glycerol. If cooling without solidification could be carried on down to the absolute zero of temperature, the liquid would be deprived of all heat and the molecules would be at rest, and, as pointed out by D. Berthelot, it may be supposed that they would be as close together as they could be brought by any possible process. If, then, the diameter were correctly extrapolated to the absolute zero point, its lower extremity would give the mean density of liquid and saturated vapour at that temperature. But the density of saturated vapour diminishes rapidly with fall of temperature, and becomes negligible not very far below the ordinary boiling point. At these low temperatures, therefore, the mean density of liquid and saturated vapour is equal to half the density of the liquid. The density of the liquid at the absolute zero would therefore be twice the mean density given by the extremity of the diameter, and the reciprocal of the density of the liquid would be the volume of a gram. This may be regarded as the actual volume occupied by the molecules themselves in one gram of the substance, and D. Berthelot has calculated these minimum volumes for a number of substances on the assumption that the diameter is straight. In the case of normal pentane there is no appreciable curva- ture between o C. and the critical temperature; and as the freezing point is very low, it would be possible and of great interest to ascertain whether the diameter remains straight CRITICAL POINT 240 160 80 022 BOILING POINT 022 026 030 03* MEAN DENSITY FIG. 37,7. 030 034- MEAN DENSITY FIG. 37/5. 170 STOICHIOMETRY down to very low temperatures, and, in other cases, whether the curvature persists. The accurate experiments of Thorpe a on some liquids of high boiling point appear to indicate that there is very slight curvature in those cases, at any rate at temperatures at which the density of saturated vapour may be neglected. The law of. Cailletet and Mathias has the same form as that of Mendeleeff, which relates to liquids only, for a is always negative ; and since the density of saturated vapour becomes negligible at low temperatures, the two laws become identical, except in so far that the s t in Mendeleeff's formula refers to the actual density of the liquid, and in that of Cailletet and Mathias to half the density. THE CRITICAL POINT. It was observed by Cagniard de la Tour, in 1822,2 that when a sufficient, but not too great, quantity of liquid was gradually heated in a sealed tube it became more ft] mobile, and at a certain temperature, depending on the liquid, it was converted into a perfectly transparent HI vapour. On allowing the tube to cool, a very thick cloud was first formed, and the liquid then reappeared. By employing a sealed tube of the form shown in Fig. 38, Cagniard de la Tour was able to make an approximate determination of the pressure at which this change occurred. He thus obtained the following results : Temperature. Pressure. Ether .... 175 C. 38 atmos. CS 2 .... 258 71 The phenomena were carefully studied by Andrews, and described in his great memoirs on the continuity of the gaseous and liquid states of matter. 3 Andrews 3 ' observed that when carbon dioxide was partially 1 Trans. Chem. Soc., 37, 141, (1880). 2 Ann. Chim. Phys., (2), 21, 127 and 178 ; 22, 410. 3 Miller's "Chemical Physics," 1863 ; Phil. Trans., 1869, pt. ii. 575 ; Royal Institution Lectures, 1871 ; Phil. Trans., 1876, pt. ii. 421. THE PROPERTIES OF LIQUIDS 171 liquefied by pressure alone, and the temperature was then gradually raised to 31, "the surface of demarcation- between the liquid and the gas became fainter,, lost its curvature, and at last disappeared. The space was then occupied by a homo- geneous fluid, which exhibited, when the pressure was suddenly diminished or the temperature slightly lowered, a peculiar appearance of moving or flickering striae throughout the entire mass." Andrews called the temperature at which these phenomena were observed the critical point. In the apparatus employed by Andrews, or the modified form of it described on p. 132 (Fig. 25), the volume of the sub- stance under investigation can be altered at will, and may be adjusted so that the critical phenomena can be seen under the best conditions. If, on the other hand, a sealed tube be employed, the quantity of liquid introduced must be within certain not very wide limits, for the following reasons : When a tube containing only a pure stable liquid and its vapour is heated, the liquid expands, but at the same time part of it is con- verted into vapour. The volume of liquid, therefore, on the one hand tends to increase, on account of the expansion, but on the other hand tends to diminish, on account of evaporation. If the quantity of liquid in the tube is small to begin with, the diminution in volume due to evaporation will, at high temperatures at any rate, be greater than the increase due to expansion, and the level of the surface of separation of liquid and vapour will fall until the whole of the liquid is con- verted into vapour. No visible change then occurs when the temperature is raised. If the quantity of liquid at low temperatures is large, the gain by expansion will be greater than the loss by evaporation, and the volume will increase until the liquid completely fills the tube. If the temperature be then allowed to rise, the pressure will increase enormously, and the tube will in all probability burst. In neither case will the critical phenomena be seen. But if the quantity of liquid is neither too small nor too great, the surface of contact will not reach either the bottom 172 STOICHIOMETRY or the top of the tube, and it will be seen that the meniscus, which at low temperatures is concave (except in the case of liquids such as mercury which do not wet the glass, when it is convex), becomes flatter at high temperatures, slowly at first, but more rapidly as the critical point is approached. The meniscus finally becomes quite flat and less distinct, and then disappears, its place being taken by a broad band of mist. At a slightly higher temperature the mist disappears, and the sub- stance becomes homogeneous throughout. On allowing the tube to cool very slowly, the mist reappears, and then the meniscus. The range of temperature over which the change takes place, from the flat but quite visible meniscus to the broad band of mist, is so small that it should be quite possible to determine the critical temperature with an error of not more than 0*1. The mist or opalescence in fluids at and near the critical temperature has been carefully observed by Travers and Usher. 1 If the temperature of a sealed tube containing a pure liquid and its vapour is very slowly raised to and then above the critical point of the liquid, the following phenomena may be observed : (1) If the surface of separation of liquid and vapour vanishes at the critical point near the bottom of the tube (in other words, if the quantity of substance is small), then at a slightly lower temperature the space below the surface becomes opalescent, appearing brownish by transmitted light, and whitish by reflected light. The nearer the surface is to the bottom of the tube, the more intense is the opalescence. When the surface vanishes the opalescence becomes gradually diffused through the whole tube, and this result may be attained at once by stirring the contents of the tube by means of an iron stirrer operated by a magnet outside the tube. (2) If the surface vanishes near the top of the tube the opal- escence appears above the surface, and the nearer the surface is to the top of the tube, the more intense is the opalescence. (3) If the surface remains stationary, or nearly so, and is near the middle of the tube, while the temperature rises to the 1 Proc. Roy. Soc., 78A, 247 (1906). THE PROPERTIES OF LIQUIDS 173 critical point, the fluid appears slightly and evenly opalescent throughout its entire length. In all cases the even distribution of the opalescence after the surface has vanished may be pro- duced at once by stirring the contents of the tube. In the case of sulphur dioxide the opalescence was first visible at 0*1 below the temperature at which the surface vanished; it attained a maximum at about 0*05 above it, and completely disappeared at a temperature o'i higher. With ether the effects persisted over about 2. Travers and Usher made a few experiments, in which the volume of the fluid could be altered ; and they point out that when the surface remains stationary near the middle of the tube before disappearing, and the temperature is within the range over which the opalescence is visible, and when the volume is increased or decreased so slowly that the temperature is not lowered or raised appreci- ably, opalescence appears below or above the surface itself or the point at which it vanished, and its intensity is inversely proportional to the space it occupies. In other words, the phenomena described under (i) and (2) can be produced in this way. Travers and Usher conclude that the opalescence is always visible in that phase l which is diminishing in volume, but ex- periments carried out by Young (loc. tit., p. 262) in a modified Andrews apparatus at the critical temperature, while in com- plete agreement with those of Travers and Usher so far as comparison is possible, seem to indicate that the position of maximum opalescence depends rather on the mean specific volume of the fluid than on the alteration of either " phase," because when the volume was reduced from that at which opalescence was first visible to that at which it finally dis- appeared, the opalescence first appeared at the bottom of the tube (that is to say, just above the mercury), and as the volume diminished it spread upwards. When the critical volume was reached the opalescence was pretty evenly distributed, though 1 Employing the term "phase" not only for liquid and vapour, but also for the fluid above or below the level at which the surface disappeared, although it is believed that the fluid is really homogeneous at and above the critical temperature. 174 STOICHIOMETRY densest about the middle, and when the volume was small the opaiescence was confined to the top of the tube. The point cannot be definitely decided without further experiments, From Young's experiments it appears that the limits of volume between which opalescence is visible at the critical temperature are nearly the same for the four paraffins (isopen- tane and normal pentane, hexane, and octane) examined, being about 1-17 or IT 8 to about 0*87 or 0-88, taking the critical volume as unity in each case. The temperature at which the liquid-vapour surface vanishes can be determined with great precision by means of the modi- fied Andrews apparatus, because while the temperature of the vapour surrounding the experimental tube is kept constant, that of the substance under investigation may be temporarily lowered or raised to a minute extent by increasing or diminish- ing the volume suddenly but slightly. The substance may be regarded as being at its critical temperature when no surface is visible so long as the temperature remains quite steady, but when a surface becomes visible for a moment on suddenly increasing the volume to a slight extent. Under favourable conditions it should be possible to determine the critical temperature by this method to within 0*05, and in many cases determinations of the critical temperatures of different speci- mens of a compound have differed from each other by less than o'o5. For example, three specimens of isopentane were examined, the first, A, obtained from Kahlbaum, who prepared it from amyl alcohol j the second, B, separated from American petro- leum ; and the third, C, prepared by reduction of amyl iodide. The specimen A was heated in the vapours of both aniline and quinoline, the specimens B and C in the vapour of aniline only. With aniline vapour as the jacket the observed critical temperatures of the three specimens were between 187*75 and 187-8, but the actual pressures (reduced to o C.) under which the aniline was boiling were only recorded in the case of speci- mens A and B. The read pressures were as follows : THE PROPERTIES OF LIQUIDS 175 Specimen. Pressure (aniline). Pressure (quinoline). B ... 827-8 A 827*4.^ 2i6x<; A A (small quantity) . . 827'45 828-35 216-6 216-85 Mean . . . 827-76 216*67 Maximum difference from mean . . O'cq o'i8 Corresponding tempera- ture difference . . . 0-028 0-030 Again, in three determinations of the critical temperature of normal pentane, one with a sealed tube and two with the modified Andrews apparatus, the pressures under which the quinoline boiled were 281*1, 281-35, and 281-2 mm. re- spectively. The maximum difference from the mean pressure is 0*13 mm., and the corresponding temperature difference 0-017. Various other methods of determining the critical tempera- ture of a substance have been devised, and are fully described by Mathias (" Le point critique des corps purs"). The question whether, for a given substance, the highest temperature at which a liquid-vapour surface is visible depends, on the one hand, on the mean specific volume of the substance, or, on the other hand, on the direction of the change of tem- perature, whether slowly rising or slowly falling, has given rise to much controversy. Battelli, Zambiasi, Galitzine, de Keen, and others have obtained very discordant results. De Heen 1 found in the case of ether that the greater was the mean density s [ , where m is the weight of ether, v the capacity of the tube] the higher was the temperature /,. at which the surface disappeared. Differences of i or 2 were observed, but it may be pointed out that the critical temperatures observed by de Heen differ widely in some cases from those of other experimenters. 2 1 Bull. deFAcad. roy. de Belgiqite, 24, 96 (1892). 2 In the case of methylacetate the error actually amounts to about 45. 176 STOICHIOMETRY Battelli, 1 on the other hand, finds at any rate, when s is either greater or not much less than the critical density that t c falls as s increases. But there were two series of determina- tions for both alcohol and ether carried out at different times, and the differences between two values of / observed at different times for the same value of s are in some cases greater than the maximum differences between the values of t e observed at the same time for different values of s. Zambiasi 2 arrives at the conclusion that t c rises as s de- creases, the maximum temperature being reached when s = s c , the critical density; but Mathias 3 shows that Zambiasi's results, if correct, indicate that t c continues to rise when s falls below s c . The total observed variation was 0*5. Hannay 4 found that for some liquids f c was independent of s, while for others a variation was noticed. He attributed this variation to the presence of impurities. Galitzine, 5 experimenting with ether, found that t e was in- dependent of s, but that //, the temperature at which the meniscus reappeared on cooling, was somewhat lower than / f , and that there was an indication of a slight rise of // with increase of s. Travers and Usher (loc. tit.) state definitely that they found the Cagniard de Latour temperature to be independent of s, and their experiments indicate that t e = //. Young, in his determinations of the critical constants of numerous carefully purified substances, has found that t c is in- dependent of s, and that f c = //, or at least that the differ- ences are within the limits of experimental error, 0*05 or at most o'i. Even as regards the results of de Heen and Battelli, the statement may be made that the observed differences, although larger, are within the limits of the larger experimental errors, and the evidence, on the whole, is therefore in favour of the 1 Nucvo Cimento, III. 33, 22 (1892). 2 Attid. R. Ace. del Lined, V. 1, 423 (1892). 3 "Le Point Critique des Corps Purs," p. 34. 4 Proe. Roy. Soc. t 30, 484 (1880). 5 Wdd. Ann., 50, 521 (1893). THE PROPERTIES OF LIQUIDS 177 conclusion that, in the case of a pure substance free from air, the Cagniard de Latour temperature is independent of the mean density and of the direction of the change of temperature. The Critical Pressure. The critical pressure may be best determined experimentally by means of the modified Andrews apparatus. The determination is carried out in the same manner as that of the vapour pressures of the liquid at lower temperatures. The critical isothermal is so nearly horizontal in the immediate neighbourhood of the critical volume that there is no difficulty in ascertaining the critical pressure if a series of readings are taken over a range which includes the critical volume. The critical pressure is altered by the presence of air or other impurities to even a greater extent than the critical temperature, and it is absolutely necessary that the utmost care be taken to purify the liquid under investigation and to remove all traces of dissolved air from it. The observed critical pressures of two specimens of a substance should not differ by 0*2 per cent. If the critical temperature is very high so that the vapour pressure of mercury is considerable, or if the substance attacks mercury at a high temperature, the modified form of experi- mental tube referred to on p. 136 may be employed; or if the critical pressure only, and not the temperature, is to be measured, the method of Altschul 1 may be employed. The apparatus required is similar in principle to that of Andrews, but the experimental tube is fixed in a nearly horizontal position. A small portion only of the liquid in it is heated by a small Bunsen flame, a sheet of metal being interposed between the flame and the glass tube. When the liquid boils there is a meniscus on each side of the vapour, and the pressure is so arranged that the two liquid surfaces are near each other. The temperature is slowly raised, and the pressure is first read when the surfaces vanish, and again when they re- appear on slow cooling. Guye and Mallet have always found the two pressures to be identical, provided that the substance 1 Zeitschr. phys. Chem., 11, 577 (1893); also Gu Y e and Mallet, Arch, de Geneve, [4], 13 (1902). N 178 STOICHIOMETRY investigated was pure and stable, and a further proof is thus afforded that the temperature at which the meniscus disappears is the same as that at which it reappears. The Critical Volume. Owing to the extreme compres- sibility of matter at and near its critical point, it is impossible to read the critical volume accurately on the critical isothermal in the pressure-volume diagram. For the same reason it is impossible, by any method yet devised, to make a direct experimental determination of the critical volume (or density) with sufficient accuracy. It is indeed impossible, as pointed out by Gouy, 1 for the whole of the fluid in a tube to be in the critical state, because, although the temperature may be the same throughout, the pressure must vary slightly at different levels; that at the bottom of a tube being greater than at the top by '; mm. of mercury, where s is the mean density of the fluid, h the height of the column, and 13*6 is the density of mercury. In a cylindrical tube the value of '-^ is, of course, independent of the temperature, since h varies inversely as s, and it may be determined once for all at any low temperature for which s and // have been determined. But at the critical temperature, when the volume is not very different from the critical volume, a very small altera- tion in pressure makes a marked difference in the density. Gouy has calculated that in a tube of 10 cms. height, con- taining pure carbon dioxide heated uniformly to its critical temperature, there may be a difference of 6 per cent, between the densities at top and bottom. The variation is greatest at the level where the pressure is exactly the critical pressure, a difference in height of 0*5 mm. being sufficient to produce a difference of i per cent, in density, and a difference in height of 0-004 mm. a difference of 0*2 per cent, in density. Strictly speaking, below the critical temperature it is only immediately above and below the surface of separation that the vapour and liquid respectively have their true (orthobaric) 1 Compt. rend., 115, 720 (1892). THE PROPERTIES OF LIQUIDS 179 densities. At a higher level the vapour is not quite saturated, and at a lower level the liquid is slightly compressed, but it is only in the neighbourhood of the critical temperature that either vapour or liquid is so compressible that the variation in density at different levels is considerable. When the temperature of a vertical tube containing a pure liquid and its vapour is very slowly raised until the critical point of the substance is reached, the meniscus, if it does not reach the top or bottom of the tube at a lower temperature (p. 171), becomes flat, then indistinct, and finally vanishes. It is evidently at the level where the meniscus vanishes that the density is the true critical density, and it is also at this level that the opalescence is most marked. Above this level the density is lower; below, it is higher. If the meniscus vanishes near the top of the tube, the mean density will be considerably higher than the critical density; if near the bottom of the tube, the mean density will be considerably lower. It follows that the critical phenomena can be observed even when the mean density of the fluid is considerably higher or lower than the critical density ; in other words, the quantity of liquid in a sealed tube may vary within moderate limits. To put the matter in another way : the condition as regards pressure and volume of a fluid enclosed in a long vertical tube and exhibiting the critical phenomena, is not represented by the point on the critical isothermal which coincides with the summit of the liquid-vapour surface, but by a length along the isothermal which includes this point. If the tube, while its temperature remained constant, were moved into a horizontal position, the variation in pressure and in specific volume would diminish and the length of isothermal represented would be greatly shortened. In a tube of narrow bore held in a horizontal position the mean density would require to be very nearly equal to the critical density for the critical point to be included in the isothermal, and if the meniscus disappeared near the top or bottom of the tube when vertical, it may be concluded that no part of the fluid would be in the critical state when it was horizontal. If the mean density of the fluid in a tube is equal to the 1 80 S TOICHIOME TR Y critical density, the meniscus will vanish at about the middle of the tube on slowly raising the temperature to the critical point, and an approximate determination of the critical volume might be made with the modified Andrews apparatus by adjusting the plunger so that the volumes of liquid and saturated vapour immediately below the critical temperature were equal. The critical temperature of normal pentane is 197*2, and four readings of the volume of vapour and of the total volume were taken by Young at each of a series of temperatures. Thus at 197*0, calling the total volume v, and the volume of vapour # v , the following values of and v were obtained : ^ . . . . 0-1363 0-3286 0-5079 0-6732 v .... 0*4271 0*4483 0*4694 0*4905. Vm Plotting -y against v, the value of v corresponding to - = 0-5 is found to be 0-4686 c.c., and this divided by the weight of substance, 0*10922 gram, gives 4*290 as the critical volume of a gram, v p , the value found by the more accurate method of Cailletet and Mathias being 4*268. The values found in a similar manner at other temperatures very near the critical point are Temperature . . 196*9 197'! 197*15 v c 4-282 4*284 4*286 mean 4*285 The method could not, however, be employed for tempera- tures far below the critical point; thus at 170 the calculated value of v c would be 4-091. The curve enclosing the liquid-vapour surface in (a) the pressure-volume, () the temperature-volume, (c) the pressure- density, and (d) the temperature-density diagram, is in each case of such a form that while the critical pressure or tempe- rature can be read with considerable accuracy, neither the critical volume nor the critical density can be estimated with any approach to exactness. THE PROPERTIES OF LIQUIDS 181 As already mentioned, however, it was stated by Cailletet and Mathias that the mean densities of liquid and saturated vapour, when plotted against the temperature, fall on a straight line, and although there is in reality, as a rule, very slight curvature of the diameter, yet their method affords by far the most accurate method of determining the critical density. To obtain the best results the curvature should be taken into account, and the critical density calculated from the formula s e = s + a(t c - / ) + (/ c - 4) 2 . In the table on the following page the critical and a few other constants are given for a number of substances. Relation between Critical Temperature and Boiling point. The question whether any simple relation exists between the boiling points under normal pressure and the critical temperatures of different substances seems to have been first discussed by Pawlevvski, 1 who arrived at the con- clusion that the difference between the two temperatures was the same for all substances, and he gave a list of seventeen esters for which the observed differences varied only between i8i'2 and 182-9; but in a later list of twenty-four widely different substances the differences varied between 150'! and 210*0. That the rule is not even roughly applicable to all substances may, however, be seen from the following table, in which the temperatures are given on the absolute scale : Critical tempe- rature = Tc Boiling-point Difference. T C -T 6 Ratio, Ik Hydrogen 35 20 15 175 Oxygen Methane 154 191 90-5 I08-3 82-7 170 176 Octane 569-2 398-8 170-4 i -43 Benzene 208-3 1-63 Water . 633 373 260 i-59 It would, indeed, as will be seen from the table, be more correct to state that the critical temperatures are roughly 1 Berichte, 15, 460 and 2460 (1882) ; 16, 2633 (1883). 182 STOICHIOMETR Y vo t^ t^ J rJ- rj- O COt^f^O O^OO w ONtoM COOO U"> tovo J^- t"^ ON ON O !-" M tovO VO >O CO u . t^ t^ t^ t^ t^ t^OO 00 00 00 00 00 00 OJO ON ON ON ON ON ON p CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO Tj- as If o-S vO N VO O ~ is .a % ^^ .OOOtoOtoQOOOOOOOtoOOOOOOOOOOOOOOO c OO to M rJ-GO ON O ** "- 1 <-* >-i VO VQ "-" i-itocOrhONCOO "-< co^OOOO M to^O O "s ^? O to cooo">o" 6 CO CO M M M CO i tooOMD ON T}-OO OOMtoO'^'ONMON'-ii-cl->.t~>. t~>.OO rJ-OO t-^OO M to >-i OO COOO COOO to O COVO ONONMOO tot-^O ONCOO tot-ON 1>.VO t-i to to O 00 t to t^ co Tt- 1 M VO ON ONOO CO ON CO *-> t- M VO O to OO>- _ i ^- CO ^-vO Ot^O^J"*- 11 - 1 - - - - x. to O f^vO t 1 O vO vO Q "* OO OO OO GO O M CO O ON Ti~ ONVO O ON ThvO M^J-Mi-iCOt^OM'-'M'^-cOMwOi-'toMMO'-.vO vp oo w p yo i>. t>.o t-ONj^>ONpNONpNpNp p^p^ P^^ op oo p *< o b b M b b '** " M HH b b b b b b b b b b b ** b b b b b b '-< c O THE PROPERTIES OF LIQUIDS 183 proportional to the boiling-points. This rough proportionality, to which attention was directed by Guldberg, 1 may, in fact, be occasionally useful in obtaining an idea of the critical point of a substance, especially if the following points are borne in mind : T (1) In any homologous series the ratios ~ diminish though i& usually at a decreasing rate with rise of molecular weight. (2) The ratios are generally nearly the same for the mem- bers of a group of closely related (not homologous) substances. (3) In the case of isomeric substances the ratios for iso-compounds are higher than for normal, and for di-iso- compounds they are still higher. Homologues. Isomers. Closely related substances. T T c T T T T~ Methane . 764 Isopentane . . l '53 l Fluorobenzene . 1-562 Ethane . 694 n-pentane . 1-520 Chlorobenzene . I-5 6 3 Propane . 6.23 n-butane . . Isopropyl ben- Silicon tetra- n-pentane 520 zene . . . 1-492 chloride I-5I3 n-hexane . . 485 Propyl benzene 1-485 Stannic chloride 1-529 n-heptane . "454 Germanium tetra- n-octane . . 427 Di-isopropyl 1-511 chloride I-532 n-nonane . . n-hexane . . 1-485 n-decane . 402 Chlorine . . I-749 Di-isobutyl . . i'443 Bromine I'734 Methyl formate . "597 n-octane . . . 1-427 Iodine . . . 1-716 ,, acetate . '535 . - ,, prop ion- Methyl isobuty- Argon . . . I-79I ate ... . 504 rate . . . 1-480 Krypton . . I'735 Methyl butyrate '475 Methyl butyrate 1-475 Xenon . . . I-756 Thorpe and Rticker's Relation. Thorpe and Riicker 2 have proposed the following formula, by which the critical temperature of a substance may be approximately calculated from the densities of the liquid at two temperatures not necessarily higher than the ordinary boiling-point : _TV LJ -TV, : 1 Zeit.phys. C/iem.,5, 374(1890). 2 Trans. Chem. Soc., 45, 135 (1884). 1 84 STOICHIOMETRY where T x and T 2 are the two absolute temperatures, s 1 and s. 2 the corresponding densities, and A is a constant which the authors take to be 1*995. Calculating the values of A for twenty-four substances for which the required data are accurately known, and taking the melting point of ice and the boiling point of the substance under normal pressure in each case, values were obtained ranging from 1-926 for ethyl propionate to 2-030 for fluoro- benzene and chlorobenzene. The mean value is 1*974, and it is only in few cases that the difference from this value exceeds 2 per cent. CHAPTER X THE KINETIC THEORY OF GASES IT was first pointed out by Bernoulli, in 1740, that the pressure of a gas is due to the impact of the molecules against the body on which the pressure is exerted. The theory was greatly extended and advanced by J. J. Waterston, but, unfortunately, his paper, which was read before the Royal Society in 1845, was not then published, and was entirely forgotten. It was found by Lord Rayleigh in the archives of the society, and was published in I892. 1 Meanwhile the theory was independently developed by Krcenig in 1856, and Clausius in 1857, and has been further extended by Clausius, Maxwell, Boltzmann, Van der Waals and others. The molecules of a gas are considered to be extremely minute, but still of finite dimensions. The volume actually taken up by the molecules of a gas under ordinary conditions of temperature and pressure is very small compared with the total volume of the gas. The molecules are, therefore, relatively to their size, very far apart, and it is assumed that they exert no appreciable attraction on each other. When they approach each other they are regarded as behaving like perfectly elastic bodies. Consider the path of an individual molecule of gas. As it is not acted on by any forces (other than gravity, which need not be considered), the molecule will move with uniform velocity in a straight line until it collides ' 2 with another 1 Phil. Trans., 183, I (1892). 2 It is not necessary to assume that actual contact between the molecules takes place ; the assumption is that the effects are the same as if the two molecules were perfectly elastic, and came into collision. 185 1 86 STOICHIOMETRY molecule. It will rebound from this in a new direction and with a different velocity, with which it will move uniformly until a second collision occurs. Thus the direction and velocity will change after each collision, but the velocities will vary about a definite mean value. The " free path " also will vary from collision to collision, but under constant conditions of tempe- rature and pressure, its mean value will remain constant. The mean kinetic energy of rectilinear motion of a single molecule = \mi?) where m is the mass of the molecule, and u its mean velocity. But besides the kinetic energy of rectilinear motion, the molecule may possess internal energy, due to rotation or oscillation of the atoms composing it. It is believed that the internal energy also varies about a definite mean value. Boyle's Law. The pressure which the gas exerts on the walls of the vessel containing it is caused by the impact of the molecules against the sides, and it is clear that, under otherwise similar conditions, the pressure will be proportional to the number of impacts in unit time, which, in their turn, will be proportional to the number of molecules in unit volume ; that is to say, to the density of the gas. The pressure will therefore vary directly as the density or inversely as the volume occupied by a given mass of the gas. Boyle's law, therefore, follows at once from the kinetic theory. In order to calculate the pressure, consider the gas in a cube of unit volume, each surface and each side being therefore equal to unity. Let m be the mass of a molecule, and N the number of molecules in the unit volume ; then mN = s, where s is the density, or mass of gas in unit volume. The pressure depends in two ways on the velocity of the molecules, for not only the force of the impacts, but also the number of them in unit time is proportional to the velocity. A molecule which collides vertically with a wall of the cube rebounds with the same velocity as before, but in exactly the opposite direction, and as the original momentum is iu, the change of momentum is 2iu. The number of impacts in unit time on the whole surface is proportional to the total number of molecules, N, THE KINETIC THEORY OF GASES 187 and to the velocity, u, and equal to Nw. But as there are six walls, the number of impacts on a single wall = JN#, and the pressure on one wall, that is to say, on Unit area, is 2mu X Take the case of hydrogen gas at o C. and 760 mm. pressure. The mass of i c.c. 0*0000899 gram, and the pressure on i sq. cm. = 1033 grams, or 1033 X 981 dynes. Therefore, since x IQ 33 X 981 s v 0*0000899 = 184,000 cms. per second. The molecules of hydrogen at o C. therefore move at the mean rate of i '84 kilometres per second ; and those of any other gas, the density of which at o C. and 760 mm. is s' t move at the rate of 1-84 /v/ -, kilometres per second; or if d is the density of the second gas, taking that of hydrogen at the same temperature and pressure as equal to unity, the molecular velocity at o = r= kilometres per second. V a The mean velocity of the molecules is independent of the pressure, but it increases with rise of temperature. It is found experimentally that the pressure of a gas at constant volume is directly proportional to the absolute temperature; but the pressure is proportional to ?/ 2 , and therefore to \mu 2 ; therefore, the mean kinetic energy of rectilinear motion of the molecules is directly proportional to the absolute temperature. Avogadro's Hypothesis. If two different gases are com- pared at the same temperature and pressure, p = ^WiN^/! 2 = 5/aN a #2 a where m t and /// 2 are the masses of the molecules of the two gases respectively, and N\ and No the number of mole- cules in unit volume. i88 STOICHIOMETRY But when two gases at the same (high) temperature and (low) pressure are mixed together, the change of pressure or temperature which occurs is so slight that it may be assumed that no change whatever would take place in the case of perfect gases. It may therefore be concluded that the kinetic energy of the molecules of different gases at the same temperature is equal, and that But since ^N^ 2 = ^ 2 N 2 # 2 2 , it follows that N x = N 2 . Avogadro's hypothesis, therefore, receives very strong support from the kinetic theory of gases. Ratio of the Specific Heats at Constant Pressure and Constant Volume. The heat energy of a gram-molecule of a gas is given by the kinetic energy of rectilinear motion of the molecules plus the internal energy of the molecules. Let e be the increase of internal energy per unit rise of temperature, and C v the molecular heat at constant volume ; then X ^ + e where J is the mechanical equivalent of heat and the molecular heat) _ ^ at constant pressure | p the latter term being due to the work done in expansion against external pressure. The ratio of the specific heats = ^ = 7 ^t 5 mu* 6 X ~T" ~~ i mil 2 , If e = o, then y = f X 2 = i'66 ; but if e has a finite value, y must be less than r66, and the higher the value of e t the more closely will 7 approach to unity. THE KINETIC THEORY OF GASES 189 If the molecules of a gas consist of single atoms, it may be concluded that there is no internal energy, and that e o. Kundt and Warburg, employing a modification of Kundt's apparatus, found that y = i'66 for mercury vapour, 1 and Ramsay and Travers have obtained values approximating closely to i *6 for the inert gases of the argon family ; it is therefore believed that the molecules of these gases are monatomic. For oxygen the value 1*404 has been obtained, and for nitrogen 1*410, and as it is practically certain that the molecules of these gases, like those of hydrogen, are diatomic, it may be concluded that the normal values of y for gases which consist of diatomic molecules is 1*40 to 1*41. Determinations of y have been made for a number of other gases and vapours, and the data obtained clearly indicate that as the complexity of molecules increases, the value of y approaches more closely to unity. This will be seen from the following table : Number of Name. Formula. atoms in y molecule. Ammonia . . . NH 3 4 1-30 Chloroform . . CHC1 3 5 I'2O Methyl ether . . (CH 3 ) 2 9 I-II3 Ethyl ether . . (C 2 H 5 ),0 15 1-029 Mean Free Path. According to Clausius the mean free path, L, is given by the equation L = where A. is the mean distance from centre to centre of two molecules regarded as spherical, so that X 3 is the size of cube that would contain one molecule, or the space inhabited by one molecule ; and / is the distance between the centres of 1 90 S TOICHIOME TR Y two molecules when in the position of closest contact for example, at the moment of collision. The question was examined by Maxwell, who in 1860 determined the values of L for some gases from their internal friction. Independent values of L were subsequently obtained by Maxwell and Clausius from the conductivities of gases for heat, and by Maxwell and Stefan from their rates of diffusion. O. E. Meyer has given the following values of L for a number of gases at 20 C. and 760 mm. L Hydrogen 18*5 millionths of a mm. Methane 8-5 Carbon monoxide 9*8 ,, dioxide 6*8 Ammonia 7*4 Ethylene 5-8 Methyl ether 4*2 THE DISSOCIATION OF GASES. Maxwell's Law of Velocities. It has been pointed out that the velocity of any individual molecule in a mass of gas at constant temperature changes after each collision with other molecules, although its mean velocity, calculated for a sufficient number of free paths, remains constant. It is clear, therefore, that the molecules cannot all be moving at the same rate, and if, at a given moment, the velocity of every molecule of the gas could be determined, and if the molecules were grouped according to their velocities, say (u -*),... (u - 2), (// - i), (?/), (u + i), (// 4- 2), . . . (n 4 n ) metres per second, where // includes all velocities from (u -) to (u 4- J) and so on, a great many molecules would be found with velocity //, a smaller number with velocities (n i) and (u 4- i), a still smaller number with velocities (u 2) and (u 4- 2), and so on. In fact, if the number of molecules in each group were plotted against the velocities, a curve of the form shown in Fig. 39 would be obtained. THE KINETIC THEORY OF GASES 191 The distribution of velocities would be similar to that of a set of observations of a constant quantity, according to their (-for ) deviations from the true value; or of the bullet- marks in and round the bull's eye on a target fired at (on a still day) by a good marksman, the marks outside the bull's- eye being counted to left and right of the centre of the target. Now, since the absolute temperature of a gas is pro- portional to the mean square of the velocities of the molecules, it may be inferred that the individual molecules are not all at the mean temperature, but that there are many molecules at temperatures near the mean and few at temperatures far above or far below the mean. The distribution of temperatures would, in fact, be of the same nature as that of velocities. FIG. 39. Take the case of a gas, such as nitrogen peroxide or iodine, which dissociates into like molecules when heated, and consider what happens to a single molecule. The attraction between the component parts of the molecule tends to keep them together, while, on the other hand, the vibration or oscillation of the parts tends to drive them asunder. As the temperature rises, the oscillation increases until the attraction between the components is no longer able to hold them together, and dissociation then takes place. If the internal energy, like the kinetic energy of rectilinear motion, is directly proportional to the absolute temperature, there must be a definite temperature, which may be called the true temperature of dissociation, T D , at which the single molecule dissociates. The same reasoning would apply to any other single molecule, and if all the molecules were at the same tempera- ture, it may be concluded that the gas would suffer no dissociation until the temperature T D was reached, but that at 192 STOICHIOMETRY that temperature complete dissociation would take place. There would therefore be an abrupt change of density at T D . If, however, when the mean temperature of the gas is considerably lower than T D , a few molecules reach that temperature, they will undergo dissociation, and the components will intermingle with the other molecules. But as the velocities, and therefore the temperatures, of the individual molecules are constantly changing, some or all of the component mole- cules will soon cool below T D , and when they happen to come in contact with each other, recombination will take place. Meanwhile other molecules will have dissociated, and for a time the number of molecules dissociated in unit time will be greater than the number re-formed ; but as the number of component molecules increases, the chances of recombination become greater, and eventually a state of equilibrium will be established, dissociation being balanced by recombination. Suppose now that the temperature is raised until it reaches T D . There will then be as many molecules with temperatures above as below T D , and it may be concluded that when equilibrium is established one-half the total number of mole- cules will be dissociated. At a still higher temperature the number of molecules dissociated will increase, but it is only when the mean temperature is far higher than T D that there can be complete dissociation. On allowing the temperature to fall again, gradual recom- bination will take place, the composition of the gas at any constant temperature depending solely on that temperature, and not on previous conditions. It follows that the curve representing the relation between the percentage number of molecules dissociated and the temperature will have the general form indicated in Fig. 40, and this conclusion is borne out by the experimental evidence. When nitrogen peroxide is undergoing dissociation, only two kinds of molecule, N. 2 O 4 and NO 2 , can be present (at temperatures below that at which the NO 2 begins to dissociate) ; but by the dissociation of phosphorus pentachloride the unlike molecules PC1 3 and C1 2 are formed. There may therefore be three kinds of molecule present in the gas, PC1 5 , PC1 3 , and C1 2 . THE KINETIC THEORY OF GASES 193 The chances of recombination are smaller in this case than with nitrogen peroxide, because while any two molecules of NO 2 may reunite, it is only when a molecule of PC1 3 comes in contact with a molecule of C1 2 that recombination can occur. But whenever a compound dissociates into unlike com- ponents the chances of recombination of either component may evidently be increased by introducing a larger number of molecules of the other component, and this without increasing the chances of decomposition. Thus in the case of phosphorus PERCENTAGE NUMBER OF 100 MOLECULES DISSOCIATED FIG. 40. pentachloride, the greater the number of PQ 3 molecules the greater the chance of a chlorine molecule meeting a PC1 3 molecule at a temperature below T D . In other words, by increasing the quantity of either component, the stability of the compound is apparently increased. Experimental evidence of the correctness of this conclusion has already been adduced (pp. 118 and 119). Calculation of the Percentage Number of Molecules Dis- sociated. If a molecule, when dissociated, forms n simpler molecules, then, when dissociation of the gas is complete, the volume of unit mass will become ;/ times as great, and the o i 9 4 STOICHIOMETRY vapour density will be - , where D is the density of the undis- sociated gas. Let d be the observed vapour density of a substance which, at the temperature of experiment, has undergone partial dis- sociation, and of every 100 complex molecules suppose that x have dissociated, giving nx simpler molecules. There will, therefore, be 100 x -\- nx or 100 + (n )x molecules 700 600 O 5O O 50 IOO MOLECULES %OF NaCU ' MOLECULES % OF NO* DISSOCIATED DISSOCIATED FIG. 4 I altogether. But the density is inversely proportional to the volume, and therefore to the number of molecules, and therefore and when n = 2 D __ 100 -\- (n i)x d loo ioo(D - d) x = X = ioo(D - d) THE KINETIC THEORY OF GASES 195 In the diagram (Fig. 41) the double dissociation N 2 O 4 = 2NO 2 , where n = 2, and 2NO a = 2NO -f O 2 , where n f, is represented, the data for the first stage in the dissociation having been obtained by Deville and Troost, 1 and for the second stage by Richardson. 2 The pressure is that of the atmosphere. In no case has the whole course of dissociation been satisfactorily observed, but this diagram shows the middle and upper parts of the first curve, and the lower and middle parts of the second curve, very satisfactorily. Deville and Troost. Richardson. Temperature. Vapour density. Molecules per cent, of N 2 O4 dissociated. Temperature. Vapour density. Molecules per cent, of NO 2 dissociated. 26-7 38/3 20'I I30-0 23*26 97'8 4 7C'/1 26"O 35 4 39'8 35"5 29*6 184-0 22-45 4'33 49-6 3 2-8 40-3 184-1 22-35 5'8o 60-2 30-0 53'3 222-1 22-52 4*17 70-0 27-7 66-0 222-5 22-40 5-26 80-6 26'O 77-0 278-4 21-53 I3-57 90*0 2 4 -8 85-4 279-2 21-59 13-10 lOO'I 24-3 89-5 358-0 21'ig 17-09 111-3 23;S 93-2 390-0 I9-57 35-05 121-5 96-6 42J2 19-63 34-48 23-1 99'2 447-0 18-98 43-28 448-2 19-20 40-63 154-0 22-8 176 466-3 18-37 50-40 183-2 22'7 2-64 485*4 17-84 490-0 18-04 55-00 494-4 17-98 55*84 17-78 58-71 619-5 15-30 lOO'OO It is, of course, quite probable that at 140 there may be a very few molecules of NO 2 dissociated, and at 150 a few molecules of N 2 O 4 remaining. It has been stated (p. 17) that for a perfect gas at constant 1 Compt. rend., 64, 237 (1867). 2 Trans. Chem. Soc. t 51, 397 (1887). 3 Molecules per cent, of NO 2 dissociated. N 2 4 1 96 6- TO 1C H 10 ME TR Y volume the pressure varies directly as the absolute temperature ; in other words, the isochors are straight lines radiating from the zero of pressure and absolute temperature. Ordinary gases and vapours under moderate or low pressures show only slight deviations from this law. In the diagram (Fig. 42^7) the theoretical isochors for isopentane representing 4000, 2000, and 1000 c.c. per gram respectively, are indicated by dotted straight lines, and actual observations (or rather points read from the isotherms constructed from actual observations) by circles, and it will be seen that the deviations for 4000 c.c. are too small to be recognizable on so small a diagram. With a substance which undergoes dissociation, however, the case is quite different. 1 Consider, for example, such a substance as nitrogen per- oxide, the molecules of which are believed to correspond to the formula N 2 O 4 at low temperatures, and to the formula NO 2 at high temperatures (140 under normal pressure). Theoretical isochors may be constructed on the assumption that the gas does not dissociate, and that the formula is (a) NO 2 , (b) N a O 4 . In Fig. 42^, the straight line AB is the theoretical isochor for 1000 c.c. of NO 2 per gram, and the line CD for 2000 c.c. NO 2 per gram. But the number of molecules in one gram of N 2 O 4 would be only half as great as in one gram of NO 2 , therefore the theoretical volume of a gram would be only half as great. The isochor CD, therefore, represents not only 2000 c.c. of NO 2 per gram, but also 1000 c.c. of N 2 O 4 per gram. Similarly the isochor EF represents 4000 c.c. NO 2 , and also 2000 c.c. N 2 O 4 . If, then, when the temperature falls, the NO 2 molecules gradually unite to form N.X) 4 molecules, the isochor representing 1000 c.c. of the real gas, nitrogen peroxide, should start at the higher temperature on the theoretical isochor AB, and descend gradually to the isochor CD. The circles representing observations by E. and L. Natanson indicate clearly that the change does proceed in this manner, although the experiments could not be carried quite far enough to show the complete passage from one theoretical isochor to the other. 1 Ramsay and Young, Phil. Mag. (V ), 24, 196 (1887). THE KINETIC THEORY OF GASES 197 4OO m.m. 30O 200 100 .-o-er o-e- cr" O 5O IOO I5O ISOPENTANE ISOCHORS FIG. 420. 600 mm 500 4OO 300 20O 100 o 100 aoo NITROGEN PEROXIDE ISOCHORS 198 STOICHIOMETRY The experiments of Ramsay and Young on acetic acid lead to quite similar results, and confirmation is thus afforded of the conclusion that the changes of vapour density in these cases are really due to dissociation. The actual data for the two substances are given in the following table : Isopentane. Nitrogen peroxide. Volume Volume in c.cs. per 4000 2000 1000 in c.cs. per 4000 200O 1000 gram. gram. Tempe- rature. Pressures. Tempe- rature. Pressures. 1075 241-5 -12-6 97' iro 6l'3 121-8 SB'S IIO'O 204-2 30-0 65-3 I30-I 258-5 497 9 6-2 1837 353-0 40'0 67-7 134-8 267-0 737 II2-5 22O'O 422-5 50*0 69-8 I39-2 275-0 99-8 I2I-2 24I-0 473-5 6o"o 7 I-8 I43-I 284-5 129-9 I36-0 271-3 540-0 7 where c and / are constants, and k = -j- 204 STOICHIOMETRY The pressure is thus a linear function of the temperature when the volume of a given mass of the substance remains constant ; in other words, the isochors are straight. They do not, however, start from zero pressure, but the pressure corre- sponding to o abs. is negative. This relation was first observed experimentally by Amagat l in the case of substances in the gaseous state, and by Ramsay and Young 2 in the case of gaseous and liquid ether. Barus 3 has shown that for some liquids it holds up to pressures of about 1000 atmos., but that there are marked deviations at higher pressures. The later experiments of Amagat 4 on carbon dioxide and ethylene and of Young on isopentane 5 and normal pentane, 6 indicate that the relation is very nearly, but not quite, true. In the case of the pentanes the isochors corresponding approximately to their critical volumes are straight, but those on either side are slightly curved. At very large volumes, however, no curvature could be detected. The constants a and b in the equation of Van der Waals may be calculated from experimental results in the gaseous and liquid states ; and from these constants the pressures may be calculated at temperatures below the critical point, and at volumes greater than the orthobaric volumes of liquid and smaller than the orthobaric volumes of saturated vapour. Or, from a number of isothermals, the pressures and tempe- ratures at a series of constant volumes may be read off, and the values of the constants k and c in the formula / = /T c may be calculated for each volume. By extrapolation the pressures at other temperatures may be determined for the same series of volumes. Whichever plan is adopted, the calculated isothermals show a continuous rise of pressure with diminution of volume above the critical temperature ; .but at any temperature below the Compi. rend., 94, 847 (1882). Phil. Mag. (V.), 23, 435 (1887). Ibid. (V.), 30, 358 (1890). Ann. Chim. Phys.> Series VI., vol. 29 (1893). Proc. Phys. Soc., 13, 602 (1895) ; Zeit. phys. Chem., 29, 193 (1899). Rose-Innes and Young, Phil. Mag. (V.), 48, 213 (1899). THE KINETIC THEORY OF GASES 205 critical point the pressure rises to a maximum (C, Fig. 44), then falls to a minimum (E), and finally rises again. If the conditions represented by these _ theoretical isothermals could be realized in practice, there should be a continuous passage from tn the gaseous to the liquid state, the substance remaining homo- - geneous throughout. Moreover, at sufficiently low temperatures VOLUME the minimum pressure should be FlG negative. Under ordinary con- ditions, when the unsaturated vapour is compressed, the pressure rises to B, remains constant during liquefaction, and then rises again, the isotherm taking the course ABFG. Conversely, when the pressure on the liquid is lowered, ebulli- tion takes place when the point F is reached, and continues at constant pressure until evaporation is complete, when the pressure again falls. If, however, the liquid is very pure, and free from dissolved air, and if the walls of the vessel are very smooth, the pressure may be lowered far below F before ebullition commences. For example, some methyl formate (B.P. 31 '9) was heated to 80 in the experimental tube in a modified Andrews' apparatus, the whole of the vapour being at first condensed. The pressure was then lowered below 800 mm. without ebullition taking place. The vapour pressure of methyl formate at 80 is 3500 mm., so that the pressure was reduced to less than a fourth of the vapour pressure. In other words, the methyl formate at 80 and under a pressure of less than 800 mm. was more than 45 above its boiling-point under that pressure. Ebullition finally took place with explosive violence. Again, Worthington l has shown that when a sealed tube nearly full of a pure liquid free from air is gently warmed, until the liquid, by expansion, completely fills the tube, a bubble of vapour will not be formed on cooling until a very large negative pressure is reached; and in some experiments 1 PhiL Trans., 183 A, 355 (1892). 206 STOICHIOMETRY the thick-walled tube actually collapsed, owing to the enormous tension. It has also been shown by Aitken 1 that when a vapour is very carefully freed from dust-particles, its temperature may be lowered many degrees below the condensing point before liquefaction takes place ; and there can be no doubt that the same effect could be produced by raising the pressure at con- stant temperature. It has therefore been proved that part of the continuous isothermal from F towards E, and from B towards C, may be realized experimentally. From E to C there would be an increase in volume, attended by a rise in pressure ; and there can be little doubt that such a change, if it could be brought about, would take place with explosive rapidity. It has been stated that when a vapour is compressed under ordinary conditions, liquefaction begins when the point B on the isothermal is reached, and that the pressure remains con- stant until all the vapour is condensed. The external work done during the process is equal to the product of the (constant) pressure into the change of volume, p(v y z> L ). It is there- fore represented by the rectangle BFHK (Fig. 45). If the change from B to F were to take place without separation into the liquid and vapour phases, that is to say, along the continuous isothermal BCDEF, the work done would be the same as before, since the initial and final states are the same. It has been pointed out by Clausius that the work in that case is represented by the irregular figure BCDEFHK, and that, since the areas of the two figures are necessarily equal, the area of the portion BDC above the rectangle must be equal to that of the portion DFE within the rectangle. If, then, the continuous isothermal be constructed in the manner described, by calculation from data at higher tempera- tures, and if a horizontal line be drawn in such a position that the areas BDC and DFE are equal, the pressure represented by this horizontal line should be equal to the observed vapour 1 Trans. Roy. Scott. Soc. of Arts, vol. 9. THE KINETIC THEORY OF GASES 207 pressure. This equality was found by Ramsay and Young (loc. dt.) to hold good in the case of ether at temperatures from 150 to the critical point 193*8, with a maximum error of only i -08 per cent, (at 150). 24 ^20 (0 u 1,6 z Ml D S K ~O 4 8 12 I6cc VOLUME (OF I GRAM OF ETHER) FIG. 45. The calculated and observed pressures are given in the following table : Vapour pressures. i emperature. Calculated. Observed. 192 26,350 26,331 11? 25,554 23,703 25,513 23,693 175 20,259 20,230 160 15,900 I5>778 150 13,405 13,262 208 STOICHIOMETR Y At all temperatures above the critical point the pressure rises continuously with diminution of volume; but below the critical point there is on each continuous isothermal a maxi- mum and a minimum pressure corresponding to the points C and E (Figs. 44 and 45), the difference between the two pressures increasing rapidly as the temperature falls, and the minimum pressures being negative, in the case of ether, below about 1 60, or only about 34 below the critical temperature. There may, therefore, be constructed two pressure-tempe- rature curves, in addition to the ordinary curve of vapour pressures, and these three curves, which are widely divergent at low temperatures, should meet at the critical point. Or from the read pressures the constants for a formula such as that of Biot may be determined, and the pressures at other temperatures may be calculated from the formulae. The read and calculated pressures for ether are given in the table. Tempe- Ordinary vapour pressures. Superior curve-pressures. Inferior curve-pressures. rature. Read. 1 Calculated. Read. Calculated. Read. Calculated. *50 13,405 13,084 I7,3 8 17,437 10,400 -10,185 1 60 15,900 15,900 19,090 19,090 2O IOO *75 20,259 20,259 22,IOO 22,100 + 14,060 + 14,060 iS 23,703 23,678 24,510 24,549 2I,66o 21,704 190 25,554 25,556 25,870 25,935 24,960 24,900 192 26,350 26,341 26,490 26,523 26,125 26,065 J 93 26,739 26,826 26,624 I93-83 27,075 27,077 27,077 The critical temperature and pressure calculated in this way are 193*83 and 27,076 mm. respectively, the observed values being 193*8 and 27,060 mm. Isochors. If the pressures corresponding to a series of definite volumes are read from the isothermals constructed from the experimental data, and if these pressures are plotted against the absolute temperatures, straight or very slightly cur-ved lines may be drawn to pass through the points corre- sponding to each volume. The isochors so constructed are 1 For equal areas. THE KINETIC THEORY OF GASES 209 shown in Fig. 46. They start from the vapour-pressure curve, those for large volumes being below and to the right of the curve, and those for small volumes above and to the left of it. If straight lines are drawn to pass as evenly as possible through the points and produced downwards, a diagram of the form shown in Fig. 47 is obtained. The vapour- pressure curve is indicated by dotted lines, and it will be seen that two other TEMPERATURE FIG. 46. curves are formed, one of them, ABC, to which the large- volume isochors are tangential, starting from the zero of temperature and pressure, and terminating at C ; the other, EDC, to which the small-volume isochors are tangential, also terminating at C, but starting from an exceedingly large negative pressure. It will be observed that outside the surface enclosed by the two curves, and above the line of zero pressure, the isochors never cut each other; in other words, only a single isochor 210 STOJCHIOMETRY FIG. 47. THE KINETIC THEORY OF GASES 211 passes through any given point in this region. Outside the surface, but below the line of zero pressure, there are no isochors. Three isochors may pass through any point within the surface and above the line of zero pressure,, but only two isochors below the zero line. Lastly, one isochor may be tangential to any point on either curve, and above the zero line a second isochor may pass through the point, but not below the zero line. In other words, there are three volumes corresponding to the pressure and temperature represented by any point within the surface ADCB ; two volumes corresponding to the pressure and temperature represented by any point within the surface ADE, or on the curves ABC and DC ; one volume only for any point outside the curvilinear triangle ADC and above the zero line, or on the curve DE. Turning to the pressure-volume diagram for ether (Fig. 48), it will be seen that at a temperature higher than the critical point there is only one volume corresponding to any pressure. At lower temperatures on each continuous isothermal between the limits of pressure corresponding to the points C and E, there are three volumes for each pressure, provided that the minimum pressure is positive; but where the pressures are negative, there can be only two volumes for each pressure. At the pressures corresponding to the point C there are only two volumes, and at that corresponding to E there are two volumes if the pressure is positive, but one only if it is negative. A comparison of the isochoral and isothermal diagrams makes it clear that the curve ABC in the former is the curve of maximum pressures, and EDC that of minimum pressures. These two curves and the ordinary vapour curve meet at C, which is the critical point. This point is the summit of the curvilinear triangle ACD, and the only isochor which passes through it is that corresponding to the critical volume. The isochors for large volumes cut the curve CD, and those for smaller volumes the curve AC. The direction and position of an isochor are defined by 212 STOICHIOMETR Y the equation / = /T are termed corresponding volumes when = -~ and = -7 respectively ; and the ^c V c U c "U c absolute temperatures are termed corresponding temperatures T T' when ^ = 7p The two substances are denned by Van der Waals as being in corresponding states when their pressures are proportional to their critical pressures, their volumes to their critical volumes, and their temperatures to their critical temperatures ; in other words, when their reduced pressures, volumes, and temperatures, respectively, are equal. Van der Waals deduced the following exceedingly important generalization regarding corresponding states from his reduced equation : When the absolute temperatures of two substances are proportional to their absolute critical temperatures, their vapour pressures will be proportional to their critical pres- sures, and their orthobaric l volumes, both as liquid and vapour, . 160. THE KINETIC THEORY OF GASES 217 to their critical volumes. The generalizations regarding corresponding temperatures, pressures, and volumes are not dependent on the particular form of the fundamental equation of state, but would follow from any modified equation which, like that of Van der Waals, is reducible, as regards volume, to one of the third degree. The fact, therefore, that the original equation of state requires modification, does not preclude the possibility that the generalizations may be strictly true, and it is necessary to investigate them independently of the equation itself. The question most easily decided is whether the vapour pressures of two substances at corresponding temperatures are corresponding pressures. The experimental data which have been obtained leave no doubt that this generalization is only strictly true in the case of certain closely related substances, such as chlorobenzene and fluorobenzene, or propyl acetate and ethyl propionate, and the critical pressures of the related substances are in both cases equal, so that corresponding pressures are equal pressures. The generalization is also very nearly true for some but not nearly all closely related substances which have different critical pressures. Thus, as will be seen from the table, it is nearly true for methyl acetate o'8a.64 Critical pressure. Substance. Ratio of vapour pressure to critical pressure. mm. 33.910 Fluorobenzene 0*00147 0-02241 0-08847 0-2949 0*5898 33,910 Chlorobenzene o '00149 0-02252 0*08744 0*2956 0-5938 25,210 Propyl acetate 0*00059 0*01404 0*06613 0*2583 0'5558 25,2IO Ethyl propionate 0-00059 0-01407 0-06697 0*2585 0*5573 35,i8o Methyl acetate 0-00093 0-01765 0-07598 0*2765 o'5757 30,440 Propyl formate 0-00094 0-01799 0*07791 0*280I 0*5772 25,100 Normal pentane 0-00154 0-02256 0*08888 0*2960 0*5933 18,730 Normal octane o- 00060 0*01406 0*06645 0*2567 o'5537 34, 1 80 ! Carbon tetrachloride 0-00203 0-02681 0*09801 0*3088 0*6022 and propyl formate, but not for methyl acetate and propyl acetate, and it is far from true for normal pentane and normal 218 STOICHIOMETRY octane. It is in some cases very nearly true, in others very far from true, for substances which have no close chemical relationship; compare, for example, on the one hand normal octane and propyl acetate or normal pentane and chloro- benzene, and on the other hand carbon tetrachloride and normal octane. If this first generalization were strictly true, it would make no difference whether the volumes were compared at corre- sponding temperatures or at the boiling points of the substances under corresponding pressures. Inasmuch, however, as the generalization is only an approximate one, it is necessary to find which method of comparing the volumes gives the better results. A preliminary investigation 1 showed that the agree- ment is better at corresponding pressures than at corresponding temperatures, and the former method of comparison will there- fore be adopted. In the following table are given the ratios T (i) of the boiling points to the critical temperatures, rp-, (2) * of the orthobaric volumes of liquid to the critical volumes, , (3) of the orthobaric volumes of vapour to the critical volumes, -^ , for thirty substances at the same reduced pressure, 0-08846. If the critical temperatures and pressures are known, but not the critical volumes, it is still possible to test the validity of the generalizations regarding corresponding volumes by means of the data at lower temperatures. For the generalization requires that -^ = ~ at corresponding pres- sures, and therefore that ^ = f = const. Now, in the case of fluorobenzene and chlorobenzene the critical pressures are equal, so that TT = i, and it is found that the ratios of the PC volumes of chlorobenzene to those of fluorobenzene at equal pressures are very nearly constant from the lowest pressures 1 Young, Phil. Mag. (V.), 33, 153 (1892). THE KINETIC THEORY OF GASES 219 to the highest at which accurate determinations were made. The ratios of the volumes of bromobenzene and of iodobenzene RATIO OF PRESSURE TO CRITICAL PRESSURE = 0*08846. Substance. T T C PL Vc v\ Vc I. Hexamethylene . . 07277 0-4090 27-7 2. Benzene .... o- 7282 0*4065 28-3 3. Isopentane . . . 4. Di-isopropyl . . . 07292 07329 0-4085 0-4093 27-7 28-4 5. Normal pentane . . Q'733 1 0*4061 28-4 6. ,, hexane . . 07406 0-4055 29-1 7. ,, heptane . 07483 0-4029 29-5 8. Di-isobutyl . . . 0-7498 0*4046 28*2 9. Normal octane . . 07544 0-4006 29-35 10. Fluorobenzene . 07334 0-4067 28-4 II. Chlorobenzene . . 07345 0*4028 ~ 28-5 12. Bromobenzene . 07343 l 0-4024 2 28-3 13. Iodobenzene . . . 07337 l O-4O2O 2 28-3 14. Carbon tetrachloride 0-7251 0-4078 27 '45 15. Stannic chloride . . 07357 0-403I 28-15 16. Ether 0-7180 O'AO^O 28-3 17. Methyl formate . . ** / O < - 7V ' 0-7348 ** T**JV 0-4001 HJ J 29' 3 1 8. Ethyl formate . . 07385 0-4003 29-6 19. Propyl formate . . 07430 0*4008 29-4 20. Methyl acetate . . 07445 0-3989 3o'i5 21. ,, propionate . 22. ,, isobutyrate . 0-7485 0-7502 0*4008 0*4014 29-6 29-15 23. Ethyl acetate . . . 07504 0-4001 30-25 24. Methyl butyrate . . 0-7522 0*4004 29'5 25. Ethyl propionate 0-7540 0-3989 3' 26. Propyl acetate . 07541 0-3985 30-35 27. Acetic acid . . . 0-7624 0*4100 25'4 28. Methyl alcohol . . 07734 0-3973 3 34'35 29. Propyl 30. Ethyl . . 0-7736 0-7794 0-4002 3 0*4061 3 30-85 32-15 1 Critical temperatures and pressures not directly determined. 2 Values of v c only approximate. Ratios of volumes to those of fluoro- benzene at corresponding pressures very constant so far as experiments extend (Phil. Mag., V. 33, 153 (1892)). 3 Values of v c only approximate, owing to marked curvature of " diameter " (Cailletet and Mathias). 220 STOICHIOMETRY respectively to those of fluorobenzene at equal pressures are practically constant, and it may be assumed with great pro- bability that their critical pressures are also equal to that of fluorobenzene. It is, therefore, most probable that the generali- zations of Van der Waals hold accurately for this group of closely related substances, although the ratio for fluoro- benzene at the reduced pressure 0-08846 given in the table is higher than those for the other halogen derivatives of benzene. In the case of ethyl propionate and propyl acetate the agree- ment is quite satisfactory whichever method of comparison is adopted. The ratios -- also show no greater differences in Z'c either case than may be attributed to errors of experiment. T Considering the ratios - as a whole, it is clear that they * c are not quite constant for a homologous series of organic compounds, but tend to rise with increase of molecular weight. Again, the ratios for iso-compounds are uniformly lower than for isomeric normal compounds, and those for di-iso-compounds are lower still. The ratio for acetic acid is higher than for any of the preceding substances, and those for the alcohols are much higher. The ratios show much smaller variations than those v c T of ~r , especially in the case of the esters, but it is evident that among homologous hydrocarbons they diminish with in- crease of molecular weight, and that among isomers the ratios for iso- compounds are higher than for normal, and those for di-iso- compounds higher than for either. The ratio for acetic acid is high ; those for the alcohols are irregular, but that for methyl alcohol is decidedly low, taking into account its small molecular weight. The ratios follow as a rule the same order as the tem- Vc perature ratios. For homologues they rise with increase of molecular weight, and for isomers, iso-, and di-iso- compounds THE KINETIC THEORY OF GASES 221 have low values. Among the esters, the variations are small and irregular, but the ratio for acetic acid is very low, and for methyl alcohol very high, the other alcohols also having high ratios. The wide variations observable in the ratios for acetic acid and the alcohols may probably be explained as follows : It is known from determinations of the vapour density of acetic acid that in the state of vapour many of the molecules of this substance are associated, the simple molecules probably uniting in pairs, thus 2G>H 4 CX. = (CoH 4 O 2 ) 2 , and that the relative number of complex molecules increases with fall of temperature. The amount of association will then be greater at a low tem- perature than at the critical point. The diminution in specific volume due to this cause will also be greater ; hence the ratio ~ will be low. In the case of the alcohols there is no molecular association in the state of vapour at low temperatures, but there is strong evidence to which reference will be made later (pp. 347, 355) that in the liquid state there is a high degree of association, particularly with methyl alcohol, that the amount of association diminishes with rise of temperature, but that there is still a moderate degree of association at the critical point. At this point, then, there will be a diminution in volume, due to association, but not with the vapours at low temperatures; hence v v may be regarded as normal, while v c is low ; hence will be high. The effect of association on the volume of a liquid is very much less marked than on that of a gas, and it is not to be expected that the variations in the ratios should be very striking. If, however, the amount of association is very much greater at a low temperature than at the critical point, one would expect the ratio to be somewhat low, and this appears to be the case with methyl alcohol. Since, however, the critical volumes of the alcohols, and perhaps also of acetic acid, cannot 222 STOICHIOMETRY be determined with great accuracy, it is not safe to attach much importance to small variations in their volume ratios. As regards the temperature ratios, it may be pointed out that with the alcohols, in the conversion of liquid into vapour, work must be done not only in increasing the volume and in overcoming ordinary molecular attraction, but also in dis- sociating the complex molecules (if the assumption of mole- cular association is correct), and it is therefore reasonable to conclude that the liquid must be raised to a higher temperature than would otherwise be necessary. Hence, as the amount of association is greater at low temperatures than at the critical T point, the temperature ratios may be expected to be high. In the case of acetic acid the molecules of vapour are associated, though probably to a smaller extent than those of the liquid ; hence the rise of temperature due to this cause is relatively T smaller than with the alcohols, and the ratio Fp is lower. -" c Van der Waals' equation of state and the generalizations deduced from it are based on the assumption that the mole- cules undergo no change when the temperature, pressure, or state of aggregation of a substance is altered ; they are, there- fore, not applicable to such compounds as acetic* acid and the alcohols, and the fact that the ^r and ratios for these sub- stances differ so widely from those observed in other cases, cannot be used as evidence against the validity of the generali- zations. There is, however, no known reason for assuming that molecular association occurs in the case of the hydro- carbons, and yet it cannot be questioned that the ratios are dependent to some extent on molecular weight and constitution. With the esters the dependence of the ratios on molecular weight is somewhat less marked than with the hydrocarbons. A possible explanation of this fact is that there is slight mole- cular association in the liquid state, and still less at the critical point, the amount of association diminishing in this homologous series, as it does in that of the alcohols and of the fatty acids, as the molecular weight increases. Thus the = and ^ ratios * c ^'c THE KINETIC THEORY OF GASES 223 would be somewhat higher, and the ratio somewhat lower for methyl formate, as compared with those for methyl butyrate and its isomers, than if there were no association. If the generalizations of Van der Waals were strictly true, the following simple laws should follow from them : la. At corresponding pressures the values of -^- should be the same for all substances. ib. At corresponding pressures the values of -^jr should be the same for all substances. p V ic. At their critical points the values of -^~ should be the same for all substances. For it is known that the saturated vapours of most sub- stances behave more and more like perfect gases as the temperature falls, and at a sufficiently low temperature the molecular volume of the saturated vapour of a substance, A, will be given almost exactly by the formula V - AX T X 76 4 273 7~ where T is the absolute temperature, and p the vapour pressure at that temperature ; and that of another substance, B, by the formula X L _ Mence -\j~i ^F> X T ' T' But if / and / are corresponding pressures, T and T' should be corresponding temperatures, and V v and V v ' corre- sponding volumes. Hence the relation should be true at any other corresponding pressure, and therefore at the critical pressures, or T; 224 STOICHIOMETR Y Again, if this relation were true for the two substances at their critical points, it should be true for the liquids at any corresponding pressures, _ T' When the critical pressures of the two substances are equal, T V V the relations take the simple form ^ = ~- t = -, at equal pressures. Thus for TT = 0*08846 the ratios for propyl acetate T V and ethyl propionate are =r, = 1*006 ; ^ = 1-015 ; and v v Y , = i'oo2. And at all pressures T v v V L T' Vv' w C 6 H 5 Cl/C a H 5 F 1-1309 1246 137 C 6 H 5 Br/C 6 H 5 F 1-1976 1802 189 C 6 H 5 I/C 6 H 5 F 1-2885 2772 282 C 6 H 5 Br/C 6 H 5 Cl . I -0590 '0494 -046 C 6 H 5 I/C 6 H 5 C1 i '1394 1357 128 C 6 H 5 I/C 6 H 5 Br i "0759 0822 -078 2 a. The ratio of the actual density of the saturated vapour to the theoretical density (calculated for the perfect gas) should be the same for all substances under corresponding pressures. For the actual density i M where v v is the volume of a gram, and V v the molecular volume ; and the theoretical density M T 760 22-41 X - X - 273 * 16 f , f .TV 22-41 X T X 760 Therefore = - ~ S 273 X / X V v = c X /V, THE KINETIC THEORY OF GASES 225 But if -^ is the same for different substances at corre- sponding pressures, ~ must also be the same (vide table, p. 228). o And if ^ is the same for all substances at corresponding pressures, then zb. The ratio of the actual density at the critical point to the theoretical density (for a perfect gas), ^-, must be the same for all substances. Graphical Representation of the Generalizations. If in a diagram showing any relation between temperature, pressure, 15 20 25 30 35 4Occ VOLUME. FIGS. 49. and volume the reduced values are plotted instead of the actual ones, the diagram should be identical for all substances. Take, for example, the relation between the orthobaric volumes of liquid or of saturated vapour and the temperature. In Fig. 49 the actual orthobaric volumes of carbon tetrachloride, normal pentane, and normal octane are plotted against the actual temperatures, and in Fig. 50 the reduced volumes against the reduced temperatures. The reduced volumes of Q 226 STOICHIOMETRY carbon tetrachloride are indicated by small circles, those of normal octane by large circles, and the single curve for the volumes of liquid up to the critical temperature is drawn through the points representing n-pentane, which are not shown. For the liquid state the deviations of the reduced volumes of carbon tetrachloride and n-octane are too small I S09 DC 0-8 O I 23456 78 REDUCED VOLUME FIG. 50. to be clearly seen on this diagram, although they are outside the limits of experimental error. The divergence of the three vapour curves is, however, very noticeable. On the other hand, it may be mentioned that of the thirty substances examined by the author all except four, methyl, ethyl, propyl alcohol, and propyl acetate, would give curves lying between those relating to carbon tetrachloride and normal octane, and the curve for propyl acetate is only slightly above that for normal octane. There is little doubt, however, that the curves for the so-called permanent gases would be lower, and for the higher paraffins higher, than those for CC1 4 and C 8 H 18 respectively. Similarly, if the generalizations were strictly true, the ratios of the densities of liquid and of saturated vapour to the critical densities, when plotted against the reduced temperatures, should THE KINETIC THEORY OF GASES 227 give coincident curves, and the diameters of these closed curves should also be coincident. In other words, if the generalizations of Van der Waals were strictly true, and the mean densities of liquid and saturated vapour were accurately represented by the formula S = A + at, rr* it would follow (3) that - - must be the same for all substances. 1 $c It has been shown, however, 2 that for most substances the diameter is slightly curved, but can be accurately represented by the formula s = A + at -f fit* where a is always negative, and /? may be either positive or negative ; and it is remarkable that there is a general relation T* between the values of ^ , and /?, as will be seen from the & S C following table. The substances are divided into groups of closely related compounds, the members of each group being arranged, as in the table on p. 219, in ascending order of the T values of =- at the reduced pressure 0*08846. The order * c would not have been very different if it had been based on the . _ s c aT c values of ~ y , or (3. O c S c The ratios ~? and - 17. Methyl formate. . j j > *r v -' v 56,000 / / 764-2 no O 3-926 v ;7/ T- 0-997 "/ J - 665 18. Ethyl . . 56,600 766-9 095 3-885 021 - 694 19. Propyl . . 56,200 766-7 105 3-868 025 - 459 20. Methyl acetate . . 56,500 746-9 "IOO 3*942 049 -1467 21. ,, propionate. 55,700 753-9 115 3-904 055 - 729 22. ,, isobutyrate 55,300 761-9 125 3-862 045 - 689 23. Ethyl acetate . . 56,2OO 743'i 105 3'944 06 1 - 764 24. Methyl butyrate 55,200 748-8 125 3-905 074 - 906 25. Ethyl propionate . 55,800 741-8 115 3-912 '090 - 784 26. Propyl acetate . . 56,300 738-5 105 3-934 088 1124 27. Acetic acid . . . 36,800 592-9 690 4-986 0-994 1191 28. Methyl alcohol . . 53,7oo 621*0 155 4-549 29. Propyl ,, . . 54,900 711-8 130 3-995 30. Ethyl ,, . . 56,300 711-9 105 4-024 ~ It may be stated that, in general, at equal reduced pressures the ratiQ ^j 1 , and ^ show slight variations among non- THE KINETIC THEORY OF GASES 229 associating substances, but that the variations are considerably greater for the ratios ^, , and -=^. 1 c V c -* The ratios ^- are obviously dependent to some extent on ^c molecular weight in the case of homologues, and on consti- tution in the case of isomers, the variations being in the same T , z/v direction as T^T and . A c V c rr\ The rise in the values of ? and the fall in those of ft are * very marked. As regards the associating substances, the ratios for acetic acid are in most cases widely different from those for normal substances, and the differences are very marked also in the case of methyl alcohol, but less so with ethyl and propyl alcohols, and the generalizations are evidently not applicable to these substances. Characteristic States of Matter. Van der Waals con- siders that all stable non-associating substances are under strictly comparable conditions at their critical points, and D. Berthelot 1 has shown that there are other conditions of matter which are equally characteristic, and that if the true equation of state is such that a reduced equation, applicable to all substances, can be derived from it, the temperatures peculiar to these conditions can be expressed in terms of the critical temperatures. Assuming, in the first place, the correctness of Van der Waals' equation, (/ -f - J (v - b) RT, the reduced equation \ v/ may be written i. Deviation from Boyle's Law. According to this law, -^ - = o at constant temperature, therefore the value of the real coefficient is equal to the deviation from the law. 1 " Sur les Thermometres a gaz," pp. 14 et seq. 230 STOICHIOMETRY For low pressures the reduced equation takes the form <*(*$) _ i/_ 27 i\ ~^T " 8" X / TT (i.) For 0! = ^ = 3-375, -^TJT = o, or the gas follows Boyle's law. For > 21, T becomes positive, and tends towards the limit J. 2. Deviation from Avogadro's Law. Reduced equation, -- X 3 = ^( i -- ~- X 7) for low 7T($> UTT O7\ O 9/ pressures. For = o, the coefficient = oc . (ii.) For 0j = zg. = 3*375, the coefficient = o. For higher temperatures the coefficient becomes positive, reaches a maximum at 2 = 6*750 ; decreases, passes through a point of inflection at 3 = 10*125, and finally tends to zero. 3. Deviation from Gay Lus sac's Law. Reduced equation, i a0 = ^ .( i - - x -* jd-n-, where ot/\ 4 ** a = -1 x -~r just as a = - X ^; and T = afl. For a gas which follows Gay Lussac's law, i aT = o. For low temperatures a > (iii.) For #2 = 675, a = >p ; and the gas follows Gay Lussac's law under low pressures. The deviation then becomes positive, reaches a maximum at 4 = 13*5, shows a point of inflection for 6 = 20*250, then diminishes, and tends towards zero. Deviation from the Law of Charles. The coefficient of increase of pressure at constant volume is /? = - X ^ and for a perfect gas, /2T i = o. THE KINETIC THEORY OF GASES 231 In reduced co-ordinates, let b = - X -^ ', "Of then 0T - i =r> ~ ' It is convenient to take densities instead of pressures as v c i cissae. Calling p = = -, th< under a very low density, dp t is abscissae. Calling p = = -, the deviation from Charles' law or the deviation from Charles' law is independent of the temperature ; in other words, the isochors are straight, and the constant-volume thermometer gives correct readings. If Van der Waals' equation were correct, this proposition should also be true for compressed gases and for liquids. Deviation from Joule's Law. According to this law, which is not strictly true, the internal energy of a given mass of gas is independent of its volume. The deviation is due simply to molecular attraction, and is expressed by the equation K 8 _ 27 i R X STT " 64 X &T where J is the mechanical equivalent of heat, and S = -Ffr. A c T3 For a gas under low pressure, -y = c lt c v ; and the equation may be written 80 _9 which indicates that there must always be a cooling effect, due to this attraction, when a gas expands into a vacuous space, and that the cooling effect tends towards zero as the temperature rises. Joule-Thomson Effect. The variation in temperature, 80, 232 STOICHIOMETRY accompanying the expansion of a gas through a porous diaphragm is due to two phenomena : the cooling, 8, due to internal work, and the cooling or heating, A0, due to the external work which results from the difference p-p^ / ^o between the pressures/! and/ - Consider the expansion from a very feeble pressure, STT, to zero pressure. The cooling due to internal work is given by the expression and the heat change due to external work by the formula (iv.) For = zj- there is no heat change due to external work on expansion ; for lower temperatures there is a cooling effect, for higher temperatures a heating effect. The resultant Joule-Thomson effect is given by the formula } C P ^ __ V 27 f ^ ~R X STT ~~ 8V 1 ' ^4 ?/ (v.) For = ^-, the temperature at which the gas follows Gay Lussac's law, the heating and cooling effects compensate each other, and there is no heat change. At lower temperatures there is a cooling effect, at higher temperatures a heating effect. This is the case, for example, with hydrogen at o C. The conclusions arrived at by D. Berthelot x are clearly indicated by the diagram (Fig. 51). It will be seen that at the reduced temperature 3*375 the gas would follow the laws of Boyle and Avogadro, and that there would be no thermal effect due to external work on expansion. At the reduced pressure 6750 the gas would follow Gay Lussac's law, and there would be no Joule- Thomson thermal effect. 1 Loc. dt. t p. 25. THE KINETIC THEORY OF GASES 233 tf>Q 3375 6750 10-125 13500 202500 02 ^ IU_ /^ -02 7 -04 / 'OFT! VJNIVE- 001 -002 /"" 1 (2) 7 -004 / 0004H (3J^ -0-004|] / vtca -0125 ^~ Te jT5u-~ A ^ -0250 // -0375 i / O 3-375 6 750 10-125 13-500 20 250 6 FIG. 51. Diagrams of the deviations from the laws relating to perfect gases which would be observed in the case of gases under low pres- sures if the formula of Van der Waals were applicable to them. Diagram i. Deviation from Boyle's law. Diagram 2. ,, Avogadro's (Ampere's) law. Diagram 3. Gay Lussac's law. Diagram 4. Thermal effects produced during expansion. Curve l c . Thermal effect due to external work, resulting from variation in value of PV. Curve Ti. Thermal effect due to internal work. Curve Tt Joule-Thomson effect. 234 STOICHIOMETRY The five reduced temperatures to which special reference has been made are the following : *i = 3*375; 2 = 20i = 6750; 03 = 3*1 = 10-125; 04 = 40i = i3'5 j 06 = 60! = 20-25 The modified equation of state proposed by Clausius - * = RT leads to similar results, but the five reduced temperatures would have the values V3 V 6 V9 v l8 If this formula were correct, the isochors would not be quite straight, and the constant-volume thermometer would not give quite correct readings. D. Berthelot points out that if the values of ^ , calculated from the equation of Van der Waals, are plotted against a straight line is obtained, whereas those derived from the equation of Clausius give a parabola. In both cases the limiting value for T = o is |. The experimental data for any one substance are not sufficiently complete to decide the question whether a straight line or parabola is correct, but Berthelot has collected all the available data for hydrogen, nitrogen, carbon monoxide, air, oxygen, nitric oxide, methane, and carbon dioxide, and calculated the values of -^ from them. These values, air plotted against T, fall satisfactorily on a parabola, which, how- ever, is quite distinct from that derived from Clausius' equation. Moreover, the limiting value is not , but J, and the value for T = i is 1*25. Inasmuch, however, as the law of corresponding states is not strictly true, the deviations from the curve cannot be entirely attributed to errors of experiment. THE KINETIC THEORY OF GASES 235 d(n-<$>} The points representing the values of ~\ , when plotted UTT against r 2 instead of r, fall satisfactorily on a straight line, and the very simple expression is thus obtained. The limiting value 0*25 represents the co-volume in reduced co-ordinates, and Berthelot points out that he had previously arrived at the same value, 0*25, by calculating the densities of liquids at the absolute zero of temperature by the method of Cailletet and Mathias 1 ; he concludes that, as the same value has been obtained from data relating to matter on the one hand in its highest state of rarefaction, and on the other hand in its highest state of condensation, the co-volume must be regarded as an absolute constant. It has been observed experimentally by Young 2 that the ratio of the actual to the theoretical density at the critical point ^ is not f, as required by Van der Waals' equation, but that in o a large number of cases it is between 37 and 3*9 (p. 228), the mean value for nine hydrocarbons being 3*783. For carbon tetrachloride the value is 3*674, and for carbon dioxide it is 3 '6, according to the measurements of Amagat. D. Berthelot points out that for oxygen and nitrogen it is probably about 3*5. For the ordinary gases Berthelot adopts the value 3*55, orf. For low pressures the equation of Clausius takes the form PV = RT| i + i I V but in place of the values 1 Compt. rend., March 12, 1900. " Phil. Mag. (V.), 50, 291 (1900). 236 STOICHIOMETRY Berthelot adopts the following, based on experimental data : a = p c v?1 c R = X ~ b = ~ From this equation with the new constants the five reduced temperatures are = 6 = 2 -45 = = = = - = - V3 V6 3 3^2 Thus the deviations from the laws of Boyle and Avogadro vanish at the reduced temperature ^ = 2*45, and the deviations from the law of Gay Lussac and also the Joule-Thomson effect vanish at 2 = 4*24. It is found that nitrogen obeys Boyle's law at about 52C., or = 2-56, and that air does so at about 54 C., or = 2*46. Olszewski l finds the inversion temperature (Joule-Thomson effect) for hydrogen to be 80*5 C., or 192-5 abs., which, taking the critical temperature of hydrogen to be 33 abs., would give the ratio 5*8. On the other hand, he has recently 2 found, on allowing air and nitrogen to expand from various high pressures to that of the atmosphere at different temperatures, that the inversion temperature depends on the initial pressure, as shown in the table below. Air. Nitrogen. Initial pressure. ti Initial pressure. a 1 60 atmos. + 259 159 atmos. +243 100 249 126 238 9 244 1 02 233 80 240 90 228 70 60 235 226 68 223 217 40 I 9 8 55 205 20 124 30 163 Modifications of the Generalizations of Van der Waals. No reduced formula can be strictly applicable to all substances, 1 Bull. Acad. Crac.y 1901, p. 453. 2 Ibid., 1906, p. 792. THE KINETIC THEORY OF GASES 237 for it has been shown that the generalizations of Van der Waals are only approximately true in most cases. It was suggested by M me K. Meyer, in iSgS, 1 that the reason why the generalizations of Van der Waals are in most cases not strictly accurate, is that the temperatures and volumes are in each case reckoned from zero. On the assumption that each substance has its own special minimum temperature and minimum volume pressures, however, being always reckoned from zero a very much better agreement between the ratios may be obtained. The reduced temperatures, volumes, and pressures on this assumption will be * T - T min . v - _ - and the modified generalizations may be stated thus 'p _ p 1. At corresponding pressures the ratio - =^ is the * A min. same for all substances, where T is the boiling point, and T m in. the minimum temperature, both on the absolute scale. 2. At corresponding pressures the ratio - -- is the V c Z>min. same for all substances, and so also is the ratio /L "" z/min - Vc - Z> mln . where v v and z> L are the orthobaric volumes of saturated vapour and of liquid, and z> min is the minimum volume. M me> Meyer took T min . = o and z> min . = o arbitrarily for fluorobenzene, and calculated the values of these constants for other substances. On then calculating the modified ratios, the agreement was found to be very much more satisfactory than is the case with the original ratios. The question has been further discussed by D. Berthelot, 2 who suggests that the volumes to be compared should be the observed volumes diminished by the co-volume ; that the co-volume may be taken as the volume which the substance would occupy at its special zero of temperature ; and that this 1 Zeit.pkys. Chem., 32, I (1900). 2 Compt. rend. (July, 1900). See also Brillouin (Journ. de Physique, VI., 2, 117 (1893) and Raveau (ibid. 6, 433 (1897) ). 2 3 8 STOICHIOMETR Y minimum volume may be calculated by the method of Cailletet and Mathias. If the minimum temperature of fluorobenzene be taken arbitrarily as o abs., those of some of the substances would be lower than the absolute zero, which of course is impossible ; thus CC1 4 - 17-26 and CS 2 -40-2. D. Berthelot takes the value of T ni in. for fluorobenzene to be 56, and has calculated the follow- ing values of T min and v min; (where v min . is the minimum volume for i gram of substance) : Vmin. Tmin. Theor. vol. at temp.Tc - T m in. and press. /,-. Vc v m in. Benzene .... 0-892 46-6 4'73 Fluorobenzene . 0767 56*0 4-69 Chlorobenzene . . 0734 6ro 4-6 7 Bromobenzene . . Q'554 69-0 4-68 lodobenzene . . "459 72-0 4'65 Carbon tetrachloride 0-490 40 "o 4-70 Ether I-OI9 5i'4 4-64 Carbon dioxide . . 0-599 2I'O 4-66 Normal pentane . . n;i 46*0 4-67 Isopentane . . . 1-179 43'3 4-68 It has been shown that if the generalizations of Van der Waals were correct, the ratio of the actual to the theoretical density at the critical point, or, in other words, the ratio of the theoretical volume (for a perfect gas at the temperature T c and the pressure p c ) to the actual critical volume should be a constant for all substances. D. Berthelot proposes the following modified law. There exists a constant ratio between the theoretical volume occupied by , unit mass of a fluid under the pressure p c and at the temperature T c T mln ., and the difference v c v mln . between the actual critical volume and the minimum volume. The numerical value of this ratio is about 4*68 (see table above). T T With the above values of T min< and v min the ratios ^ _ T m '"' AC * min. ^ for different substances at corresponding pres- and V min. sures show good agreement. CHAPTER XII PROPERTIES OF SOLIDS WHEN a liquid is cooled below its freezing point, or when a gas, under sufficiently reduced pressure, is cooled below its condensing point, the substance assumes the solid state. The internal friction of solid substances is much greater than that of liquids, and a much greater expenditure of work is required to alter their form. Moreover, when the form of a solid is forcibly altered but not beyond a certain amount the particles are put into a state of strain, so that the system acquires potential energy. When the force causing the strain ceases to act, the solid reverts to its original form : it is said to be elastic as regards shape. Some solids, such as tempered steel or indiarubber, are extremely elastic ; others, such as lead or antimony, only to a very slight extent. Solids vary also very greatly in their hardness, malleability, tenacity, and other properties. Their compressibility is exceedingly slight, much less, even , than that of liquids. Melting points of Solids. When a pure solid substance is heated, it melts, as a rule, at a definite temperature. The melting point depends on the nature of the substance, but was thought, until 1849, to be independent of the external pressure. It was shown, however, by James Thomson, that the melting point of ice should, theoretically, be slighty lowered by raising the pressure, and he calculated the rate of change of tempe- rature per unit rise of pressure by means of the formula . x or _ x ~ x ' - ' V L - v s j ,*T dp' 239 240 S TOICHIOME TR Y where L' is the heat of fusion, V L and v s the volumes of a gram of liquid and solid respectively, J the mechanical equivalent of heat, T the melting point on the absolute 7/T scale of temperature, and -rr, the rate of change of temperature per unit rise of pressure. ^T Since T, J, and L' are always positive, it follows that -rr, will be either positive or negative, according as V L is greater or less than v g . Most solid substances expand on fusion, and V L is therefore generally greater than v s . The melting point in these cases should be raised by increasing the pressure. Ice, however, contracts on fusion ; v s is therefore greater than V L , and the melting point should fall when the pressure is raised. In the case of ice, T = 273, v = 0*00100 (litre), v s = 0*00109, L' = 79*6 calories = - litre atmospheres. 0T .*. -TT, 0*0075 per atmos. 7fTl * This value of -ry , calculated by James Thompson, agrees well with that found experimentally by Sir William Thomson l in 1850, and it has subsequently been confirmed by Dewar, Goosens and other observers. >rp The most striking case of a positive value of -^ yet observed is that of carbon tetrachloride, the melting point of which has been found by Amagat 2 to rise from -i9'5 to + 19-5 on increasing the pressure from 210 to 1160 atmos., so //T 1 that --jz = 4-0*04 per atmos. The rise in the melting point of acetic acid caused by increasing the pressure was measured by de Visser 3 by means of the simple apparatus shown in Fig. 52. 1 Phil. Mag., 37, 123 (1850). z Compt. rend., 105, 165 (1887). 3 Zeit.phys. Chem., 9, 767, (1892). PROPERTIES OF SOLIDS 241 A thick-walled bulb, C, is fused to a long piece of capillary tubing, which is bent three times at right angles, as shown in the diagram. The tube is sealed at A, and the horizontal portion is graduated and calibrated. The tube from A to B contains air, the volume of which at a known temperature and pressure has been measured. From B to C there is mercury, and the bulb contains acetic acid, which should be partly fused at its ordinary melting point, 16-6; that is to say, when the pressure of the air in the tube is about i atmosphere. On raising the temperature of the bulb slightly, some of the solid melts ; expansion takes place on fusion, and the air is compressed. FIG. 521 Fusion goes on, and the pressure rises until equilibrium is established. On raising the temperature again, more of the solid melts until the pressure reaches the maximum corre- sponding to the new temperature. In this way a series of readings of temperature and pressure may be taken. The 7rp value of -j-r-y o'o2435 per atmos., ascertained in this way by de Visser, agrees very well with that calculated by the formula of Clapeyron, 0*0242. According to Damien, 1 the effect of pressure on the melt- ing point of a solid may in general be expressed by the formula Compt. rend., 112, 785 (1891). 242 STOICHIOMETRY where / is the melting point under atmospheric pressure, and / the melting point under pressure /. The constant b was found to be negative in every case investigated, and if the formula holds up to sufficiently high pressures, the melting point must reach a maximum, and then diminish with further rise of pressure. Such a maximum was actually observed in the case of naphthylamine, the melting point of which rises from 49*750 under atmospheric pressure t 50*543 under a pressure of 81 atmos., and falls again to 49'646 when the pressure is further raised to 173 atmos. Vapour Pressure of Solids. A solid substance, like a liquid, gives off vapour, and the vapour pressure, like that of a liquid, depends on the temperature. It is, however, in many cases too small to be measured. The term volatilization may conveniently be applied to the vaporization of a solid, the term sublimation to the double process of volatilization and condensation, just as the term distillation is applied in the case of a liquid to the double process of vaporization and condensation. The vapour pressure of a solid, if high enough, may be measured by the statical method, some of the solid being placed over the mercury in a barometer tube. The curve representing the relation between vapour pressure and tempe- rature is of the same form for solids as for liquids. The Triple Point. The vapour pressures of both ice and water were very carefully determined by Regnault, 1 and he was inclined to attribute the small differences observed to errors of experiment; but James Thomson, 2 in 1851, arrived at the conclusion, based on theoretical grounds, that at the melting point the vapour pressures of ice and water should be identical, but that at any lower temperature the vapour of water should be higher than that of ice. In fact, the curves representing (a) the vapour pressures of water, AC, Fig. 53, (b) the vapour pressures of ice, BA, and (c) the pressures under which ice melts at different temperatures, AD, should intersect at a point 1 Ann. Chim. Phys. [3], 11, 273 (1844) ; " Relation des Experiences " (Paris, 1847), pp. 465-633- 2 Trans. Roy. Soc. Ediu. t 1851. PROPERTIES OF SOLIDS 243 A, which he called the triple point. The same conclusion was arrived at independently by Kirchhoff in 1858.* A care- ful examination of Regnault's results showed that the vapour pressures of ice observed by him were in fact slightly lower than those of water at the same temperature, except at the melting point. Volatilizing Points. In the year 1880, Carnelley 2 observed that ice, when exposed to exceedingly low pressures, could not be melted by the application of heat, but that rapid volatili- zation, without fusion, took place. It was thought at first that the temperature of the ice rose above o, but it was suggested by Young 3 that if the ice did not really become hot, the curve repre- senting the vapour pressures of ice at different tempera- tures might also represent the volatilizing points of ice under different pressures. In 1883 and 1884 Ramsay and Young 4 proved experi- mentally (a) that the volatilizing points of ice and other vaporizible solids depend on the pressure ; (b) that the same curve represents the volatilizing points and the vapour pressures of a given solid ; and (c) that the curve for ice agrees with that based on the formulae employed by James Thomson. Experi- mental confirmation of the correctness of James Thomson's conclusions was obtained by Fischer 5 in 1886 in the case of ice, and by Ferche 6 in 1891 in that of benzene by the statical method. 1 Pogg. Ann., 103, 206 (1858). 2 Chem. News, 42, 130 and 313 (1880) ; 43, 19 (1881). 3 Nature, 24, 239 (1881) ; (cf. Pettersson, ibid., p. 167). 4 Phil. Trans., 175, 37 and 461 (1884) ; Phil. Mag. [5], 23, 61 (1887). 5 Wied. Ann., 28, 400 (1886). ti Ibid., 44, 265 (1891). PRESSURE FIG. 53. 244 STOICHIOMETRY dp" The value of -^ for a volatilizing solid was calculated by James Thomson in the following manner : The heat of volatilization of a solid is given by the equation L" = (v v - v s )^ X ~, Where v v and v s are the volumes of a gram of vapour and solid dp 1 ' respectively, and -7 is the rate of increase of the vapour pressure of the solid per unit rise in temperature. Since the vapour pressure is usually very low, the volume v v is very large relatively to v s , and the equation may be written L" - X T X ^ J_l Vy XS V~ A " rp At the melting point the heat of volatilization must be equal to the sum of the heats of fusion, L', and the heat of vaporization, L, or L" = L' + L and L' - L" - L. T dp But L = v v X , X ^p T /dp" dp \ T ' v v \s I ___ __ r ] v ] \ are mixed together at constant temperature, the volume of the mixture being v t the pressure p exerted by the mixture is equal to the sum of the original pressures p\ + pi + and the partial pressures of the gases in the mixture A'A' . . . j are equal to the original pressures / lf / 2 This law, like the others already considered, is only strictly applicable to perfect gases. According to Leduc 1 it would be more correct to state the law, as applicable to ordinary gases, in the following form. " The volume occupied by a mixture of gases is equal to the sum of the volumes which the com- ponent gases would separately occupy at the same temperature and under the same pressure as the mixture." Thus the composition of atmospheric air, free from moisture 1 Compt. rend., 123, 805 (1896) ; January, 1898. 254 STOICHIOMETRY and carbon dioxide, may be calculated with sufficient accuracy from the densities of oxygen, "atmospheric" nitrogen 1 and air if compared at the same temperature and pressure, but not if compared at the same temperature and volume. The first calculation gives 23-21 per cent, by weight of oxygen, the second 23-33 per cent, by weight, the direct determinations of Leduc for air at Paris giving values between 23 '18 and 23*23 per cent., mean 23-20. D. Berthelot and Sacerdote 2 show that when two gases, originally at the same pressure, are mixed in such a manner that the temperature and the total volume remain unaltered, the pressure of the mixture may be calculated, if the coefficients of deviation from Boyle's Law, A 2 = ( *~ i ) X - \ A^i / p\ A between the common pressure fa and zero pressure / are known for the mixture and for each of the two gases. There is found to be usually a very slight increase of pressure on admixture, hardly measurable except in the case of the more condensible gases. Thus for a mixture of SO 2 and CO 3 the increase of pressure, A/, was found to be 1*36 mm. ; calculated 1-52. For atmospheric air the calculated increase is only 0*01 mm., so that Leduc's law is confirmed for this mixture. Just as the pressure of a mixture of gases may be calculated with but slight error from those of its components, so also other physical properties of mixtures, the refractive power, the power of absorbing light, the specific heat, the solubility in liquids, and so on, may be predicted. When two gases at the same temperature and pressure are allowed to diffuse into each other, no evolution or absorption of heat is observed, and the total energy therefore remains unaltered. This statement, however, is only strictly applicable to perfect gases ; it is very nearly true for ordinary gases under low pressures, but not when the pressure is high. 1 The term " atmospheric nitrogen " is conveniently employed to denote the mixture of nitrogen with argon and its associated gases, which is obtained in the ordinary manner from air. 2 Compt. rend.> March and May, 1899. MIXTURES 255 MIXED LIQUIDS. The molecules of a liquid are much closer together than those of a gas under ordinary pressures, and the attractive forces between their molecules cannot be left out of account. Consider a mixture of two liquids, A and B. The properties of the mixture will be affected (a) by the attraction of the like molecules those of A for each other, and those of B for each other and (b) by the mutual attraction of the molecules of A and B. If the attraction of the unlike molecules is relatively very slight indeed, it may be expected that the liquids will be non- miscible, or nearly so, as in the case of benzene and water, or mercury and either benzene or water. If the attraction between the unlike molecules is greater than in the cases just considered, but still relatively small, miscibility within limits may be expected, as, for example, with aniline and water or ether and water. In such cases there is frequently slight expansion and slight absorption of heat on admixture. Comparing together various pairs of liquids, as the mutual attraction of the unlike molecules increases relatively to that of the like molecules, the following changes may be expected : (a) increasing and finally infinite miscibility ; (b) slight expansion, diminishing to zero and followed by increasing contraction; (c) diminishing absorption of heat changing to increasing heat evolution. These changes do not, in many cases, run strictly part passu, and among liquids which are miscible in all proportions, it is not unusual to find a small amount of contraction attended by slight absorption of heat, as, for example ; when a little water is added to normal propyl alcohol; but when certain compounds which are chemically closely related are mixed together, there is neither any appreci- able change of volume nor any measurable evolution or absorption of heat. For such substances it is probable that the different molecular attractions, A for A, B for B, and A for B, are very nearly equal, and that the relation suggested 256 STOICHIOMETRY by Galitzine 1 and by D. Berthelot, 2 namely, that # A . B = J a A .d E holds good [where 'a A . B represents the attraction of the unlike molecules, and a A and a B the respective attractions of the like molecules]. It would appear, then, that there are two very simple cases 1. That in which the attraction of the unlike molecules is so slight that the liquids are practically non-miscible. In this case there can, naturally, be no heat or volume change when the liquids are brought together, but the vaporization of such pairs of liquids must be considered. 2. That of two infinitely miscible and closely related liquids which show no heat or volume change on admixture. In the latter case the properties of a mixture can be accurately calculated from those of the components, and the term " additive " has been applied by Ostwald to such properties. Density and Specific Volume of Mixtures. Let v be the volume of the mixture, and V A and V B the volumes of the com- ponents; v, V A and V B the corresponding specific volumes (volumes of a gram) ; and m A and m B the weights of the com- ponents. Then v = v(m A + m B ), V A = V A W A> z/ B = v B m B And if v = V A 4- V B v = A 4- and the density s = - The changes in volume observed on mixing various pairs of liquids are given in the following table, together with the (uncorrected) temperature changes, which show the direction and give a rough indication of the magnitude of the correspond- ing heat changes. The substances were mixed in equimolecular proportions, except in the four cases marked with an asterisk in which the molecular percentage of water was 40. 1 Wied. Ann., 41, 770 (1890). 2 Compt. rend., 126, 1703 (1898). MIXTURES 257 It will be seen that with closely related substances the changes are very small, in other cases they are usually but not invariably much larger. There are five cases in which con- traction is accompanied by a fall in temperature and one in which a very slight expansion is attended by a rise in temperature. Substances. Changes on admixture. A. B. Volume per cent. Temperature. Bromobenzene Chlorobenzene O O Ethyl propionate Ethyl acetate + 0'OI5 O'O2 Ethyl benzene n-Octane Toluene n-Hexane -0-034 -0-053 + 0'05 + 0'06 Ethyl alcohol Methyl alcohol + 0-004 O'lO Toluene Benzene + o'i6i - 0-45 Ethylene dichloride j +0-34 - 0-35 Benzene Carbon tetrachloride -0-13 0-69 Toluene j> 0*07 + 0-25 Ethyl acetate >5 +0-03 + '55 Chlorobenzene V 0'12 0-4 Benzene n-Hexane + 0-52 - 47 Carbon disulphide Methylal + 1-22 - 6-5 Acetone Carbon disulphide + T2I - 9'85 Chloroform Acetone ' 2 3 + 12-4 Water * Methyl alcohol -2-98 + 7^5 * Ethyl -2-56 + 2-95 * i ? Propyl ,, -1-42 - 1*15 Isobutyl alcohol * Water 0-90 - 3*i5 Benzene Methyl alcohol O'OI - 3'8 5 > Ethyl O - 4'2 Propyl alcohol Benzene +'5 - 4'65 Isobutyl ,, ,, +0-16 - 6-35 Isoamyl ,, " +0-23 -5-25 Specific Heat. The specific heat of a mixture may be approximately calculated from the specific heats of the com- ponents. Let c be the specific heat of the mixture, and B The vapour density of chlorobenzene = 56*2, and that of water 9, and at 90*23 the relative masses of vapour will be m' A 56*2 x 210*1 = = 2*47^, and the percentage mass of mm 9 X 530*1 chlorobenzene will be 71*2. 1 Naumann, Ber. y 10, 1421, 1819, 2015, 2099 (1877) ; Brown, Trans. Chem. Sec., 35, 547 (1879). 262 STOICHIOMETRY In the actual experiment to which reference has already been made, the percentage of chlorobenzene in the distillate was found to be 71*6, or, correcting for water left adhering to the tubes, 71*4. Both the boiling point and the composition of the vapour, therefore, agree very well with the calculated values. INFINITELY MISCIBLE AND CLOSELY RELATED LIQUIDS. In the case of liquids which are miscible in all proportions, the simplest relations are observed when the substances are chemically closely related to each other. Vapour Pressures. The vapour pressure of a mixture of two such liquids, A and B, is given by the formula ioo/ = M/ A + (too M)/ B where M is the molecular percentage of A, and /, / A , and / B are the vapour pressures of the mixture and of A and B respectively at the same temperature, /. In other words, the relation between vapour pressure and molecular composition is represented by a straight line. Van der Waals 1 considered that this relation should be true when the critical pressures of the two liquids are equal and the molecular attractions agree with the formula of Galit- zine and D. Berthelot, = M/ A + (100 M)/ B holds good. It is probable, also, that for such liquids the constant c is equal, or nearly equal, to A A* The strongest evidence is afforded by two pairs of liquids, ethylene and propylene dibromides, and benzene and ethylene dichloride, investigated by Zawidski, 1 for both of which the relation between vapour pressure and molecular composition is accurately represented by a straight line. For the two dibro- mides /= 85-05; 2 at 85= 1-357, and ^=1-31; for ^B benzene and ethylene dichloride /= 49-99; 7^50 = 1*135, P* and c= 1*134. Zawidski states that the errors of experiment were much greater in the first case than the second. It has been stated that the formula ioo/ = M/ A -f (100 M)/ B is generally applicable to closely related liquids 1 Loc. cit. 268 STOICHIOMETR Y (and occasionally to others), and it may perhaps be concluded that Brown's formula is generally true for such liquids, and probably also that c = T^ PR The number of closely related liquids so far examined is, however, very small, and further investigation is required before a definite statement can be made. INFINITELY MISCIBLE LIQUIDS WHICH ARE NOT CLOSELY RELATED. Vapour Pressures. The relation between vapour pressure and molecular composition of mixed liquids which have no very PA PB MOLECULAR PERCENTAGE OF B I0 FIG. 59. close chemical relationship to each other is usually represented by a curve, and it may be stated generally that when the attraction of the unlike molecules is small, relatively to that of the like molecules, the vapour pressures will be higher than those calculated from the formula/ = M/ A 4- (i M)/ B (where M is the molecular fractional amount of A), while if the mutual attraction of the unlike molecules is relatively great, the vapour pressures will be lower. Or, adopting the formula of Galitzine and D. Berthelot, it may probably be stated that when # A . B < vWtf B > then p> M/ A + (i - M)/ B , and vice versa. The relations are shown diagramatically in Fig. 59. MIXTURES 269 The greater the difference between # A . B and V 'a A .a& the greater will be the curvature, and it will be seen that, for any given values of/ A and/ B , if the deviation from the straight line exceeds a certain amount, there must be a point of maximum or minimum pressure on the curve. It is obvious, also, that the smaller the difference between / A and / B , the smaller will be the deviation required to give a maximum or minimum pressure. The influence of chemical relationship is well seen by the behaviour of the monohydric, aliphatic alcohols towards water. These alcohols may be regarded as derivatives of water formed by the replacement of a hydrogen atom by the group C n H 2u + 1 , thus HO H -> HO C M H 2n + 1 ; or as derivatives of the paraffins, formed by replacement of a hydrogen atom by a hydroxyl group, thus C n H 2jl+1 H->C n H 2n+1 OH. The smaller the alkyl group, the closer is the relationship to water ; the larger the alkyl group, the smaller is the influence of the hydroxyl radical, and the closer is the relationship to the corresponding paraffin. At the ordinary temperature methyl alcohol is miscible with water in all proportions, as also are ethyl and propyl alcohols. Normal butyl alcohol dissolves in about 12 parts of water, and isobutyl alcohol in about 10*5 parts, and the solu- bility of the higher alcohols in water diminishes as the mole- cular weight rises, cetyl alcohol, for example, being practically insoluble in water. The volume and temperature changes (p. 257) similarly indicate that the mutual attraction of the unlike molecules diminishes as the molecular weight of the alcohols increases. Lastly, the deviation of the vapour- pressure curves from straightness increases, 1 as may be seen from Fig. 60, in which the vapour pressure-molecular composition curves for four alcohols are given. The temperatures are such that the vapour pressure of each pure alcohol is 400 mm. The maximum differences between the pressures represented by the actual curves 'and the theoretical straight lines are roughly as follows : 1 Konowalow, Wied. Ann., 14, 34 (1881). 270 STOICHIOMETRY Methyl alcohol and water Ethyl n-Propyl Isobutyl 43 mm. 112 203 8OO m.m. IOO O 2O ^O 6O 8O IOO MOLECULAR PERCENTAGE OF ALCOHOL FIG. 60. The miscibility of the alcohols with the paraffins from which they are derived has not yet been studied, because the MIXTURES 271 lower paraffins are gaseous, but the behaviour of a single paraffin, normal hexane, towards the alcohols has been investi- gated. Methyl alcohol and n-hexane at the ordinary tem- perature are only miscible within limits, but the higher alcohols at any rate, up to isoamyl alcohol are miscible with the hydrocarbon in all proportions. Again, the fall in temperature on mixing hexane with the alcohols in equimolecular propor- tions diminishes slightly as the molecular weights of the alcohols rise (ethyl alcohol, 2-55; n-propyl alcohol, 2-40; isobutyl alcohol, 2'35; isoamyl alcohol, 1*85). Lastly, n-hexane forms mixtures of maximum vapour pressure with the lower alcohols, but not with isoamyl alcohol or any other of "higher boiling point. The behaviour of benzene towards the alcohols is very similar to that of n-hexane, and has been more com- pletely studied. The temperature and volume changes are given in the table, p. 257; the percentage differences between the observed and calculated pressures (p' and / respectively) for equimolecular mixtures both with water and with benzene are given below. Mixtures with Water. Benzene. Alcohol. 4f i> ioo(/-/) & 4> ioo(/'-/) P P Methyl 282 247-0 + 14-2 760 475 - +60-0 Ethyl . n-Propyl 372 57 6 2857 387-0 + 30-2 + 48-8 760 760 507-3 535-4 +49-8 +41-9 Isobutyl 792 476^ +66-2 760 562-2 +35-2 Isoamyl 760 579'6 +31-1 Mixtures of minimum vapour pressure are of comparatively rare occurrence. The few which have been studied are mentioned on p. 273. Boiling Points. It has been stated (p. 263) that the boil- ing points of mixtures of closely related liquids under a pressure #can be calculated with considerable accuracy from the. vapour 272 STOICHIOMETRY pressures of the components by means of the formula M = A -A In the case of liquids which are not closely related the observed boiling points of mixtures do not, as a rule, agree with those calculated in this way. If, as is usually the case, the vapour pressures of the mixtures are higher than are given by the formula ioo/ = M/ A + (100 - M)/ B the observed boiling points will be lower than the calculated ; if the vapour pressures are lower, the boiling points will be higher. Moreover, when there is a point of maximum pressure on the curve which shows the relation between vapour pressure and molecular composition, there must be a corresponding point of minimum temperature on the boiling point molecular com- position curve, the composition of the mixture which exerts a maximum vapour pressure / at f being the same as that of the mixture which has a minimum boiling point f under the pressure /. So, also, two substances capable of forming mixtures of minimum vapour pressure will also form mixtures of maximum boiling point. Such mixtures of either minimum or maximum boiling point, when distilled, boil at a constant temperature like pure substances, and they have frequently been mistaken for chemical compounds. The composition, however, depends on the pressure, which would not be the case with a definite com- pound and, moreover, mixtures of minimum boiling point are formed owing to the relatively small attraction of the unlike molecules for each other. A table of mixtures of constant (minimum and maximum) boiling point is given in Young's " Fractional Distillation," pp. 67-69. In the great majority of cases one of the two liquids is a hydroxyl compound an alcohol, an acid, or water, or both liquids may be hydroxyl compounds ; and it may probably be MIXTURES 273 concluded that mixtures of constant boiling point are most readily formed when one or both of the liquids exhibit molecular association. There is some evidence of molecular association in the case of acetone and probably of the lower . aliphatic esters, and the following pairs of liquids are stated by Ryland 1 to form mixtures of minimum boiling point : carbon disulphide and acetone, carbon disulphide and methyl acetate, carbon disulphide and ethyl acetate, acetone and methyl acetate, acetone and ethyl iodide, ethyl iodide and ethyl acetate. Mixtures of minimum boiling point are not confined to associating liquids, but they only occur among normal liquids when the difference between the boiling points of the components, A,, is small. Thus it is almost certain that benzene and normal hexane (A, = 11*3) and benzene and carbon tetrachloride (A, = 3 -44) form such mixtures, and Ryland states that a mixture of carbon disulphide and ethyl bromide (A, = about 7*6) boils 0*5 lower than ethyl bromide. Again, Zawidski finds that methylal and carbon disulphide (A, = 4- 1 5) form a mixture of maximum vapour pressure. Mixtures of maximum boiling point are not so frequently met with. In most of the known cases one of the substances is an acid and the other a base or a compound of basic character formic, acetic, or propionic acid with pyridine (Zawidski), hydrochloric acid with methyl ether (Friedel) ; or the liquids are water and an acid formic, hydrochloric, hydro- bromic, hydriodic, hydrofluoric, nitric, or perchloric acid (Roscoe); but Rylands finds that such mixtures are also formed by chloroform and acetone (A, = 4'8), and chloroform and methyl acetate (A, = about 4*3), and these results have been confirmed by other observers. In the case of three liquids, if each of the three possible pairs is able to form a mixture of minimum boiling point, it may happen that a particular mixture of all three liquids will boil constantly at a lower temperature than any of the pairs or single liquids. Thus benzene and water form such ternary mixtures of minimum boiling point with ethyl, n-propyl, iso- 1 Amer. Chem.Journ., 22, 384 (1899). T 274 STOICHIOMETRY propyl, and tertiary butyl alcohols, and normal hexane and water do so with ethyl and n-propyl alcohols, and no doubt with the other two also. Composition of Liquid and Vapour Phases. The whole question of the relations between the composition of liquid mixtures and (a) the partial pressures of the vapours of the components, (b) the composition of the vapour, has been dis- cussed mathematically by Duhem and by Margules, and they have arrived independently at the same formula d log M d log (i M) where / A and / B are the partial pressures of the vapours of the two liquids A and B, and M and (i M) their molecular fractional amounts in the liquid mixture, taking the normal molecular weights as correct. Starting from this equation, Lehfeldt adopts the formula < {m ' X where m' A and m' E are the weights of A and B in the vapour, and m^ and /% the weights in the liquid, and k and ; are constants. = In this formula, when r = i, r = k X , or Brown's m B WB formula holds good. On the other hand, if k is positive and r is less than unity, there must be a particular value of ^ , for which log(^) = log ( mA \ and there must therefore be a \m B/ V#B/ possible mixture of constant boiling point. Thus for benzene and carbon tetrachloride Lehfeldt gives log ( r j = 0-065 -f- o'947 log ( ). In this case the logarithms of the ratios are MIXTURES 275 equal when log = 1-2264, or = 16-84. There should M B m B thus be a mixture of constant boiling point containing 94-4 per cent, by weight of carbon tetrachloride. Zawidski adopts the following equations to express the relations between the partial pressures /' A and/' B of the com- ponents in the vapour from the mixture, the vapour pressures A and/ B of the pure components, and the molecular fractional amounts M and i M of the two substances in the liquid mixture : and ? 2 = a where a. 2 and a 3 are constants, the values of which can be ascertained from the partial-pressure curves, or, by a method suggested by Margules, from the total-pressure curve. Zawidski points out that if a and ft vanish, the equations become /A = AM and / B = / B (i - M) P\ A M M whence = x =* x but for substances of normal molecular weight the pressures are proportional to the number of molecules present, and the ivr' IVT equation may be written r= k X -, which is Brown's M B M B formula, expressed in gram-molecules. For ethylene and propylene dibromides, and for benzene and ethylene dichloride, Zawidski shows the corr ectness, not only of the relation / =/A +/ B = AM + A(i - M) but also of the formulae /A = A M and/ B =/ B (i - M) 2 7 6 STOICHIOMETR Y as may be seen from the diagram (Fig. 61), which is taken from his paper. In the case of other mixtures of liquids with normal molecular weight investigated by Zawidski, the constants a and ft were found to have finite values, and the simple formulae /' A =/ A M and /' B = / B (i M) were not found to be applicable ; the relations between molecular composition and pressure, whether total or partial, are, in fact, represented by curves which could be well represented by the formulae given 200 m.m. 150 u K D 0) cn ,00 50 O 2O 4O 6O 80 100 MOLECULES PER CENTOFPROPYLENE DIBROMIDE FIG. 61. on p. 275. In the case of associating substances, Zawidski's formulae could only be applied if the average molecular weights of the associating substances under the varying conditions of the experiment were known. Investigations of the relation between the composition of liquid and vapour have, as a rule, been carried out at constant temperature, but in practice a liquid is almost always distilled under constant pressure. The ratio A varies slightly with the /B temperature even for closely related substances, so that if Brown's formula were strictly true for a distillation at constant MIXTURES 277 temperature, it could not be applicable without slight error to an ordinary distillation under constant pressure, or rather the value of ^ ought, theoretically, to be calculated for any given /B temperature during the distillation. Distillation of Mixtures. It has been stated that for closely related liquids, Brown's formula, r= c x , in all M B M B probability holds good with a close approximation to accuracy, and that the constant c is probably equal to the ratio of the vapour pressures ~ at the boiling point of the mixture. The /B value of the constant is always such that the vapour is richer than the liquid in the more volatile component. The distillate obtained by condensation of the vapour will therefore be richer, and the residual liquid will be slightly poorer, than the original liquid mixture in that component. Continuing the distillation, the vapour evolved from the residual liquid will again be richer than the liquid in contact with it in the more volatile component, but it will contain a relatively smaller amount of it than the first portion of vapour. If successive portions of vapour be condensed, the percentage of the more volatile component in the distillates or fractions will steadily diminish until, if the constant c differs greatly from unity, in other words, if there is a great difference between the vapour pressures of the pure components, the residual liquid will con- sist of the liquid of lower vapour pressure and higher boiling point in a pure or almost perfectly pure state. If the distillation is carried out under constant pressure, the boiling point will rise continuously until only the one component is left ; if it is carried out at constant temperature, the vapour pressure will fall until it reaches that of the less volatile component. If the components are not closely related, or, more generally, if the formula is not applicable, the composition of the vapour cannot be 278 STOICHIOMETRY calculated from that of the liquid by Brown's formula, but the percentage of the more volatile component in the vapour will be greater than in the liquid, and the separation by distilla- tion will take place in a similar manner unless the deviation from the formula M/ =/ A + (i M)/ B is so great that a mixture of minimum or maximum vapour pressure is formed. If the fractions obtained by the first distillation were re- distilled, each fraction could be separated into smaller fractions, the first richer and the last poorer in the more volatile com- ponent, and by a process of systematic fractional distillation it should, theoretically, be possible to effect a separation of the two components. The mathematical investigation 1 of the behaviour on dis- tillation of mixed liquids which follow Brown's law, show that with two components it is the liquid of higher boiling point which is the easier to separate, and that if there are three or more components boiling at fairly equal intervals of tempera- ture, the substances of intermediate boiling point are the most difficult to separate, and the least volatile substance is the easiest. For such substances, also, it may be stated quite generally that the greater the difference between the boiling points of the components, the more readily can a separation be effected by distillation. These rules do not necessarily apply to liquids which do not follow Brown's law, but the form of the curve representing the relation between boiling point and composi- tion must be taken into account. If the curve for two com- ponents were of the form a (Fig. 62), the substance of higher boiling point could be separated very easily, but the more volatile component only with great difficulty, if at all. On the other hand, if the curve were of the form b, nearly horizontal at the higher temperature, the more volatile component would be comparatively easy and the less volatile difficult to separate. The first case is frequently met with, the second seldom. With curves of the forms c and d (Fig. 63), it would, under no conditions, be possible to separate both components by distillation of any given mixture, but it would be possible to 1 Barrell, Thomas, and Young, Phil. Mag. (V.), 37, 8 (1894). MIXTURES 279 a o 100 MOLECULAR PERCENTAGE OF A FIG. 62. UJ S UJ o q r 100 MOLECULAR PERCENTAGE OF A FIG. 63. 28o STOICHIOMETRY separate the mixture of maximum or minimum boiling point from that component which was in excess. In a case represented by curve <:, where the minimum temperature corresponds to the molecular composition ^, the distillation might proceed in either of three ways: (i) If the liquid mixture had the composition ^, it would distil un- changed in composition and at a constant temperature like a pure liquid. (2) If the molecular percentage of A were less than q, the liquid would tend to separate into two compo- nents, the more volatile of which would be the mixture of minimum boiling point, and the less volatile the substance B. (3) If the molecular percentage of A were greater than ^, the components separated by distillation would be, first, the mixture of minimum boiling point, and, second, the liquid A. A well-known case of this kind is that of normal propyl alcohol and water. The boiling points under normal pressure are : water, 100; n-propyl alcohol, 97*2; mixture of minimum B.P. 87*7. This mixture contains 71*7 per cent, by weight, or 43*2 molecules per cent, of propyl alcohol. It was described for many years as a hydrate of propyl alcohol. If the boiling point composition curve has the form d (Fig. 63), the mixture will distil like a pure liquid at constant temperature if it has the composition r, or it will tend to separate into two components, the first being either A if the molecular percentage of A in the original mixture is greater than ;-, or B if it is less, and the second the mixture of maximum boiling point. Formic acid and water behave in this manner, as shown by Roscoe. 1 JS oiling points : water, 100, formic acid, 99*9; mixture of maximum boiling point, 107*1. Composition of mixture : percentage of acid by weight, 77 ; molecular percentage, 567. If, as in the case of ethyl alcohol and water (Fig. 64), the mixture of constant boiling point distils at very nearly the same temperature as one of the two pure liquids, it is im- possible to separate that component in a pure state by distilla- tion. In this case the curve is also exceedingly flat at the lower temperatures, and it is practically impossible to separate 1 Trans. Chem. Soc., 13, 146 (1861) ; 15, 270 (1862). MIXTURES 281 the mixture of minimum boiling point in a pure state even when water is in excess, although it is quite easy to separate pure water from such a mixture. O 2O 40 60 80 IOO MOLECULAR PERCENTAGE OF WATER FIG. 64. The apparatus required for carrying out the distillation of a liquid consists essentially of five parts (Fig. 65) : A, the still; B FIG. 65. B, the still-head ; C, the Liebig's condenser ; D, the receiver ; E, the thermometer. Each of these parts may be modified to meet special requirements, such as distillation under 282 S TOICHIOME TR Y reduced pressure, distillation of large quantities of liquid, of very volatile liquids, and so on; but the most important modifications are those of the still-head, by which a more complete separation of the components can be obtained in a single distillation than with the plain vertical still-head. For the chief modifications of the still-head and other parts, and for an account of the methods of systematic fractional distillation, and of the interpretation of the experimental results, Young's " Fractional Distillation " may be consulted. CRITICAL CONSTANTS OF MIXED LIQUIDS. The behaviour of mixed liquids at or near the critical point has been investigated mathematically by Van der Waals, 1 and Duhem, 2 while the most valuable experimental work has been carried out by Kuenen 3 in Leiden and Dundee, Hart- mann and Verschaffelt in Leiden 4 and Caubet 5 in Bordeaux. Kuenen 3 pointed out that inasmuch as during the evapora- tion or condensation of the components of a mixture, change of composition is constantly taking place, and as the process of diffusion is exceedingly slow, it is practically impossible for either the liquid or gaseous phase to be homogeneous unless complete admixture is brought about by vigorous stirring. He therefore placed in his experimental tube a little stirrer con- sisting of a fine rod of soft iron, about 2 cm. in length, provided 1 "Die Continuitat des gasformigen und fliissigen Zustandes " (1881) ; Zeit. phys. Chem., 5, 133 (1890) ; " Statique des fluides (Melanges)," Congres internal, de physique (Paris, 1900), vol. i. p. 583. 2 Trav. el Mem. des Facultes de Lille, 11, 90 (1892) ; ibid. [3], 13 (1893), and other papers (vide Caubet). 3 Archives Neerlandaises, 26, 354 ; Communications from the Physical Lab. Leiden, Nos. 4, 7, 8, n, 13, 16, 17 ; Zeit. phys. Chem. 11, 38(1893) ; 24, 667 (1897) ; 41, 43 (1902) ; Phil. Mag. (5), 40, 173 (1895) ; 44, 174 (1897); (6) 4, 116 (1902); Arch. Neerland., set. exact, nat. (2), 5, 306 (1900). 4 Communications from Physical Lab. Leiden (Professor H. Kamer- lingh Onnes, director). 5 "Liquefaction des Melanges gazeux " (Paris, 1901); Zeit. phys. Chem., 40, 257 (1902). MIXTURES 283 at each end with a bead of enamel. This stirrer could be moved rapidly up and down by means of an electro-magnet outside the apparatus. Earlier experiments carried out without such a stirring arrangement are of little value, and need not be described. When a mixed vapour is compressed at a constant tem- perature below its critical point it behaves like a pure substance, the pressure rising as the volume diminishes, until condensation begins. The process of condensation differs, however, from that of a pure vapour unless, indeed, a mixture of maximum or minimum vapour pressure is formed for a mixed liquid differs in composition from the vapour in contact with it (p. 266), being richer in the less volatile component. As con- densation proceeds the successive quantities of liquid formed will be poorer and poorer in this component, and the vapour pressure will rise until condensation is complete, when the composition of the liquid as a whole will, of course, be the same as that of the original vapour. If both liquid and vapour are constantly stirred during the process, so that each phase is always homogeneous, the true relation between pressure and volume will be observed, but if the electro-magnetic or other stirrer is not used, and especially if the experiment is carried out in a long narrow tube, admixture of the successive portions of liquid formed by condensation will take place with extreme slowness, and the observed vapour pressures will be always too high. In any case there will be a rise of vapour pressure during condensation, and the diagram representing the relation between pressure and volume for a given mixture at a series of tempe- ratures will be of the form shown in Fig. 66. The relation between vapour pressure and temperature will not be represented by a simple curve, as in the case of a pure substance, but by a surface enclosed by a border curve (Kuenen). The general form of the vapour-pressure surface is indicated by the curves VRPL in Figs. 67, 68, and 70. It may safely be assumed that the relations between pres- sure, temperature, and composition are simplest in the case of mixtures of substances which are chemically closely related ; 284 STOICHIOMETR Y but, unfortunately, the only determinations which have so far been made with such substances 1 are not sufficiently complete, as regards . range of composition, to allow of definite conclu- sions being drawn regarding the relation between composition and critical pressure or critical temperature. Several pairs of infinitely miscible liquids which do not 100 p 90 80 70 60 50 5 VOLUME FIG. 66. 9 form mixtures of maximum or minimum pressure have, how- ever, been carefully examined by Kuenen and by Caubet, and the results obtained by the latter observer with mixtures of carbon dioxide and sulphur dioxide are shown in Fig. 67. The vapour-pressure curves of the two pure substances ter- minate in their critical points, Q and C 2 respectively. The vapour-pressure areas enclosed by the border curves (VRPL) Kuenen, " Ethane and Butane," Proc. Roy. Soc. Edin., vol. 21. MIXTURES 285 for the mixtures investigated lie between these curves, and a third curve, called by Kuenen the plait point curve, drawn between Q and C 2 is tangential to the border curves. The point of contact P between a border curve and the plait point curve is termed by Kuenen the plait point temperature, and by Caubet the critical temperature. The point R at which the border curve has a tangent parallel to the/- axis is termed by Kuenen the critical point of contact ; it gives the maximum temperature on the border curve. 4O 20 ^o 60 8O IOO I2O TEMPERATURE CENTIGRADE FIG. 67. I6O At all temperatures below the plait point / P , vaporization or condensation at constant temperature takes place in the ordi- nary manner ; starting with saturated vapour and compressing the mixture, condensation takes place, and the volume of liquid continuously increases and the pressure rises until all the vapour has disappeared. At temperatures higher than the maximum / R the substance behaves like a pure substance above its critical point, no liquid being formed under any pressure. At intermediate temperatures a remarkable phenomenon is observed, condensation beginning at the lower pressure at 286 STOICHIOMETRY which the vertical line of constant temperature intersects the border curve, the liquid increasing in amount with rise of pressure_to a maximum, then diminishing and finally disappear- ing at the pressure corresponding to the point where the vertical line intersects the upper branch of the border curve. This phenomenon was observed by Cailletet in iSSo, 1 in the case of a mixture of carbon dioxide and air, and subse- quently by Van der Waals, and by Andrews. It was carefully and thoroughly investigated by Kuenen, by whom it was termed retrograde condensation. Several observers 2 described the appearance of three phases, two liquid and one vapour. Ramsay and Young 3 found that with a mixture of alcohol and ether, two liquid phases could be temporarily produced at 210 by allowing some of the vapour in the upper part of the tube to cool so as to promote separation by distillation. When, however, the vapour was condensed by diminishing the volume, and the upper part of the tube was again cooled, convection currents were formed, and the apparent meniscus between the two liquid layers was seen to descend the tube until it became lost at the surface of the mercury. By the use of his electro-magnetic stirrer, Kuenen (loc. tit.} was able to prove still more conclusively that the appearance of the two liquid phases was merely due to the temporary partial separation of the two components by a process of distillation, and that only one liquid phase remained after stirring. Kuenen 4 has pointed out that a second kind of retro- grade condensation during compression is possible, a vapour phase appearing, reaching a maximum, diminishing, and finally disappearing. The question which kind of retro- grade condensation will occur is decided by considering whether, on passing along the border curve, starting from 1 Compt. rend., 90, 210. 2 Pictet, Compt. rend., 100, 329 (1885) ; Wroblewski, Wied. Ann., 26, 134 (1885) ; Dewar, Proc. Roy. Soc., 30, 538 (1880). 3 Trans. Chem. Soc., 51, 760 (1887). 4 Communications, No. 16. MIXTURES 287 its lower branch, the point R or P is first reached. In Fig. 68, A, B, and C, three possible relative positions of plait- point curve and border curve are shown. In A and B the point R is encountered before P, and the conditions are those under which retrograde condensation of the first kind is met with. In C, on the other hand, the border curve is above and to the left of the plait point curve, and the point P is reached before R. Under these conditions, retrograde condensation of the second kind should be observed. The conditions would B be fulfilled if the plait point temperatures were between the critical temperatures of the pure substances for all mixtures and the component of higher critical temperature had the higher critical pressure, a case which does not frequently occur. They may also be fulfilled when the plait point curve is less simple. Kuenen has investigated a considerable number of mixtures in the hope of observing retrograde condensation of the second kind ; but although he has succeeded in finding mixtures which 288 STOICHIOME TR Y fulfil the conditions (Figs. 69 and 70, plait point curve between B and A), yet the difference in temperature between / r and / R in the case of ethane and nitrous oxide (Fig. 69) l was never 70 | 60 u D 50 0) 30 10 20 TEMPERATURE C. FIG. 69,' 30 100 80 60 40 hi cr a- 20 0" 20" 40 60 80 100 120 140 160 TEMPERATURE C. FIG. 70. greater than o'i, and the difficulties due to minute variations in temperature and to the action of gravity on the highly compressible fluid (Gouy) made it impossible to observe the 1 Phil. Mag., Aug. 1897, 174. MIXTURES 289 phenomenon, or, indeed, to distinguish between the two tempe- ratures. In the case of methyl ether and hydrochloric acid (Fig. 70), there was some chemical action at the higher temperatures, and trustworthy observations could not be made. Kuenen, however, has succeeded in bringing to light several interesting facts. It has been stated that many pairs of infinitely miscible liquids form mixtures of minimum boiling point, and that a smaller number form mixtures of maximum boiling point. Kuenen has shown that certain pairs of sub- stances also form mixtures of minimum, and others mixtures of maximum, critical point. To the first class belong ethane and nitrous oxide (Fig. 69), ethane and acetylene, and ethane and carbon dioxide ; to the latter, methyl ether and hydrogen chloride (Fig. 70). The results further showed that two substances which at a low temperature form a mixture of maximum or minimum vapour pressure form a similar mixture at higher temperatures up to the critical point. If the composition of the mixture of maximum or minimum pressure were the same at all temperatures there would be three vapour pressure curves on the P.T. diagram, the curves for the two pure substances, and a third for the mixture of maximum or minimum vapour pressure. The composition, however, does vary with the temperature, although very slightly in the case of nitrous oxide and ethane. In the neighbourhood of the curve of maximum pressure, and also of the vapour pressure curves for the pure substances, the border curves are very narrow, that is to say, the rise of pressure during condensation is very slight. Under these conditions there is great difficulty in observing retrograde condensation of either kind. RELATION BETWEEN COMPOSITION AND CRITICAL TEMPERATURE OR CRITICAL PRESSURE. By the critical point of a mixture is usually understood the plait pointy or the point at which the border curve touches the plait point curve. At the temperature and under the pressure u 290 STOICHIOMETRY corresponding to the plait point, the critical phenomena opalescence, striae, etc. are visible.; but the plait point tempe- rature is not the highest at which condensation of vapour can be brought about, for retrograde condensation may take place at temperatures between the plait point and the " critical tempe- rature of contact," that is to say, the maximum temperature on the border curve. It would therefore, perhaps, be more correct to speak of the critical region than the critical point of a mixture; but when the term critical point is employed, it must be understood to refer to the plait point. It was stated in 1882 by Pawlewski 1 that the critical tem- perature of a mixture could be calculated by the formula T c = mTj + (i - w)T," where T c , T c ', T c " are the critical temperatures of the mixture and of the two components A and B respectively, and m is the fractional weight of A. That Pawlewski's rule, however, cannot be of general applicability has been clearly proved by Kuenen, who has shown that the critical temperature of a mixture may in certain cases be considerably lower, in others considerably higher, than that of either component (Figs. 69, 70). For such pairs of liquids it is obvious that the relation between critical temperature and composition is not represented by any such formula as that of Pawlewski^ It was pointed out by Kuenen that the substances which form mixtures of minimum or maximum critical temperature form also mixtures of minimum or maximum boiling point under lower pressures; and it is very probable that many such mixtures of minimum or maximum critical temperature will be met with in the future. The data at present available are insufficient to allow of any very definite conclusions being drawn, but it may be assumed that the relations between pressure, temperature, and composition will be simple in the case of mixtures of sub- stances which are chemically closely related, and it is not improbable that they may be found to be even simpler when 1 Berichte, 15, 460. MIXTURES 291 the critical pressures of the two substances are equal as in the case of fluorobenzene and chlorobenzene than when they are unequal as in the case of homologous compounds. It may, indeed, be conjectured that all mixtures of fluoro- benzene and chlorobenzene will be found to have the same critical pressure; but the question whether any such simple rule as that of Pawlewski applies to the critical pressures of mixtures of homologous organic compounds, or to the critical temperatures of closely related substances of either equal or unequal critical pressure can only be decided by experiment. It seems not unlikely, also, that the formula should take the form T c = MT C ' + (i - M)T C " or p c = M// -f (i - M)/ C ", where M is the molecular fractional amount of A. CHAPTER XIV SOLUBILITY AND MISCIBILITY IT is customary to speak of a mixture of two or more gases or of two or more liquids, and the term mixed solids is also employed ; but a mixture formed by bringing together a gas and a liquid or a solid and a liquid is usually termed a sohition. There is, however, no real difference between miscibility and solubility; for example, tertiary butyl alcohol melts at 25*53, and it is easy to cool the alcohol a few degrees below its freezing-point without solidification taking place. We may then mix the liquid alcohol with water at 20, or dissolve the solid alcohol in water at the same temperature, the product being precisely the same in the two cases, and it would be permissible to speak either of a mixture of the alcohol with water or of a solution of the alcohol in water. SOLUBILITY OF GASES IN LIQUIDS. Some gases, such as ammonia, are exceedingly soluble in water; others, like hydrogen, very slightly. Thus at o and 760 mm., i volume of water dissolves 1050 volumes of ammonia gas, but only 0*02 of hydrogen. It may, perhaps, be stated that no gas is absolutely insoluble in any liquid ; but the solubility may be almost inappreciable, as, for example, that of hydrogen in mercury. On the other hand, no gas under ordinary pressures is known to be infinitely soluble in any liquid. The solubility of gases in liquids diminishes with rise of temperature. Thus on warming a saturated solution of 292 SOLUBILITY AND MISCIBILITY 293 ammonia in water, gas is freely evolved, and may be ob- tained free from moisture by passing it over quicklime. On boiling the solution for some time, the whole of the ammonia gas is expelled. In the case of gases such as hydrogen or nitrogen, which are only slightly soluble in water, the amount dissolved at a given temperature is directly proportional to the pressure ; but the density varies directly as the pressure, and the volume of gas dissolved is therefore independent of the pressure. This law, first stated by Henry, is, however, subject to limitations similar to those observed in the case of Boyle's few. It is not absolutely true for any gas under ordinary pressure, and the deviations increase with rise of pressure ; they are greater, also, for the more soluble gases, such as carbon dioxide or ammonia, but it is probable that some chemical action takes place in these cases. Dalton's law of partial pressures was first applied to solu- tions of mixed gases in water. The solubility of each gas depends on its own partial pressure, not on the total pressure of the mixture. Thus, in the case of air in contact with water, the amount of each gas dissolved depends on its specific solu- bility and on its partial pressure, that is to say, about one-fifth of the total atmospheric pressure for the oxygen, and about four-fifths for the nitrogen. The deviations from Dalton's law are of the same kind as from Boyle's and Henry's laws. MISCIBILITY OF LIQUIDS, AND CRITICAL SOLUTION POINT. It has been stated that if the mutual attraction of the molecules of two liquids, A and B, is very slight compared with the attractions of the like molecules, those of A for each other, and those of B for each other, or, making use of the formula of Galitzine and D. Berthelot (p. 256), if # A . B is very much smaller than V a\ X # B , the two liquids are likely to be either non-miscible or only miscible within limits. If, on the other hand, # A . B = vV\ X a* or > V '# A X a^ the liquids will be miscible in all proportions. 294 STOICHIOMETRY It is found, however, that the miscibility of two partially miscible liquids is dependent on the temperature, usually increasing, but in some cases diminishing with rise of tem- perature. If the relation between A . B and *J a^ X # B remains the same, it is to be expected that the miscibility will increase with rise of temperature, because the kinetic energy of rectili- near motion of the molecules increases with rise of temperature, and also the mean distance between the molecules increases. It may, in short, be said that the penetrating power of the molecules becomes greater as the temperature rises. The general increase in miscibility with rise of temperature may then be attributed to this purely physical cause. An increase in the ratio of # A .B to Vtf A X # B will also tend to cause increased miscibility ; but the ratio may increase as the temperature falls, and the increase in miscibility due to this change may be greater than the decrease due to the diminution in kinetic energy and specific volume, so that the miscibility may actually become greater as the temperature falls. The subject was first studied experimentally by Alexeeff, 1 who found that several pairs of liquids, which at the ordinary temperature are only partially miscible, become infinitely miscible at some higher temperature. This temperature has been termed the critical solution temperature by Orme Masson, who has drawn attention to the close analogy between the critical point of a pure liquid and the critical solution point of a pair of liquids. This analogy will be discussed after the laws of osmotic pressure have been considered. Since the publication of Alexeeff s results many cases have been observed of liquids, which are partially miscible at ordinary temperatures, becoming infinitely miscible at a higher temperature. It has also been found that with certain liquids, notably derivatives of ammonia, the miscibility increases with fall of temperature, and Rothmund 2 has observed several cases of 1 Wied. Ann., 28, 305 (1886). 2 Zeit.phys. Ckem. y 26, 433 (1898). SOLUBILITY AND MISCIBILITY 295 partial miscibility at high temperatures increasing to infinite miscibility at a lower temperature. 1 Many lactones are characterized by the fact that an aqueous solution saturated at the ordinary temperature becomes turbid when warmed, but, on raising the temperature still higher, becomes clear again. There is thus a temperature of minimum miscibility, generally about 40, for these substances. Lastly, nicotine and water are stated by Hudson to be partially miscible between 61 and 210, but miscible in all proportions above and below these temperatures. This pair of substances has therefore both a superior and an inferior critical solution temperature. We may thus have the three cases represented in Figs. 71-73. The first shows the superior critical solution point, the second the inferior point, and the third both superior and inferior critical solution points. It has been shown by Crismer 2 that the critical solution temperature of a pair of liquids is greatly altered by the presence of even a small quantity of a third substance, soluble in one or both of the liquids, and he recommends the determination of this temperature as a delicate test of the purity of a liquid. This subject has been further studied by Timmermans, 3 who points out that the critical solution temperature is raised by the addition of a substance which is soluble in only one of the two liquids, but is lowered when the added substance is soluble in both. The observation of a superior or inferior critical solution point may thus be rendered possible at a convenient temperature. To take a single example, normal hexane and ethyl alcohol are miscible in all proportions at the ordinary tem- perature, but they become only partially miscible on addition of a very small quantity of water, which is miscible with alcohol but not with hexane. The critical solution temperature may thus be raised to, say, 30 or 40. On the other hand, the critical solution temperature of 1 See also Centnerszwer and Zoppi, Zeit. phys. Ghent., 54, 690 (1906). - Compt. rend, du Congrls de Chimie de Liege, 1905. 3 Bull. Soc. Chiin. Belg., 1906 ; and Zeit. phys. Chem., 58, 129 (1907). 2 9 6 STOICHIOMETR Y phenol and water was found by Alexe'eff to be 66, but by adding a little soap, which dissolves in both liquids, the critical temperature may be so greatly reduced that infinite miscibility at the ordinary temperature results. The disinfectant known as lysol is prepared in this way. The influence of pressure on the miscibility of liquids has not been much studied, but it is probable that the question whether the miscibility is in- creased or diminished by rise of pressure depends partly on the change of volume on admixture and partly on the heat change. There is little doubt that when the volume of the mixture is PERCENTAGE OF A. FIG. 71. 100 O IOO PERCENTAGE OF A. FIG. 72. O IOO PERCENTAGE OF A FIG. 73: considerably smaller than the sum of the volumes of the components, miscibility is increased by raising the pressure. SOLUBILITY OF SOLIDS IN LIQUIDS. Influence of Temperature. As a general rule the solubility of a solid in a liquid is increased by raising the temperature, SOLUBILITY AND MISCIBILITY 297 but the rate of change differs widely for different substances, and there are many cases in which the rate for a given substance alters abruptly at a definite temperature a rapid increase of solubility being followed by a much slower increase, or even by a decrease. The influence of change of temperature on the solubility of a few typical substances is indicated in Fig. 74, temperatures o I 8 100 - 80 60 cS cn 2O 4O 6O 8O TEMPERATURE FIG. 74- I00< being measured as abscissae, and the weights of anhydrous salt dissolved in 100 parts of water as ordinates. The fact that there are two distinct solubility curves for strontium nitrate and for sodium sulphate is, no doubt, to be explained by the existence of hydrates, Sr(NO 3 ) 2 ,4H 2 O 298 STOICHIOMETRY and Na 2 SO 4 ,ioH 2 O, respectively, in solution at the lower temperatures, and of the anhydrous salts at the higher tem- peratures. The point of intersection of the curves indicates in each case the temperature of dissociation of the hydrate, but it is not to be assumed that complete dissociation .takes place at that temperature. There are doubtless molecules of the anhydrous salt present at lower temperatures, and of the hydrate at higher temperatures, and the diminution in the apparent solubility of sodium sulphate is probably due to the gradual dissociation of the residual hydrate with rise of temperature. Tilden and Shenstone x proved, in fact, by heating solid sodium sulphate with water in closed tubes of gun-metal, that the solubility reaches a minimum at about 120, and increases .slowly at higher temperatures, the actual measurements having been taken to 240. Influence of Pressure on Solubility. According to Sorby, 2 the solubility of a solid in a liquid increases with rise of pressure when there is contraction on dissolution, but diminishes when there is expansion. Braun, however, 3 basing his reasoning on the mechanical theory of heat, concludes that the change in solubility depends, not only on the alteration of volume on dissolution, but also on the temperature, the heat of dissolu- tion, and the temperature coefficient of solubility. SOLIDIFICATION OF LIQUID MIXTURES. It will be convenient to include under the heading " liquid mixtures," not only mixed liquids, but also solutions of gases and solids in liquids. There is a fairly close analogy between vaporization and solidification. A pure liquid under a given pressure has a definite boiling point and a definite freezing point, although under certain conditions the liquid may be heated above its boiling point or cooled below its freezing point. A mixed liquid may either boil at a constant temperature, when the 1 Phil. Trans., 1884, 23. 2 Proc. Roy. Soc., 12, 538 (1863). 3 Wicd. Ann., 30, 250 (1887). SOLUBILITY AND MISCIBILITY 299 composition of the vapour must be the same as that of the liquid ; or the temperature may rise during distillation, when the vapour will be richer than the residual liquid in the more volatile component. So, also, a mixed liquid may freeze at a constant temperature, in which case the solid will have the same composition as the residual liquid (mother liquor), or the temperature may fall during solidification, the composition of the solid differing from that of the mother liquor. Again, the freezing point of a liquid mixture may lie between the freezing points of the pure components, or it may be lower or, rarely, higher than either of them. When the two substances are chemically closely related and are isomor- phous, they separate together from the liquid, but as a rule the solid which separates differs in composition from the remaining liquid (mother liquor), and the temperature falls steadily during solidification. If the freezing points of all mixtures lie between those of the pure compounds, it is theoretically possible to separate both components from the mixture by fractional crystallization. If, on the other hand, the curve representing the relation between freezing point and com- position shows a maximum or minimum point it is only possible to separate the mixture of maximum or minimum freezing point, termed the eutectic mixture, from that component which is in excess. Here, again, there is a close analogy between solidification and distillation. In the case of substances which are closely related but of different crystalline form, or of substances which are not closely related, the freezing point of a mixture is usually lower than that of either component. This, for example, is the case with aqueous solutions of most salts and of many other substances. When a dilute solution of common salt, for example, is cooled below o, solid ice begins to separate when the freezing point of the mixture is reached. The mother liquor thus becomes richer in salt, and its freezing point falls. If the solution is further cooled, more ice continues to separate, and the concentration of the residual liquid increases, but the solu- bility of sodium chloride in water diminishes as the temperature 300 STOICHIOMETRY falls, and a point is finally reached at which the residual solu- tion is saturated. Further removal of ice would then cause the solution to become supersaturated, and though the con- centration might increase and the temperature fall to a small extent, separation of solid salt would soon occur, and the temperature would rise again until the point was reached at which the solution first became saturated. After this, the solution being now in contact with both solid ice and solid salt, both components would continue to separate at a constant temperature,, and the composition of the residual solution would undergo no further change. A mixture or solution of constant freezing point would, in fact, be obtained. Starting with a saturated solution of sodium chloride at o and cooling the solution, the solubility diminishes, solid salt separates, and the concentration of the mother liquor falls. This process goes on until the freezing point of the residual solution is reached. It may be possible to cool the solution a few degrees below its freezing point before solidification takes place, but as the temperature continues to fall, the con- centration diminishes owing to further separation of salt, and the freezing point of the mother liquor therefore rises. A point is therefore very soon reached at which ice begins to form, when the temperature at once rises, and equilibrium is finally attained under the same conditions as in the previous case, both solid ice and solid salt being in contact with the solution. In such a case there is not a continuous freezing point temperature curve, but the minimum freezing point is given by the inter- section of the freezing point curve AB with the solubility curve CB (Fig. 75). The freezing of such solutions was first studied by Guthrie, who termed the mixtures of constant freezing point " cryohydrates." They are, however, not hydrates in reality, for the ice and salt crystallize separately, and not in the form of hydrates or even of mixed crystals. Many substances, when they crystallize from aqueous solu- tion, form definite hydrates, such, for example, as MgSO 4 ,- 7H 2 O; Na 2 SO 4 ,ioH 2 O. On cooling solutions of such sub- stances either ice or the solid hydrate separates, and a point SOLUBILITY AND MISCIBILITY 301 is finally reached at which the solid hydrate, solid ice, and the residual solution are in equilibrium. Some substances, such as ferric chloride, form more than one hydrate, and the freezing of solutions of these substances may be a, less simple process, because the final equilibrium may be between ice, the highest hydrate, and the residual solution, or between two solid hydrates and solution, or lastly between a solid hydrate, the 10 -301 10 20 30 CONCENTRATION FIG. 75. solid anhydrous salt, and the solution, according to the concen- tration of the original solution. When an aqueous solution of two or more salts is concen- trated by evaporation, or when the solubility of the salts is diminished by cooling, the dissolved substances solidify sepa- rately unless they are isomorphous, in which case mixed crystals are formed. In the former case, if the saturation point of one substance is reached before that of the other, the first substance separates in a nearly pure state, and by repeated dissolution and crystal- lization may be obtained quite pure. In the latter case the relative quantities of the salts in the 302 STOICHIOMETRY mixed crystal may differ from those in the solution, and sepa- ration by fractional crystallization may be possible, though more difficult. Some salts, such as chrome alum and ordinary alum, are miscible in all proportions in the solid state, so that the com- position of the mixed crystal may vary indefinitely from that of the one pure salt to that of the other. In other cases the solids are only miscible within limits, and in some cases the pure salts crystallize normally in quite different forms ; for example, magnesium sulphate, MgSO 4 ,- 7H 2 O and ferrous sulphate, FeSO 4 ,7H 2 O. Mixed crystals of these salts may be obtained in either form ; thus from a solution rich in magnesium sulphate the crystals will take the rhombic form of that substance, but if the original solution contains a large excess of ferrous sulphate, the crystals will take the monoclinic form of that salt. Rhombic crystals containing more than 18*8 per cent, of ferrous sulphate and monoclinic crystals with more than 54 per cent, of magnesium sulphate cannot be obtained by evaporation of mixed solutions at the ordinary temperature. The specific volumes of mixed crystals may usually be calculated without great error from those of the components by the method described on p. 256, and other physical properties appear to be approximately additive. For a fuller account of the solidification of mixed liquids, see Findlay, "The Phase Rule," in this series. See also Roozeboom, Zeit.phys, Chem., 30, 385 (1899). Absorption of Gases by Solids. Certain metals, notably palladium and platinum, when in a finely divided state, have the power of absorbing or occluding hydrogen and oxygen. There is experimental evidence l that when oxygen is absorbed by platinum black or palladium black, chemical combination with the metal takes place. On the other hand, there appears to be no evidence of the formation of a hydride of either metal. One volume of pure spongy palladium occluded 852 volumes of hydrogen under atmospheric pressure, and of this 1 Mond, Ramsay, and Shields, Proc. Roy, Soc., 62, 50 and 290 (1898). SOLUBILITY AND MISCIBILITY 303 92 per cent, could be extracted in a vacuum at the ordinary temperature. When the palladium contained oxygen, a larger amount of hydrogen was absorbed, the excess forming water with the oxygen. Charcoal and other porous substances possess the property of absorbing gases ; it is found that the denser forms of charcoal have greater absorptive power than the lighter, and that cocoanut charcoal gives especially good results. At a given temperature and pressure, gases which are easily condensed are absorbed much more freely than those which have very low critical temperatures ; but Dewar has shown that under atmospheric pressure the volumes of different gases absorbed by unit volume of charcoal at their respective condensing points do not show wide differences. At constant temperature the quantity of any given gas absorbed increases with rise of pressure, but is not directly proportional to the pressure. At constant pressure the quantity absorbed increases greatly with fall of temperature. Miss Homfray l has measured the volumes of argon and of nitrogen absorbed at definite pressures and temperatures, and finds that the " isosteric " curves, showing the relation between temperature and pressure for equal volumes of either gas absorbed, have the same form as a vapour pressure curve. Moreover, if the isosteric curve for argon or nitrogen is com- pared with the vapour pressure curve for a pure liquid, the relation T ' T T"" 7 = 1 f r ~f~ *f^*A T A ) AB AB (p. 142) is found to hold good. Very good vacua can be obtained, as pointed out by Dewar, by the removal of the last traces of air by means of cocoanut charcoal cooled to the temperature of liquid air. 1 Brit. Ass. Rep. for 1906. CHAPTER XV PROPERTIES OF DILUTE SOLUTIONS Freezing Points. It has long been known that the freezing point of sea-water is lower than that of fresh water, and Blagden/ in 1788, observed that the depression of the freezing point of water is, within limits, proportional to the amount of a salt, such as sodium chloride, dissolved in it ; and that if two different substances are dissolved together, the observed depression of the freezing point is equal to the sum of the depressions which the two would cause separately. These results were, however, entirely overlooked until atten- tion was called to them by de Coppet 2 in 1871. Meanwhile, in 1 86 1, similar observations had been made by Riidorff. 5 De Coppet himself proceeded further, and by taking quantities of different salts proportional to their molecular (formula) weights, he was able to show that, for analogous substances, the molecular depression of the freezing point is constant. The whole subject was investigated with great care and thoroughness by Raoult, 4 who employed not only water, but also benzene, acetic acid, and other liquids as solvents, and examined solutions of more than two hundred different substances. If A^ 1 is the observed depression of the freezing point caused by dissolving m grams of substance of molecular weight M in 100 grams of solvent, the molecular depression of the 1 Phil. Trans., 78, 277 (1788). 2 Ann. Chim. Phys. (4), 23, 366 (1871) ; 25, 502 (1872) ; 26, 98 (1872). 3 Pogg. Ann., 114, 63 (1861) ; 116, 55 (1862) ; 145, 599 (1871). 4 Compt. rend., 94, 1517 (1882) ; 95, 188 and 1030 (1882) ; Ann, Chim. Phys. (5), 28, 137 (1883) ; (6), 2, 66 (1884 \ 304 PROPERTIES OF DILUTE SOLUTIONS 305 freezing point is given, according to Raoult, by the equation , A/. M E = ~^r Raoult found that in the majority of cases E' is constant for a given solvent, but a number of exceptions were met with. With water as solvent, for example, organic compounds and many weak acids and bases gave values of E' about 18*5 or 19, but inorganic acids and bases and the salts derived from them gave higher values ; thus for strong monobasic acids, monacid bases, and the salts derived from them double values were obtained, while hydroxides and halides of the dyad alkaline earth metals gave nearly triple values. On the other hand, with organic solvents, the higher value of E' was generally observed, but with certain substances the value was only half as great. Raoult thought it probable that these exceptional values of E' were due to molecular association of the dissolved substance. Van't Hoff l showed that E' may be calculated for any solvent from its heat of fusion, L', expressed in gram-calories, and its melting point on the absolute scale of temperature ; thus 0-02T* In the table on page 30 6 the values of E' are given for a few solvents. The *' observed " values are obtained from Raoult's A/ M formula, E' = '- > a large number of substances of known molecular weight having been dissolved in the solvent, and the mean value of E' being adopted; the calculated values are derived from Van't HofFs formula. The experimental method of determining the freezing points of solvent and solution has been perfected by Beckmann 2 (Fig. 76). A weighed quantity of the pure solvent is placed in the tube A, and is cooled by water, ice, or a freezing mixture in the large bath B, direct contact between the tube A and the 1 Zeit.phys. Chem., 1,481 (1887). 2 Ibid., 2, 638 (1888) j 7, 323 (1891) ; 21, 239 (1896) ; 44, 169 (1903). X STOICHIOMETR Y 1 :' Calculated. Observed. Water. . . l8'9 18-5 to 19 Acetic acid . 38-8 39 -o Benzene . . 51-0 49 -o Phenol . . 76-0 74-0 Formic acid . 28-4 277 Nitrobenzene 76-3 71-0 material in the bath being prevented by means of the tube C, which contains only air. Two stirrers are provided, one, D, for the solvent, the other, E, for the bath. The temperature is read on a very delicate thermometer, F, of a special form devised by Beckmann. The actual freezing points of the solvent and solutions are not required, but only the differences, and the ther- mometer has a range of only five or six degrees. The amount of mercury in the bulb may be adjusted so that readings may be taken on the same thermometer with liquids of widely different freezing points. After the freezing point of the solvent has been determined, a weighed quantity of the substance is introduced through the side tube G, the solvent having previously been melted ; and the freezinglpoint of the solution is determined. It is usual to make a series of determinations, FIG. 76. a series further small quantities of the substance being added. Vapour Pressures. It seems to have been first observed by Gay Lussac that the vapour pressure of an aqueous solution of sodium chloride is lower than that of pure water, and it was found by Princep that the ratio of the vapour pressure of the PROPERTIES OF DILUTE SOLUTIONS 307 solution, /, to that of pure water, /, was constant at different temperatures. Von Babo afterwards obtained similar results with aqueous solutions of other salts. In 1856 Wiillner 1 concluded, from his experiments, that the lowering of the vapour pressure of water produced by a dissolved non-volatile substance is proportional to the amount of solute. Tammann, in i885, 2 determined the vapour pressure of aqueous solutions of a great number of salts. He found that Wiillner's law was strictly true in only a few cases, but, on the other hand, he showed that the molecular lowering of the vapour pressure, E" = > is approximately the same for similar salts (M is the molecular weight of the salt, and m its percentage weight in the solution). Further experiments by Moser, 3 v. Helmholtz, 4 Emden, 5 Bremer, 6 and J. Walker 7 indicated that Von Babo's law was correct, but that Wiillner's law was only approximately true. In all the older experiments aqueous solutions had been examined, but Raoult 8 employed other solvents, notably ether, and carried out a long series of investigations, employing the barometric method for the measurement of the vapour pressures. Raoult found that Von Babo's law was true for ethereal solutions between o and 20, that Wiillner's law was true for moderate concentrations, and that the molecular lowering of , tf A/T the vapour pressure - *- X (where m is the weight of sub- stance in 100 parts of ether) was the same for different substances. After making similar experiments with other solvents, he was led to the wider generalization that the molecular lowering Pogg. Ann., 103, 529 ; 105, 85 (1858) ; 110, 564 (1860). Wied. Ann., 24, 523 (1885). Ibid., 14, 72 (i 88 1 ). Ibid., 27, 508 (1886). Ibid., 31, 145 (1887). Rec. tr. Pays-Bas., 6, 122 (1887) Zeit.phys. Chem., 2, 602 (1888). 8 Compt. rend., 103, 1125 (1886) ; 104, 976 and 1430 (1887) ; 107, 442 (1888) ; Zeit. phys. Chem., 2, 353 (1888). 3o& STOICHIOMETRY of the vapour pressure is equal to the ratio of the number of molecules of solute to the total number of molecules, or p-p' _ N p ~ n + N which may be written It has been stated (p. 262) that for closely related substances, when mixed in any proportions ^ where /, / A , and / B are the vapour pressures of the mixtures and the two substances, A and B, respectively, and M is the fractional number of gram-molecules of A. If A = o, p = M/ A , or A = - , -M) / M n an equation which is identical with Raoult's (A and / in the above equation corresponding to / and /', respectively, in Raoult's). But the equation / = M/ A -{- (i M)/ B does not, as a rule, hold for substances which are not closely related, and one would therefore not expect Raoult's law to be true for such substances even when A = o. It appears, however, that for dilute solutions the errors are small, and the law may be taken as, at any rate, approximately true. Raoult found that while the molecular lowering of the vapour pressure was generally constant for a given solvent, 1 Raoult first gave the equation in the form /-/ = N p ~ n but this he afterwards found to be incorrect. PROPERTIES OF DILUTE SOLUTIONS 309 there were exceptions similar to those observed in the case of the molecular depression of the freezing point. The chief experimental methods which have been employed for the determination of the vapour pressures of solutions or mixtures of liquids are the following : 1. The statical method, in which the difference between the vapour pressures of the pure solvent and of solutions or mixtures of known composition is measured at a known temperature, the vapour pressures of the pure solvent having been previously determined. This method was employed by Konowalow 1 in his research on the vapour pressures of mix- tures of water with the lower alcohols and fatty acids, by Emden, Raoult, and others. The statical method is open to the serious objection that there is great difficulty in getting rid of traces of air from a solution without altering its concentration, and there is also some danger that the surface layer of solution may differ in composition from the liquid below. 2. The dew point method. Air in presence of pure water gives a mist when very slightly cooled by sudden expansion, but in presence of a salt solution a greater cooling is required before the dew point is reached. A method based on this principle has been devised by R. von Helmholtz (loc. at.}. 3. Dry air is passed through two Liebig's absorption tubes containing the salt solution, then through one containing pure water, and lastly through a drying tube, in which the moisture is completely absorbed. In passing through the first Liebig's tube the air takes up moisture, and the solution gradually becomes slightly more concentrated; but the amount of moisture taken from the second solution is very small, and the concentration of this solution remains almost constant. The air becomes fully saturated in passing through the pure water. The ratio of the loss of weight of the water-tube to the increase of weight of the absorption tube is equal to the ratio P This method was first suggested by Ostwald, and was 1 Wied. Ann., 14, 34 (1881). 3io STOICHIOMETRY employed by J. Walker (loc. tit.}. Will and Bredig * used a similar method for alcoholic solutions, determining the loss of weight of the solution and of the pure solvent, and thus obtain- .1 ing the ratio -,, and the method has since been employed by many experimenters. 4. A small flask, containing firstly the pure solvent, and secondly the solution, is brought into contact with an exhausted globe, and the loss of weight is determined in each case. In this method, which was employed by Beckmann, 2 the ratio of / to f is directly obtained. Boiling Points. The four methods described above are somewhat inconvenient, and are not very accurate, and Beck- mann 3 proposed to determine the boiling points of the solvent and solution under the same pressure, instead of the vapour pressures at the same temperature. The molecular rise of the boiling point, E, is given by the equation E = A/xM m where M is the molecular weight of the dissolved substance, m is the weight of substance in 100 grams of solvent, and A/ is the observed rise of the boiling point. The value of E for a given solvent may be ascertained by determining the rise of boiling point for a number of substances of known molecular weight ; or, as pointed out by Van't Hoff, 4 it may be calulated from the equation where T is the boiling point of the solvent on the absolute scale of temperature, and L is its heat of vaporization. 1 Berichte, 22, 1084 (1889). 2 Zeit. phys. Chem., 4, 532 (1889). 3 Loc. cit. and ibid., 8, 223 (1891) ; 21, 239 (1896) ; 40, 129 (1902) ; 44, 161 (1903). 4 Loc. cit, PROPERTIES OF DILUTE SOLUTIONS 311 The following are the values of E for a few useful sol- vents : Solvem E Benzene . 267 Chloroform 36-6 Acetic acid 25*3 Ether . . 21-2 Water . . 5'2 Aniline . 32-2 There are two methods in general use for the determination of the boiling points of solutions. In that of Beckmann (Fig. 77) a weighed quantity of the pure solvent is first boiled in a glass tube, A, the tem- perature being registered by a delicate thermometer, simi- lar to that employed for the determination of freezing points. Ebullition is facili- tated by fusing a short length FIG. 77. FIG. of stout platinum wire, B, into the bottom of the tube, and by placing in the tube a number of glass beads or crystals of garnet. The glass tube is placed inside a wider vessel, C (Fig. 77#), in which some of the pure solvent is boiled. Both the experimental tube and the jacketing vessel are provided with reflux condensers, either spiral in form or fitted with water-jackets (D and E). 312 STOICHIOMETRY After reading the position of the mercury when the thermo- meter bulb is immersed in the boiling solvent, a small quantity of the substance under investigation is introduced through the side tube, and after the temperature has become constant, a second reading is taken. Additional small quantities of the substance are introduced, and the rise of boiling point deter- mined in each case. The relation between concentration and rise of boiling point may thus be studied. Landsberger 1 has devised a somewhat different method. The solvent and solution respectively are not heated directly by a flame, but by passing the vapour of the pure solvent through them. Modifications of the original method have been proposed by Walker and Lumsden, 2 Smits, 3 Riiber, 4 and Ludlam. 5 The apparatus devised by Ludlam is shown in Fig. 78. A quantity of the pure solvent is boiled in the flask A ; the vapour passes through the opening in the side of the tube B, up through the valve C (shown separately on a larger scale) in the bottom of the experimental tube D (which is graduated in cubic centimetres), and out by the side tube E, which is connected with a Liebig's condenser. If necessary, a little of the pure solvent is first placed in D. Condensation takes place at first in the tube B and in the lower part of D, but after the apparatus has become thoroughly heated, the amount of condensation is very small. Any liquid formed by con- densation of vapour in the upper part of D is carried off into the condenser. It is usual to employ a thermometer graduated in tenths or fifths of a degree. The boiling point of the pure solvent is first determined, and then a small quantity of the substance is introduced through the side tube F. When the thermometer bulb is quite covered with liquid and the tempe- rature has become steady (the time required is much shorter than with the Beckmann apparatus), the current of vapour is 1 Berichte, 81,458(1898). 2 Trans. Chem. Soc., 77, 503 (1898). 3 Proe. K. Akad. Wetensch. Amsterdam, 3, 86 (1900). 4 Berichte. 34, 1060 (1901). 5 Trans. Chem. Soc., 81, 1194 (1902). PROPERTIES OF DILUTE SOLUTIONS 313 stopped for a few moments by cooling the flask A by touching it with the hand. The liquid is prevented by the valve C from flowing out of the experimental tube, and a reading of the volume of the solution is taken. The vapour is allowed to pass through the solution again, and successive readings are FIG. 78. taken with larger volumes of solution. In the Beckmann apparatus the quantity of substance is gradually increased, the solution becoming more concentrated ; in the Landsberger- Ludlam apparatus the quantity of solvent is gradually in- creased, the solution becoming more dilute. When the last reading has been taken, the clip G is opened in order to admit air into the flask. DIFFUSION OF LIQUIDS AND OSMOSIS. Just as two gases, when brought into contact or when separated only by a porous diaphragm, diffuse into each other 3H STOICHIOMETRY until a homogenous mixture is produced, so also admixture of two liquids will take place under similar conditions. The process of diffusion, however, in the case of liquids is exceedingly slow, as may be seen by carefully pouring a strong solution of a coloured substance, such as copper sulphate, through a thistle funnel, so as to form a layer at the bottom of a cylinder of water. Weeks or even months will elapse before the salt is evenly distributed through the water. The processes are similar in this respect also, that they are not reversible. The gases or liquids may, indeed, be separated again, but not by a simple reversal of the process by which admixture was effected. It is possible, however, by the employment of what are termed semipermeable diaphragms, to make the process a strictly reversible one. Imagine a cylinder (Fig. 79) divided by AB b FIG. 79. means of two pistons into two chambers, a and b. Let each piston consist of a solid rod attached to a semipermeable dia- phragm, such that the diaphragm A will allow a gas placed in the chamber a to pass freely through it, but not a gas placed in b. Conversely, let B be permeable to the gas in b, but not to that in a. The gas in a will then pass freely through A, but it will exert a pressure on B tending to move it to the right, while the gas in b will pass freely through B, but will tend to force A to the left. If the pistons were frictionless, they would therefore move apart until they reached the extremities of the cylinder, and a mixture of the two gases would then be obtained (Fig. 80). Let the two pistons be now brought together again by the application of external force. As B moves to the left, it compresses the gas originally present in UGAR SOLUTION FIG. 81. FIG. 82. from above, water would pass through it, and the solution remaining below the piston would become more concentrated. The work done by the cane-sugar in raising the piston would be equal to that done in forcing the piston down to its original position. The pressure exerted on the piston by the dissolved sugar is termed the osmotic pressure of the solution. It would be very difficult to make a frictionless and semi- permeable piston strong enough and fitting the cylinder well enough to allow of this experiment being actually performed, but semipermeable membranes exist in nature, and others can be prepared in the laboratory. Traube, 1 in 1867, observed that a membrane of copper 1 Archiv. f. Anatomie u. Physiologic* 1867, p. 87. PROPERTIES OF DILUTE SOLUTIONS 317 ferrocyanide, formed by the action of copper sulphate on potassium ferrocyanide in aqueous solution, is permeable to water, but not to cane-sugar, nor to many other dissolved substances. A copper ferrocyanide membrane would not be strong enough to withstand even moderate pressures, but this difficulty was overcome by Pfeffer, 1 who caused the precipitation to take place in the interior of the walls of a porous earthenware cell. The porous cell is immersed in water, and all air is removed from the walls by boiling the water under greatly reduced pres- sure, after which the cell is placed in a three per cent, solution of copper sulphate, until the walls are thoroughly impregnated with the salt ; it is then rinsed with distilled water, wiped with filter-paper, filled with a three per cent, solution of potassium ferrocyanide, and immersed in a solution of copper sulphate of the same strength. Diffusion takes place so that the two salts meet each other, and the precipitate is formed in the interior of the walls near the inner surface. The cell is then thoroughly washed with water. In the earlier experiments the cell was fitted with a stopper, through which passed a long vertical glass tube. The cell was filled with a dilute solution of cane-sugar to a height a little above the top of the stopper, and was immersed in pure water. Under these conditions the water slowly enters the cell, and the solution rises in the vertical tube until equi- librium is established between the hydrostatic pressure of the column of solution and the osmotic pressure which tends to cause the passage of more water into the cell from outside. There is, in fact, a tendency for a dissolved substance to expand by diffusion into a solvent, just as there is a tendency for a gas to expand either into a vacuous space,' or, by diffusion, into another gas. But the sugar cannot pass through the membrane of copper ferrocyanide, and dilution of the solution can only take place by the entry of water into the cell from outside. In this experiment, as in that with ammonia gas and air, the semipermeable diaphragm is fixed, and it may be stated 1 " Osmostiche Untersuchungen." Leipzig, 1877. STOICHIOMETR Y that the ammonia passes through the moistened bladder and the water through the copper ferrocyanide membrane until their partial pressures inside the funnel and cell respectively are equal to their pressures outside. The simple apparatus first devised by Pfeffer is not suitable for accurate measurements of osmotic pressure for two reasons. In the first place, the pressures to be measured are so great that glass tubes of inconvenient height would be required; thus the osmotic pressure of an aqueous solution containing one per cent, of cane-sugar was found to be 0*649 atmos. at o, which would correspond to a column of water 67 metres in height. In the second place the solution becomes diluted as the process goes on, and, diffusion being a very slow process, the concentration would not become uniform until after the lapse of a long period of time, even though admixture would doubtless be facilitated to some extent by convection currents. It would, therefore, not be easy to ascertain the true concentration of the solution in the cell itself. Pfeffer overcame these difficulties by the employment of an air manometer in place of the open water manometer. The ap- i ,. ^ paratus, as further modified by Adie, 1 is n shown in Fig. 83. The glass cover B is fixed to the porous cell by means of sealing wax ; the manometer is closed above, and contains air above C, and mercury from C to D. A solution of cane-sugar of the required strength is poured into the cell through the tube E until the remainder of the apparatus is completely filled, the tube E is then sealed at the blowpipe, and the cell is immersed in a vessel of pure water. The water enters slowly, and the pressure of the air in the manometer rises until it becomes constant after several days or perhaps weeks. The quantity of water 1 Trans. Client. Soc.> 59, 344 (1891). FIG. 83. PROPERTIES OF DILUTE SOLUTIONS 319 which enters the cell is so small that the dilution is of little importance, and it may, of course, be estimated by the diminution in volume of the air. Quantitative experiments with cane-sugar solutions of different concentrations and at different temperatures, carried out by Pfeffer, and later by Adie and others, prove that for dilute solutions the osmotic pressure is directly proportional to the concentration, and, approximately at any rate, to the absolute temperature. The osmotic pressure of a dilute cane-sugar solution may, in fact, be calculated by the formula p = n X 0*649(1 + o'oo367/) atmos. where n is the percentage of cane-sugar. Other substances, for example, ferric hydroxide, tannate of gelatine, calcium phosphate, prussian blue, or silicic acid, may be employed in place of copper ferrocyanide, and semi- permeable membranes are found naturally in plant cells, such as those in the leaves of Trades cantia discolor^ in red blood- corpuscles, and in bacteria. The osmotic pressure in such cells frequently amounts to four or five atmospheres, and may be considerably higher when the cells contain dissolved reserve materials, such as the sugar in beetroot. It was noticed by Pringsheim that when a vegetable cell is placed in a salt solution, the cell wall remains unaltered in shape, but the protoplasm contracts, breaking away from the cell wall. This is explained by assuming that the protoplasm is enclosed in an outer skin which, like the copper ferrocyanide membrane, allows water to pass through it, but is impermeable to many dissolved substances. Water therefore flows out of the protoplasm into the outer solution, and the protoplasm shrinks. De Vries * prepared solutions of different substances of such strengths that they were just in equilibrium with the cell contents, producing no effect on the protoplasm. Such solutions, having the same osmotic pressure as the contents of 1 Pringsheims Jahrbiicher, 14, 427 (1884). 320 S TOICHIOME TR Y the protoplasm, have the same osmotic pressure as each other, and are termed isosmotic^ or isotonic. An optical method of finding whether solutions are isotonic or not has been devised by Tammann. 1 A drop of potassium ferrocyanide at the end of a capillary pipette is placed in a solution of copper sulphate, when it becomes covered at once with a membrane of copper ferrocyanide. According as the osmotic pressure inside is greater or less than outside, the cell so formed will expand or contract, as water enters or escapes. At the same time striae may be seen owing to the change in concentration, and therefore in density, of the copper sulphate solution round the cell. If water enters the cell, the copper sulphate solution becomes more concentrated, and the striae may be seen to descend ; if water leaves the cell, the copper sulphate solution becomes more dilute, and the striae move upwards. When no striae are visible, the solutions are isotonic. Solutions of copper sulphate and potassium ferrocyanide of various strengths may be thus examined, or other substances may be dissolved in either or both solutions before the cell is formed. LAWS OF OSMOTIC PRESSURE. It has been pointed out by Van't HorT 2 that the laws of osmotic pressure are similar to those relating to gaseous pres- sure. Pfeffer, as already stated, found that the osmotic pressure of a dilute cane-sugar solution was directly propor- tional to the weight of cane-sugar in 100 grams of the solu- tion, which may be taken, without sensible error, to occupy 100 c.c. Let c be the number of gram-molecules of cane-sugar dissolved in one litre of solution at a given temperature; then p = c X constant > Wied.Ann.,Mt, 299, (1888). 2 Arch, Norland, 20 (1885) ; K. Svensk. Ak, Hand., 21 ; Zeit. phys. Chem., 1, 481 (1887). PROPERTIES OF DILUTE SOLUTIONS 321 But c = ^, where V is the volume of solution in litres that contains i gram-molecule of sugar ; therefore pV = const, at constant temperature The range of temperature over which experiments are possible is small, and it can only be stated that the results obtained by Pfeffer are not inconsistent with the statement that the osmotic pressure is directly proportional to the abso- lute temperature, or for a i per cent, cane-sugar solution T p = 0-649 X This conclusion has been confirmed by experiments with living cells, which showed that solutions of different substances in osmotic equilibrium with the cell contents at o were also in equilibrium at 34. The relation of osmotic pressure to temperature is therefore the same for aqueous solutions of different substances. The equation for gases PV = T x constant representing the laws of Boyle and Gay Lussac, is therefore found to hold good for substances in dilute solution. The value of the constant in the above equation may be deduced from Pfeffer's observation that the osmotic pressure of a i per cent, cane-sugar solution is 0*649 atmos. The volume of 100 grams of solution at o = 99*7 c.c. ; that is to say, i gram of cane-sugar is present in 997 c.c. of solution, and therefore i gram-molecule, or 342 grams of sugar in 342 x 997 c.c., or 34-1 litres. But in the equation for gases _ RT P = -yr atmos. R = 0*0821, and if V = 34*1 litres for i gram-molecule of gas, and T = 273, then 0-0821 x 271 P = - -- = 0*658 atmos. 34 i 322 STOICHIOMETRY The agreement of this pressure with that found by Pfeffer 0-649 atmos. is as close as could be expected from the nature of the experiments, and the conclusion is therefore apparently justified that the equation P _ RT "V is applicable not only to gases under moderate or low pressures, but also to dilute solutions ; in other words, that the osmotic pressure of a substance in dilute solution is equal to the pressure which it would exert as a gas at the same tempera- ture and occupying the same volume as the solution, if it could exist as a gas under such conditions. Griffiths has determined the osmotic pressures of very dilute solutions of cane-sugar, and has obtained an excellent agreement between the observed pressures and those calculated from the formula PV = RT. It would be of great interest to find whether the osmotic pressures of more concentrated solutions show deviations from the simple laws similar to those observed in the case of com- pressed gases ; in other words, whether some such formula as that of Van der Waals is applicable to the osmotic pressures of strong solutions. PferTer's cells would not be strong enough, however, to withstand the high pressures required, and a special form of apparatus has been devised by the Earl of Berkeley and Mr. Hartley, 1 by means of which pressures exceeding 100 atmos. could be measured, the semipermeable membrane employed being copper ferrocyanide. The Earl of Berkeley 2 has considered how far the results obtained could be represented by an equation similar to that of Van der Waals. Among the numerous equations tried, the two following were found to give good results over the range of the actual observations : (A/z;~p + ^ 2 K^-^) = RT . . . (i) (A/ + p - alv^(v - b) = RT . . . (2) 1 Phil. Trans., 2o6A, 481 (1906). 2 Proc. Roy. Soc., 79A, 125 (1907). PROPERTIES OF DILUTE SOLUTIONS 323 The units adopted were the atmosphere and the litre, and R was taken as equal to 0*08207. In the first equation v = the volume of solvent which contains i gram-molecule of solute, and in the second equation v = the volume of solution which contains a gram-molecule. The temperature was o C. The calculated and observed results for cane-sugar are given below ; the concentration is in grams per litre of solution. The highest osmotic pressure was not directly measured, but was calculated from vapour-pressure measurements. The constants for the equations were calculated from the three highest pressures, and were used for the calculation of the lower pressures. j Concen- tration. V Osmotic pressure. Ofeqn. (r). Ofeqn. (2). From eqn. (i). From eqn (2). Observed. 850 760 660 540 420 300 i So O'l8270 0^23656 0-29883 0-41431 o - 5947 1 0-91883 1-67368 0-39722 0-45025 0-51177 0-62570 0-80492 1-12764 1-88094 (183-0) (1337) (ioo-8) 68-4 45'o 277 14-6 (183-0) (1337) (100-8) 67-7 43'4 25 '4 , 2 - 2 183-0 1337 100-8 67-5 44-0 26-8 14-0 The constants are A a b For equation (i) . . 45-3689 . . 3*5696 . . 0*05266 ,, (2) . . 67166 . . 7-2960 . . 0-25139 The values of T, p, v for the critical point derived from the two equations are impossible ones, and it therefore appears, as the Earl of Berkeley points out, that the equation can only be regarded as holding good over a limited range of values. Kahlenberg 1 has carried out a large series of qualitative experiments on osmosis in which various liquids and septa were employed. The process of admixture of solution and solvent in the cell was accelerated by stirring. Kahlenberg states that osmotic pressures are equilibrium pressures, and that in the osmotic process there is always a 1 fourn. Phys. C/iem., 10, 141 (1906). 324 STOICHIOMETRY current in both directions, though the major current may, in specific cases, be so much stronger than the minor that the latter almost sinks into insignificance. He terms the septum " semipermeable " in such cases, and he found that vulcanized caoutchouc was " semipermeable " when used as a septum separating a pyridine solution of silver nitrate, lithium chloride, or cane-sugar from the pure solvent. Kahlenberg made quanti- tative measurements of osmotic pressure with these solutions, and found that the laws relating to gases did not hold ; he therefore concludes that these laws cannot, serve as a basis for a satisfactory theory of solutions. It may be pointed out, however, that the theory assumes that the membrane is absolutely impermeable to the solute, and that deviations from the laws relating to gases must occur if the solute is able to penetrate the septum. An imperfectly semipermeable membrane would, in fact, behave like a piston which was not quite air-tight, the measured pressures of a com- pressed gas being necessarily too low. That the osmotic pressure must be measurable by the hydrostatic pressure of the column of solution in a cell of Pfeffer's original simple form, and that it is simply related to the vapour pressures of the solution and solvent, is evident from the following considera- tions : 1 Let a vessel, A (Fig. 84), containing a small quantity of a solution, be placed in a shallow cylindrical vessel, B, containing the pure solvent; let the apparatus be covered by a bell- jar, C, connected with a pump, and let all air be removed from the vessel and the liquids. The vapour pressure of the pure solvent will be higher than that of the solution, and distil- lation will therefore take place. The volume of the solution will increase, and if the temperature be kept quite constant, and time enough be allowed for diffusion of the condensed solvent into the solution to take place completely, a state of equilibrium will finally be attained when the diluted solution has reached a certain height, /*, measured from the level of the pure solvent. The vapour pressure of the pure solvent will still be higher 1 Arrhenius, Zeit. phys. Chem., 3, 115 (1889). PROPERTIES OF DILUTE SOLUTIONS 325 than that of the solution at their respective surfaces, but the pressure of the saturated vapour just above the surface of the solvent is greater than that of the vapour at the height H, by the pressure of the column of vapour between the two levels, ^-$T- atmos., where s is the mean mass of i c.c. of the vapour, ;6/ and s' is the mass of i c.c. of mercury. Calling the vapour pressure of the solvent and solution / and /' respectively, equilibrium takes place when p p' = B H Imagine, now, that, without disturbing the apparatus, the bottom of the cylinder is re- placed by a truly semipermeable diaphragm. The solvent could now pass into or out of the cylinder, but if it were to do so the height of the column of solution above the level of the solvent would be altered, and there would no longer be equili- brium between the vapour pres- sure of the solution and the pressure of the vapour of the pure solvent at the new height H'. Distillation in one direction or the other would therefore take place, and would go on continuously. There would, in fact, be a perpetual circulation, the solvent passing in one direction by osmosis through the diaphragm, and in the other direction by distillation. It is, in fact, evident that the osmotic pressure of a solu- tion, as measured by the hydrostatic pressure of the solution in the vessel with a semi-permeable base, must be definitely related to the difference between the vapour pressures of solvent and solution at the same temperature. The osmotic FIG. 84. 326 6" TOICHIOME TR Y pressure may, indeed, be calculated from the lowering of the vapour pressure. The theory of this relation is discussed in Donnan's " Thermodynamics," and it is there shown that the osmotic pressure may also be calculated from the depression of the freezing point, the rise of the boiling point, and also, as Nernst l has shown, by the diminution in the solubility of one liquid in another caused by the dissolution in it of a third substance. It will be sufficient here to give the formulas expressing these relations. The osmotic pressure may be calculated (1) From the lowering of the vapour pressure, by the equation /-/ 82-iT x s P -""/" X ~ "IvF" * atmos - where T is the absolute temperature, s is the specific gravity of the solution at T, and M is the molecular weight of the solvent ; or, for stronger solutions, with greater accuracy by the formula 82-iTx-y, p P= - M log. ^ atmos. (2) From the rise of the boiling point, by the equation IOOQS X L A/ P = 24-17 . X T atmos - where L is the heat of vaporization of the solvent, A/ the rise of the boiling point, and T the boiling point of the pure solvent on the absolute scale of temperature ; (3) From the depression of the freezing point, by the equation IOOO.T x L' A/ p = - - X TT, atmos. 24-17 1 where L' is the heat of fusion of the solvent, T its freezing point, and A/ the depression of the freezing point ; 1 Zeit.phys. Che in., 6, 16 (1890). PROPERTIES OF DILUTE SOLUTIONS 327 (4) From the diminution in solubility, by the equation S-S' 82-iT + j p ' X- ~M atmos ' where S is the solubility of the first liquid in the second before the addition of the solute, and S' the solubility after its addition, T is the absolute temperature, and s and M are the specific gravity and molecular weight, respectively, of the first liquid. CHAPTER XVI DISSOLUTION AND VAPORIZATION IT has been pointed out (pp. 294, 296) that the miscibility of two liquids and the solubility of a solid in a liquid generally increase with rise of temperature, and that Alexeeff l was the first to observe the gradual change from partial miscibility of two liquids at a low temperature to infinite miscibility at a higher temperature. This temperature, at which two liquids become miscible in all proportions, has been termed by Orme Masson 2 the critical solution temperature ; and he has called attention, not only to the analogy between the critical solution temperature of two liquids and the critical temperature of a pure substance, but also, more generally, to that between dissolution (or admixture) and vaporization. Consider two liquids, miscible within limits at the ordinary temperature, placed in contact with each other. For conve- nience, call the liquid A the solute, and B the solvent, Exerting a definite osmotic pressure, the liquid A proceeds to dissolve until, if there is sufficient present, the maximum osmotic pressure is reached and the solution becomes saturated ; just as a liquid, when placed in a vacuous space, proceeds to evaporate until the maximum vapour pressure is exerted. At the same time dissolution of the solvent in the solute takes place until equilibrium is reached. Two layers will thus be formed one, which may be termed the A layer, consisting of solute A, containing a little of the solvent B in solution ; the other, the B layer, consisting of 1 Loc. cit. 2 Nature, 43, 345 (1891) ; Zeit. phys. Ghent., 7, 500 (1891). 328 DISSOLUTION AND VAPORIZATION 329 solvent with some dissolved solute. If the amount of solute is insufficient, the whole of it will dissolve, and a single layer of unsaturated or just saturated solution will be formed ; just as an unsaturated or just saturated vapour may be formed when a small amount of liquid is placed in a vacuous space. The volume occupied by i gram of solute is termed by Masson the specific solution volume ; that occupied by i gram- molecule the molecular solution volume. It is clear that the specific solution volume of the solute in the A layer must be relatively small, and in the B layer relatively great, just as the specific volume of a liquid under ordinary conditions is small compared with that of its saturated vapour. The specific solution volume of A in the unsaturated solution must also obviously be greater than in the saturated solution, just as the volume of vapour is greater when unsaturated than when saturated. Suppose, now, that the temperature is raised when both layers are present. The osmotic pressure increases, and more solute dissolves, until the solution again becomes saturated j at the same time more of the solvent dissolves in the solute. The specific solution volume of the solute in the A layer thus increases, while that in the B layer diminishes. [The changes in specific solution volume due to expansion by heat are generally inconsiderable compared with those due to increase in miscibility ; the increase in specific solution volume of the A layer is slightly greater, and of the B layer very slightly less, than if there were no expansion.] The case of a pure liquid is quite analogous ; on raising the temperature further evapo- ration takes place until the vapour again becomes saturated. The specific volume of the liquid becomes greater owing to expansion, that of the liquid less owing to increased evapo- ration. Each time that the temperature is raised, the osmotic pressure and the miscibility increase; the specific solution volume of the solute in the A layer increases, while it diminishes in the B layer. If either solute or solvent is present in insufficient quantity, it will eventually be completely dissolved in the other layer. 330 STOICHIOMETRY In the same way, if the liquid placed in the vacuous space is too small in quantity, it will completely evaporate, and if too large it will completely fill the space. If, however, the quantities are such that the two layers remain, the specific solution volume of the solvent in the A layer will at last become equal to that in the B layer. The two layers will, in fact, become identical, and the two liquids infinitely miscible, and the critical solution temperature will be reached. There is thus a close analogy with the critical temperature of a pure substance, the temperature at which the specific volume of the liquid becomes equal to that of its saturated vapour. In many cases the substance is solid at the ordinary tem- perature, but the solution melting point ', that is to say, the temperature at which the solid in contact with a solvent melts, is generally lower than the ordinary melting-point, because the melted solid dissolves a portion of the solvent, and the freezing point of a solution is generally lower than that of a pure substance. Among other solutions Alexeeff examined those of phenol, salicylic acid, benzoic acid, aniline phenylate, and aniline in water, and of chlorobenzene, benzene, toluene, aniline, and mustard oil in molten sulphur, and in each of these cases he observed reciprocal partial solubility at lower temperatures, leading to infinite miscibility at some definite higher tempera- ture. In several cases, also, he observed that the solution melting point was lower than the melting point of the pure substance. Alexe'eff determined the temperatures at which different relative quantities of the same two liquids are just converted into homogeneous liquids ; in other words, he determined the strengths of the saturated solutions corresponding to different temperatures. From Alexeeff's results Masson calculated the weight of water capable of dissolving or of being dissolved by i gram of aniline at each observed temperature so as to form a saturated solution. From the known specific volumes of aniline and water Masson then calculated the approximate specific solution DISSOLUTION AND VAPORIZATION 331 volumes of aniline, on the assumption that the volume of solution is equal to the sum of the volumes of the components. Finally, he plotted the specific solution volumes against the temperatures. The actual data are given in the table on p. 332, and the curves are shown in Fig. 85. The specific volumes of 200 5 IO 15 20 25 SPECIFIC SOLUTION VOLUME FIG. 85. 5 IO 15 2O SPECIFIC VOLUME FIG. 86. isopentane are plotted against the temperatures in Fig. 86, in order that the two diagrams may be compared. In the isopentane diagram a few isobaric curves for liquid and saturated vapour are given. The corresponding curves for aniline and water cannot be drawn, because the osmotic pressures have not yet been determined. It is also impos- sible as yet to draw the diagram representing the relations between osmotic pressure and specific solution volume at constant temperature, but with regard to these relations and to the comparison of the diagram with the isothermal diagram 332 STOICHIOMETR Y for gases and liquids (Figs. 19 and 20), the following points may be noticed. Specific solution volume of aniline. Temperature. In aniline layer. In water layer. 8-0 I "OI 5 _ 16-0 32-I6 25-0 1-036 39*o 1*053 5o 28-27 68 'o I '087 77*o 19*55 137-0 1-297 142-0 7-696 156*0 5-248 |57]5 I-498 3-4I2 When unsaturated isopentane vapour is compressed at constant temperature the volume diminishes and the pressure rises until the vapour becomes saturated. Liquefaction then takes place, and the pressure remains quite constant until it is complete, the volume diminishing greatly during this process. Lastly, the pressure rises again, but the volume of liquid diminishes very slowly. The specific solution volume of aniline in the B layer depends on the concentration of the solution ; it may be diminished by removal of water, and for dilute solutions, as Pfeffer has shown, the osmotic pressure is directly proportional to the concentration, or inversely proportional to the specific solution volume. For stronger solutions there is little doubt that the pressure rises somewhat more slowly ; in other words, the product p# falls in the same way that it does for com- pressed gases. In any case, the specific solution volume diminishes and the osmotic pressure increases until the solution becomes saturated. On further removal of water the second phase the A layer, consisting of aniline saturated with water appears, and its volume slowly increases, while that of the B DISSOLUTION AND VAPORIZATION 333 layer rapidly diminishes. The concentration, and therefore the osmotic pressure, of each layer remains unaltered during this process, and, as the two layers are in equilibrium, the osmotic pressure must be the same for both. The layer B finally disappears, and, as the remaining A layer contains very little water, hardly any further change in the specific solution volume of the aniline can be effected by removal of solvent, but the corresponding rise in osmotic pressure is very great. The process may be exactly reversed by the gradual addi- tion of water to aniline. There is thus a very close analogy between the changes produced by compressing unsaturated isopentane vapour and those caused by concentrating an aqueous solution of aniline by gradual removal of water. But the analogy is even closer, for by careful removal or addition of solvent it is generally possible to obtain super- saturated solutions. Thus, starting with the unsaturated B layer, it would be possible to obtain a supersaturated solution of aniline in water, or, beginning with the unsaturated A layer, a supersaturated solution of water in aniline would be obtained. In neither case, however, could the process, as a rule, be carried very far; after a time an abrupt separation into the A and B layers would take place. The osmotic pressure of the supersaturated B layer would be greater, and of the super- saturated A layer less than that of the saturated solutions, and with the sudden formation of the two layers the osmotic pressure would at once fall or rise to that of the saturated solution. The formation of the supersaturated aqueous solution of aniline is precisely analogous to the formation of a super- saturated vapour by compression beyond the condensing point at constant pressure, as observed by Aitken. On the other hand, the supersaturated A layer is analogous to a superheated liquid, which may be obtained either by lowering the pressure below the vapour pressure of the liquid at constant tempera- ture, or by raising the temperature above the boiling point at constant pressure. In either case the change of state, when it occurs, takes place abruptly, and the pressure at once falls 334 STOICHIOMETRY or rises to the true vapour pressure (or the temperature falls or rises to the true boiling point). If the compression of the vapour or the concentration of the solution is carried out at a higher temperature, but still below the critical or critical solution temperature, the changes observed are similar in kind, the only differences being that the specific volume and specific solution volume of the saturated vapour and B layer respectively are smaller, while those of the liquid and A layer respectively are greater than at the lower temperature. When the process is carried out at the critical and critical solution temperatures respectively, the separation into two phases does not take place, but in both cases, between certain limits of volume, the opalescence so characteristic of the critical state is observed. This opalescence is also to be seen in both cases at temperatures slightly above and slightly below the critical temperature. At still higher temperatures no visible change whatever occurs during compression, but there is a continuous rise of gaseous or osmotic pressure. Law of Cailletet and Mathias. Rothmund, 1 who has carried out an important investigation of the influence of tem- perature on the miscibility of liquids, discusses the question whether the law of Cailletet and Mathias is applicable to mix- tures of liquids. Strictly speaking, the density of one of the substances, that is to say, the mass of it in one cubic centi- metre of liquid, should be determined for each layer at each temperature. The two densities would then correspond to those of liquid and saturated vapour in the case of a pure substance. The mean densities should then be plotted against the temperature. In order to do this, however, a knowledge not only of the composition but also of the density of each layer would be required, and in most cases these densities have not been ascertained. Rothmund, however, points out that if the concentration of the liquid A is expressed by the equation /-* ^A C = : X TOO m A. T m B Zeit.phys. Chem., 26,433 (1898). DISSOLUTION AND VAPORIZATION 335 where ;;/ A and ;;/ B are the masses of the two liquids, and if C x and Q are the concentrations of the liquid A in the two layers, then the mean concentration at any temperature, /, should be given by the formula and the critical concentration would be C, = A + B/ c The law of the rectilinear diameter, stated in this form, was found to hold in the case of eight pairs of substances which became infinitely miscible at high temperatures. In the case of aniline and water, investigated by Alexe'eff, Masson has calculated the approximate specific solution volumes of aniline in the two layers, and the reciprocals of these values give the required densities. The densities were plotted against the temperatures, and the values given in the table below were read from the curves. The mean densities given in the last column were calculated from the equation s t = 0*512 Densities of aniline. Temperature. In A layer. In B layer. Mean. Mean calculated. 20 0-972 0*030 0*501 0*502 40 0-951 0-033 0-492 0'493 60 0*928 0*040 0-484 0-483 80 0-902 0*050 0-476 0-474 100 0-867 0*067 0-467 0-464 1 2O 0-821 0-089 '455 0-454 I4O 0762 0-127 Q'445 0-445 ISO 0719 0-160 0-440 0-440 1 60 0-633 (?) 0'22I 0-427 (?) '435 The agreement is very good except at 160, but the number of observations is small, and the density of aniline in the A layer at 160 was obtained by extrapolation. 336 STOICHIOMETRY It may be noticed that, as in the case of pure liquids, the coefficient B in the formula s t = A + B/ is negative, and that it is of the same order of magnitude ; thus for normal pentane the value of B is 0*00046. In the case of two pairs of liquids, triethylamine and water, and /?-collidine and water, Rothmund found that the miscibility increased with fall of temperature, reaching infinity at about 1 8* 7 with the first pair, and at about 6-4 with the second. If, as has been suggested (p. 294), the increasing miscibility with fall of temperature is due to the attraction between the unlike molecules becoming greater relatively to that between the like molecules, there would be no close analogy between the inferior and superior critical solution temperatures, and it could not be expected that the law of the rectilinear diameter should hold. In point of fact, the diameter is markedly curved in both these cases. CHAPTER XVII THE DETERMINATION OF MOLECULAR WEIGHT FROM CHEMICAL CONSIDERATIONS IF the percentage composition of a substance and the atomic weights of its component elements are known, the empirical formula of the compound may be calculated by dividing the percentage amounts of the elements by their respective atomic weights, and the quotients so obtained by the lowest of them. Taking acetic acid as an example- C . . H . . O 4o*o 6 7 53' 3 lOO'O = 3-3 3-3 67 - 2 (approximately) O O g- the empirical formula is CH 2 O. But | of the total hydrogen is replaceable by a metal, and ^, l, or | of the hydrogen by chlorine, and the substitution cannot be effected in any other proportions. It is therefore concluded that there are 4 atoms of hydrogen in the molecule, and the molecular formula C 2 H 4 O. 2 is adopted, the correspond- ing molecular weight being 60 (taking as atomic weights C = 12, H = i, O = 1 6). Again, the empirical formula of benzene is found to be CH, and as the hydrogen can be replaced by chlorine in six equal stages, it is concluded that the mole- cular formula is C G H 6 , and that the molecular weight is 78. 337 z 338 STOICHIOMETRY From the percentage composition of ammonia, its empirical formula is found to be NH 3 , that of ammonium chloride is similarly found to be NH 4 C1, and of platinic chloride PtCl 4 , and the two latter substances unite to form a crystalline compound which has the empirical formula N 2 H 8 PtCl 6 , thus 2NH 4 Ci + PtCl 4 = (NH 4 ) 2 PlCl 6 But the hydrogen in ammonia can be replaced in three equal stages by various monovalent groups of carbon and hydrogen atoms, such as CH 3 , C 2 H 5 , etc., forming amines, while the hydrogen in hydrochloric acid can be replaced in only one stage ; and the molecular formulae of ammonia, ammonium chloride, and ammonium platinichloride, for these and other reasons, are taken to be the same as their empirical formulae, namely, NH 3 , NH 4 C1, and (NH 4 ) 2 PtCl 6 . The amines unite with hydrochloric acid to form substituted ammonium chlorides, and these will combine with platinum chloride to form crystalline compounds similar to ammonium platinichloride. All these platinichlorides, when strongly heated, decompose and leave a residue of pure platinum. Therefore the weight of platinichloride is to the weight of platinum as the molecular weight of the platinichloride is to the atomic weight of platinum ; and as the atomic weight of platinum is known, the molecular weight of the platinichloride may be calculated. Writing the formula of the platinichloride (NRR'R"H),- PtCl 6 (where R, R', and R" may be monad radicals or hydro- gen), and subtracting from its molecular weight the atomic weights of Pt, 6C1 and 2H, there is left twice the molecular weight of NRR'R". This method is commonly employed for determining the molecular weights of amines. So, also, the silver salts of organic acids, when strongly heated, decompose and leave a residue of metallic silver. The equivalent of the acid may thus be directly determined, and its molecular weight may be calculated by multiplying the equivalent by the basicity. By one or other of these various methods it is frequently possible to determine what may be called the chemical molecular weight of a compound, but it DETERMINATION OF MOLECULAR WEIGHT 339 does not necessarily follow that this molecular weight is identical with that of the smallest particle of the compound that exists in the free state. The methods of determining the physical molecular weight of a substance will now be con- sidered. MOLECULAR WEIGHTS OF GASES AND VAPOURS. The molecular weight of a gas or vapour is usually cal- culated from its density compared with that of a standard gas, hydrogen, oxygen, or air, at the same temperature and pressure. It is now customary to take the atomic weight of oxygen as 1 6, and as the molecules of this gas are diatomic, the molecular weight of oxygen = 32. The densities of gases and vapours were formerly almost invariably expressed in terms of that of air, but this method of comparison has the obvious disadvantage that air is a mixture of slightly variable composition and density. If Traube expresses much less confidence in his theory, and states his opinion that the phenomena observed at and near the critical point can best be explained by Bakker's purely physical theory (Zeit. phys. Chem., 49, 616 (1904)) of the broadening of the surface layer as the critical temperature is approached. 2 A 354 STOICHIOMETRV in a long vertical column of fluid at its critical temperature, when the mean density does not differ greatly from the critical density, has been proved on theoretical grounds by Gouy (p. 178), the reasoning being based on the almost infinite compressibility of a fluid at its critical point, and its very great compressibility in the neighbourhood of that point. An elegant and ingenious method of determining the densities at different levels of such a column of fluid, and of demonstrating their remarkable differences, has been devised by Teichner, 1 who places a number of minute coloured glass bulbs in the rather wide sealed tube containing the liquid under investiga- tion. The density of such a bulb depends on the ratio of the volume of glass to that of glass plus enclosed air, and this ratio is capable of great variation. The bulbs can be dis- tinguished by the shapes of the bits of capillary tubing left attached to them, and their densities are determined once for all by placing them in a liquid of very low specific gravity, such as isopentane, heating the liquid in a sealed tube, and observing the temperatures at which the bulbs sink. It is necessary to employ a liquid of high specific gravity for the experiments at and near the critical point, and Teichner chose carbon tetrachloride for the purpose. In his earlier experiments Teichner observed very great differences in density at different levels, and found that these differences persisted for many hours at temperatures far higher than that at which the meniscus disappeared. There was no doubt, however, that the carbon tetrachloride had not been purified with sufficient care, and it is probable that the removal of dissolved air was not complete. Even in the later experiments, in which great care was taken in purifying the liquid and removing air, much greater differences were observed for a considerable time in some cases than could be accounted for by Gouy's explanation. Teichner admits that after a sufficient length of time, or after stirring, the observed densities are not too great, and he attributes the extreme slowness with which the change to the final state of equilibrium occurred to the 1 Inaug. Dissert., Vienna, 1903; Ann. d. Phys. (4), 13, 595 (1904); also Traube, Zeit, anorg. Chern., 38, 399 (1904). DETERMINATION OF MOLECULAR WEIGHT 355 perfection of his method of heating the tubes. Other experi- menters place their tubes either in a bath of well-stirred liquid heated by a flame, or in the vapour from a boiling pure liquid ; Teichner places his tube in a rather wider one containing paraffin, and this is heated by the vapour from a boiling liquid. Teichner insists on the purity of his carbon tetrachloride both before and after being heated ; but there is reason to think that this substance undergoes very slow decomposition at high temperatures, such as 280 or 290; and Verschaffelt l has clearly shown that Teichner's results may be explained by the presence of a minute amount of permanent gas or very volatile impurity in the liquid. In any case, the question is merely that of the length of time required to bring about the final state of equilibrium, and it does not appear to the author that any sufficient reasons have been advanced for rejecting the simple theory of Andrews and Van der Waals. MOLECULAR ASSOCIATION. For the reasons which have been given in the preceding section of this chapter, it will be assumed that the molecules of what may be termed a normal liquid are simple, like those of its vapour ; but it has been pointed out that with some sub- stances, such as acetic acid, there is molecular association in the gaseous state, as shown by the changes in vapour density, and there must undoubtedly be association in the liquid state also. There are reasons, also, for believing that with some other substances, notably water and the alcohols, there is molecular association of some kind in the liquid state, though not in that of vapour. The criteria for the existence of molecular association have been discussed by Guye, 2 who refers especially to the following points : 1 Communications from the Physical Laboratory, Leiden, suppl., No. 10 (1904). 2 Archives des Sciences phys. et nat. t Geneva, (3), 31, pp. 38, 164, 463 (1894). 356 STOICHIOMETRY 1. The variation of the constant k in the equation yV 1 = k(r - A) from the mean value 2*12 (Ramsay and Shields, p. 634). Very low values, indicating a high degree of association, were observed in the case of water, the alcohols, and the fatty acids, moderately low values in the case of acetone, propionitrile, and nitroethane. In the homologous series of alcohols and fatty acids, the amount of association diminishes at a given temperature as the molecular weight increases, and in all cases the association diminishes as the temperature rises. 2. Molecular association at the critical temperature is indicated when the ratio of the actual to the critical density is much higher than 3*85 (p. 228). The four highest values observed were 4*986, 4*549, 4*024, and 3 '99 5 , respectively, for acetic acid, methyl alcohol, ethyl alcohol, and propyl alcohol. The values for the lower aliphatic esters are also somewhat high 3-862 to 3*944 and it seems not improbable that there may be a slight degree of association in these cases also. 3. According to the law of Cailletet and Mathias (p. 165), the mean densities of liquid and saturated vapour are a recti- linear function of the temperature. It has been shown by Young that the law requires modification to this extent that there is in most cases very slight curvature, the mean densities being accurately given by the formula s = s + *t+(Bt the coefficient /3 being very small. In the case of the alcohols, the curvature of the diameter is very marked, and a fourth term, y/ 3 , would have to be added to reproduce the mean densities at all satisfactorily. The simpler formula suffices for acetic acid ; but with this substance there is association not only in the liquid, but also in the gaseous state. The conclusion arrived at by Guye is that marked curvature indicates molecular association, but that the absence of marked curvature does not preclude the possibility of molecular association. DETERMINATION OF MOLECULAR WEIGHT 357 4. When there is no change in molecular complexity on the passage of a substance from the liquid to the gaseous state , the work done in vaporizing the liquid is wholly expended in overcoming the mutual attraction (cohesion) of the molecules and in causing expansion against external pressure. In such a case the heat of vaporization, L, always diminishes with rise of temperature. But when the molecules of vapour are less complex than those of the liquid, work is also required to over- come the selective or chemical attraction between individual molecules. An irregularity is thus introduced into the relation between heat of vaporization and temperature, and in the case of acetic acid the values of L show a well-defined maximum at about 110 (Ramsay and Young). Ethyl alcohol shows a similar but less striking maximum at about 10; and although no maximum has been observed in the case of methyl alcohol, it is not improbable that it may exist at some temperature lower than o C. Acetic acid. Ethyl alcohol. t L t L cal. o cal. 20 84-05 22O'9 50 88-14 10 221-2 80 91*59 2O 220-6 100 92-32 3 22O'I 110 92-79 40 2I8-7 120 92-71 5o 2l6'0 I 3 92-42 70 209-9 150 91-91 100 197-1 From these results Guye concludes that the heats of vapori- zation do not show a maximum unless there is molecular association ; but it is, of course, possible that there may be association when a maximum has not been observed. 5. Regnault l called attention in 1862 to the fact that the vapour-pressure curves of different substances do not usually cut each other, but that water, the alcohols, and acetic acid 1 Mem. Acad. Sc. Paris, vol. 26. 358 STOICHIOMETRY form exceptions to the rule. The question is discussed, in the light of more recent investigations, by Guye, who arrives at the general conclusion that when the vapour-pressure curve of a given substance cuts the curves for normal substances, the first substance is associated. It is more convenient, however, to consider the ratios of the boiling points (on the absolute scale) of the liquid to those of a normal substance at a series of equal pressures (Ramsay and Young, p. 142). If the relation T ' T* - 4- f(T ' T ^ r / ' rp T * *B -IfiJ J A A does not hold (where T B ' and T B are the boiling points of the T ' normal substance), in other words, if the relation between y and T B ' T B is not represented by a straight line, 1 it may be concluded that there is molecular association (or dissociation) in the case of the substance A. 6. It may also be noticed that for the alcohols, water, and acetic acid, the values of ~ X T at the boiling point under atmospheric pressure are very high. There is, however, con- dp siderable variation in the values of , X T among normal substances; thus for oxygen it is 6854, and for anthracene 9240. In a homologous series the value rises as the molecular weight increases ; for example, methane 7434, n-pentane 7980, n-octane 8415. For ethyl alcohol, water, and acetic acid the values are 10,660, 10,150, and 9357 respectively. 7. Dunstan and Thole 2 point out that the quantity viscosity _ *. ___ vx , ,-.6 molecular volume 1 If c has not an exceptionally high value, the somewhat more conve- rp 9 r*r\ nient equation * = _, A + f(T B '- T B ) may be employed without sensible IB IB error (p. 143). 2 Proc. Chem. Soc., 23, 19 (1907) ; Zeit.phys. Chem., 51, 732 (1905). DETERMINATION OF MOLECULAR WEIGHT 359 is nearly constant, namely, about 60 for the liquids which are generally regarded as unimolecular, but that for h'ydroxyl com- pounds, which are considered to be associated, the values are much higher ; thus Benzene 65 Chloroform 67 Carbon disulphide .... 60 Water 493 Methyl alcohol Ethyl Acetic acid . Glycerol . . 138 189 195 106,000 In many other respects the properties of water, the alcohols, and the fatty acids differ from those of normal substances, but with regard to the homologous series of alcohols and acids, it is to be noted that these differences become less marked as the molecular weight increases. It seems probable that with these substances the tendency for molecular association to occur is due to the presence of the hydroxyl group, and that the in- fluence of this group becomes less marked as the complexity of the alkyl or other group increases. MOLECULAR WEIGHTS OF DISSOLVED SUBSTANCES. The methods of determining molecular weights so far described are not generally applicable to substances which are only volatile at very high temperatures, or which decompose when vaporized. Such substances may, in most cases, be dissolved in water or some other solvent, and the following methods are now known by which their molecular weights may be determined : i. From the Osmotic Pressure. Let m grams or ^ gram- molecules of a substance be present in one litre of solution, and call the osmotic pressure, measured in atmospheres, p It has been shown that for i gram-molecule p x v = 0*082 iT litre-atmos. therefore for ^j gram-molecules P m v = o'o82iT X TT M 360 STOICHIOMETRY If v = i litre, then and M = 0*082 iT x But the direct measurement of osmotic pressure is difficult, and is rarely employed in practice. 2. From the Depression of the Freezing Point. Let m grams of a substance be dissolved in 100 grams of solvent, and call the observed depression of the freezing point A Then M = E * (Raoult) where E' is the molecular lowering of the freezing point of the particular solvent employed, and M is the molecular weight of the dissolved substance. Also E' = - (Van't Hoff) where T is the melting point of the solvent on the absolute scale of temperature, and L' is its heat of fusion in gram- calories. Values of E' for a few useful solvents are given on p. 306, and the apparatus required is shown in Fig. 76. 3. From the Lowering of the Vapour Pressure, It was found by Raoult (p. 308) that for dilute solutions where / and /' are the vapour pressures of solvent and solution respectively at the temperature of observation, and N and n the relative number of molecules of substance and solvent. Let m grams of substance be dissolved in 100 grams of solvent ; then AT m I0 N = M and *= M' DETERMINATION OF MOLECULAR WEIGHT 361 where M and M' are the molecular weights of solute and solvent respectively. N _ __ Then 7i ~ i ooM - P< 4. From the Rise of the Boiling Point. Let m grams of substance be dissolved in 100 grams of solvent, and call the observed rise of boiling point A/; then E X m M = -^- and, as shown by Van't Hoff 0-02T 2 ~L~ where T is the boiling point of the solvent on the absolute scale of temperature, and L is its heat of vaporization in gram- calories. Values of E for a number of useful solvents are given on p. 3 1 1, and the apparatus required is shown in Figs. 77 and 78. 5. From the Diminution in Solubility of one Solvent in another. Consider two liquids such as ether and water, miscible only within comparatively small limits, and call the solubility of pure ether in water j at the temperature of observation. Let ;;/ grams of a substance be dissolved in 100 grams of ether, and call the solubility of the impure ether in water S' at the same temperature, and the molecular weights of sub- stance and ether M and M' respectively ; then M = MlX_ w x S/ (Nernst, p. 326) ioo S - S DISSOCIATION, MOLECULAR ASSOCIATION, AND ELECTROLYTIC DISSOCIATION. The molecular weights of many substances may be deter- mined by several of the methods described : (i) from their chemical behaviour, (2) in the gaseous state, (3) in the liquid 362 STOICHIOMETRY state, and (4) in solution ; and the same value is frequently found by each method. There are, however, numerous cases in which discordant results are obtained. For example, from the chemical properties of acetic acid, together with its per- centage composition, chemists are led *to adopt the molecular formula C 2 H 4 O 2 , and the molecular weight corresponding to this formula is 60 (approximately). Determinations of the vapour density of acetic acid at high temperatures and low pressures give the constant value 30, and the molecular weight 60; but at low temperatures higher values are obtained, and from the curve (Fig. 87, p. 343) it is clear that the density of the saturated vapour would reach, if not exceed, the double value 60, corresponding to the mole- cular weight 120 and the formula C 4 H 8 O 4 . In the liquid state, a very high factor of association has been observed by Ramsay and Shields at low temperatures (x = 2-13 and M = 137*8 at 20). The molecular weights of acetic acid calculated from the depression of the freezing points and the rise of boiling points of solvents are very variable, depending on the concentration of the solutions, and still more on the nature of the solvent. Thus with benzene as solvent, and when the solution is not too dilute, the molecular weight 120 is obtained; with ether the molecular weight 60 ; while with water, when the solution is very dilute, the value 30 is obtained. As already stated, the high values are in all probability to be explained by the association of the chemical molecules C 2 H 4 O 2 or CH 3 .COOH. It is known that oxygen, although usually divalent, acts in some cases as a tetravalent element, and such formulae as CH 3 C OH CH 3 OH ii X o c o o HO\ f~* p. ^ f* ..CH 3 CH 3 C OH CH 3 > < OH and so on, are possible. DETERMINATION OF MOLECULAR WEIGHT 363 But the lower molecular weight, 30, indicates dissociation or decomposition; and as the acetic acid can be recovered from the dilute solution, the change must be one of dissociation rather than decomposition. Many oxy-acids, when heated, break up into the anhydride and water; but acetic acid can be strongly heated without undergoing this change, and it is only by the action of a powerful dehydrating agent that the anhydride can be prepared from the acid. It is exceedingly unlikely that such a change would occur in dilute aqueous solution ; and, in any case, no explanation of the facts would be afforded by it, for the number of molecules must be doubled to reduce the apparent molecular weight to one-half, whereas the formation of anhydride and water from the acid is expressed by the equation 2 CH 3 .COOH = (CH 3 .CO) 2 + H 2 O The amount of solvent, water, would be slightly increased, and the number of molecules of anhydride would be only half as great as the number of molecules of acid. A similar difficulty arises in the determination of the mole- cular weights of strong mineral acids and bases, and of salts derived from them. Thus the molecular weight of hydro- chloric acid calculated from the freezing point or boiling point of a dilute aqueous solution is only half as great as that calcu- lated from the chemical formula HC1, that of sulphuric acid is only one-third, and so on. But the equations which represent the dissociation which these substances suffer on heating are 2HC1 = H 2 + Cl a and H,SO 4 = SO 3 + H 2 O respectively. With hydrochloric acid there is no change in the number of molecules, and with sulphuric acid the number is only doubled. Moreover, in a dilute solution of hydrochloric acid there is certainly no free hydrogen or chlorine present. Theory of Electrolytic Dissociation. It was observed that those substances which cause abnormally large alterations in the freezing point, boiling point, and vapour pressure of water behave as electrolytes in aqueous solution, while others, 364 S TOICHIOME TR Y such as the sugars and many other organic compounds, which produce the normal effect when dissolved in water, do not act as electrolytes. Again, while pure water and pure liquefied hydrogen chloride are non-conductors of electricity, aqueous hydro- chloric acid conducts electricity freely, hydrogen gas being evolved at the negative pole and chlorine l at the positive pole. On the other hand, carbon tetrachloride is not an electrolyte either in the pure (liquid) state or when dissolved in dilute alcohol (it is practically insoluble in water). When an aqueous solution of silver nitrate is added to aqueous hydrochloric acid, a precipitate of silver chloride is at once formed ; but when added to a solution of carbon tetra- chloride in dilute alcohol, no change whatever occurs. In the light of these and other facts, Arrhenius 2 was led to his theory of electrolytic dissociation. According to this theory, when a substance such as carbon tetrachloride, which is not an electrolyte even in solution, is dissolved in water (water and alcohol in this case), no decomposition or dissociation occurs ; the molecules of dissolved carbon tetrachloride differ in no respect from those of the substance in the gaseous state. On the other hand, when hydrogen chloride is dissolved in water, some of the molecules of the chloride are at once dis- sociated, not into ordinary atomic hydrogen and chlorine, but into tons, that is to say, into atoms of these elements endowed with very large electrical charges. So long as the atoms retain these charges, they do not behave like free atoms ; but when the solution is electrolyzed, the hydrogen ions carry their positive charges to the negative electrode, and, giving ' them up, become free atoms, which unite together to form diatomic molecules of gaseous hydrogen. Similarly the chlorine ions travel to the positive electrode and surrender their negative charges, and the atoms of chlorine then either unite together to form molecules or they act on the water, forming oxyacids of chlorine or hydrochloric acid and free oxygen. 1 From strong solutions ; when the solution is dilute, the nascent chlorine may act chemically on the water. 2 Zeit. phys. Chetn., 1, 631 (1887). DETERMINATION OF MOLECULAR WEIGHT 365 In the case of very dilute aqueous solutions of hydrochloric acid, the molecular weight of the acid calculated from the depression of the freezing point of the water has half the normal value, and it is concluded that electrolytic dissociation is complete or very nearly so j that there are, in fact, very few, if any, molecules of dissolved hydrogen chloride, but only hydrogen and chlorine ions. With stronger solutions the calculated molecular weight is somewhat higher, but still far below that corresponding to the formula HC1, and it is con- cluded that dissociation is not complete. So also with other strong acids, with strong bases, and with salts derived from them, and even with salts derived from strong acids and weak bases or strong bases and weak acids ; in very dilute aqueous solution the molecular weight calculated from the depression of the freezing point or the rise of the boiling point is in general a simple sub-multiple of that corre- sponding to the molecular formula. In all such cases it is concluded that complete or nearly complete electrolytic dis- sociation occurs. Thus, in dilute aqueous solution Number of ions from mole- cule of acid, base, or salt. NaCl = Na- + Cl' 2 HN0 8 = H- + NO; , . 2 AgN0 3 = Ag- + N0 3 ' 2 KOH = K- + OH' 2 FeS0 4 = Fe" + S0 4 " 2 Na 2 SO 4 = 2Na-f-SO 4 " ...... 3 K 2 Q0 4 = 2 K- + Q0 4 " 3 K 4 Fe(CN) 6 = 4 K- + Fe(CN) B ' 1 ' 5 and so on The dot, ', represents the -f sign ; the dash, ', the - sign. In the case of weak acids, weak bases, and the salts derived from them, the molecular weights (M') calculated from the depression of the freezing point or the rise of the boiling point approach more closely to those (M) corresponding to the chemical formulae, and it is believed that electrolytic 366 S TQICHIOME TR Y dissociation is incomplete, the solutions containing both undis- sociated molecules and ions. Let n be the number of ions derived from one molecule of substance, and x the fractional number of molecules dissociated; then (M-M^ ~ (n - i)M' It is believed that the changes which are observed in quali- tative analysis take place through interaction of the ions, and not of the molecules. Thus when aqueous solutions of silver nitrate and hydrochloric acid are mixed together, the formation of insoluble silver chloride is expressed by the equation Ag' 4- N0 3 ' + H- 4- Cl' 4- Aq = AgCl + H- + NO 3 ' 4- Aq. If none of the substances which would be formed by such a reaction are insoluble, no change at all takes place. Again, on adding silver nitrate to a solution of carbon tetrachloride in dilute alcohol, the substances present are Ag- 4- NO 3 ' 4- CC1 4 4- Aq(+ alcohol) and no reaction is possible. The theory of electrolytic dissociation is supported by the following, among other considerations : i. When equivalent quantities of strong acids and bases are mixed together in dilute aqueous solution, the amount of heat evolved is almost independent of the nature of the acid or base. According to the theory, the reactions which occur are expressed by such equations as the following : H- 4- Cl' 4- Na- + OH' = Na- + Cl' + H 2 O H- + N0 3 ' 4- K- + OH' = K- 4- NO 3 ' + H 2 O {2H- + SO 4 " + 2Na- + 2(OH)' = 2Na* + SO 4 " + 2H a O} f{ 2 H- + 2C1' 4- Ca" + 2(OH)' = Ca- + 2C1' + sH.O) The change combination of hydrogen with hydroxyl to form water is the same in each case. DETERMINATION OF MOLECULAR WEIGHT 367 On the other hand, with a weak acid and a weak base, the amount of heat evolved is smaller ; and this is accounted for by the assumption that the solutions contain not only ions but undissociated molecules. The number of hydrogen and hydroxyl ions which unite to form water is therefore smaller. For details of this subject, see Thomsen's " Thermo-Chemistry/' translated by Miss Burke (this series). 2. The molecular (electrical) conductivity of an electrolyte may be denned in the following manner : Imagine a vessel formed of two very large electrodes i cm. apart, the other two walls and the bottom of the vessel being formed of non-conducting material. Let an aqueous solution containing one gram-molecule of the electrolyte be placed in the cell. The conductivity of the system will then be called the molecular conductivity of the electrolyte. 1 The molecular conductivity depends on the substance and on the temperature, increasing about 2 per cent, per degree. For a given substance at constant temperature it increases with the dilution, the increase being small with good conductors, but considerable with bad ones. In all cases it approximates with increase of dilution to a limiting value, which can be reached in practice with good conductors, but not with bad ones. If the electricity is conveyed by the ions, the conductivity of a given electrolyte must be proportional to the number of ions present; and it is believed that when the maximum molecular conductivity is reached in very dilute solutions, electrolytic dissociation is complete. It was discovered by Hittorf in 1853 that when aqueous solutions of different substances are electrolyzed, the change in concentration in the neighbourhood of the two electrodes is usually different, and in order to explain the facts he advanced the theory that the velocities of migration of the ions are different. He showed, also, how the relative velocities could be calculated from the relative changes in concentration. Kohlrausch, in 1 For a full account of the methods of determining molecular con- ductivity, and of the results obtained, see Lehfeldt's " Electro-Chemistry " (this series). 3 68 STOICHIOMETR Y 1876, pointed out that the conductivities of salts, acids, and bases may be regarded as the sum of two values, one depend- ing on the positive, the other on the negative ion ; and that, when dissociation is complete, the conductivity of electrolytes afford a measure of the relative velocities of migration of the ions. In the following table the conductivities of equivalent quantities of a few electrolytes are given for different states of dilution at the same temperature : Conductivity. Dilution. KC1. NaCl. K 2 S0 4 . MgS0 4 . litres. 91-9 69-5 6 7 -2 27-0 10 1047 86-5 897 47 '4 IOO 1147 9 6-2 109-8 yi'5 I,OOO 119-3 100-8 1207 93'5 10,000 I20'9 102-9 124-9 103-4 50,000 I2I-7 1 02 '8 I26-Q 105-2 100,000 121*6 102*4 127-5 105*6 In each case the conductivity is nearly constant for the three highest states of dilution, and the mean of the three values maybe taken as the maximum; namely, KC1, 121-4; NaCl, 102-7; |K 2 SO 4 , 126-1; fMgSO 4 , 104-7. With solutions of potassium chloride the concentration is very nearly the same at both electrodes, and it is therefore concluded that the velocity of migration of the K and Cl ions is the same. Adopting the arbitrary value 1 21 -4 = 60-7 as the velocity of these ions, that of the Na ions, 102*7 60*7 = 42 ; of the SO 4 ions, 126'! 607 = 65*4; and of the Mg ions, 105-6 - 607 = 44-9. The conductivity of the strong acids and bases is greater than that of salts; thus for HC1 the maximum value is about 346 ; hence the velocity of the H ions is about 346 61 = 285, and that of the OH ions, derived from the conductivity of potassium hydroxide, about 154. DETERMINATION OF MOLECULAR WEIGHT 369 Strong acids and bases obey the law of Kohlrausch, but weak acids and bases do not ; and it has already been stated that the dissociation of these substances appears to be incom- plete. On the other hand, the law applies to salts derived from strong acids and weak bases, or from weak acids and strong bases, and the velocities of all the ions can therefore be determined. If ju, is the molecular conductivity, and u and #' are the velocities of migration of the ions, the equation ju, = u -f- u' holds for very dilute solutions of strong acids and bases and of salts derived from a strong acid or a strong base ; but for stronger solutions of these substances and for dilute solutions of weak acids and bases and of salts derived from them the equation should be written where x is the fractional number of molecules dissociated. If the solution is infinitely diluted, dissociation is complete, and jU-oc = U + I/ It would, of course, be impossible to directly determine the conductivity of a solution of infinite dilution ; but, as already stated, the values of u and u' may be indirectly deter- mined for all ions, and thus the value of p x may be ascer- tained. From the two equations //, = x(u -f rf) and /x, K = u + */ the degree of electrolytic dissociation may be calculated, for The values of x determined in this way agree satisfactorily with those calculated from the depression of the freezing point and the rise of the boiling point. From what has been mentioned with regard to the influence 2 B 37o STOICHIOMETRY of temperature on the solubility of salts (p. 296), it follows that in strong solutions there may be at the same time (a) ions formed by electrolytic dissociation, (Z>) molecules of the anhy- drous salt, (V) molecules of the salt in one or more states of hydration. NOTE. An important memoir by E. Buckingham, "On the Establish- ment of the Thermodynamic Scale of Temperature by means of the constant pressure Thermometer" (Bulletin of the B^lrea^l of Standards, Washington, vol. iii., p. 237, 1907), has just been received by the author (Nov. 28th, 1907). Buckingham makes use of the recent measurements of the specific heat of nitrogen by Holborn and Austin (Phys. Rev.) 21, 209, 1905), and, as a result of his own calculations and of those of D. Berthelot, he deduces the value 273' 13 for the melting point of ice on the centigrade thermodynamic scale of temperature. This value is slightly higher than that obtained by D. Berthelot, 273*09 (p. 39). NAME INDEX Adams, 4 Adie, 318, 319 Aitken, 206, 333 Alexeeff, 294, 296, 328, 330, 335 Altschul, 177 Amagat, 19, 26, 29, 33, 124, 135, 161, 165, 202, 204, 215, 235, 240, 351 Ampere, 48 Andrews, 122, 126, 132, 152, 170, 286, 352, 355 Arrhenius, 324, 364 Avogadro, 47, 48, 58, 187, 230, 340 B Babo, von, 307 Bakker, 353 Baly, 28, 30, 33 Barrell, 278 Bartoli, 51 Barus, 27, 204 Battelli, 31, 33, 126, 175, 353 Baynes, 202 Beckmann, 305, 310, 311 Becquerel, 3, 4 Behn, 153 Berkeley, Earl of, 322 Bernini, 249 Bernoulli, 48, 185 Berthelot, 53, 151, 266 Berthelot, D., 15, 35, 38, 50, 78, 88, 89, 168, 215, 229, 232, 237, 254, 262, 293, 340, 351 Berthollet, 5 Bertrand, 143 Berzelius, 71 Biot, 129, 213 Black, 148 Blagden, 304 Bodenstein, 119 Bohr, 30, 33 Boltzmann, 185 Bondin, 36 Boyle, i, 12, 186, 229, 321, 340 Braak, 24 Braun, 298 Bredig, 310 Bremer, 307 Brillouin, 237 Briner, 115 Brix, 152 Brown, F. D., 261, 265, 266 Brown, J. C., 153 Burke, 367 Cagniard de la Tour, 170 (~!jiliniir<:. TT*7 Cahours, 117 t, 19, 165, 170, 181, 238, 1 A tt(\ 371 Cailletet, .-,, .. 286, 334, 356 Cannizzaro, 249 372 INDEX Carnelley, 91, 243 Carveth, 266 Caubet, 282, 284 Cavendish, 46 Centnerszwer, 295 Chappuis, 36, 38, 49, 152 Charles, 14, 230 Chatelier, le, 53 Clapeyron, 148 Clarke, F. W., 70, 75, 79, 83, 86 Clausius, 148, 185, 189, 190, 206, 215, 234 Clement, 54 Cooke, 73, 76 Coppet, de, 304 Crafts, 42, 119, 158 Crismer, 295 Curie, M. and Mme., 3, 4 Dale, 258 Dalton, 5, 8, 13, 48, 58, 253, 293 Damien, 241 Davies, 88 Davila, 88 Democritus, 8 Desormes, 54 Despretz, 154 Deville, 114, 116, 120, 195 Dewar, 150, 153, 240, 286, 303 Dieterici, 215 Dittmar, 72, 75, 76 Dixon, H. B., 89 Donnan, 326 Duhring, 142 Duhem, 274, 282 Dulong, 65, 71, 247 Dumas, 43, 71 Dunstan, 358 E Edgar, 89 Elsasser, 160 Emden, 307, 309 Eotvos, 346 Erdmann, 73 Estreicher, 153 Eve, 4 Favre, 152 Ferche, 243 Find lay, 302 Fischer, 243 Fortey, 263 Friedel, 273 Gahl, 266 Galitzine, 175, 176, 293, 353 Gally-Cazalat, 20 Gamier, 249 Gartenmeister, 160 Gay-Lussac, 13, 35, 44, 46, 48, 52, 58, 230, 306, 321, 340 Gladstone, 258 Goosens, 240 Gouy, 178, 288, 354 Graham, 251 Gray, 88, 89 Griffiths, 152, 322 Guldberg, 183 Guthrie, 263, 300 Guye, 88, 177, 355, 356, 358 H Hannay, 176 Harker, 249 Hartley, 322 Hartmann, 282 Keen, de, 175, 176, 353 Helmholtz, von, 307, 309 Henderson, 72, 75, 76 INDEX 373 Henry, 293 Heydweiller, 2 Hittorf, 367 Hoff, van't, 305, 310, 320, 360, 3 6i Hofmann, 43 Homfray, 303 Hudson, 295 Humboldt, 46 Irvine, 148 Jahn, 152 Jaquerod, 33, 36, 49, 88, 89 Joly, S3, '53 Joule, 52, 200, 231 K Kahlenberg, 152, 323 Keiser, 73 Kelvin, Lord, 52, 200, 231, 240 Kirchhoff, 243 Kohlrausch, 367, 369 Konowalow, 269, 309 Kopp, 1 60, 250 Kroenig, 185 Kuenen, 282, 283, 285, 286, 289, 290 Kundt, 54, 61, 189 Landolt, 2, 258 Landsberger, 312 Laplace, 54 Leduc, 33, 43, 50, 75, 76, 77, 87, 89, 253 Lehfeldt, 265, 274, 367 Lemoine, 118 Leucippus, 8 Linebarger, 266 Lorentz, 258 Lorenz, 258 Louguinine, 152 Lucretius, 8 Ludlam, 312 Lumsden, 312 M Makower, 36 Mallard, 53 Mallett, 177 Marchand, 73 Margules, 274 Mariotte,' 12 Marks, 36 Marshall, 152 Masson, 294, 328, 330, 335 Mathias, 152, 153, 161, 165, 170, 175, 176, 181, 227, 238, 334, 351, 356 Maxwell, 185, 190 Meier, 119 Melsens, 72 Mendeleeff, 29, 91, 97, 102, 112, 164, 170 Mettler, 115 Meyer, K. 237 Meyer, L., 79, 83, 91, 97, 102 Meyer, O. E., 190, 200 Meyer, V., 43, 45 Mills, J. E., 129, 153, 201, 212 Mitscherlich, 65 Mond, 302 Morley, 43, 47, 48, 69, 72, 75, 76, 77,87 Morren, 115 Moser, 307 N Natanson, E. and L., 120, 196 Natter er, 19 374 INDEX Naumann, 261 Nernst, 315, 326, 361 Neumann, 249 Newlands, 91 Nilsson, 112, 249 Noble, 36 Noyes, 74, 76 Onnes, Kamerlingh, 24, 27, 36, 215, 282 Ostwald, 79, 81, 86, 256, 309 Olszewski, 236 Pawlewski, 181, 290 Pebal, u 6 Perkin, 159 Perman, 88 Perrot, 36 Petit, 65, 247 Pettersson, 112, 249 Pfeffer, 317, 318, 319, 320, 332 Pictet, 155, 286 Pierre, 160 Plaats, van der, 83 Porter, 143 Pouillet, 19 Preston, 53, 148 Princep, 306 Pringsheim, 319 Proust, 5 Ramsay, 4, 27, 28, 30, 33, 44, 45, 67, 112, 117, 120, 139, 142, 152, 1 5S> !5 6 189, 196, 204, 207, 2 43, 286, 302, 340, 346, 349, 350, 356, 357, 358, 362 Raoult, 304, 307, 308, 360 Raveau, 237 Rayleigh, Lord, 18, 32, 33, 34, 42, 43, 49, 73, 74, 76, 87, 185, 201, 340 Regnault, 19, 33, 35, 36, 42, 71, 141, 148, 152, 242, 260, 357 Reinganum, 215 Richards, 36, 73, 76, 89 Richardson, 121, 195 Richter, 6 Robinson, 117 Rontgen, 54 Roozeboom, 302 Roscoe, 273, 280 Rose-Innes, 204, 215 Roth, 27 Rothmund, 294, 334, 336 Rowland, 51 Riiber, 312 Riicker, 183 Riidorff, 304 Rutherford, 3, 4 Ryland, 273 Sacerdote, 33, 50, 87, 89, 254 Schalkwijk, 27 Schuster, 4 Scott, 47, 77, 89 Seubert, 79, 83 Shearer, 153 Shenstone, 298 Sheuer, 33, 49, 88, 89 Shields, 302, 346, 350, 356, 362 Silbermann, 152 Siljestrom, 29 Smiles, 247 Smits, 312 Soddy, 3, 4 Sorby, 298 Sprengel, 159 Stas, 79, 83, 85, 86, 89 Steele, 44, 340 Stefan, 190 INDEX 375 Stewart, 247 Stracciati, 51 Tait, 8, 215 Tammann, 307, 320 Teichner, 354 Than, 116 Thiesen, 31 Thole, 358 Thomas, 161, 278 Thomsen, 75, 76, 83, 367 Thomson, J., 239, 242, 244 Thomson, W. v. Lord Kelvin Thorpe, 1 60, 170, 183 U Usher, 172, 176 Ven, van der, 30 Verschaffelt, 282, 355 Vieille, 53 Visser, de, 240 Vries, de, 319 W Waals, van der, 27, 78, 185, 199, 201, 203, 215, 216, 229, 236, 262, 282, 286, 322, 341, 353, 355 Walker, 307, 310, 312 Wanklyn, 117, 266 Warburg, 61, 189 Waterston, 185 Watt, 148 Weber, 248 Wells, 89 Wenzel, 5, 6 Will, 310 Winkelmann, 266 Wirtz, 153 Witkowski, 24, 25 Wollaston, 7, 9 Worthington, 205 Wroblewski, 286 Wiillner, 307 Wurtz, 117, 118 Young, S., 27, 45, 117, 120, 127, 139, 142, 156, 161, 165, 173, 176, 180, 196, 204, 207, 218, 227, 235, 243, 262, 265, 278, 286, 351, 356, 357, 358 Young, Thos., 145 Zambiasi, 175, 176 Zander, 160 Zawidski, 259, 263, 265, 267, 273, 275 Zoppi, 295 SUBJECT INDEX Absorption of gases by solids, 302 Acetic acid, dissociation of, 120, 198 Acids, aliphatic, abnormal behav- iour of, 154, 156, 220, 229, 260, 272, 342, 347, 35 , , molecular association of, 144, 203, 221, 260, 273, 350, 355 Alcohols, abnormal behaviour of, 154, 156, 158, 167, 220, 229, 260, 272, 341, 346, 347, 350 , molecular association of, 144, 203, 221, 260, 273, 350, 355 Ammonia gas, effect of sparking, 1 14 Ammonium chloride, dissociation of, 115 Amyl bromide (tertiary), dissocia- tion of, 117 Association factor, 349, 362 Association, molecular, 144, 203, 221, 260, 273, 350, 355, 361 Atomic heat, 65, 245 theory, 8 volumes, 91 of elements, table of, 92 weight and equivalent, 56 weights, 9, 56, 86 - , determination of, 56, 68 , table of, 92 Attraction, molecular, 199, 255 Attraction, molecular, variation of, with distance, 154 Avogadro's hypothesis, 47, 187, 230 B Boiling point, correction of, to normal pressure, 157 -- , definition of term, 141 , determination of, 139 -- of pure liquid, 136 relations, 142, 358 points of dilute solutions, 310, of mixed liquids, 263, 271 of non-miscible liquids, 260 Border curves, 283 Boyle's law, 12, 186 , deviations from, 18, 229 Bromine, atomic weight of, 84 Cailletet and Mathias' law, 165, 334, 356 Carbon dioxide, dissociation of, 115 ! Carbon monoxide, dissociation of, "5 Characteristic states of matter, 229 Chlorides of elements, 99 Chlorine, atomic weight of, 83 377 378 INDEX Coefficient of expansion of gases, 25, 35 of increase of pressure, 26, 35 Combination, laws of chemical, I Composition of liquid and vapour phases, 266, 274 of vapour from non-miscible liquids, 260 Compounds, I Compressibility of gases, 19, 29 Conductivity, molecular, 367 Conservation of matter, i Constant, R, for perfect gases, 50 Corresponding temperatures, pres- sures, and volumes, 216 Critical constants, calculation of, 213 of mixed liquids, 282 - density, 167, 354 , actual and theoretical, 225, 228, 235, 238, 356 point, 170 pressure, 177 and composition of mixtures, 289 solution point, 293 temperature, 294, 328 temperature, 123, 172, 353 and boiling point, 181 and composition of mixtures, 289 volume, 167, 178 Cryohydrates, 300 Crystalline form, 245 Crystals, mixed, 301 Definite proportions, law of, 5 Densities of gases and vapours, 40, 60 Densities of liquids, 159 of saturated vapours, 164 of mixtures, 256 Density, critical, 167, 354 Despretz, law of, 154 Diffusion of gases, 251, 314 of liquids, 313 Dilatation, coefficient of, 25, 35 Dissociation, electrolytic, 361 factor, 369 of gases and vapours, 114, 190, 193, 36i Dissolution and vaporization, 328 Distillation of mixtures, 277 Dulong and Petit's law, 65, 247 Electrolytic dissociation, 361 , theory of, 363 Element, definition of term, 2 Elements, I , electrochemical character of, 97 , physical properties of, 91, 100 , valency of, 100 Equivalent, 9 and atomic weight, 56 , definition of term, 7 weights, law of, 6 Error, probable, 69 Errors constant, 69 ,, experimental, 68 Eutectic mixtures, 299 Expansion, coefficient of, 25, 35 Freezing point of dilute solutions, 304. 3 60 of mixed liquids, 299 Gallium, atomic weight of, 66 Gas constant, R, 50 INDEX 379 Gaseous and liquid state, continuity of, 204 states of matter, 352 state of matter, 1 1 Gases, compressibility of, 19, 29 , densities of, 40, 60 , dissociation of, 114, 190, 193 , general properties of, 1 1 , kinetic theory of, 185, 199 , perfect, 18, 37 , specific heat of, 5 1 under high pressures, 18, 199 under very low pressures, 28 Gay Lussac's law, 13 , deviations from, 1 8, 230 of volumes, 46 H Halides of elements, 99 Heat, atomic, 65, 245 of neutralization, 366 of vaporization, 146, 357 , calculation of, 148, [48 -, determination of, , specific, v. specific heat. Hydrides of elements, 99 Hydrogen, density of, 43, 77 iodide, dissociation of, 118 , molecular weight of, 50, 60 Iodine, atomic weight of, 84 , dissociation of, 119 Isochors, 204, 208 Isomorphism, 65, 301 J Joule's law, deviation from, 231 Joule-Thomson effect, 231 K Kinetic theory of gases, 185, 199 Liquefaction, 122 Liquid state of matter, 1 1 Liquids, boiling points of, 136 , densities of, 159 , heats of vaporization of, 146 , general properties of, 122, 159 , specific volumes of, 159 , surface tension of, 144, 346, 356 , vapour pressure of, 124 Lithium, atomic weight of, 85 M Melting point, 239 Minimum values of pv, 23 Miscibility of liquids, 255, 293 Mitscherlich's law, 65 Mixtures, 251 of constant boiling point, 272 freezing point, 300 of maximum or minimum vapour pressure, 269 Molecular association, 144, 203 221, 260, 273, 350, 355, 361 attraction, 199, 255 , variation with distance, 154 weights, determination of, 337 of dissolved substances, 359 of gases and vapours, 48 60, 339 of liquids, 346 of saturated vapours, 341 of substances at critical point, 341 3 8o INDEX Molecule, 58 Molecules, actual volumes of, 168, 199, 200 Multiple proportions, law of, 5 N Neutralization, heat of, 366 Nitrogen, atomic weight of, 85, 87, 90 , density of, 43 - , molecular weight of, 50 peroxide, dissociation of, 120, 192 Octaves, law of, 91 Opalescence at critical point, 172 at critical solution point, 334 Orthobaric volumes of liquid, 160 of saturated vapour, 164 Osmosis, 313 Osmotic pressure, 316 and molecular weight, 359 and vapour pressure, 328 , direct measurement of, 317 , indirect measurement of, 326 , laws of, 320' Oxides of the elements, 104 Oxygen, atomic weight of, 63, 71 , density of, 43, 49, 76, 77 , equivalent of, 71 Path, mean free, 189 Periodic law, 91 Periodic table, 103, 104 , utility of, 112 Phosphorus pentachloride, dissocia- tion of, 117 Plait point, 285 curves, 285 Potassium, atomic weight of, 84 Pressure, coefficient of increase of, 26, 27, 35 , critical, 177 , differential of, 26, 27 -, vapour, v. vapour pressure. Pressure- volume diagram, 122 , theoretical, 204 Pressures, law of partial, 253, 293 Proportions, law of definite, 5 , of multiple, 5 Quantivalence, 56 R Radium, 3 Refractive power, 258 Retrograde condensation, 286 Semipermeable diaphragms, 314, 316 Silver, atomic weight of, 79 Sodium, atomic weight of, 85 Solid state of matter, 1 1 Solidification of mixed liquids, 298 Solids, melting points of, 239 , properties of, 239 , specific heat of, 247 , vapour pressures of, 242 , volatilizing points of, 243 Solubility and miscibility, 292 , diminution of, 326, 361 of gases in liquids, 292 INDEX 38i Solubility of solids in liquids, 296 Specific gravity of elements, table of, 92 of liquids, 159 heats of gases, 5 1 of mixed liquids, 257 of solids, 245 of elements, 65 , ratio of, 54, 188 solution volume, 329 volumes of liquids, 159 of mixed liquids, 257 Vapour pressure, determination of, 130 pressures of dilute solutions, 306, 360 of mixed liquids, 262, 268 of non-miscible liquids, 262, 268 of solids, 242 >, saturated, densities of, 164 , , specific volumes of, 164 of saturated vapours, 164 | Velocities, Maxwell's law of, 190 State, equation of, 201 , of, reduced, 215 Sulphur, atomic weight of, 84 dioxide, dissociation of, 115 Sulphuric acid, dissociation of, 117 Surface tension, 144, 346, 356 Temperature, absolute scale of, 15 , critical, 123, 170 , measurement of, 14 of dissociation, 191 Triple point, 242 Trou ton's law, 155 V Valency of elements, 100 Vaporization, heat of, 146, 357 , - , calculation of, 148, 153 , , determination of, 148 of mixed liquids, 260 Vapour densities, 40, 60 , abnormal, 115 , determination of, 43 pressure, 124 curves, 128, 357 Velocity of migration of ions, 368 Viscosity and molecular volume, 358 Volatilization of solids, 243 Volume, critical, 167, 178 of molecules, actual, 168 Volumes, atomic, 91 - , Gay Lussac's law of, 46 , specific, v. specific volumes W Waals, Van der, theory of, 199 , , equation of, 201 , , generalizations of, 216 , - , of, deduc- tions from the, 223 , - , of, graphical representation of the, 225 , ; of, modifica- tions of the, 236 Water, abnormal behaviour of, '54. I5 6 IS 8 , 260, 272, 347, 350 , composition of, 71, 76 , formula for, 59 , molecular association of, 144, 203, 260, 273, 350, 355 vapour, dissociation of, 114 PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLES. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. BIOLOGY LIBRARY 1938 APR 6 MAY t LD21-5m-7,'33 RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (510)642-6753 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW DD20 15M 4-02