UC-NRLF O XT CM O GIFT OF MICHAEL REESE ON THE CALCULATION OF THERMO-CHEMICAL CONSTANTS H. STANLEY REDGROVE, B.Sc. (LOXD.), F.C.S. LONDON EDWARD ARNOLD 1909 [All rights reserved] QD5// PREFACE THE following monograph has its origin in several short papers, published by the author in the Chemical News (see Chemical News, xcv, 193, 301 ; xcvi, 188 ; xcvii, 183, 253, and 266 ; xcviiL 25 and 80). The earlier papers have been rewritten to some extent, and considerably amplified. Some entirely new sections will be found as well, namely, those dealing with the calculation of thermal constants for sulphur and for nitrogen compounds. In the opening chapter of this work e On the Cal- culation of Physico-Chemical Constants ' the author puts forward a proof that the usually adopted method of calculating ' additive ' physico-chemical constants is fundamentally wrong, and outlines a more logical method. The rest of the work is concerned with the application of this method to thermal constants. The study of the thermal behaviour of polymethylenes leads to important evidence for the validity of von Baeyer's Strain Theory. Thomsen's method of cal- culating thermal constants, not coming under the objections mentioned in the first chapter, but, never- theless, being unsatisfactory, is dealt with briefly in an Appendix. The unit of heat employed throughout is the large calorie, written Cal. (1 Gal. = 1,000 cals.). As a rule 284514 iv PREFACE the figures given are correct to the first decimal place, i. e. jo Cal. only, as the second place is beyond the limit of experimental accuracy. The abbreviations M. H. C. for molecular heat of combustion, and M. II. F. for molecular heat of forma- tion, are used occasionally throughout this book. The author's heartiest thanks are due to Mr. F. E. Weston, B.Sc. (Lond.), F.C.S., for his kind help in reading the proofs, &c. H. S. R. January, 1909. CONTENTS PAGE PREFACE iii ON THE CALCULATION OF PHYSICO-CHEMICAL CONSTANTS . 1 Ox THE CALCULATION OF THEKMO- CHEMICAL CONSTANTS . 9 1. Introduction ........ 9 1. Choice of Data. 2. The Data employed. 2. Thermal Constants of the Hydrocarbons . . . .12 3. Molecular Heats of Combustion of the Hydrocarbons. 4. Thermo-Chemical Evidence for von Baeyer's Strain Theory. 5. The Constitution of Benzene. 3. Thermal Constants of the Hydrocarbons (continued) . . 22 6. Molecular Heats of Formation of the Hydrocarbons. 7. Relative Theoretical Value of Molecular Heats of Combustion and Formation. 4. Thermal Constants of Organic Halogen Compounds . . 30 8. Molecular Heats of Combustion of Organic Halogen Compounds. 9. Molecular Heats of Formation of Or- ganic Halogen Compounds. 10. Calculation of the Mole- cular Heats of Combustion and Formation of Aromatic Compounds. 5. Thermal Constants of Organic Oxygen Compounds . . 38 11. Molecular Heats of Combustion of Ethers. 12. Molecular Heats of Formation of Ethers. 13. Molecular Heats of Combustion of Alcohols. 14. Molecular Heats of Formation of Alcohols. G. Thermal Constants of Organic Oxygen Compounds (con- tinued) . . . .48 15. Molecular Heats of Combustion of Ketones and Aldehydes. 16. Molecular Heats of Formation of Alde- hydes and Ketones. 1 7. Molecular Heats of Combustion of Esters. 18. Molecular Heats of Combustion of Acids. 19. Molecular Heats of Formation of Esters and Acids. vi CONTENTS PAGE 7. Thermo-Chemical Evidence for von Baeyer's Strain Theory 59 20. Thermal Equivalents of the Intramolecular Strain in Polymethylenes. 21. Thermal Equivalent of the Intramolecular Strain in Ethylene Oxide. 8. Thermal Constants of Organic Sulphur Compounds . . 66 22. Molecular Heats of Combustion of Organic Sulphur Compounds. 23. The Constitution of Thiophene. 24. Molecular Heats of Formation of Organic Sulphur Compounds. 9. Thermal Constants of Organic Nitrogen Compounds . . 76 25. Molecular Heats of Combustion of Organic Nitrogen Compounds (Nitrogen linked eotirely to Carbon). 26. Molecular Heats of Combustion of Organic Nitrogen Compounds (Nitrogen linked to Carbon and Hydrogen). 27. Molecular Heats of Formation of Organic Nitrogen Compounds. 28. The Constitution of Pyridine. 10. Summary and Conclusion . . . . . .91 APPENDIX. A Short Criticism of Thomson's Method of Calcu- lating the Thermal Constants of Organic Substances . 96 INDEX OF SUBSTANCES . 101 LIST OF TABLES PAGE Table 1. Calculation of ft 14 2. Calculation of y . 15 3. Calculation of y . . . . . . .15 4. Calculation of 8 16 5. Calculation of 8 16 6. Molecular Heats of Combustion of Hydrocarbons 18,19 ,, 7. Angles of Deviation for Polymetbylenes ... 20 ., 8. Calculation of /?' 24 ., 9. Calculation of y' 24 ,, 10. Calculation of y' ....... 25 11. Calculation of 8' 25 12. Calculation of 8' 26 13. Molecular Heats of Formation of Hydrocarbons . 28 ,, 14. Regularities in the Molecular Heats of Combustion of Halogen Compounds 31 ,, 15. Regularities in the Molecular Heats of Combustion of Halogen Compounds 32 ., 16. Molecular Heats of Combustion and Formation of Organic Halogen Compounds ... 34, 35 ,, 17. Molecular Heats of Combustion and Formation of Aromatic Compounds ..... 36, 37 ,, 18. Molecular Heats of Combustion and Formation of Ethers . . 40,41 ,, 19. Molecular Heats of Combustion and Formation of Alcohols . . . . . . . 46, 47 ,, 20. Molecular Heats of Combustion and Formation of Aldehydes and Ketones .... 52, 53 ., 21. Molecular Heats of Combustion and Formation of Esters 54, 55 22. Molecular Heats of Combustion and Formation of Acids 56, 57 23. Calculation of the Thermal Equivalents of Intramole- cular Strain in Polymethylenes . . . .60 viii LIST OF TABLES PAGE Table 24. Calculation of the Thermal Equivalents of Intramole- cular Strain in Polymethylenes . . . .61 ., 25. Intramolecular Strain and Angles of Deviation for Polymethylenes . . . . . . .62 26. Molecular Heats of Combustion and Formation of Organic Sulphur Compounds . . . 70, 71 27. The Constitution of Thiophene . . . .73 ,, 28. Molecular Heats of Combustion and Formation of Organic Nitrogen Compounds (Nitrogen linked entirely to Carbon) 78, 79 ,, 29. Apparent Anomalies exhibited by the Molecular Heats of Combustion of Amines . . . .80 ,, 30. Apparent Anomalies exhibited by the Molecular Heats of Combustion of Amines. . . .83 ., 31. Molecular Heats of Combustion and Formation of Organic Nitrogen Compounds (Nitrogen linked to Carbon and Hydrogen) . . . . 86, 87 32. The Fundamental Molecular Heats of Combustion and Formation Constants . . . . 92, 93 Plate. Curve showing the Variation of the Intramolecular Strain ('') with Change in the Angle of Deviation, for Polymethylenes 64 ERRATA Page 14. In Table 1 the formula for propylene should read Page 84, line 13, for determined, Thomsen read determined by Thomsen Page 85, line 17, for 90-0 read 89-9 Reclgrove : Thei'mo-Chemical Constanta. ON THE CALCULATION OF PHYSICO- CHEMICAL CONSTANTS IT has been found that the ' double ' or ethene link and the ' treble ' or ethine link each exerts a definite specific influence on certain physico-chemical properties (e. g. molecular refractivity, molecular heat of com- bustion, &c.), that oxygen exerts a different specific influence according to its mode of combination, &c. ; in view of these facts it seems surprising that chemists in general l so persistently ignore the ' single ' or ethane and certain other links. A priori we should not regard physico-chemical constants in general as ad- ditive in the sense of depending solely upon the number and kind of atoms in the molecule. It follows from the fact, that as we employ the term ' link ' to designate that which holds the atoms together in a definite configuration (although of course not rigidly), therefore the total internal energy of a substance will depend largely upon the number and kind of links in the molecule ; and also, as it seems evident that the distance between any given atoms will bear some relation to the link between these atoms, therefore energy and volume properties (which include practically all physico-chemical properties) will, if additive at all, be so only in the sense of depending upon, not only the number and kind of atoms, but also the number and kind of links in the molecule ; a conclusion we 1 See Appendix. B CONSTANTS might have inferred from the facts noted above. We shall therefore term ' additive ' all properties showing the above regularity, that is to say, which are not affected (or at the most, negligibly so) by the position of the atoms in the molecule, in so far as such re- arrangement of the atoms does not alter the number and kind of links. The object of the present method of calculation is to avoid as many assumptions as possible, and it is surely logical to insist that proof should be given that the value of, say, the ethane link is zero, before it can be ignored. The assumption that certain differ- ent links possess the same value (without evidence) carried to its logical conclusion that all links have the same value is pure nonsense, contradicted by experi- mental data : we shall regard each different link as exerting a definite specific value. It may be, that in so far as some particular additive property is concerned, certain links may possess the same value, or even, that certain links may exerpise a negligible influence, but this must first be proved before any method of cal- culation is based thereon. It is, of course, true that, in the application of the usual ' ethane-link-ignoring ' methods of calculation, the errors thus arising balance one another in general ; for the same errors are committed in obtaining the constants as are made in applying them ; but this procedure seems hardly scientific. It can also be shown, if we logically insist on the principles already laid down, that the alleged physico- chemical constants are not only incorrect, but that the simple atomic and link physico-chemical constants are, at our present state of knowledge, unobtainable ; a proof of which follows later. PHYSICO-CHEMICAL CONSTANTS 3 Nevertheless, the examination of physico-chemical constants does throw much light on questions of con- stitution and other matters of interest ; an outline method of calculation and application of the constants in general is given herein ; to be applied in detail later in so far as thermo-chemical constants are con- cerned. The method makes but one assumption, namely, that the physico-chemical constants in question are additive in the wider sense explained above. In so far as certain properties are concerned this assumption will be found, in general, correct ; those properties that diverge greatly from it are without the domain of our consideration ; and any slight or peculiar diver- gences shown by the in-general-concordant properties can be allowed for in the particular application of the method. Let H l be the value of a hydrogen atom plus the link joining it to a carbon atom. Let C be the value of a carbon atom, not including the value of its valencies. Let Lj, L 2 , L 3 , be the values of the ' single ' (ethane), ' double ' (ethene) and ' treble ' (ethine) links respec- tively. If the constants for four hydrocarbons (in which each series ethane, ethene, and ethine is represented) are known, the value of the following can be calcu- lated : 1 The symbol H (not italicized) "will be used later to represent the value of a hydrogen atom not including the value of a C . H or other link. B 2 4 PHYSICO-CHEMICAL CONSTANTS thus, suppose we know the values of methane, ethane, ethylene and acetylene : a = C + 4: H = value of methane. the value of methane less that of ethane. the value of methane less that of ethylene. 8 = 6 H-L 3 = 2 (C + 4 H) - (2 C + 2 JT-f L 3 ) = twice the value of methane less that of acetylene. If a larger amount of experimental data is at hand, the method can be modified to suit such data, means can be struck, and greater accuracy obtained, as will be shown below. It is proposed to call the above the ' fundamental constants ' (for carbon and hydrogen). We have above a set of four equations, involving five unknowns, namely, C, H, L u L 2 , L 3 ; these equa- tions cannot be solved for these unknowns, unless another equation, not derivable from these four, can be obtained. To see if this be possible, it is necessary to develop a general expression for all hydrocarbons. It is evident that represents all open-chain saturated hydrocarbons. The removal of two hydrogen atoms (joined to adjacent carbon atoms) would cause the replacement of a C . C link by a C : C link ; thus a (2 H + Lj ) must be re- placed by a L 2 (a being some integer) to give a general expression ; namely, n C + 2 (n + 1 - a) H+ (n - a - 1) L x + a L 2 representing all open-chain hydrocarbons, not containing ' treble ' links. PHYSICO-CHEMICAL CONSTANTS 5 The removal of four hydrogen atoms (joined in pairs to two adjacent carbon atoms) from the saturated hydrocarbon would cause the replacement of a C . C link by a C : C link ; thus b (4 H + Lj) must be replaced by b L 3 (b being some integer) to give a general ex- pression, namely nC + 2(n+l-2b)H+(n-b-l)L l + aL, representing all open-chain hydrocarbons, not con- taining ' double ' links. Combining the two operations we get nC + 2(n + l-a-2b)H + (n - a - b - 1) L! + aL. 2 + b L 3 the general expression representing all open-chain hydrocarbons. The removal of two hydrogen atoms (joined to different non- adjacent carbon atoms, which become joined by a C . C link) gives a ring hydrocarbon ; thus 2p H must be replaced by p L x (p being some integer) to give a general expression, namely, n C + 2 (n + 1 - a - 2 b - p) H representing all hydrocarbons. But nC + 2(n i l-a-2b-p)H -h (n +p a b 1) L^ + a L 2 + b L 3 = noi-(n+pa-b-i)/3-ay-bS. Therefore, the expression for any and every hydro- carbon can be expressed in terms of the fundamental equations (i. e. C + 4 H= a, 2 H- L L = /3, 4 H- L 2 = y, 6JT L 3 = 8), consequently, no equation, not derived therefrom, is obtainable ; so that the equations cannot 6 PHYSICO-CHEMICAL CONSTANTS be solved : that is to say, neither the values of the separate atoms nor of the separate links can be ob- tained. The proof has only been given for hydrocarbons, but it can easily be extended for other compounds. Dealing with organic compounds, their formulae can all be derived from that of the general hydrocarbon ; and for every different group introduced, which means the introduction of at least one unknown, only one new equation can be obtained, and so the equations are still indeterminate. Thus, suppose we introduce a group whose value, together with the link (or links) joining it to carbon, is R. The general expression for the group of com- pounds thus obtained will be found by replacing mvH by mR (v being the valency of the group), giving + (n+p a b = n a - (n +p - a - 6 - 1) /J - a y & 8 - w (vH- R). The value of (vH R) can be found, and will con- stitute the fundamental constant for this group of compounds ; but the equation vHT\, = k, where k is the known value of this fundamental constant, together with the other fundamental equations will constitute a set of five equations involving six unknowns, and therefore indeterminate. The above identities, however, enable us at once to write the formula of any compound in terms of the * fundamental constants ', and the theoretical value thus obtained can be compared with the value found experi- mentally. It should be noticed that the expression for any PHYSICO-CHEMICAL CONSTANTS 7 hydrocarbon in terms of the ' fundamental constants ' is such that Coefficient of a = number of carbon atoms in the substance. Coefficient of /8 = number of ' single ' links, with the negative sign. Coefficient of y = number of ' double ' links, with the negative sign. Coefficient of 8 = number of c treble ' links, with the negative sign. This will apply, as a rule, to other compounds. In the following pages this method will be applied to the calculation of the molecular heats of combustion and formation of organic substances. ON THE CALCULATION OF THERMO- CHEMICAL CONSTANTS 1. INTEODUCTION. 1. CHOICE OF DATA. IT is of the utmost importance that the data from which it is proposed to calculate physico-chemical constants are accurate and consistent ; the ideal ex- perimental data are obtained only from a large number of accurate experiments, all of which must be carried out under exactly the same conditions ; otherwise the various results will not be comparable with one another. Fortunately, in so far as Thermo-chemistry is con- cerned, such an ideal state of affairs is to a great extent realized in the unique work of Julius Thornsen. A priori one is justified in regarding much physico- chemical data, and particularly thermo- chemical data, with a certain want of reliance, owing to the experi- mental difficulties to be overcome in gaining such data ; we find, however, as w r ill be evident later, at the very outset of our examination of thermo-chemical constants, that out of fifteen aliphatic hydrocarbons the difference between the results calculated by the method already outlined for their molecular heats of combustion, and Thomsen's experimental results, is, in the case of twelve, less than 0-2 per cent. We do not always find so excellent an agreement as this, but with a few isolated exceptions, it is always satisfactory. 10 THEEMO-CHEMICAL CONSTANTS This can be no chance relationship, and proves, not only the correctness of our method of calculation, but also the reliability of Thomsen's experimental data. The calculations given hereinafter are based solely upon Thomsen's experimental results (which will be found in his Thermochemische Untersuchungen ; English translation by Miss Katherine Burke, B.Sc.), with the exception of data relating to the poly- methylenes. 2. THE DATA EMPLOYED. Thomsen determined the heats of combustion of volatile organic compounds. The experiments were carried out, as far as possible, in a uniform manner : with the same apparatus and under the same external conditions ; namely, the compound was volatilized by a current of gas at 18 C., and burnt in Thomsen's universal burner ; the experiments were carried out at constant pressure. Such combustions, however, generally produce change of volume, more generally, diminution which results in evolution of heat ; so that to obtain correct molecular heats of combustion (i. e. at constant volume) a correction must be applied to the molecular heats of combustion at constant pressure for this change of volume. This is given by the equation : h = 7i (0-543 + 0-0020 Gals. where h is the amount of heat due to diminution of volume, and must be subtracted from the molecular heat of combustion at constant pressure ; n the number of gas molecules disappearing, and t the temperature. The products of combustion are assumed to be cooled to 18 C. so that carbon dioxide, sulphur dioxide, and nitrogen appear as gases, water on the other hand INTRODUCTION 11 as a liquid ; the halogens are also assumed gaseous. All the experiments being carried out at 18 C. the above formula simplifies to : h = 0-58^ Gals. All the molecular heats of combustion given later have been corrected thus for constant volume. The heats of formation of organic compounds cannot, as a rule, be obtained directly ; this is, however, not necessary, for the molecular heats of formation of these substances equal the molecular heats of formation of the products of their combustion, less the molecular heats of combustion of the substances themselves. Therefore having given : M. H. F. of Carbon dioxide (constant pressure or volume) from amorphous carbon =96-96 Cals. M.H. F. of Sulphur dioxide (constant pressure or volume) from rhombic sulphur =71-08 Cals. M. H. F. of Water (constant volume) from gaseous hydrogen =6749 Cals. the molecular heats of formation (at constant volume) referring to amorphous carbon, rhombic sulphur, and gaseous molecules of hydrogen, nitrogen, chlorine, bromine, and iodine, can be obtained at once from the molecular heats of combustion (at constant volume) of any organic compounds. Thus :- M. H. C. of Methane (CH 4 ) = 210-77 Cals. Therefore M. H. F. of Methane (CH 4 ) = 96-96 Cals. + 2 x 67-49 Cals. - 210-77 Cals. = 21-17 Cals, &c. Hereinafter, molecular heats of formation obtained as above are referred to as 'found' or 'experimental', in contradistinction to those calculated by our method. 2. THEEMAL CONSTANTS OF THE HYDRO- CARBONS. I 3. MOLECULAR HEATS OF COMBUSTION OF THE HYDROCARBONS. THE heat of combustion of a hydrocarbon consists of several factors. Consider the case of the general hydro- carbon : + (n+p a b - The heat of combustion of one molecule of this hydrocarbon is the algebraic sum of the following heats (of which nos. 1, 2, 4, 5, 6 and 7 are negative) : (1) The heat due to the severance of 2 (n + 1 - a - 26 -^)C.H links. (2) The heat due to the decomposition of \(n + 1 a 2b p) oxygen molecules into free atoms. (3) The heat of formation of (n+ 1 a 2b p) molecules of liquid water from hydrogen and oxygen atoms. (4) The heat due to the severance of (n +p a -b-l)C.C links. (5) The heat due to the severance of a C : C links. (6) The heat due to the severance of b C C links. HYDROCARBONS 13 (7) The heat due to the decomposition of n oxygen molecules into free atoms. (8) The heat of formation of n molecules of carbon dioxide from carbon and oxygen atoms. The coefficients of the heats 1, 2 and 3 are always in the ratio 2:f:l; therefore their algebraic sum can be considered as one constant ; likewise the algebraic sum of heats 7 and 8 can be considered as one constant. Dealing with grm. -molecular weights, and using the notation already adopted for physico-chemical constants in general : 2 Heats 1, 2 and 3 = 2(n + 1 -a-2b-p) HCals., Heat 4 = (n +p a b 1) L x Gals., Heat 5 = aL 2 Gals., Heat 6 = 6L 3 Gals., 2 Heats 7 and 8 = nC Gals. It has already been shown, that unless more or less unlikely assumptions are made, 1 the values of these constants cannot be obtained at our present state of knowledge ; the values of the ' fundamental con- stants ' a(=C + 4#), j8(=21T-L 1 ), r( = 4#-L 2 ), S (= 6H L 3 ), however, can be calculated easily, using the molecular heats of combustion of the hydrocarbons (determined by Thomsen, and corrected for constant volume), as follows : a = C + 4T=the molecular heat of combustion of methane = 210-8 Gals. The difference between the molecular heats of com- bustion of two adjacent homologues gives C + 2JET+L! as in the following table : 1 See Appendix. THEEMO-CHEMICAL CONSTANTS TABLE 1. CALCULATION OF 3. Substance. Formula. Mol. Heat of Combustion. Difference : Methane .... Ethane 2 C + 6 // + Lj Cals. 210-8) 369-0 [ Cals. 158-2 Propane .... Trimethylmethane . Tetramethyl methane Ethylene . . . Propylene . . . wo-Butylene Acetylene . . . Allylene . . . 3C+8//+2LJ 4C+ 10//+3L t 5C+12//+4L! 4C+8//+2L 1 + L 2 2C-f 2#+L 3 3C+4fl r +L 1 + L 3 Mean 527-5 | 685-2; 844-8} 332-21 491-3) 648-9* 309-2, 466-4' .. C+2//+L! 158-5 157-7 159-6 159-1 157-6 157-2 = 158-3 L 1 = /3. Therefore /8 = (210-8 - 158-3) Cals. = 52-5 Cals. But this value, although appearing at first sight to be the true mean, depends only upon the first and last member of each series. It is, however, possible to obtain a value of /B depending upon the values of all the saturated hydrocarbons given, as follows (and as it so happens the value thus obtained is identical with the one above), thus summing the values of all these hydrocarbons, we have 15C + 40jfiT-f 10 Lj = 2637-3 Cals., whence 15a- 100 .= 2637-3 Cals., so that putting a = 210-8 Cals., we have 10/3 = 15 x 210-8 Cals. - 2637-3 Cals. = 524-7 Cals., whence /3 = 52-5 Cals., as before. The method of least squares applied to these five hydrocarbons gives results which differ only slightly from the above. The difference between the molecular heats of combustion of a saturated (ethane) hydrocarbon n C + (2n -f 2) H+ (n 1) L x and the corresponding un- HYDKOCAKBONS 15 saturated (ethene) hydrocarbon nC + 2nH+(n-2) L, + L 2 gives 2 H + L x L 2 , as in the following table : TABLE 2. CALCULATION OF y. Substance. Formula. Mol. Heat of Combustion. Difference : 2H+L 1 -L 2 . Cals. Cals. Ethane . . . Ethylene . . . 2C+QH+L l 2C+4#+L 2 369-0) 332-2} 36-8 Propane . . . 3C+8//+2LJ 527-5) of* 9 Propylene . . 3C + 6H+L 1 + L 2 491.3} OO-^ Trimethylmethane 4C + 1QH+3L! 685.2) oft q f'so-Butylene . 4C + 87/+2L 1 + L 2 648-9] oU-o Mean ... 2H+L 1 -L 2 = 36-4 H- L 2 = There- (2H+ L, - L 2 ) + (2ST- L,) = fore y = (364 + 52-5) Cals. = 88-9 Cals. The value of y can also be obtained directly from these unsaturated hydrocarbons, for, writing the formula nC + 2nH + (n 2) L x + L 2 in the form n a (n 2)/3 y, and knowing the values of a and & that of y can be obtained, as in the following table : TABLE 3. CALCULATION OF y. Substance. Formula. Mol. Heat of Combustion. 7 Calculated. Ethylene .... Propylene wo-Butylene . 2a-y Sa-^-y 4a-2/3-y Cals. 332-2 491-3 648-9 Cals. 89-4 88-6 89-3 Mean ... y = 89-1 The final mean value of y is therefore 89-0 Cals. The difference between the molecular heats of combustion of a saturated (ethane) hydrocarbon nC + (2n + 2)H+(n-l)L L and the corresponding unsaturated (ethine) hydrocarbon nC + (2n 2) H 16 THERMO-CHEMICAL CONSTANTS + (n 2) L! + L 3 gives 4H+ L x L 3 , as in the following table : TABLE 4. CALCULATION OF 8. Substance. Formula. Mol. Heat of Combustion. Difference : Cals. Cals. Ethane .... Acetylene .... 2C+6H+L l 2C+2#+L 3 369-0) 309-2) 59-8 Propane .... 3C+8//+2L! 527-5) fil .1 Allylene .... 3C + 4#+L 1 + L 3 466-4] Mean ... 4//+L t -L 3 = 60-45 L 3 = S. There- fore 8 = (6045 + 52-5) Cals. = 112-95 Cals. The value of 8 can also be obtained directly from these unsaturated hydrocarbons, for, writing the formula nC + (2n- 2) H + (n 2) I^ + Lg in the form n a (n 2) /3 8, and knowing the values of a and /3, that of 8 can be obtained, as in the following table : TABLE 5. CALCULATION OF 8. Substance. Formula. Mol. Heat, of Combustion. S Calculated. Cals. Cals. Acetylene. . . . Allylene .... 2a-8 3a-/?-8 309-2 466-4 112-4 113-5 Mean ... 8 = 112-95 The value of 8 is therefore 113-0 Cals. In Table 6 will be found the molecular heats of combust icn (corrected for constant volume) of all the hydrocarbons determined by Thomson, herein are also exhibited the molecular heats of combustion calculated by means of the values of the ' fundamental constants ' obtained above, namely a= 210-8 Cals., P = 52-5 Cals., y = 890 Cals., 8 = 113 Cals., HYDROCARBONS 17 together with the differences between them and the experimental ; and the percentage errors. Out of fifteen aliphatic hydrocarbons, the error in the ease of twelve is belotv 0-2 per cent., proving (at least in so far as the hydrocarbons are concerned) the additive nature of molecular heats of combustion. The errors in the cases of di-isopropyl and tso-amylene are also quite small, and are probably experimental. The very large difference between the experimental and calculated values for trimethylene cannot be thus explained. I 4. THERMOCHEMICAL EVIDENCE FOE VON BAEYER'S STRAIN THEORY. Before attempting to explain the abnormal behaviour of trimethylene, a consideration of the ' double ' and ' treble ' link is necessary. If a C : C link were a double link in an arithmetical sense we should have L 2 2L X = 0, whereas actually L, - 2L L = 2 (2H- L,) - (H- L,) = 2/3 - y = (105-0 - 89-0) Gals. = 16-0 Gals. Similarly if a C C link were a treble link in an arithmetical sense we should have L 3 31^ = 0, whereas actually = (157-5-113-0) Gals. = 4:4-5 Gals. We know, however, from pure chemistry, that a 1 double ' link is not an arithmetical double link, and that a ' treble ' link is not an arithmetical treble link, but in so far as stability is concerned each is less than a ' single ' link. The instability of C : C and C : C links finds a mathematical interpretation in von Baeyer's Strain Theory, which states that the four valencies of the carbon atom act normally in the direction of the four c 18 THERMO-CHEMICAL CONSTANTS TABLE 6. MOLECULAR HEATS OF 1. Substance. 2. 3. Formulae. C+47/ 2C-I-6//4-L! 4C+ 1077+ 3L L 5C+127/+4LJ GC+147/+5L! 2C + 47/+L 2 3C+677+3LJ 4C+8//+2L 1 + L 2 5C+ 107/+3L 1 + L 2 6C+107/+3L 1 + 2L 2 2C+277+L 3 3C+ 477+ Lj + L 3 6C+G7/+3L 1 +3L 2 GC+67/+9L! 7C+87/+4L 1 + 3L 2 7C+87/+10L! 9C+127/+12L! 9C+1277+GL 1 + 3L, 9C+127/+12L! a 2a-/2 3a-2^8 2a-y 5a-3j3-y Ga-3y8-2y 2a-8 6a-3y8-3y| 7a-4^-3y| 9a-12/? j Trimethyl methane . Tetrame thy 1 methane . . Di-f'sopropyl .... Ethylene Trimethylene .... wo-Amylene Diallyl Acetylene Allylene Dipropargyl Benzene . . -: / 7 1 ((b) Toluene - >,< nr -i. i (() Mesitylene . . . j / *( Pseudocumene . . -,/J (a) Kekule"s formulae. (b~) Ladenburg's or Claus's formulae (without adding the value due to the intramolecular strain). lines drawn from the centre to the four corners of a regular tetrahedron (i. e. making an angle of 109 28' with one another). If the directions of the valencies are different from this normal condition, a state of intramolecular strain is set up, depending upon the angle through which the directions of the valencies are diverted. The tendency of the strain is to sever the link, hence the instability of such links ; moreover, the molecular heat of combustion of a compound which is HYDKOCARBONS 19 COMBUSTION OF HYDROCARBONS. 4. M. H. C. constant volume (Thomsen). 5. M. H. C. Calculated. 6. Difference between cols. 4 and 5. 7. Error. Cals. Cals. Cals. Per cent. 210-8 210-8 + 0-0 + 0-00 369-0 369-1 + 0-1 -f 0-03 527-5 527-4 -0-1 -0-02 685-2 685-7 + 0-5 + 0-07 844-8 844-0 -0-8 -0-09 996-6 1002-3 + 5-7 + 0-57 332-2 332-6 + 0-4 + 0-12 491-3 490-9 -0-4 -0-08 498-0 474-9 -23-1 -4-64 648-9 649-2 + 0-3 + 0-05 805-6 807-5 + 1-9 + 0-24 930-8 929-3 -1-5 -0-16 309-2 308-6 -0-6 -0-19 466-4 466-9 + 0-5 + 0-11 881-4 881-3 -0-1 -0-01 797-9 ( 840-3 1 792-3 + 42-4 -5-6 + 5-31 -0-70 953-9 ( 998-6 ( 950-6 + 44-7 -3-3 + 4-69 -0-35 1280-0 (1315-2 (1267-2 + 35-2 -12-8 + 2-75 -1-00 1279-2 J1315-2 (1267.2 + 36-0 -12-0 + 2-81 -0-94 in a condition of intramolecular strain will be greater than the calculated value by the thermal equivalent of this strain. Hence, if we represent this thermal equivalent for the ' double ' link by T 2 , and for the treble link by T 3 , then 2L 1 + T 2 = L 2 , whence T 2 = 16-0 Cals., and 3L 1 + T 8 = L 3 , whence T 3 = 44 5 Cals. In the polymethylenes, although there are no ' double ' or ' treble ' links, it can be seen by con- structing models of the molecules that they are in a condition of strain. Assuming that they possess a regular configuration, the atoms constituting the c 2 20 THERMO-CHEMICAL CONSTANTS ring being all in one plane, the following formula can be obtained for the angle of deviation D = 5444'- -90 n where n is the number of carbon atoms in the ring, and D the angle of deviation. The values of the angle of deviation in various rings, &c., are given in Table 7. TABLE 7. ANGLES OF DEVIATION FOR POLYMETHYLENES. Ring. Angle of Deviation (= D). Dimethylene (= Ethylene) .... 54 44' Trimethylece 24 44' Tetramethylene 9 44' Pentamethylene 44' Hexamethylene -5 16' Also Acetylene +70 32' This explains to a great extent the relative stabilities of the various groups of polymethylenes. Consequently, the excess of the actual molecular heat of combustion of trimethylene over the calculated (which we will express by T U1 ) is the thermal equivalent of the intramolecular strain in this substance, so that T m = (498-0 -474-9) Gals. = 23-1 Cals. Thomsen's determinations (save that of the heat of combustion of ethylene oxide) do not afford further data for testing the validity of von Baeyer's Strain Theory. Stohmann, however, has carried out a research on the heats of combustion of polymethylene carboxylic acids, which will be considered later (see 20 and 21). 5. THE CONSTITUTION OF BENZENE. As would be expected, in that it represents an un- saturated substance, Kekule's formula for benzene HYDROCARBONS 21 gives too high values for the molecular heats of com- bustion of the aromatic hydrocarbons, on the other hand Ladenburg's or Claus's formula (i. e. benzene is 6C + 6JY+9L,) gives fairly good values apparently. Applying, however, the knowledge gained relative to intramolecular strain, we are led to the conclusion that Ladenburg's formula would give very much higher values than those calculated as above, for a substance having Ladenburg's formula would contain two tri- methylene and three tetramethylene rings ; con- sequently we must add to the values calculated as above the thermal equivalent of the total intramolecular strain due to these rings. The trimethylene rings alone would cause a difference of 46-2 (circa) Gals. ; the true values for Ladenburg's formula would be, therefore, very much higher than the experimental. Claus's formula also contains tetramethylene rings, which would cause the true theoretical values to be higher than the experimental. The thermo-chemistry of benzene is in agreement with the pure chemistry of the substance, showing, as it does, its saturated and stable nature. Comparing the molecular heat of combustion found experimentally with that calculated for a fully saturated compound (6 C + 6 H+ 9 Lj), we are led to the conclusion that the molecules of benzene are in a state of only very slight strain, less than would be accounted for by one C : C link. It may be that this has been best ex- pressed, up to the present time, by Armstrong's and Baeyer's centric formula, although this is not altogether satisfactory. An empirical method of calculating the molecular heats of combustion of aromatic compounds will be explained later (see $ 10). 3. THERMAL CONSTANTS OF THE HYDRO- CARBONS (continued). fi 6. MOLECULAR HEATS OF FORMATION OF j THE HYDROCARBONS. A SET of constants will be necessary for the cal- culation of molecular heats of formation entirely analogous to those required for the calculation of molecular heats of combustion, but as the symbols will have different specific significations when employed in calculating molecular heats of formation from those when employed in calculating molecular heats of com- bustion, they will be dashed in the former case to avoid confusion. Consider the case of the general hydrocarbon, nC + 2(n + l-a-2b-p)H + (n +p - a - b - 1) L! + a L 2 + b L 3 . The heat of formation of one molecule of this hydrocarbon from molecular carbon (amorphous) and molecular hydrogen (gaseous), is the algebraic sum of the following heats (of which nos. 1-2 are negative) (1) The heat due to the decomposition of a sufficient number of carbon molecules to provide n free carbon atoms. (2) The heat due to the decomposition of (n + l-a 26-jp) hydrogen molecules into free atoms. HYDBOCARBONS 23 (3) The heat of formation of 2 (n + 1 - a - 2 b -p) G . H links. (4) The heat of formation of (n +p a b ~L) C . C links. (5) The heat of formation of a C : C links. (6) The heat of formation of & C C links. The coefficients of heats 2 and 3 are always in the ratio 1 : 2, therefore their algebraic sum can be con- sidered as one constant. Dealing with grm.-molecular weights, and using the notation already adopted Heat l = nC'Cals., 2 Heats 2 and 3 = 2 (n + 1 - a -2 b -p) H' Gals., Heat 4: = (n +p a b 1) L/ Cals., Heat 5 = a L 2 ' Cals., Heat 6 = &L 3 ' Cals. It should be noticed that L/= L 1? L/= L 2 , L;= -L 3 . The fundamental molecular heat of formation con- stants are therefore : S^GH' L 3 X , and can be calculated from the mole- cular heats of formation (corrected for constant volume) of the hydrocarbons, given by Thomsen, in a similar manner as were the fundamental molecular heat of combustion constants from the molecular heats of com- bustion of the hydrocarbons. Thus, a = C' + 4 IT - the molecular heat of formation of methane = 21-2 Cals. The difference between the molecular heats of formation of two adjacent homologues gives C x + L/ as in the following table : 24 THERMO-CHEMICAL CONSTANTS TABLE 8. CALCULATION OF (?. Substance. Formula. Mol. Heat of Formation. Difference : C' + 2H'+L 1 '. Gals. Cals. ]\ [ethane .... C'+4//' 21- 2i 6-2 Ethane .... 2C'+6//'+L 1 ' 27-4 f fi.O Propane .... 3C / +8//+2L/ 33-4 O* \J 67 Trimethyl methane . 4C'+10//+3L 1 ' 40- 1{ i Tetramethylmethane 5C / +12/r+4L 1 / 45-0* 4-9 Ethylene .... 2C'+4#' + L 2 / -3-3) K d. Propylene 3C / +6 J H' + L 1 / +L 2 ' + 2-1 [ D-'t 6Q ?'so-Butylene . . 4C'+8/f+2L 1 / + L,' 8-9* o Acetylene 2C'+2#'+L 3 ' -47-8) 7.3 Allylene .... 3C / +4// / + L/ + L 3 / -40-5' Mean ... C / +2// / + L/ = 6-2 L 1 / = /3 / . There- fore ' = (21-2 - 6-2) Cals. = 15-0 Cals. 1 The difference between the molecular heats of formation of a saturated (ethane) hydrocarbon n C' + (2n + 2}H'+(n-l)L l ' and the corresponding un- saturated (ethene) hydrocarbon n C' + 2n H' + (n 2)L 1 / + L/ gives 2H' + L/ - L/, as in the following table : TABLE 9. CALCULATION OF y. Substance. Formula. Mol. Heat of Formation. Difference : Cals. Cals. Ethane .... 2 C' + 6 H f + L/ 27-4} o f\ i-r Ethylene. . . . 2C' + 47/' + L 2 ' -3-3] o(J' 1 Propane .... 3C / + 87/+2L 1 / + 33-4) 010 Propylene . . . 3CT+6// + L/ + L/ 2.1} Trimethylmeth ane . ?so-Butylene . . . 4C'+107/'+3L 1 ' 4C'+8//'+2L 1 / + L 2 / 40.1) 8.9] 31-2 Mean ... 2// + L/-L/ = 31-1 1 As pointed out in the case of /?, this apparent mean depends only upon the first and last members of each series. However, precisely the same value for f? will be obtained later by a more reliable method. It is for this reason that this value is employed in the calculations which follow. HYDEOCAEBONS 25 Therefore / = (81-1 + 15-0) Gals. = 46-1 Gals. The value of y can also be obtained directly from these unsaturated hydrocarbons, for, writing the formula nC' + 2nH' + (n-2) L/ + L/ in the form n of (n 2) ft' y, and knowing the values of a and /3', that of y can be obtained, as in the following table : TABLE 10. CALCULATION OF y. Substance. Formula. Mol. Heat of Formation. y Calculated. Cals. Cals. Ethylene .... Propylene. . . . wo-Butylene . . . 2a '~ 7 / -3-3 + 2-1 8-9 45-7 46-5 45-9 Mean ... /= 46-0 The difference between the molecular heats of combustion of a saturated (ethane) hydrocarbon n C' + (2 n + 2) T+(n- 1) L/ and the corresponding unsaturated (ethine) hydrocarbon n C' + (2 n 2) H' + (n-2)L 1 ' + L 3 / gives 4 1T + L/-L;, as in the following table : TABLE 11. CALCULATION OF S'. Substance. Formula. Mol. Heat of Formation. Difference : Cals. Cals. Ethane .... Acetylene . Propane. . . Allylene. . . 2C'+2// / +L 3 ' 3C'+4#'+L 1 / -fL 3 / 27-4} -47-8J + 33-4} -40-5) 75-2 73-9 Mean ... 4// / +L/-L 3 / = 74-55 ' + L/ - L 3 ') + (2H'- L/) = H' - L/ = S'. There- fore % = (74-55 + 15-0) Cals. = 89.55 Cals. 26 THERMO-CHEMICAL CONSTANTS The value of S' can also be obtained directly from these unsaturated hydrocarbons, for, writing the formula n .a H} < J- K r^l ] 1 1 CO CO M CO CO + v + v v + ^^^i-Ti-r CO CO t>> CM M W Q O CO T^ bbbbbbbbbbbbbbbbbbb ' g ^ o To o ^o o to c llliitllsiiii * p S .p? S o <1Pm EH HYDROCARBONS 29 that a small percentage error made in determining a molecular heat of combustion will occasion very often a large percentage error in the corresponding molecular heat of formation. To take an example, consider benzene : the experi- mental molecular heat of combustion (constant volume) is 797-9 Gals. ; suppose the mean error to be only 0-2 per cent., this would amount to 1-6 Gals.; so that supposing the heats of combustion of carbon and hydrogen in the molecular condition to be known accurately, we get, even in this extreme case, a value, 13-7 Gals., for the molecular heat of formation with a mean error of 1-6 Gals. ; that is to say, 11-6 per cent. ! This increase in percentage error will be found in general. Moreover the absolute error is also unreliable as a criterion of accuracy ; for, to take an example : an absolute error of, say, 2-0 Gals, in the case of a sub- stance with a low M. H. G. like formic acid (M. H. C. = 691 Gals., M. H. F. = 954 Gals.) means a large per- centage error, nearly 3 per cent, in the experimental determination ; whereas the same absolute error in the case of, say, mesitylene (M. H. C. = 1280-0 Gals., M. H. F. = - 24) is negligible, being occasioned by an experimental error below 0-2 per cent. On the other hand, dealing with molecular heats of combustion the percentage error is a good criterion of accuracy. Therefore, in preference to molecular heats of formation, we employ molecular heats of com- bustion upon which to base any arguments ; however, for the sake of completeness, molecular heat of forma- tion constants have been obtained, and the molecular heats of formation of the various substances calculated therefrom. THERMAL CONSTANTS OF ORGANIC HALOGEN COMPOUNDS. $ 8. MOLECULAR HEATS OF COMBUSTION OF ORGANIC HALOGEN COMPOUNDS. ALL halogen-substituted hydrocarbons can be ob- tained theoretically by replacing f hydrogen atoms by f halogen atoms, where/ is some integer ; the following constant will therefore be required : X = the algebraic sum of the following heats: (i) due to the severance of a C . H link ; (ii) due to the combustion of a hydrogen atom (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of a C . Cl (C . Br, C . J) link ; (iv) one-half that due to the formation of a gaseous chlorine (bromine, iodine) molecule ; or, as it can be written more simply : X = the sum of the following heats : (ii) due to the combustion of a hydrogen atom (to liquid water) ; (iii) due to the formation of a C . Cl (C . Br, C . J) link, minus the sum of the following heats : (i) due to the formation of a C . H link ; (iv) one-half that due to the formation of a gaseous chlorine (bromine, iodine) molecule. So that the general halogen-substituted hydro- carbon : + aL. + 6L, +/C . 01 (C . Br, C . J) links +/C1 (Br, J), OKGANIC HALOGEN COMPOUNDS can be written : -a-2b-p)H+(n+p-a-b-l)'L l 31 = na (n+p a b 1)$ ay b8 where x is used for chlorine, Xi f r bromine, and X2 f r iodine. Before proceeding to calculate the values of these constants, a few regularities in the molecular heats of combustion (at constant volume) of the compounds under consideration will be pointed out, using the experimental results of Thomsen. 1. The effect on the molecular heat of combustion produced by replacing a hydrogen atom in any hydro- carbon by a chlorine atom, is constant ; similarly, the effects produced by replacing the chlorine by bromine, and the bromine by iodine, are respectively constant ; as shown in the following table : TABLE 14. Hydride. Difference. Chloride. Difference. Bromide. Difference. Iodide. Cals. Cals. Cals. Cals. Cals. Cals. Cals. Methyl . Ethyl . Propyl . 210-8 369-0 527-5 -34-6 -35-9 -36-4 176-2 333-1 491-1 + 7-8 7-7 7-9 184-0 340-8 498-0 + 11-4 11-9 195-4 352-7 2. The effect on the molecular heat of combustion produced by replacing in turn 1, 2, 3 hydrogen atoms in any hydrocarbon by chlorine is constant. Ap- parently the replacement of a fourth hydrogen atom produces a less effect, but as the data is scanty, and the difference is in any case small, it has been neglected in the calculations to follow. 32 THEKMO-CHEMICAL CONSTANTS This regularity is shown in the following table : TABLE 15. M.H.C. Cals. Difference. Cals. Methane CH 4 210-8) 34-6 Methyl chloride CH 3 C1 176-2[ Chloroform . CHC1 3 107-2} x 34-5 Carbon tetrachlor de CC1 4 76-5/ 30-7 Ethane C H 369-0 l Ethyl chloride C 2 H 5 C1 333-1 35-9 37-3 Ethylene chloride C 2 H 4 C1 2 295-8* QO.C Monochlorethylene chloride . C 2 H 3 C1 8 262-33 3. The mere position of the halogen has no effect on the molecular heat of combustion. This is shown by the fact that the results for monochlorpropylene ( = 4524 Cals.) and for allyl chloride ( = 453-7 Cals.) are practically equal, and the result for ethylene chloride (=295-8 Cals.) identical with that for ethyli- dene chloride ( = 295-8 Cals.). In Table 16 will be found the molecular heats of combustion (corrected for constant volume) of fourteen chlorine, four bromine, and two iodine compounds, determined by Thomsen ; from these the values of X, Xi> and X2 have been calculated; thus, methyl chloride is CH 3 C1, i. e. a - x ; M. H. C. found = 176-2 Cals. Therefore, x = a- 176-2 Cals. = (210-8- 176-2) Cals. = 34-6 Cals., &c. The values thus obtained are given in Table 16, and means have been struck so as to give the lowest average error. The values thus obtained are : X = 35-5 Cals., Xi = 28 ' 6 Cals., X2 = 15< These are the fundamental molecular heat of com- bustion halogen constants. ORGANIC HALOGEN COMPOUNDS 33 Using these values, the molecular heats of com- bustion of all the halogen compounds given have been calculated, and are exhibited, together with the differences between them arid the experimental, and the percentage errors, in Table 16. Excepting chloroform, perchlorethylene, and carbon tetrachloride, the results are quite satisfactory, although not exhibiting the extraordinary exactness with which it was found possible to calculate the molecular heats of combustion of the hydrocarbons. I 9. MOLECULAR HEATS OF FORMATION OF ORGANIC HALOGEN COMPOUNDS. The constants required will be entirely analogous to the molecular heat of combustion constants, so that : X' = the algebraic sum of the following heats : (i) one-half that due to the decomposition of a hydrogen molecule ; (ii) due to the formation of a C . H link, minus the algebraic sum of the following heats : (iii) one-half that due to the decomposition of a chlorine molecule ; (iv) due to the formation of a C . Cl link; or, as it can be written more simply : x' = the sum of the following heats : (ii) due to the formation of a C . H link ; (iii) one-half that due to the formation of a chlorine molecule, minus the sum of the following heats : (i) one-half that due to the formation of a hydrogen molecule ; (iv) due to the formation of a C . Cl link. Similarly, ^i' for bromine, and ^/ for iodine. It follows, therefore, that x + X = Xt' + Xi = X-/ + X2 = the heat due to the combustion of a hydrogen atom (to liquid water), less half the heat due to the formation of a hydrogen molecule = the heat of combustion of one D 34: THERMO-CHEMICAL CONSTANTS TABLE 16. ORGANI 1. Substance. 2. Formula. Molecular Heals 3. Formula. 4. M.H.C. (Thomsen N constant vol. 5. X calcu- ' lated. 6. M.H.C calculate Chlorides. Methyl chloride .... Ethyl chloride .... Propyl chloride .... 250-Butyl chloride . . Monochlorethylene . . . Monochlorpropylene . . . Allyl chloride CII,C1 C 2 H 5 C1 C,H 7 C1 C 4 H 9 C1 C 2 H,Cl C 3 H 6 C1 CJl-.Cl CJI 4 CI 9 C 2 U 4 C1 2 c 4 n ci a CHCl, C 9 T1 3 C1 3 a O v CC1 4 C 2 CI 4 CLI 8 Br C 2 H 5 Br C 3 H 7 Br C 3 II 5 Br CH 3 J C 2 T1-J a-x 2a-/?- X 3a-2/?- X 4a-3/?- X 2a-y- X 3a-/?-y~x 3a-/?-7-X 2a-/?-2 X 2a-/3-2 X 3a-2/3-2x a-3 X 2a-/3-3 X a-4 X 2a-y-4 X a ~Xl 2a-/3- X i 3a-2/3- Xl 3a-/3-y-Xi a ~X^ 2a-^- X2 Cals. 176-2 3334 491-1 648-5 297-6 452-4 453-7 295-8 295-8 453-0 107-2 262-3 76-5 195-7 Mean ... 184-0 340-8 498-0 461-1 Mean ... 195-4 352-7 Mean ... Oak. 34-6 36-0 36-3 37-2 35-0 38-5 37-2 73-3x4 73-3x^ 74-4x4 103-6XJ 106-8X| 134-3 xj 136-9XJ x = 35.5 Xi 26-8 28-3 29-4 29-8 Xi = 28-6 Xa 15-4 16-4 X2 = 13'9 Cals. 175-3 333-6 491-9 650-2 297-1 455-4 455-4 298-1 298-1 456-4 104-3 262-6 68-8 190-6 182-2 340-5 498-8 462-3 194-9 353-2 Ethylene chloride . . . Ethylidene chloride . . . Dichlorpropane .... Chloroform Monochlorethylene chloride Carbon tetrachloride . . Perchlorethylene .... Bromides. Methyl bromide .... Ethyl bromide Propyl bromide .... Allyl bromide Iodides. Methyl iodide . . Ethyl iodide ... atomic gram weight of molecular hydrogen to liquid water - 1 x 67-5 Cals. - 33-75 Cals. Whence : x ' = (83-75 - 35-5) Cals. = - 1-75 Cals. x / = (33-75 -28-6) Cals. = +5-15 Cals, x ; = (33-75 - 15-9) Cals. = 17-85 Cals. In Table 16 will be found the molecular heats of ORGANIC HALOGEN COMPOUNDS 35 HALOGEN COMPOUNDS. Combustion. Molecular Heats of Formation. 7. Difference between cols. 4 and 6. 8. Error. 9. Formula. 10. M. H. F. (Thomson) constant vol. 11. x' calcu- lated. 12. M. H. F. calculated. 13. Difference between cols. 10 and 12. Cals. Per cent. Cals. Cals. Cals. Cals. -0-9 -0-51 a'-/ 22-0 -0-8 22-9 + 0-9 + 0.5 + 0-15 2a'-y3'-x' 29-6 -2-2 294 -0-5 + 0-8 + 0-16 3 a 2 ft x 36-0 -2-4 35-3 -0-7 + 1.7 + 0-26 4a'-3/3'-x' 43-1 -3-3 41-5 -1-6 -0.5 -047 o / / ' 2a -y - X -2-5 -1-1 -1-9 + 0-6 + 3-0 + 0-66 3a'-/T-/-x' + 7-3 -4-7 + 4-3 -3-0 + 1-7 + 0-37 3a' /?' y' x' 5-9 -3-3 4-3 -1-6 + 2-3 + 2-3 + 0-78 + 0-78 2a'-/3'-2 X ' 2a'-/J'-2x' 33-1 33-1 -5-7x4 30-8 30-8 -2-3 -2-3 + 3-4 + 0-75 3 a 2 ft' 2 x' 40-3 - 6-7x4 37-0 -3-3 -2-9 + 0-3 -2-71 + 0-11 a'-3 X ' 2a'-/3'-3 X ' 23-5 32-8 -2-3x4 26-3 32-5 + 2-8 -0-3 -7-7 -10-07 a'-4 x ' 20-5 + 0-7 x J 28-0 + 7-5 -5-1 -2-61 2a'-/-4x' -1-7 -1-9XJ 3-2 + 4-9 Mean ... x'= -1-7 Xi -1-8 -0-98 a! x\ + 14-2 + 7-0 16-0 + 1-8 -0-3 -0-09 2a ft' X/ 21-8 5-6 22-2 + 0-4 + 0-8 + 0-16 3 a 2ft' Xi 29-1 4-5 28-4 -0-7 + 1-2 + 0-26 oa-ft'-y'-xi' -1-5 4-1 -2-6 -14 Mean ... x/ = + 5 '3 -0-5 -0-26 a'-x/ + 2-8 18-4 2 + 3-3 + 0-5 + 0-5 + 0-14 2a'-/T-x/ 9-9 17-5 9-5 -0-4 Mean ... x 2 '= 17-95 formation of the halogen compounds under considera- tion, given by Thomsen ; from these the values of ^', X/, and x* have been calculated in a similar manner as were the molecular heat of combustion constants. The values thus obtained are x '= _ 1-7 Cals., x /= +5-3 Cals., x /- 17-95 Cals., agreeing with the above. D 2 36 THERMO-CHEMICAL CONSTANTS Using the mean values : X' = -1-7 Cals., x/ = +5-2 Cals., x/ = 17-9 Cals., which are the fundamental molecular heat of for- mation halogen constants, the molecular heats of formation of all the halogen compounds given have been calculated, and are exhibited, together with the differences between them and the experimental, in Table 16. 10. CALCULATION OF THE MOLECULAR HEATS OF COM- BUSTION AND FORMATION OF AROMATIC COMPOUNDS. Thomsen has determined also the molecular heat of combustion of phenyl chloride ; if we attempt to cal- TABLE 17. AROMATIC 1. Substance. 2. Formula. Molecu'ar Hca's of 3. Formula. 4. M. H. C. (Thomsen) constant vol. 5. M. H. C calculated. Toluene . . . C..H-.CH, t+a-P +3a-3 +3a-3 C-x Cals. 953-9 1280-0 1279-2 762-9 Cals. 956-2 1272-8 1272-8 762-4 Mesitylene Pseudocumene . Phenyl chloride . C H 3 'CH 3 ) 3 C 6 H 3 'CH 3 ) 3 C C H 5 .C1 culate either the molecular heat of combustion or formation of this substance by means of our funda- mental constants, we are beset by the same difficulty as in the case of the aromatic hydrocarbons : the constitution of benzene is unknown, such formulae as those of Kekule, Ladenburg, &c., giving inaccurate results. It would be useful, therefore, to adopt some means of calculation in which the question of the constitution of benzene is not introduced, where the primary object is to find out whether various groups ( Cl in the above case) exhibit the same thermal behaviour in aromatic as in aliphatic compounds. OKGANIC HALOGEN COMPOUNDS 37 This can readily be done by referring such com- pounds back to benzene, using the constants = the M. H. C. of benzene as determined by experiment (and corrected for constant volume), and ' = the corre- sponding M. H. F. of benzene ; whence = 797-9 Cals., '= 13-7 Cals. (Thomsen). Phenyl chloride can then be written ^ ; and similarly for other aromatic compounds. Using this method, the molecular heats of com- bustion and formation of this substance and the aromatic hydrocarbons given in Tables 6 and 13 have been calculated, and are exhibited, together with the COMPOUNDS. Combustion. Molecular Heats of Formation. 6. 7. 8. 9. 10. 11. Difference M. H. F. Difference between cols. 4 & 5. Error. Formula. (Thomsen) constant vol. M. H. F. calculated. between cols. 9 & 10. Cals. Per cent. Cals. Cals. Cals. + 2-3 + 0-24 rw-/3' -5-3 -7-5 -2-2 -7-2 -0-56 '+3a'-3/?' -2-4 + 4-9 + 7-3 -6-4 -0-50 '+3a'-3/T -1-6 + 4-9 + 6-5 -0-5 -0-07 r-x -12-1 -12-0 + 0-4 differences betwen them and the experimental, and the percentage errors (in the case of molecular heats of com- bustion) in Table 17. The results are quite satisfactory. The values given to % and % ' m the above table are those already obtained for aliphatic halogen compounds ; the excellent agreement between the experimental and calculated results shows that ^ and % have the same values in aromatic compounds, and hence that chlorine exhibits a like thermal behaviour in aromatic and in aliphatic compounds. Other aromatic com- pounds will be considered later. 5. THERMAL CONSTANTS OF ORGANIC OXYGEN COMPOUNDS. WE find generally in compounds of carbon, hydrogen and oxygen, that the oxygen is combined in three primary ways, namely : the etheric, in which the oxygen atom is ' singly ' linked to two different carbon atoms ; the hydroxylic, in which the oxygen atom is singly linked to a carbon and to a hydrogen atom ; the ketonic, in which the oxygen atom is ' doubly ' linked to one carbon atom ; each of these three classes will require a different constant, as follows : 11. MOLECULAR HEATS OF COMBUSTION OF ETHERS. 1 All ethers can be obtained theoretically by replacing 2c hydrogen atoms in one or more hydrocarbons by c oxygen atoms, each linked to two different carbon atoms, where c is some integer ; the following constant will therefore be required : o) = the algebraic sum of the following heats : (i) due to the severance of two C . H links ; (ii) due to the combustion of two hydrogen atoms (to liquid water), minus the algebraic sum of the following heats :- (iii) due to the severance of two C . links ; (iv) one- half that due to the formation of an oxygen molecule ; or, as it can be written more simply : 1 A consideration of Ethylene Oxide is postponed until 21. OEGANIC OXYGEN COMPOUNDS 39 o) = the sum of the following heats : (ii) due to the combustion of two hydrogen atoms (to liquid water) ; (iii) due to the formation of two C . links, minus the sum of the following heats : (i) due to the forma- tion of two C . H links ; (iv) one-half that due to the formation of an oxygen molecule. So that the general ether : nC + 2(n+l-a-2b-p-c) H+ (n + p - a - b - 1) L, + aL, + &L 3 + cO + 2c(C.O) links 1 can be written : In Table 18 will be found the molecular heats of combustion (corrected for constant volume) of eight ethers, determined by Thomsen ; from each of these a value of a> has been calculated thus Methyl ethyl ether is CH 3 . . C 2 H r i. e. 3a - ft - w. M. H.C. found = 5044 Gals. Therefore, a) = 5a-/3 - 5044 Gals. = (6324 - 52-5 - 5044) Gals. = 75-5 Cals., &c. ; the values of w thus obtained are given in the table ; the mean of the six more consistent values is oj = 754 Cals. Using this value, the molecular heats of combustion of all the ethers given have been calculated, and are exhibited, together with the differences between them and the experimental, and the percentage errors, in Table 18 ; the agreement is quite satisfactory, except perhaps in the case of methylal. The agreement in the case of anisol shows that w o has the same value in aromatic as in aliphatic sub- stances. 1 For common ethers put p = - 1. 40 THERMO-CHEMICAL CONSTANTS TABLE Ii 1. Substance. 2. Formula. Molecular He 3. Formula. 4. M. H. C. found vThomsen" constant volume. 5. C 2 H-.O.CJI- CII 3 -.O.C 3 H fl C 3 TI 5 .O.C,I1 5 CH 3 .O.C 3 H 3 C II 5 . . CH 3 CM 2 (OCTT 3 ) 2 2a-w 3a j3 to 4a-2-w 4a j3 y to Qa-2/3-2y-co 4a-/2-S-u> + a a> 3a 2 to Cals. 348-2 504-4 657-9 625-7 909-4 602-7 934-8 474-9 Mean ... a Cals. 73-4 75-5 (80-3) 76-0 (72-4) 75-0 73-9 78-75 > = 754 Cals. 346-2 504-5 662-8 626-3 906-4 602-3 933-3 481-6 Methylal . 12. MOLECULAR HEATS OF FORMATION OF ETHERS. The molecular heat of formation constant corre- sponding to a} is o/ = the algebraic sum of the following heats: (i) due to the decomposition of a hydrogen molecule ; (ii) due to the formation of two C . H links, minus the algebraic sum of the following heats : (iii) one-half that due to the decomposition of an oxygen molecule ; (iv) due to the formation of two C . links ; or, as it can be written more simply : co = the sum of the following heats : (ii) due to the formation of two C . H links ; (iii) one-half that due to the formation of an oxygen molecule, minus the sum of the following heats : (i) due to the formation of a hydrogen molecule ; (iv) due to the formation of two C . links. ORGANIC OXYGEN COMPOUNDS 41 ETHEES. of Combustion. Molecular Heats of Combustion. 7. 8. 9. 10. 11. 12. 13. MTT F Difference between cols. 4 and 6. Error. Formula. found (Thomsen) constant volume. ' calcu- lated. M. H. F. calcu- lated. Difference between cols. 10 and 12. Cals. Per cent. Cals. Cals. Cals. Cals. -2-0 -0-57 2a'-to' 48-2 -5-8 50-2 + 2-0 + 0-1 + 0-02 3 a' y8' to' 56-4 -7-8 56-4 + 0-0 + 4-9 + 0-74 4 a - 2 ft' to' 67-4 (-12.6) 62-6 -4-8 + 0-6 + 0-10 4 of ft' Y M' 32-1 -8-3 31-6 -0-5 -3-0 -0-33 6a -2/3' - 2/-a/ 9.9 (-4-7) 13-0 + 3-1 -0-4 -0-07 A f ' ' ' 4a p o to -12-4 -7-3 -11-9 + 0-5 -1-5 -0-16 ' + of - to' + 13-8 -6-3 + 15-3 +1-5 + 6-7 + 1-41 3 a 2 to 85-9 -11-15 79-2 -6-7 Mean ... to'= - 7-8 Therefore, w + a/ = the heat due to the combustion of two hydrogen atoms (to liquid water), less the heat due to the formation of a hydrogen molecule the molecular heat of combustion of hydrogen gas to liquid water = 67-5 Cals. ; whence, / = 67-5 Cals. - a) = (67-5 - 754) Cals. = - 7-9 Cals. In Table 18 will be found the molecular heats of formation (at constant volume) of eight ethers, given by Thomsen, from these the value of a/ has been cal- culated in a similar manner as was the value of at. The mean value is o/ 7-8 Cals., agreeing with the above. Using this value (a/ = 7-8 Cals.), the molecula-r heats of formation of all the ethers given have been calculated, and are exhibited, together with the dif- ferences between them and the experimental, in Table 18. 42 THEEMO-CHEMICAL CONSTANTS 13. MOLECULAR HEATS OF COMBUSTION OF ALCOHOLS. All alcohols can be obtained theoretically by re- placing d hydrogen atoms in the corresponding hydro- carbons by d hydroxyl groups each linked to carbon, where d is some integer ; the following constant will therefore be required : o>i = the algebraic sum of the following heats: (i) due to the severance of a C . H link ; (ii) due to the com- bustion of a hydrogen atom (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of a C . link ; (iv) due to the severance of an . H link ; (v) one-half that due to the forma- tion of an oxygen atom ; (vi) due to the combustion of a hydrogen atom (to liquid water) ; or, as it can be written more simply : e^ = the sum of the following heats : (iii) due to the formation of a C . link ; (iv) due to the formation of an . H link, minus the sum of the following heats : (i) due to the formation of a C . H link ; (v) one- half that due to the formation of an oxygen molecule. So that the general alcohol : can be written : n C + 2 (n + 1 - a - 2 b - -p) H + (n + - p-a-6-l)L 1 + a L 2 + b L 3 d 01, = n a (n +p a b l)^ 1 See footnote, p. 3. ORGANIC OXYGEN COMPOUNDS 43 Now, the heat of combustion of two hydrogen atoms to water vapour = the heat due to the formation of two O . H links, less one-half that due to the forma- tion of an oxygen molecule. Therefore, the heat due to the formation of two O . H links = the heat of com- bustion of two hydrogen atoms to water vapour, plus one-half the heat due to the formation of an oxygen molecule. Now, 2 OH, i.e. a -co,. M. H. G. found = 1814 Gals. Therefore, e^a-1814 Gals. = (210-8 - 1814) Gals. = 29-4 Gals., &c. These values are given in the table. It is seen that the alcohols divide themselves into two groups, thus : 44 THERMO-CHEMICAL CONSTANTS The first group contains the primary alcohols and phenol, and gives a value for o^ somewhat below the theoretical (32-8 Gals.). The mean of the five more consistent values is o^ = 29-7 Gals. Using this value the molecular heats of combustion of the members of this group have been calculated, and are exhibited, together with the differences between them and the experimental, and the percentage errors, in Table 19. The agreement is quite satisfactory. The second group contains the secondary and ter- tiary alcohols, ethylene glycol and a primary alcohol (propargyl alcohol), and gives a value for o^ somewhat above the theoretical. The mean value (neglecting trimethyl carbinol) for this group is 35-9 Gals. It will be shown, however, in 18 that the mean value of CO L in mono-carboxy acids is 37-0 Gals., agreeing with this value above ; the final mean, namely 36-4 Gals., is used in the calculations ; and the molecular heats of combustion of the alcohols in this group have been calculated thereby, and are exhibited, together with the differ- ences between them and the experimental, and the percentage errors, in Table 19. The agreement is quite satisfactory, except in the case of trimethyl- carbinol. This behaviour of the alcohols in thus dividing themselves into two groups with respect to the value of O) L is remarkable, inasmuch as it appears that the mere position of the hydroxyl group exercises an influence upon its thermal equivalent, and is in marked contrast to the behaviour of the chlorine substituted hydrocarbons (see 8). It may be, however, that the two hydrogen atoms in water are not bound to the oxygen atom with ORGANIC OXYGEN COMPOUNDS 45 equal affinity (see the case of ammonia, 26) in some alcohols one hydrogen atom being replaced, in others, the other hydrogen atom being replaced, depending pos- sibly upon the configuration of the rest of the mole- cule, whilst the thermal value of the C . link is constant. This would explain why the value of o) l deduced from a consideration of the ether constant and water is practically the arithmetic mean between the two values of ^ obtained from the two groups of alcohols above. 14. MOLECULAR HEATS OF FORMATION OF ALCOHOLS. The molecular heat of formation constant corre- sponding to coj is : & i = the algebraic sum of the following heats : (i) one-half that due to the decomposition of a hydro- gen molecule ; (ii) due to the formation of a C . H link, minus the algebraic sum of the following heats : (iii) one-half that due to the decomposition of an oxygen molecule ; (iv) one-half that due to the de- composition of a hydrogen molecule ; (v) due to the formation of a C . link ; (vi) due to the formation of an O . H link ; or as it can be written more simply: a)/ = the sum of the following heats : (ii) due to the formation of a C . H link ; (iii) one-half that due to the formation of an oxygen molecule, minus the sum of the following heats : (v) due to the formation of a C . link ; (vi) due to the formation of an O . H link. Hence, a>/ = co l . In Table 19 will be found the molecular heats of formation (at constant volume) of twelve alcohols, &c., given by Thomsen ; from these the values of &>/ have THERMO-CHEMICAL CONSTANTS TABLE 19. 1. Substance. 2. Formula. Molecular Heats 3. Formula. 4. M. H. C. found (Thomsen) constant vol. 5. ! 767-6 30-3 Primary Alcohols. Methyl alcohol . . . CH 3 . OH a-wj 181-4 29-4 Ethyl alcohol .... C 2 H 5 . OH 2a /? coj 339-4 29-7 Propyl alcohol . . . C 3 H 7 .OH 3a-2/?- Wl 497-2 30-2 ?6'oButyl alcohol . . . (CH 3 ) 2 CH . CH 2 OH 4a-3/2-(o 1 656-7 29-0 wo Amy 1 alcohol . . Allyl alcohol .... ,CH 3 ) 3 CH.CH 2 .CH 2 OH C 3 H 5 .OH 5(1-4/3-0)! 3a-/2- 7 - Wl 818-0 463-6 (26-0) (27-3) Mean Wl =29-7 GKOUP 2. Propargyl alcohol . C 3 H 3 . OH 3a-/3-3- Wl 430-2 36-7 Ethylene glycol . C 2 H 4 (OH) 2 2 a - (3 - 2 coj 297-2 71-9xi Secondary Alcohol. /soPropyl alcohol . . (CH 3 ) 2 CH . OH 3a-2^-a> 1 491-9 35-5 Tert iarij A Icohols. Trimethyl carbinol . (CH 3 ) 3 C.OH 4a-3-a> 1 639-6 (46-1) Dimethyl ethyl carbinol (CH 3 ) 2 C(OH)C 2 H, oa-4/3-a)! 808-4 35-6 Mean ... wj = 35-9 Final Mean (see text) ... Wl = 36-4 been calculated similarly as were the values of w,. The mean values obtained are : for the first group a>i = -29-6 Cals. ; for the second group &)/= -35-8 Cals., in agreement with the above relation. Using the values obtained from this relation (/ 71-7 (-25.7) 75-7 + 4-0 461-2 -2-4 - 0-52 3 a ft y (*>! 29-8 (-27-2; 32-3 + 2-5 Mean...o) /- -29-6 430-5 4 0-3 + 0-07 Sa'-p'-S'-a)!' -4-4 -36-5 -4-5 -0-1 296-3 -0-9 -0-30 2a'-/?'-2a> 1 ' 1 + 99-2 -71-8XJ + 100-2 + 1-0 491-0 -0-9 -0-18 3 a' -2/3' -co/ 69-0 -35-4 70-0 -f-1-0 649-3 + 9-7 + 1-52 la'-S/S'-co/ 85-7 (-45-9) 76-2 -9-5 807-6 -0-8 -0-10 5 a' 4/3' w/ 81-3 -35-3 82-4 + M Mean...oj 1 / = -35-8 the first and second groups respectively, the mole- cular heats of formation of all the alcohols, &c., given have been calculated, and are exhibited, together with the differences between them and the experimental, in Table 19. 6. THERMAL CONSTANTS OF ORGANIC OXYGEN COMPOUNDS (continued). $15. MOLECULAR HEATS OF COMBUSTION OF KETONES AND ALDEHYDES. ALL ketones and aldehydes can be obtained theo- retically by replacing 2 e hydrogen atoms in the corresponding hydrocarbons by e oxygen atoms each 'doubly linked' to carbon, where e is some integer; the following constant will therefore be required : o> 2 = the algebraic sum of the following heats : (i) due to the severance of two C . H links ; (ii) due to the combustion of two hydrogen atoms (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of a C : link ; (iv) one-half that due to the formation of an oxygen molecule ; or, as it can be written more simply : W, = the sum of the following heats : (ii) due to the combustion of two hydrogen atoms (to liquid water) ; (iii) due to the formation of a C : O link, minus the sum of the following heats : (i) due to the formation of two C . H links ; (iv) one-half that due to the formation of an oxygen molecule. So that the general ketone and aldehyde : n C + '2 (n + 1 - a - 2 b -p - e) //+ (ti + p-a-l>- 1)L, + a L 2 + 1) L 3 + e O + e (C : O) links can be written : n C + 2(n+l-a-2& -p) H + (n +p --&-!) LI + a L 2 -I- b L 3 e co 2 = na (n+p a & 1)$ ay 68 ea> 2 . OKGANIC OXYGEN COMPOUNDS 49 The value of o> 2 can be shown from a consideration of carbon dioxide to be identical with that of ^, in J either of the following ways : (1) a = the molecular heat of combustion of methane (to gaseous carbon dioxide and liquid water). = the algebraic sum of the following heats : (i) due to the combustion of one carbon atom ; (ii) due to the severance of four C . H links ; (iii) due to the com- bustion of four hydrogen atoms (to liquid water). But as carbon on combustion gives O : C : 0, the heat of combustion of one carbon atom = the heat due to the formation of two C : O links, less the heat due to the formation of an oxygen molecule. Therefore, a = the sum of the following heats : (iii) due to the combustion of four hydrogen atoms (to liquid water) ; (i) due to the formation of two C : links, minus the sum of the following heats : (ii) due to the formation of four C . H links ; (i) due to the formation of an oxygen molecule. Therefore, a = 2 w 2 , whence a>_, = ~ = 1054 Gals. ~ (2) Otherwise: CO 2 can be written a 2w 2 , its heat of combustion is zero, whence a 2 a>^ = 0, so that o) 2 = ~ = 1054 Cals. as before. tL This value of o> 2 , as will be shown later, is in excellent agreement with the values obtained for the carbonyl oxygen in certain acids and esters (see $17 and 18). In Table 20 will be found the molecular heats of combustion (corrected for constant volume) of three aldehydes and two ketones determined by Thomsen. These give lower values for o> 2 , thus : Acetaldehyde is CH 3 .CHO, i.e. 2 a - - *>,. M.H.C. found = 281-0 Gals. E 50 THERMO-CHEMICAL CONSTANTS Therefore o), = 2 a - /3 - 281-0 Cals. = (421-6 - 52-5 - 281-0) Cals. = 88-1 Cals. The values of o> 2 calculated thus are given in the table. The mean value for the aldehydes is w 2 = 87-7 Cals., for the ketones, w 2 = 914 Cals. ; using these values, the molecular heats of combustion of all the aldehydes and ketones given have been calculated, and are exhibited, together with the differences between them and the experimental, and the percentage errors, in Table 20. The agreement is excellent. It must, however, be noticed that probably the above two latter values are not the true values of o> 2 , but are purely empirical, inasmuch as it seems very probable that all (or at least, many) ketones and aldehydes are, under ordinary conditions, mixtures of true carbonyl-oxygen compounds the true ketones and aldehydes and unsaturated secondary alcohols (i. e. mixtures of the keto and enol forms) : these latter, it is worth while noticing, have theoretically relatively high molecular heats of combustion. 16. MOLECULAR HEATS or FORMATION or ALDEHYDES AND KETONES. The molecular heat of formation constant corre- sponding to a) 2 is : o). 2 ' = the algebraic sum of the following heats : (i) due to the decomposition of a hydrogen molecule ; (ii) due to the formation of two C . H links, minus the algebraic sum of the following heats : (iii) one-half that due to the decomposition of an oxygen molecule ; (iv) due to the formation of a C : link ; or, as it can be written more simply: o>/ = the sum of the following heats : (ii) due to the OKGANIC OXYGEN COMPOUNDS 51 formation of two C . H links ; (iii) one-half that due to the formation of an oxygen molecule, minus the sum of the following heats : (i) due to the formation of a hydrogen molecule ; (iv) due to the formation of a C : O link. Therefore, a). 2 + w 2 ' = the heat due to the combustion of two hydrogen atoms (to liquid water), less the heat due to the formation of a hydrogen molecule = the molecular heat of combustion of molecular hydrogen to liquid water = 67-5 Cals., whence co/ 67-5 Cals. co. 2 . Therefore, co/ (C0 2 , acids and esters, see hereinafter) l = (67-5 - 1054) Cals. = - 37-9 Cals. o>/ (aldehydes) = (67-5 - 87-7) Cals. = 20-2 Cals. 2 : Co,' (aldehydes) = - 201 Cals. co/ (ketones) = 23-55 Cals. Using the mean values, co/ (aldehydes) = 20-2 Cals., co/ (ketones) = 23-7 Cals., the molecular heats of formation of all the aldehydes and ketones given have been calculated, and are exhibited, together with the differences between them and the experimental, in Table 20. 1 The molecular heat of formation of carbon dioxide calculated by means of this value of o> 2 ' (M. H. C. of C0 2 = a - 2w 2 ' = 97-0 Cals.) is in agreement, as follows necessarily from the method of calculation, with the actual experimental result (= 96-96 Cals.). E 2 52 THERMO-CHEMICAL CONSTANTS TABLE 20. ALDEHYDES 1. Substance. 2 > Formula. Molecular Heats of 3. Formula. 4. M. H.C. found (Thomson) constant vol. 5. 2 calcu- lated. 6. M. H. C. calcu- lated. Aldehydes. Acetaldehyde . . Propion aldehyde . . ?so-Butylaldehyde Ketones. Dimethyl ketone . . Methyl propyl ketone CH 3 . CHO C 2 H 5 .CHO C 3 H 7 . CHO (CH 8 ) 2 CO CH 3 . CO . C 3 H 7 2a-/3-co 2 3a-2/?-a> 2 4 a 3/? w 2 3a-2/3-w 2 5 a 4 (3 w 2 . \.(J . 0.0.3 M. H. C. found = 240-6 Cals. 1 For common esters put p = 1. OKGANIC OXYGEN COMPOUNDS 53 AND KETONES. Combustion. Molecular Heats of Formation. 7. Difference between cols. 4 and 6. 8. Error. 9. Formula. 10. M. H. F. found Thomsen) constant vol. 11. a>2 calcu- lated. 12. M. H. F. calcu- lated. 13. Difference between cols. 10 and 12. Cals. + 0-4 + 04 -0-4 Per cent. + 044 + 0-02 -0-07 2 a ft a>2 3a'-2ft'-o> 2 ' Cals. 47-9 53-8 59-3 Cats. -20-5 -20-2 -19-5 Cals. 47-6 53-8 60-0 Cals. -0-3 0-0 + 0-7 Mean ... o> 2 ' = -204 -04 + 04 -0-02 + 0-01 3 a 2 ft o>2 57-3 69-4 -23-7 -23-4 57-3 69-7 + 0-0 + 0-3 Mean ... o> 2 ' = -23-55 Therefore, o> + w 2 = 2 a - 240-6 Cals. (421-6 - 240-6) Cals. = 181-0 Cals. The value of co + 2 the value 1054 Cals., obtained from a consideration of carbon dioxide, a value for o>, namely 75-8 Cals., is obtained in excellent agreement with that obtained from the molecular heats of combustion of ethers, namely, 75-4 Cals. It is evident, therefore, that as the value of a). 2 in these esters is equivalent to , their formulae, in so far THEKMO-CHEMICAL CONSTANTS TABLE 21. Molecular Heats of 1. 2. 3. 4. 5. 6. M. H. C. found cy + = 754 Cals., the molecular heats of combustion of all the esters given have been calculated, and are exhibited, together with the differences between them and the experimental, and the percentage errors in Table 21. The agree- ment is quite satisfactory except in the case of ethyl acetate, which gives an exceptional molecular heat of OKGANIC OXYGEN COMPOUNDS 55 ESTERS. Combustion* Molecular Heats of Formation. 7. 8. 9. 10. 11. 12. 13. Difference between cols. 4 and 6. Error. Formula. M. H. F. (Thomson) constant vol. u>' + co 2 ' calcu- lated. M. H. F. calcu- lated. Difference between cols. 10 and 12. Cals. Per cent. Cals. Cals. Cals. Cals. + 0-2 + 0-08 o ' ' ' A a w o> 2 88-3 -45-9 88-1 -0-2 + 0-7 + 0-18 3a'-y3'-a/-co 2 ' 95-0 -46-4 94-3 -0-7 + 4-6 + 0-83 4a'-2/3'-a/-w/ 105-0 -50-2 100-5 -4-5 + 0-2 4-0-03 5tt'-3'-a/-co 2 ' 106-8 -45-8 106-7 -0-1 -0-1 -0-03 o / /o/ / / o a p (o 0)2 94-2 -45-6 94-3 + 0-1 + 12-0 + 2-20 4a'-2/3'-a/-a> 2 ' 112-4 (-57-6) 100-5 -11-9 -0-2 -0-04 4a'-2/2'-a/-w 2 ' 100-2 -45-4 100-5 + 0-3 -2-7 -0-35 5a 3 ft w a>2 103-8 -42-8 106-7 + 2-9 -6-1 -146 A f r>f ft f 4a p y w a> 2 63-3 (-39-5) 69-5 + 6-2 Mean ... w + o^' = -46-0 combustion, which has not yet been satisfactorily explained. 1 18. MOLECULAR HEATS OF COMBUSTION OF ACIDS. The general formula for all mono-basic carboxy acids is : + a L, -t- 1 L 3 + 2 + 1 (C : 0) link + 1 (C . O) link = l(6.H)link 1 Thomson found that ethyl acetate would not fit in with the rest of his system, see Thermocliemuclie UntersucJningen, iv. 310. 56 THEEMO-CHEMICAL CONSTANTS TABLE 22. Molecular Heats of 1. 2. 3. 4. 5. 6. M. H. C. found 1 + W 2 M. H. C. Substance. Formula. Formulae. (Thomson) calcu- calcu- constant lated. lated. vol. A cids. Cals. Cals. Cals. Formic acid . . H.C0 2 H | a coj w 2 ] 69-1 141-7 69-0 I 9 n Q , 4 , , 1 Acetic acid . . . CH 3 . C0 2 II I t ft p (Oj W 2 {lift-/? -a,! 224-8 144-3 227-3 Propionic acid . . C 2 II 5 . C0 2 H ( 3 u. 2 LJ coi o>o ) 385-6 141-8 385-6 Mean ... Wl + w 2 = 142-4 Anhydride. Acetic anhydride . (C 2 II a O) 2 J 4a-2y8-co-2o> 2 | ( ( 3a-2/?- 2 In Table 22 will be found the molecular heats of combustion (corrected for constant volume) of three acids, given by Thomsen, from these the value of o>! + o). 2 has been calculated thus : Formic acid is H . C \ ^-p- i. e. a a^ a/, . M. H. C. found = 691 Cals. Therefore, ^ + e, = a - 691 Cals. = (210-8 - 691) Cals. = 141-7 Cals. The value of co l + ^ obtained from each acid is given in the table. Mean value of c^ + w 2 = 1424 Cals. It is at once evident that, if we assign to w 2 the values obtained from the molecular heats of combustion of either aldehydes or ketones, values for v^ will be obtained which are much higher than obtained before ($ 13) ; but if, on the other hand, we assign to o> 2 OKGANIC OXYGEN COMPOUNDS 57 ACIDS. Combustion. Molecular Heats of Formation. 7. 8. 9. 10. 11. 12. 13. Difference between cols. 4 and 6. Error. Formula. M. H. F. (Thomson) constant vol. calcu- lated. M. H. F. calcu- lated. Difference between cols. 10 and 12. Cals. Per cent. Cals. Cals. Cals. Cals. -0-1 -0-14 a'- 2 ' 95-4 -74-2 95-5 + 0-1 + 2-5 + 1-11 2> ft fj w-i Wo 104-1 -76-7 101-7 -2-4 0-0 0-00 q / n nf / / oa &p a>j o>2 107-7 -74-1 107-9 + 0-2 Mean ... w/+ a> 2 ' = -75-0 -7-5 -1-63 4a / -2/r-a/-2a>o / 130-8 - 138-4 + 7-6 the value 1054 Cals., obtained from consideration of carbon dioxide, we obtain for c^ a value, 37-0 Cals., in agreement with that found for the second group of alcohols, namely 35-9 Cals. The mean of these two values, namely 364 Cals., is taken therefore as the value of aji for these classes of compounds. It is evident, therefore, that as the value of &>., in these acids is equivalent to 5, their formulae, in so far u as molecular heats of combustion are concerned, can be simplified, as were the formulae of their esters with mono-hydroxy alcohols, the general formula becoming: (n-\}a-(n +p -a-b-l) p-ay~-b- w^ Both sets of formulae are given in Table 22 ; using the simplified formulae and the value w l = 364 Cals., the molecular heats of combustion of the acids (and also similarly, that of acetic anhydride, using a) = 754 Cals.) have been calculated, arid are exhibited, 58 THEKMO-CHEMICAL CONSTANTS together with the differences between them and the experimental, and the percentage errors, in Table 22. The agreement in the cases of the acids is quite satisfactory. 19. MOLECULAR HEATS OF FORMATION OF ESTERS AND ACIDS. The values of &/ + 2 ' = 75-0 Gals, in agreement with the values of a>' } cu/ and o>/ obtained respectively from ethers, alcohols (group 2), and carbon dioxide. Using these latter values, whence a/+G>/= -45-7 Gals., &{ + <;= -74-3 Gals., the molecular heats of formation of all these esters, acids, &c., given have been calculated, and are exhibited, together with the differences between them and the experimental, in Tables 21, 22. 7. THERMO-CHEMICAL EVIDENCE FOR YON BAEYER'S STRAIN THEORY. IT has been shown in ^ 4 that the apparently anomalous result obtained by Thomsen for the mole- cular heat of combustion of trimethylene is explicable in terms of von Baeyer's Strain Theory. It has also been shown that the thermal data relating to ethene and ethine hydrocarbons is in agreement with this theory. And the thermal equivalents of the intra- molecular strain in these substances have been cal- culated from Thomsen's experimental data. We proceed to the examination of Stohmann's experimental data relating to the thermal behaviour of the poly- methylenes, and Thomsen's experimental result for the molecular heat of combustion of ethylene oxide. 20. THERMAL EQUIVALENTS OF THE INTRA- MOLECULAR STRAIN IN POLYMETHYLENES. The procedure adopted by Stohmann and his collaborators in their thermo-chemical researches on the polymethylenes l was to determine the heats of combustion of polymethylene carboxylic acids (these being prepared more readily than other polymethylene derivatives), and of the corresponding open- chain acids, 1 For which, see Stohmann, Kleber, and Langbein, J. Prakt. Client., xl. 202, 341 ; Stohmann and Kleber, ibid., xliii. 1, and xlv. 475. 60 THEKMO-CHEMICAL CONSTANTS TABLE 23. 1. Dimethylenes (Ethylenes). Fumaric acid * . Succinic acid .... Dimethyl fumaraie . Dimethyl succinate . 2. Trimethylenes. aa-Trimethylenedicarboxylic acid a/?-Trimethylenedicarboxy]ic acid Glutaric acid . Methylsuccinic acid . Ethylmalonic acid . . . . Dimethylmalonic acid . . aa/?/?-Tetramethyl trimethylenetetra- carbonate . . . . . Tetramethyl methylenedimalonate 3. Tetramethylenes. aa-Tetramethylenedicarboxylic acid a/?-Tetramethylenedicarboxylic acid Adipic acid .... Methylglutaric acid . Ethylsuccinic acid Sym. Dimethylsuccinic acid Unsyni. Dimethylsuccinic acid . Propylmalonic acid . ^so-Propylmalonic acid Methylethylmalonic acid . 4. Pentamethylenes. a/3-Pentamethylenedicarboxylic acid Pimelic acid 5. Hexamethylenes. cis. Hexahydroterephthalic acid trans. Hexahydroterephthalic acid Suberic acid M. H. C. constant vol. (Stoh- mann). Mean. Cals. Cals. 320-7 320-7 357-1 357-1 Therefore ft - T 2 = 36-4 Cals. C G II 8 4 664-7 664-7 C G H 10 4 703-3 703-3 Therefore ft - T 2 - 38-6 Cals. Mean /2-T 2 =37-5 Cals. C 4 H 4 4 C 4 H 6 4 C 5 H G 4 C 5 H G 4 C 5 H 8 4 C 5 H 8 4 483-5 484-4 515-0 515-2 C 5 II 8 4 517-91 C 5 H 8 4 515-3 1 Therefore ft - T m = 31-9 Cals. 483-95 515-85 1170-7 1202-2 1170-7 1202-2 Therefore - T = 31-5 Cals. C 6 H 8 4 C 6 H 8 4 SS) - C C H ]0 4 668-6 C I1 10 4 670-5 671-9 cXoX C C II 10 4 670-7 671-4 [ 671-84 C H I0 4 674-7 C 6 H 10 4 674-9 C H W 4 672-0 Therefore /2-T,v = 29-4 Cals C 7 H 10 4 775-7 775-7 C 7 II 12 4 828-3 828-3 Therefore yS-T v = 52-6 Cals . C 8 11 12 4 928-0) 928-9f y ^ b 982-8 982-8 Therefore ft - T VI = 54-35 Cals. Malei'c acid is omitted as it gives a divergent result. C 8 H 12 4 C 8 II H 4 VON BAEYEE'S STRAIN THEORY 61 using a bomb- calorimeter. The difference between the molecular heats of combustion of any polymethylene derivative and of the corresponding open-chain com- pound is due to the breaking of the ring and the addition of two hydrogen atoms linked to carbon ; in terms of our constants, this difference equals 2 H- L! - T, that is to say, ft - T. In Table 23 are given these molecular heats of combustion (for constant volume), and the values of TABLE 24. King. Stohmann. Thomsen. Acetylene T 3 44-5 Cals Ethylene . . . j T 9 = 52-5 Cals. - 37-5 Cals. ) - 15-0 Cals j T 2 = 16-0 Cals. Trimethylene . ! T nl = 52-5 Cals. - 31-7 Cals. ]. = 20-8 Cals ) T IM = 23-1 Cals. Tetrametliylene j ' I Tiv = 52-5 Cals. - 29-4 Cals. ) = 23-1 Cals. j Pentamethylene T v = 52-5 Cals - 52-6 Cals. \ = 0-1 Cals., i e zero ) Hexamethylene j 1 T VI = 52-5 Cals. - 54-35 Cals. ) = 1-85 Cals., i.e. zero j ft T calculated for the various rings. The notation employed is to denote the number of carbon atoms in the ring by a Roman numeral affixed to T. T 2 and T :5 will be employed with the significations applied to them in 4. The value of ft being known, the values of T can readily be obtained, as in Table 24. Perfectly accurate results cannot be expected, for the value of ft employed (namely 52-5 Cals.) is calculated from the molecular heats of combustion of gases, whereas the values of ft T are for solids. However, as ft T is always 62 THERMO-CHEMICAL CONSTANTS found as the difference between two (or two sets) of Stohmann's experimental results, this error will be at a minimum, and fairly good approximate results may be hoped for. On comparing with the above those values of T which have also been calculated entirely from Thomsen's experiments (namely T 2 and T m ), we see that the above error amounts to only 1-0 Cal. in the case of T 2 , and 2-3 Cals., in the case of T m . Now as in the above rings different numbers of links are concerned, it is evident, that, in order to obtain comparable results, it will be necessary to TABLE 25. King. Thermal Equivalent of Strain for each link. Angle of Deviation. Stohmann. Thomson. Mean. D. Acetylene Ethylene . . . Trimethylene . Tetramethylene Pentamethylene ^ = 7-5 Cals. t~ m = 6-9 Cals. f IV = 5-8 Cals. t v = 0-0 Cals. ? 3 = 14-8 Cals. f 2 = 8-0 Cals. t m = 7-7 Cals. t z = 7-8 Cals. * m =7-3Cals. 70 32' 54 44' 24 44' 9 44' 044' divide the thermal equivalent of the total strain in each ring by the number of links in that ring which are in a condition of strain, thereby obtaining the thermal equivalents of the strains set up by deviating one C . C link through various angles, represented by t in Table 25. The regularity is at once apparent, for, whichever set of results we use, it is seen that increase in the angle of deviation causes a rise in t, while a decrease in the angle of deviation produces a corresponding fall in t, indicating the probable existence of some mathematical relation (although clearly not a simple proportion) between D and t. This regularity is exhibited more VON BAEYEE'S STEAIN THEOEY 63 clearly by a curve in which D and t are plotted along coordinate axes. This curve is shown in the plate, the values used being derived from Thomsen's data for t 3 and t. 2 , from Stohmann's for t iy and t v , and the mean value for t lu . Its regular nature is at once apparent, and constitutes, in the author's opinion, very striking evidence for the validity of von Baeyer's Strain Theory ; but up to the present he has not been able to represent satisfactorily the relation between D and t by any simple mathematical formula. 21. THE THERMAL EQUIVALENT or THE INTRA- MOLECULAR STRAIN IN ETHYLENE OXIDE. Chemical evidence shows that the ethylene oxide molecule has the constitution GIL, I ">0 OH/ so that its molecular heat of combustion is represented by the expression 2 a /3 co. The molecular heat of combustion (corrected for constant volume) of this compound was found by Thomsen to be 311-7 Cals., whereas the calculated molecular heat of combustion amounts to only (2 x 210-8 - 52-5 - 75-4) Cals. = 293-7 Cals., so that the experimental is considerably greater (by 18-0 Cals.) than the calculated molecular heat of com- bustion. The molecular heat of formation deduced from the experimental heat of combustion, namely 17-2 Cals., is correspondingly less than the calculated value, namely, 2 a - p - a/ = (2 x 21-2 - 15-0 + 7-8) Cals. = 35-2 Cals. 64 THEEMO-CHEMICAL CONSTANTS < 1C 8 tCals. 1O M 30 SO 60 10 Curve showing change in the value of t with change in the angle of deviation. YON BAEYEE'S STEAIN THEOEY 65 This apparently anomalous result would be expected, however, from the standpoint of von Baeyer's Strain Theory ; for, from analogy with trimethylene, the ethylene oxide molecule must be in a condition of strain. The thermal equivalent of this strain is now given as 18-0 Gals. ; that it is not identical with that for trimethylene is only to be expected from the fact that carbon has an affinity for carbon differing from that which it has for oxygen, and, moreover, it is not unlikely that the normal directions of the oxygen valencies are different from the normal direction of carbon valencies. The general conclusion to be drawn from the thermal data considered is that a perfect agreement with von Baeyer's Strain Theory is shown ; and that it supplies satisfactory evidence of the validity of this theory. 8. THERMAL CONSTANTS OF ORGANIC SULPHUR COMPOUNDS. THE organic sulphur compounds being quite analogous to the organic oxygen compounds, we shall require an analogous set of constants as follows : J 22. MOLECULAR HEATS OF COMBUSTION OF ORGANIC SULPHUR COMPOUNDS. (1) Sulphides (analogous to ethers). These sulphides can be obtained theoretically by replacing 2 g hydrogen atoms in one or two hydrocarbons by g sulphur atoms, each singly linked to two carbon atoms, where g is some integer ; the following constant will therefore be required : o- = the algebraic sum of the following heats : (i) due to the severance of two C . H links ; (ii) due to the combustion of two hydrogen atoms (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of two C . S links : (iv) due to the combustion of a sulphur atom ; or, as it can be written more simply : o- = the sum of the following heats : (ii) due to the combustion of two hydrogen atoms (to liquid water) ; (iii) due to the formation of two C . S links, minus the sum of the following heats : (i) due to the formation of two C . H links ; (iv) due to the combustion of a sulphur atom. ORGANIC SULPHUR COMPOUNDS 67 So that the general (etheric) sulphide nC-\-2(n + I-a-2b- p- g)H+ (n+p-a-b-1) L, + aL 2 + bL 3 + 2g (C. S) links +gS l can be written 2(n+l-a-2b-p)H+(n+p-a-b-l)L l = n a (n + p a b l)/3 ay b$ g cr. In Table 26 will be found the molecular heats of combustion (corrected for constant volume) of two (etheric) sulphides, determined by Thomsen, from each of which a value of cr has been calculated thus : Dimethyl sulphide is (CH 3 ),S, i.e. 2 a - cr. M. H. C. found = 455-9 Gals. Therefore, o- = 2 a - 455-9 Gals. = (421-6 - 455-9) Gals. = - 34-3 Gals., &c. ; mean value for cr= 33-1 Gals. (2) Mercaptans (analogous to alcohols). All mercap- tanscanbe obtained theoretically by replacing h hydrogen atoms in the corresponding hydrocarbons by h SH groups singly linked to carbon, where h is some integer ; the following constant will therefore be required : cr l = the algebraic sum of the following heats : (i) due to the severance of a C . H link ; (ii) due to the combustion of a hydrogen atom (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of a C . S link ; (iv) due to the severance of a S . H link ; (v) due to the combustion of a sulphur atom ; (vi) due to the combustion of a hydrogen atom (to liquid water) ; or, as it can be written more simply : Mean... 0-= -33-1 Mercaptans. ff Methyl mercaptan . PTT CTT ^iJ^ .Oil a o"j 297-6 -86-8 295-9 Ethyl mercaptan . C 2 H 5 .SH 2 a fi 2 = o> so ^at 0-'C:S is represented by | a cr 2 ; this gives a satisfactory result. Mean value of = the sum of the following heats : (ii) due to the combustion of three hydrogen atoms (to liquid water) ; (iii) due to the formation of three C . N links, minus the sum of the following heats : (i) due to the formation of three C . H links ; (iv) one-half that due to the formation of a nitrogen molecule. So that the general nitrogen compound of this class : (C.N) links + &N can be written : l-a-2b-p)H+(n+p-a-b-l)L l = na-(n +p - a - b - 1) /3 - ay - bS - 3k v. To formulate some examples : (1) Nitriles of mono-basic aliphatic carboxy acids : p = 0, =1, so that their general formula is na (n a b-1) ft ay 18 3 */. For thiocyanates subtract cr. (2) Aliphatic mcno-iso-thiocyanates, R . N : C : S : p = 1 (because two hydrocarbon residues are linked through the nitrogen atom), k = l, and a- 2 must be subtracted for the ' doubly linked ' sulphur atom ; so that their general formula is na (n a - b 2)/3 ay 68 cr 2 Sv. (3) Aliphatic mono-tertiary amines : p = 2 (be- cause three hydrocarbon residues are linked through the nitrogen atom), k = 1 ; so that their general formula is na (n a b 3) ft ay b 8 3i>, &c. In Table 28 will be found the molecular heats of combustion (corrected for constant volume) of nine 78 THERMO-CHEMICAL CONSTANTS TABLE 28. ORGANIC (Nitrogen linked Molecular Heats of 1. 2. 3. 4. 5. 6. M. H. C. found 3v M. H. C. Substance. Formula. Formula. ^Thomson) calcu- calcu- coiistant lated. lated. vol. Ci/anides Cals. Cals. Cals. (linking C j N). Cyanogen .... C 2 N 2 2 a /3 - 6 v 259-6 54-75 256-3 Hydrogen cyanide MCN (II . NC) a-3i/ 158-2 (52-6) 154-4 Acetonitrile . . . cn 3 . CN 2 a ft 3 311-4 57-7 312-7 Propionitrile . . . C 2 H 5 .CN 3a-20-3y 470-4 57-0 471-0 Methyl thiocyanate . CH 3 . S . CN 2 a cr 3 v 398-2 56-9 398-7 Iso-thiocyanates (linking C : N . C). Methyl wo-thiocyanate CHo . N : C : S 2 a = 56-3 Therefore v = 18-8 such nitrogen compounds. From these, using the above formulae, the values of 3v have been calculated in the usual manner and are given in the table. It is at once evident that each of the three groups gives the same value for this constant. Taking the mean of the seven more consistent we obtain v= 18-8 Cals. Using this value, the molecular heats of combustion of all these nitrogen compounds have been calculated, and are exhibited, together with the differences between them and the experimental, and the percentage errors, in Table 28. Excepting hydrogen cyanide ORGANIC NITROGEN COMPOUNDS 79 NITROGEN COMPOUNDS. entirely to Carbon.} Combustion. Molecular Heats of Formation. 7. 8. 9. 10. 11. 12. 13. Difference between cols. 4 and 6. Error. Formula. M. H. F. found (Thomsen, constant vol. calcu- lated. M. H. C. calcu- lated. Difference between cols. 10 and 12. Cals. Percent Cals. Cals. Cals. Cals. -3-3 -1-27 2a '_/3'-6i/ -65-7 46-55 -62-6 + 34 -3-8 -2-40 a'-3/ -27-5 (48-7) -23-8 +3-7 + 1-3 + 0-42 2 a' /?' 3/ -16-3 43-7 -17-6 -1-3 + 0-6 + 043 3 a 2 8' 3 v -10-8 44.4 -11-4 -0-6 + 0-5 + 043 -\ / / o ' 2 a o- 3 v - 32-0 44-5 -32-5 -0-5 + 0-2 + 0-05 ' ' O ' Methylamine . NH 2 (CH 3 ) 257-3 [ 167-4 Dimethylamine NH(CH 3 ) 2 419-2! 9 Trimethylainine N(CH 3 ) 3 5810* 161-8 Ammonia . . NH 3 89-9) 094 K Ethylamine . NH 2 (C 2 H 5 ) 414-4! o 1 o o Diethylamine . Triethylamine NH(C 2 H 5 ) 2 N(C 8 H B ), 732-6 [ 1 049-9 f olo-J 317-3 shown the effect in the molecular heat of combustion by successively replacing the hydrogen atoms in ammonia by methyl and by ethyl. In both cases we find that the replacement of the second and third hydrogen atoms produces an equal effect, appreciably less than that produced by the replacement of the first. How is this to be explained ? That the amines have the constitution usually assigned to them is ORGANIC NITROGEN COMPOUNDS 81 amply demonstrated by pure chemistry, and to assign them other formulae on account of the above anomalous behaviour is unwarranted. In explanation we wish to depart from our fundamental assumption as little as possible. The following explanation is not the only one that could be put forward, but it is simple, it does explain the facts, and it leads to perfectly satisfactory numerical results. It is as follows : the three affinities of nitrogen for hydrogen in ammonia are not identical, two being weaker than the third, whereas the affinity of trivalent nitrogen for carbon is constant ; and will be employed in the following calculations. It follows, therefore, that 1674 Gals, represent the change in molecular heat of combustion by replacing the strongly -}&\m&. hydrogen in ammonia by methyl and 324-5 Gals, by ethyl, whereas 161-8-9 Gals, re- present the change in molecular heat of combustion by replacing one of the weakly-bound hydrogen atoms in ammonia by methyl and 317-3 8-2 Gals, by ethyl. So that writing ammonia HN^ where the thick \H stroke represents the strong affinity, methyl and ethyl amines are represented by II . N<^ and dimethyl and \H diethylamines by '. N H. All primary amines can be obtained theoretically by replacing one or more hydrogen atoms in the corre- sponding hydrocarbon by the same number of NH 2 groups, and similarly all secondary amines can be obtained theoretically by replacing an even number of hydrogen atoms by half the number of N H groups. 82 THERMO CHEMICAL CONSTANTS So that the primary -amine constant = the algebraic sum of the following heats : (i) due to the severance of a C . H link ; (ii) due to the combustion of a hydrogen atom (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of a C . N link ; (iv) due to the severance of two N . H links ; (v) one-half that due to the formation of a nitrogen molecule ; (vi) due to the combustion of two hydrogen atoms (to liquid water) ; or, as it can be written more simply : The primary-amine constant = the sum of the follow- ing heats : (iii) due to the formation of a C . N link ; (iv) due to the formation of two N . H links, minus the sum of the following heats : (i) due to the formation of a C . H link ; (v) one-half that due to the formation of a nitrogen molecule ; (vi) due to the combustion of a hydrogen atom (to liquid water). Also, the secondary-amine constant = the algebraic sum of the following heats : (i) due to the severance of two C . H links ; (ii) due to the combustion of two hydrogen atoms (to liquid water), minus the algebraic sum of the following heats : (iii) due to the severance of two C . N links ; (iv) due to the severance of a N. H link ; (v) one-half that due to the formation of a nitrogen molecule ; (vi) due to the combustion of a hydrogen atom (to liquid water) ; or, as it can be written more simply : The secondary-amine constant = the sum of the following heats: (ii) due to the combustion of a hydrogen atom (to liquid water) ; (iii) due to the for- mation of two C . N links ; (iv) due to the formation of a N . H link, minus the sum of the following heats : (i) due to the formation of two C . H links ; (v) one- half that due to the formation of a nitrogen molecule. ORGANIC NITROGEN COMPOUNDS 83 Granting that the affinity of trivalent nitrogen for carbon is constant, from the definition of 3i/ 3 i/ = the sum of the following heats : (ii) due to the combustion of a hydrogen atom (to liquid water) ; (iii) due to the formation of a C . N link, minus the sum of the follow- ing heats : (i) due to the formation of a C. H link ; (iv) one-sixth that due to the formation of a nitrogen molecule ; = 18-8 Gals. Put JLL = the sum of the following heats : (i) one- TABLE 30. Substance. Formulae. M. H C. /j. calculated. Ammonia . . NH 8 * Cals. 89-9 Cals. /A =30-0 250-Butylamine Ally lam ine . Aniline . . C 4 H 9 . NH 2 C 3 ri- . NH 2 C;H 5 .NU 2 '-"'" 723-5 530-0 837-2 Mean .. 56-6 57-9 584 . 2fjL = 57-5 Piperidine C 5 H 10 .NH 5a-4/3-2v + / , 831-9 ^ = 25-5 sixth that due to the formation of a nitrogen molecule ; (ii) due to the combustion of a hydrogen atom (to liquid water), minus the heat of formation of a N . H link. (So that if the three affinities of nitrogen for hydrogen are not equal, p will have corresponding different values.) It is evident, therefore, that Primary-amine constant = v - 2 />t, Secondary -amine constant = 2 v - ft, Mole- cular heat of combustion of ammonia = sum of three /x (any difference in value of /x being allowed for). G 2 84 THERMO-CHEMICAL CONSTANTS The general primary mon-amine : = nC + 2(n - a - 2 1 -p)H+ (n +p-a-l>-l)L l = na (n+p a 1) 1))8 ay &S v + 2jji. And the general secondary mon-amine similarly is expressed by : na - (n +p - a - I - l)/3 - ay - IS - 2 v + p.. 1 In Tables 30 and 31 are given the molecular heats of combustion (corrected for constant volume) of am- monia, seven primary and three secondary amines determined, Thomsen ; from these we proceed to cal- culate the values of ^, and test our theory regarding the nitrogen hydrogen affinities. Thus methylamine is CH 3 . NH 2 , i.e. a *>-f-2//,. M. H. C. found = 257-3 Gals., therefore 2/* = (257-3 - 210-8 + 18-8) Gals. = 65-3 Gals., &c. Group 1 Amines (see Table 31). The following primary amines : methyl, ethyl, propyl, and amylamine give a constant value for 2/x. Mean 2 p. = 64-5 Gals. Diethylamine gives /A = 32-0 Gals, almost exactly half the above, so that the two //, in the above primary amines are equal, the final mean gives p, a = 32-2 Gals., writing p, a for this value of /x. Using this value, the molecular heats of combustion of all the above amines (and dimethylamine) have been calculated and are exhibited, together with the differences between them and the experimental, and the percentage errors, in Table 31. The agreement is perfectly satisfactory. The conclusion that the two //, 1 For aliphatic secondary mon- amines put p 1. OEGANIC NITROGEN COMPOUNDS 85 in methyl and ethyl amines are identical in value is in agreement with the conclusion drawn from Table 29. Group 2 Amines (see Table 30). If we assume the equivalence of the values of /* for this group of amines we obtain the following contra- dictory results : Ammonia gives 3/i = 89-9 Gals., hence /x = 3OO Cals., iso-butylamine, allylamine, and aniline give an almost constant value for 2/x,, mean 2/x = 57-5 Cals., hence /x = 28-8 Cals., and piperidine gives //, = 25-5 Cals. On the other hand, representing this value of JK, given by piperidine by ^ b (its value it should be noticed corresponds to a stronger affinity between nitrogen and hydrogen than /A a ), if we write ammonia, 2ju, tt -h/* 6 we get a value 89-9 Cals. in perfect accord with its experimental molecular heat of combustion above (90-0 Cals.), and also if we write the 2//, constant obtained from the primary amines above, ft a 4-^, we get a value 57-7 Cals. also in perfect agreement with that found above (57-5 Cals.). Ammonia is therefore represented by the formula H N<^ , the above primary amines by R . N\ \H ^H .gv CH 2 CH 2 and piperidine by CH 2 CH 2 , the results being in H agreement with the theory already laid down. That cases of isomerism do not occur owing to this non- equivalence of the three nitrogen hydrogen affinities is 86 THERMO-CHEMICAL CONSTANTS TABLE 31. ORGANIC (Nitrogen linked Molecular Heats of 1. 2. 3. 4. 5. 6. M. H. C. found M.H.C. Substance. Formula. Formula. (Thomsen) /* calcu- calcu- constant lated. lated. vol. Cals. Cals. Cals. GROUP 1. Primary Amines. P'O, Methylamine . . CH 3 NH 2 a v + 2fjL 257-3 65-3 x^ 256-4 Ethyl am ine Propylamine . . C 2 H 5 NH 2 C 3 ILNH 2 2a-/?-v+V rt 414-4 64-lx| 574-1 65-Sxi 414-7 573-0 Amylamine . . C 5 H n NH 2 5a~4/3-v+2/x a 888-4 63-2xi 889-6 Secondary Amines. Dimethylamine CH 3 ) 2 NH 2a 2i/+ IL 419-2 (35-2) 416-2 Diethylamine . (C 2 H 5 ) 2 NH 4a-2/2 2v + fji a 732-6 ; 32-0 732-8 Mean ... /x ft = 32-2 GROUP 2. ^ Ammonia . . NH 3 2 /* + /*& 89-9 25-5 90-0 Primary Amines. /5o-Butylamine C 4 H 9 .NH 2 4 a 3 /? - v + p a + fJL b 723-5 ;(24-4) 724-7 Allylamine . . . C 3 H 5 . NH 2 3 a __y_ l/ 4.. t + ^ 530-0 25-7 529-9 Aniline .... C 6 H 5 .NH 2 -v + t*a + Pb 837-2 25-9 836-9 Secondary Amine. Piperidine . . C 5 H 10 .NH 5a-4^-2v + /x ?> 831-9 25-5 832-0 Mean ... fi b = 25-6 due to the fact that probably the configuration of the rest of the molecule determines the hydrogen atom or atoms substituted. Knowing the value of p a the mean value of /x 6 can be calculated from the amines of group 2 as in Table 31, and is found to be 25-6 Cals. (agreeing with the value, 25-5 Cals. obtained from piperidine and used above). Using these values : p a = 32-2 Cals., fji b = 25-6 Cals., and v = 18-8 Cals., OKGANIC NITEOGEN COMPOUNDS 87 NITROGEN COMPOUNDS. to Hydrogen.) Combustion. Molecular Hta's of Formation. 7. Difference between cols. 4 and 6. 8. Error 9. Formula. 10. M. H. F. found (^Thomsen) constant vol. 11. p! calcu- lated. 12. M. H. F. calcu- lated. 13. Difference I etwten cols. 10 and 12. Cals. Percent. Cals. Cals. Cals. Cals. -0-9 + 0-3 -0-35 + 0-07 -p3i^ 8-4 15-8 Ma' 2-2 x i 3.4 xi 9-2 15-4 + 0-S -0-4 -M -0-19 3 of 2 ft v f + 2 fa' 20-4 1.8x* 21-6 + 1-2 + L2 + 0-14 5a '_ 4 ^-/ +2 ^' 35-1 4-1 x4 34-0 -11 -3-0 + 0-2 -0.72 + 0-03 #:& + -t/ +ftl ' 11-0 26-4 -1.4) 1-6 13-9 26-3 + 2-9 Mean ...ft/ = 1-5 + 0-1 + 0-11 W+*' 11-3 8^3 11.1 -0-2 + 1-2 -0-1 + 0-17 -0-02 4 < /-3/8'-/+yi a '+^' 35-6 -2-9 (9-3) 8-0 34-4 -2-8 -1-2 + 0-1 -0-3 -0-04 r-/w+M(/ -19-2 8-0 -19-1 + 0-1 + 0-1 + 0-01 5a'-4/3'-2/ + ^' + 24-1 84 + 24-1 + 0-0 Mean ... /V = 8-1 which are the fundamental molecular heat of com- bustion nitrogen constants, the molecular heats of combustion of the amines given have been calculated, and are exhibited, together with the differences between them and the experimental, and the percentage errors, in Table 31. All the results are perfectly satisfactory, demonstrating the validity of the theory put forward. 88 THERMO-CHEMICAL CONSTANTS I 27. MOLECULAR HEATS OF FORMATION OF ORGANIC NITROGEN COMPOUNDS. The molecular heat of formation constants analogous to v and p, are as follows : v = the algebraic sum of the following heats : (i) one-half that due to the decomposition of a hydrogen molecule ; (ii) due to the formation of a C . H link, minus the algebraic sum of the following heats : (iii) one-sixth that due to the decomposition of a nitrogen molecule ; (iv) due to the formation of a C . N link ; or, as it can be written more simply : i/ = the sum of the following heats : (ii) due to the formation of a C . H link ; (iii) one-sixth that due to the formation of a nitrogen molecule, minus the sum of the following heats : (i) one-half that due to the formation of a hydrogen molecule ; (iv) due to the formation of a C . N link. Also, // = the heat (i) due to the formation of a N . H link, minus the sum of the following heats : (ii) one- sixth that due to the formation of a nitrogen molecule ; (iii) one-half that due to the formation of a hydrogen molecule. It follows, therefore, that i/ + v = // -f /^ = the heat due to the combustion of a hydrogen atom (to liquid water), less half the heat due to the formation of a hydrogen molecule = the heat of combustion of a gram atomic weight of molecular hydrogen to liquid water = \ x 67-5 Cals. = 33-75 Cals. Whence : v = (33-75 - 18-8) Cals. = 14-95 Cals. H a ' = (33-75 - 32-2) Cals. = 1-55 Cals. p b ' = (33-75 -25-6) Cals -8-15 Cals. OEGANIC NITEOGEN COMPOUNDS 89 In Tables 28 and 31 will be found the molecular heats of formation of the nitrogen compounds under consideration, given by Thomsen ; from these the values of v' 9 and have been calculated in a similar manner as were the molecular heat of combustion constants. The values thus obtained are v 15-0 Cals., //,/ = 1-5 Cals., /V = 8-l Cals., agreeing with the above. Using these values : i/ = 150 Cals., ^ = 1-5 Cals., /V = 8-1 Cals., which are the fundamental molecular heat of formation nitrogen constants, the molecular heats of formation of all the nitrogen compounds given have been calculated, and are exhibited, together with the differences between them and the experimental, in Tables 28 and 31. 28. THE CONSTITUTION or PYRIDINE. The molecular heat of combustion of pyridine (cor- rected for constant volume) is 674-1 Cals. (Thomsen). Below are shown certain constitutional formulae which have been proposed for this substance, with the cal- culated molecular heat of combustion corresponding to each formula : CII CH " CII / \ / \ / \ CH CH PIT PFT V>>11 L/xl PIT rri l^ilv s\jl\ 1 II CH CH II II CII CH 1 >< 1 CIK \CH \ / \ / \ / N N N 5a-2/2-2y- 3i/ = 714-6 Cals. 5a-6-: CII CH \ CH N How r ever, the effect due to any intramolecular strain, other than that due to the C : C links, has been omitted in the above calculations. Probably, as it seems that 90 THERMO-CHEMICAL CONSTANTS C . N links are not subject to strain, this effect would be less than in the case of the corresponding benzene formulae, but it would still be sufficient to invalidate these formulae. From the thermo-chemical, as also from the purely chemical, point of view, pyridine shows a similarity to benzene, and the true constitutional formula of pyridine can be hoped to be forthcoming only with the solution of the ' benzene-problem '. 10. SUMMARY AND CONCLUSION. IN the foregoing pages, from a consideration of the molecular heats of combustion of volatile organic compounds determined by Thomsen, twenty funda- mental molecu]ar heat of combustion constants have been calculated, and by means of these the molecular heats of combustion of all the above substances (with the exceptions noted below T ), which number above one hundred, have been calculated ; with the exception of a few isolated cases the agreement between the calculated and experimental results is quite satisfactory. A similar, although less detailed procedure has been employed in the case of molecular heats of formation. Valuable evidence has been obtained of the validity of von Baeyer's Strain Theory, and a theory has been put forward in explanation of the peculiarities mani- fested by certain nitrogen compounds. In Table 32 is given a complete list of the Funda- mental Molecular Heat of Combustion and Molecular Heat of Formation Constants. The arrangement of the table is as follows : 1 These exceptions are as follows: Carbon monoxide (exact formula doubtful C : or C I ? see Appendix) ; carbonyl chloride, trimethyl ortho-formate, dimethyl- and diethyl-carbonates (these four substances give anomalous results, due probably in the cases of the last three to the accumulation of oxygen atoms in the molecules, the data is however too scanty to test this suggestion) ; nitromethane and nitroethane, ethyl and amyl nitrites, and ethyl nitrate (the data relating to oxygen-nitrogen links is too scanty, and in the cases of the last three compounds, not sufficiently accurate owing to their explosive nature to base any fundamental constants upon). 92 THERMO-CHEMICAL CONSTANTS i~ CO l> to co 00 CO (M W 1 D H 8 ii II . ?- II ^C II II X ii >< II : x II II II 3 3^ 3^ 00 O o O O fc cS r . 1 ;_, ^ ^ ^) O .... i H % X u ijj 8 CO I s OJ g CO 1 H PH O ^ l 1 1 1 a o 9 P^ ^ C3 g fu ^ ^ < 1 CO o M O fl j j >* a >, 73 >> S H ?R % Cfl r-j r-J * o H ^ % 1 > ^3 O> -iJ "d x-v^-x s 3 a nic substanc< "5 T 'S ^ i cS *-*j !S 1 ^ rt 'P 1 T3 c substances fine substitu line substitu ae substitute o fe 03 OQ 1 S g A s .2 'r3 ' a o | 1 & W ^ js pj g S ^^ o 53 o o 73 ^ -g ^ J3 *o rv. 3 H S ^ 3 ^ <3 g H ^5 ^ w H i i i n N n a> ^ to M O I SUMMARY AND CONCLUSION CM 6 CM 1 J I' 00 II I 1 h- o CO t^. CM CO 1 1 Jl II 3* 3'' 6 rH S sic. 'L ', I' 3* 1 9 CM CO cc 1 H t o J b" 1 ! 00 1 II h~ Ol I CO CM 1 II M b 10 T 1 II op 00 i-H II 11 v CM CM CO II { pH II II """"' x < ^ j s H- s B . < j i C S S 1 f ^, | i H 3 a 1 'C ' a 5 s . . C 3 ^ ^ s ^^. "J CO f 1 *. ^ co^co S CO 4. (M I =S i i 1 ft. ^ "5^ 03 <^ " ^. o CM -. CM -> Primary amines Secondary amines Secondary amines I I (M cc CM I I I w '^ I I a s a H a K CO CO CO CM 94 THERMO-CHEMICAL CONSTANTS Column 1 gives the general definition of the funda- mental constants in an abbreviated form. In the text, except in the cases of a, ft, y, and 8, the general definitions have, for the purposes of simplification, not been given, whereas the specific definitions for both molecular heats of combustion and molecular heats of formation have been given for all constants from the general definition the specific ones are obvious and if stated fully, vice versa. The following abbreviated form of notation is used : for whatever physico-chemical pro- perty we are considering : (i) the symbol for any element represents the value due to one gram atom of that element not including the value due to any links. Thus S = the value due to a gram atom of sulphur, (ii) A dot between two atoms represents the value due to such links, contained in a gram molecule of a substance of which the molecule con- tains one such link, (iii) A dot other than between two atoms represents the value due to a link between the atom before which it is placed and a carbon atom, as in (ii). Two or three dots near together represent the value due to a * double ' or * treble ' link respec- tively, but isolated dots represent so many single links. In accordance with this notation we write -H in this Table, where in the foregoing pages we have written H. LJ, L 2 , and L 3 have the same meanings as throughout this work, (iv) A plus sign between two symbols indicates the sum of their respective values, and a minus sign the difference between these values. Column 2 gives the classes of compounds for which each constant is applicable, and Columns 3 and 4 give the values of the fundamental molecular heat of com- bustion and formation constants respectively. A slightly different procedure has been adopted in SUMMARY AND CONCLUSION 95 the case of nitrogen constants. The definitions given are those of the actual groupings of the constants which are employed for the several classes, and after each class is given in brackets the grouping of constants in question. In conclusion : the most conclusive evidence is afforded of the additive nature (in the wider sense) of thermal constants by the fact that the various atomic groupings deport themselves, from the thermal point of view, similarly in relatively complex molecules, as in the simpler, provided that they are linked in precisely the same way; as shown by the following examples : The values of the carbon and hydrogen constants obtained from the hydrocarbons are success- fully used throughout the calculations ; the constant involving (i. e. co) has the same value in esters as in ethers ; the constant involving : O (i. e. w_,) has the same value in esters and acids as in carbon dioxide ; the constant involving S (i. e. or) has the same value in thiocyanates as in sulphides (of the form H S R) ; the constant involving : S (i. e. o- 2 ) has the same value in ^o-thiocyanates as in carbonyl sulphide and carbon disulphide, &c. APPENDIX A SHORT CRITICISM OF THOMSEN'S METHOD OF CAL- CULATING THE THERMAL CONSTANTS OF ORGANIC SUBSTANCES. THOMSEN, in his method of calculating thermal constants, has not committed the common error of neglecting the value of certain links (e. g. the C . C link) ; it is necessary, therefore, to show wherein this system fails to be satisfactory. From the fact that the successive replacement of the hydrogen in methane by methyl brings about a constant difference in the molecular heat of com- bustion (see Table 1), Thomsen infers the identity of the four valencies of carbon. He finds also that the difference between other successive hornologues is nearly constant. The formula where f C a H 2b represents the molecular heat of com- bustion of the hydrocarbon C a H, b ; x, y, i\, v 2 , v & , have precisely the same meanings as our constants C, H, L/, L/, Lg', respectively ; p. 2 is the number of ethene links, and p 3 the number of ethine links in the molecule of this hydrocarbon is developed. The values of x 2v l} 2y-i-v 1 , 2-v l v 2) and 3v\ v 3 are calculated from the molecular heats of combustion of the hydrocarbons, and the theoretical values of these heats of combustion obtained thereby compared with APPENDIX 97 the experimental. The method so far is similar to ours, and is perfectly valid and accurate. Thomsen, however, does not continue this method, but attempts to determine the actual values of the constants x, y, v l9 v. 2 , and v 3 , in the following in- genious manner : ( . . . The heat of combustion of carbon monoxide . . . at constant volume amounts to 67-67 Gals. The one atom of oxygen that carbon monoxide takes up on oxidation is linked to the carbon by two valencies that is, in the same manner as the oxygen atom already present in the molecule of carbon monoxide. The heat of formation of carbon dioxide must there- fore be 2 x 67-67 or 135-34 Gals., provided always that the carbon atom from which the molecule of carbon dioxide is to be formed is present as the constituent of a gaseous compound ; whilst the formation of 1 gram-molecule of carbon dioxide by the combustion of amorphous carbon produces only 96-96 Gals. This difference of 38-38 Gals, must therefore be the amount of heat which is consumed in detaching a gram-atom of carbon from the complex molecule of amorphous carbon and converting it into the gaseous state.' l Granting the above, it is easy to calculate the con- stants required from the molecular heats of combustion of the hydrocarbons ; and they are found to be x = 135-34 Gals, 2?/ = 37-69 Gals., ^ = 14-71 Gals., v 2 = 13-27 Gals., and v 3 = -0-16 Gals. (i. e. zero). Thomsen develops his constants in order to calculate, not molecular heats of combustion, but molecular heats of formation from gaseous carbon atoms, which are also obtained from the molecular heats of formation 1 Thomsen, Thermochemistry (English translation by Miss Burke), p. 448. II 98 THERMO-CHEMICAL CONSTANTS derived from the experimental data by means of the above constant for the ' heat consumed in detaching a gram-atom of carbon from the complex molecule of amorphous carbon and converting it into the gaseous state '. Our objections to his method are as follows : 1. The whole system of calculation depends on two assumptions : (i) that the oxygen in carbon monoxide is bound to the carbon by two links, or bonds of affinity. There is little evidence either way as to the exact formula of carbon monoxide, but what evidence there is appears to indicate the tetravalency of the two atoms in the carbon monoxide molecule, i. e. that it is represented by the formula C : O and not C : 0. (ii) Granting, however, for the sake of argument, that this latter formula (C : 0) is correct, Thomsen assumes that the two carbon affinities, when carbon functions as a divalent element, are exactly equivalent to two of the affinities of tetravalent carbon. These assumptions, may, of course, be true ; but they are without any evidence, and appear to be unlikely. Moreover, they lead to the improbable result that the thermal value of the ethine link is negative or zero. If this is so what right have we to say that this link (by which term we understand some attractive or bind- ing force exerted between two atoms) exists ? On the other hand,, these unlikely assumptions are entirely avoided in our method of calculation. 2. Thomsen applies his method to calculate heats of formation only (see $ 7). 3. Several objections could be urged against many of the incidental applications of this method ; we will mention only two : (i) The influence of intramolecular strain due to the geometrical configuration of certain APPENDIX 99 molecules is not taken into account, and hence the thermal behaviour of trimethylene remains a mystery, and a wrong conclusion is drawn relative to the con- stitution of the ethylene oxide molecule, (ii) The calculation of oxygen constants is based to a great extent on the ketones most unsuitable substances owing to the fact that they are probably mixtures of dynamic isomers and the results obtained are by no means consistent with themselves. Thus, for the C:O group, ketones give the value 53-52 Cals., and this value is used for determining the constitution of certain substances (e. g. the aldehydes), and is not treated as purely empirical, as we have treated our corresponding constant. But Thomsen's whole system is based upon the value 67-67 Cals. for the C : group (see above) ! This procedure leads him to assign to the C . . C group in esters the value 52-72 Cals., whereas the ethers give for the same constant the value 34-31 Cals. 1 Thus, whilst assigning with all chemists the highest praise to Thomsen for his unique and very accurate experimental work in Thermochemistry, we cannot, although admiring its ingenuity, and the absence of the usual ethane-link-ignoring error, regard his method of calculating the thermal constants of organic sub- stances and the theoretical results based thereon with a like degree of confidence. 1 See Thomsen, Thermochemistry (English translation by Miss Burke), chap, xiv, especially pp. 402-10, 415-18. INDEX OF THE SUBSTANCES WHOSE THERMAL CONSTANTS HAVE BEEN CONSIDERED IN THE FOREGOING PAGES. [The numbers refer to pages.] Acetic acid, 56. aldehyde, 49, 52. anhydride, 56, 57. Acetonitrile, 78. Acetylene, 4, 14, 16, 18, 24-6, 28, 61 et seq. Adipic acid, 60. Allyl alcohol, 46. Allylamine, 83, 85, 86. Allyl bromide, 34. chloride, 32, 34. Allylene, 14, 16, 18, 24-6, 28. Allyl formate, 54. isothiocyanate, 78. methyl ether (see methyl allyl ether), 40. Ammonia, 80, 81, 83, 85, 86. Amylamine, 84, 86. Aniline, 83, 85, 86. Anisol, 39, 40. Benzene, 18, 20, 21, 28, 29, 37. Carbon dioxide, 11, 49, 51, 97, 98. - disulphide, 69, 70, 72. monoxide, 97, 98. oxysulphide (see carbonyl sul- phide), 69, 70, 72. tetrachloride, 32-4. Carbonyl sulphide, 69, 70, 72. Chloroform, 32-4. Cyanogen, 78, 80. Diallyl, 18, 28. ether, 40. Dichlorpropane, 34. Diethylamine, 80, 81, 84, 86. Diethyl ether, 40. sulphide, 70. Di-isopropyl, 17, 18, 28. Dimethylamine, 80, 81, 84, 86. Dimethyl ether, 40. ethyl carbinol, 46. fumarate, 60. ketone, 52. malonic acid, 60. succinate, 60. succinic acid, 60. sulphide, 67, 70. Dipropargyl, 18, 28. Ethane, 4, 14-16, 18, 24, 25, 28, 31, 32. Ethyl acetate, 54, 55. alcohol, 46. Ethylamine, 80, 81, 84, 86. Ethyl bromide, 31, 34. chloride, 31, 32, 34. Ethylene, 4, 14, 15, 18, 20, 24, 25, 28, 61 et seq. chloride, 32, 34. glycol, 44,- 46. - oxide, 63, 65, 99. Ethyl formate, 54. Ethylidene chloride, 32, 34. Ethyl iodide, 31, 34. - malonic acid, 60. mercaptan, 70. - methyl ether (see methyl ethyl ether), 39, 40. succinic acid, 60. Formic acid, 29, 56. Funiaric acid, 60. Glutaric acid, 60. Hexahydroterephthalic acid, 60. Hydrogen cyanide, 78-80. - sulphide, 68-70. Isoamyl alcohol, 46. 102 .INDEX Isoamylene/lT, 18) SC' ' Isobutyl alcohol, 46. aldehyde, 52. Isobutylamine 83, 85, 86. Isobutyl chloride. 34. Isobutylene, 14, 15, 18, 24, 25, 28. Isobutyl formate, 54. Isopropyl alcohol, 46. - malonic acid, 60. Mesitylene, 18, 28, 29, 36. Methane, 4, 11, 13, 14, 1?, 23, 24, 28, 31, 32. Methyl acetate, 54. Methylal, 39, 40. Methyl alcohol, 43, 46. allyl ether, 40. Methylamine, 80, 81, 84, 86. Methyl bromide, 31, 34. chloride, 31, 32, 34. - ethyl ether, 39, 40 malonic acid, 60. formate, 52, 54. glutaric acid, 60. - iodide, 31, 34. isobutyrate, 54. isothiocyanate, 78. mercaptan, 68, 70. phenyl ether (see anisol), 39, 40. - propargyl ether, 40. propionate, 54. propyl ketone, 52. succinic acid, 60. thiocyanate, 78. Monochlorethylene, 34. chloride, 32, 34. Monochlorpropylene, 32, 34. Pentamethylenedicarboxylic acid, 60. Perchlorethylene, 33, 34. Perchlormethane (see carbon tetra- chloride), 32-4. Phenol, 44, 46. Phenyl chloride, 36, 37. methyl ether (see anisol), 39, 40. Pimelic acid, 60. Piperidine, 83, 85, 86. Propane, 14-16, 18, 24, 25, 28, 31. Propargyl alcohol, 44, 46. Propionaldehyde, 52. Propionic acid, 56. Propionitrile, 78. Propyl alcohol, 46. Propylamine, 84, 86. Propyl bromide, 31, 34. chloride, 31, 34. Propylene, 14, 15, 18, 24, 25, 28. Propyl formate, 54. malonic acid, 60. Pseudo-cumene, 18, 28, 36. Pyridine, 89, 90. Suberic acid, 60. Succinic acid, 60. Sulphur dioxide, 11. - Tetram ethylenedicarboxylic acid, 60. Tetramethyl methane, 14, 18, 24, 28. methylenedimalonate, 60. trimethylenetetracarbonate, 60. Thiophene, 72, 73. Toluene, 18, 28, 36. Triethylamine, 78, 80. Trimethylamine, 78, 80. Trimethyl carbinol, 46. Trimethylene, 17 et seq., 28, 59 et seq., 99. Trimethylenedicarboxylic acid, 60 Trimethyl methane, 14, 15, 18, 24, 28. Water, 11, 43-5. THE END. Oxford : HORACE HAKT, Printer to the University AUTHORIZED ENGlilSfl: $tiilf$$$ \ /:-, viii + 286 pages. Demy 8vo, cloth, price 10s. 6d. net Experimental Researches with the Electric Furnace by Henri Moissan Professor of Chemistry at the Sorbonne Membre de 1'Institut Translated by A. T. de Mouilpied B.Sc. (Lond.), M.Sc. (Viet.), Ph.D. THIS book is divided into five chapters. In the first are described the different types of electric furnaces used in these researches, and their application to the study of the fusion and the volatilization of a number of refractory bodies. The second chapter contains a study of the three varieties of carbon : amorphous carbon, graphite, and the diamond. Chapter III deals with the preparation of some elements in the electric furnace. The elements investigated were Chromium, Manganese, Molybdenum, Tungsten, Uranium, Vanadium, Zirconium, Titanium, Silicon, and Aluminium. Chapter IV contains an account of the researches carried out on some new series of binary compounds the carbides, the silicides, and the borides. The preparation, properties, and analyses of hitherto unknown compounds are given. More especially the preparation of calcium carbide has been subjected to fresh investigation, and this is dealt with in some detail. Finally come a number of general conclusions. LONDON : EDWARD ARNOLD, 41 & 43 MADDOX STREET, W. 8vo 9 cloth, 4s. 6d. net Electrolytic Preparations Exercises for use in the Laboratory by Chemists and Electro-Chemists By Dr. Karl Elbs Professor of Organic and Physical Chemistry at the University of Giessen Translated by R S. Hutton, M.Sc. Demonstrator and Lecturer on Electro-Chemistry at the University of Manchester A LARGE number of works are available for the education of students in preparations of a purely chemical nature. In the numerous recent introductions to practical electro- chemistry, although the physical side of the teaching of the electro-chemist is fully dealt with, the chemical prepar- ative portion is usually little developed. 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DALBY, M.A., B.Sc., M.lNST.C.E., M.I.M.E., Professor of Engineering, City and Guilds of London Central Technical College. SECOND EDITION, REVISED AND ENLARGED. xii-(-283 pages. With upwards of 180 Illustrations. Demy 8vo., cloth, IDS. 6d. net. CONTENTS. CHAP. I. The Addition and Subtraction of Vector Quantities. II. The Balancing of Revolving Masses. III. The Balancing of Reciprocating Masses. Long Connecting-rods. IV. The Balancing of Locomotives. CHAP. V. Secondary Balancing. VI. Estimation of the Primary and Secondary Unbalanced Forces and Couples. VII. The Vibration of the Supports. VIII. The Motion of the Connecting-rod. APPENDIX. EXERCISES. INDEX. Valves and Valve Gear Mechanisms. BY W. E. DALBY, M.A., B.Sc., M.lNST.C.E., M.I.M.E., Professor of Engineering, City and Guilds of London Central Technical College. xviii + 366 pages. With upwards of 200 Illustrations. Royal 8vo., cloth, 2 is. net. Valve gears are considered in this book from two points of view namely, the analysis of what a given gear can do, and the design of a gear to effect a stated distribution of steam. The gears analyzed are for the most part those belonging to existing and well-known types of engines, and include, amongst others, a link motion of the Great Eastern Railway, the straight link motion of the London and North- Western Railway, the Walschaert gear of the Northern of France Railway, the Joy gear of the Lancashire and Yorkshire Railway, the Sulzer gear, the Meyer gear, etc. The needs of students and draughtsmen have been kept in view throughout. " No such systematic and complete treatment of the subject has yet been obtainable in book form, and we doubt if it could have been much better done, or by a more competent authority. The language is exact and clear, the illustrations are admirably drawn and reproduced." The Times. The Strength and Elasticity of Structural Members. BY R. J. 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This collection of Tables has been .selected for use in the examinations of the University of London. " This is a most valuable contribution to the literature of Mathematical refer- ence .... To anyone engaged in almost any form of higher physical research this compilation will be an enormous boon in the way of saving time and labour and collecting data. . . . The five-figure tables of roots and powers are, perhaps, the most useful features of the work." Mining Journal. Logarithmic and Trigonometric Tables (To Five Places of Decimals). By JOHN BORTHWICK DALE, M.A., Assistant Professor of Mathematics at King's College, London. Demy 8vo., cloth, 2s. net. Traverse Tables. With an Introductory Chapter on Co-ordinate Surveying. BY HENRY LOUIS, M.A., AND G. W. GAUNT, M.A., Professor of Mining and Lecturer on Surveying, Lecturer in Mathematics, Armstrong College, Newcastle-on-Tyne. xxviii + 92 pages. Demy 8vo., flexible cloth, rounded corners, 45. 6d. net. 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The great achievements of modern Organic Chemistry in the domain of the synthesis or artificial production of compounds which are known to be formed as the result of the vital activities of plants and animals have not of late years been systematically recorded. The object of the present book is to set forth a statement, as complete as possible, of the existing state of knowledge in this most important branch of science. The Chemistry of the Diazo-Compounds. BY JOHN CANNELL CAIN, D.Sc. (Manchester and Tubingen), Editor of the Publications of the Chemical Society. Demy 8vo. los. 6d. net. Lectures on Theoretical and Physical Chemistry. BY DR. J. H. VAN T HOFF, Professor of Chemistry at the University of Berlin. Translated by R. A. LEHFELDT, D.Sc, Professor of Physics at the Transvaal Technical Institute, Johannesburg. In three volumes, demy 8vo., cloth, 285. net, or separately as follows : PART I. CHEMICAL DYNAMICS. 254 pages. 125. net. PART II. CHEMICAL STATICS. 156 pages. 8s. 6d. net. 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Translated by R. S. HUTTON, M.Sc., Demonstrator and Lecturer on Electro-Chemistry at the University of Manchester. xii+ ioo pages. Demy 8vo., cloth, 45. 6d. net. The book contains a complete course of examples on the application of electrolysis to the preparation of both inorganic and organic sub- stances. It will be found useful as filling a distinct gap in the text- book literature suitable for use in chemical laboratories, and should enable the chemist to make use of the many valuable and elegant methods of preparation which have been worked out during recent years, the advantages and ease of application of which he cannot appreciate without such a guide. Introduction to Metallurgical Chemistry for Technical Students. BY JT. H. STANSBIE, B.Sc. (LOND.), F.I.C., Associate of Mason University College, and Lecturer in the Birmingham University Technical School. SECOND EDITION. xii + 252 pages. Crown 8vo., cloth, 45. 6d. An Experimental Course of Chemistry for Agri- cultural Students. By T. S. DYMOND, F.I.C., Lately Principal Lecturer in the Agricultural Department, County Technical Laboratories, Chelmsford. New Impression. 192 pages, with 50 Illustrations. Crown 8vo., cloth, 2s. 6d. A History of Chemistry. BY DR. HUGO BAUER, Royal Technical Institute, Stuttgart. Translated by R. V. STANFORD, B.Sc. (LOND.), Priestley Research Scholar in the University of Birmingham. Crown 8vo., cloth, 33. 6d. net. Technical and Scientific Publications 7 The Becquerel Rays and the Properties of Radium. BY THE HON. R. J. STRUTT, F.R.S., Fellow of Trinity College, Cambridge. SECOND EDITION, REVISED AND ENLARGED. viii + 222 pages, with Diagrams. Demy 8vo., cloth, 8s. 6d. net. " If only a few more books of this type were written, there might be some hope of a general appreciation of the methods, aims, and results of science, which would go far to promote its study. ... A book for which no praise can be excessive." Athenaeum. Astronomical Discovery. 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BOULGER, F.L.S., F.G.S., A.S.I., Professor of Botany and Lecturer on Forestry in the City of London College, and formerly in the Royal Agricultural College. NEW EDITION. Revised and Enlarged and profusely illustrated. Demy 8vo., 123. 6d. net. " It is just the book that has long been wanted by land agents, foresters, and wood- men, and it should find a place in all technical school libraries." Field. Manual of Alcoholic Fermentation and the Allied Industries. BY CHARLES G. MATTHEWS, F.I.C., F.C.S., ETC. xvi + 295 pages, with 8 Plates, and 40 Illustrations. Crown 8vo., cloth, 73. 6d. net. " This is a book worthy of its author, and well worth perusing by every student. . . . The student, both old and young, as well as the practical brewer, will find this book gives him some very useful information." Brewers' Guardian. 8 Mr. Edward Arnold 's Technical & Scientific Books The Evolution Theory. By DR. AUGUST WEIS- MANN, Professor of Zoology in the University of Freiburg in Breisgau. Translated, with the Author's co-operation, by J. ARTHUR THOMSON, Regius Professor of Natural History in the University of Aberdeen ; and MARGARET THOMSON. Two vols., xvi + 4i6 and viii + 396 pages, with over 130 Illustrations. Royal 8vo., cloth, 325. net. " The subject has never been so fully and comprehensively expounded before ; and it is not necessary to subscribe to all the author's tenets in order to recognise the value and the absorbing interest of his exposition, with its prodigious -wealth of illustration, its vast store of zoological knowledge, its ingenious interpretations and far-reaching theories. English readers have reason to be grateful to Professor and Mrs. Thomson for their admirable translation." The Times. The Chances of Death and Other Studies in Evolution. By KARL PEARSON, M.A., F.R.S., Professor of Applied Mathematics in University College, London, and formerly Fellow of King's College, Cambridge. 2 vols., xii + 388 and 460 pages, with numerous Illustrations. Demy 8vo., cloth, 25*. net. The Life of the Salmon. With reference more especially to the Fish in Scotland. By W. L. CALDERWOOD, F.R.S.E., Inspector of Salmon Fisheries for Scotland. Illustrated. Demy 8vo., 7s. 6d. net. " We have no hesitation whatever in advising all persons interested in the salmon, whether as fishermen, naturalists, or legislators, to add this book to their libraries." Nature. Animal Behaviour. By Professor C. LLOYD MORGAN, LL.D., F.R.S., Principal of University College, Bristol. viii+344 pages, with 26 Illustrations. Large crown 8vo., cloth, IDS. 6d. This important contribution to the fascinating subject of animal psycho- logy covers the whole ground from the behaviour of cells up to that of the most highly developed animals. BY THE SAME AUTHOR. Habit and Instinct, viii + 352 pages, with Photo- gravure Frontispiece. Demy 8vo., cloth, i6s. Professor ALFRED RUSSEL WALLACE : " An admirable introduction to the study of a most important and fascinating branch of biology, now for the first time based upon a substantial foundation of carefully observed facts and logical induction from them." BY THE SAME AUTHOR. The Springs of Conduct. Cheaper Edition. viii + 317 pages. Large crown 8vo., cloth, 33. 6d. This volume deals with the Source and Limits of Knowledge, the Study of Nature, the Evolution of Scientific Knowledge, Body, and Mind, Choice, Feeling) and Conduct. BY THE SAME AUTHOR. Psychology for Teachers. New Edition, entirely rewritten, xii + 308 pages. Crown 8vo., cloth, 45. 6d. An Introduction to Child Study. By Dr. W. B. DRUMMOND. Crown 8vo., cloth, 6s. net. The Child's Mind: Its Growth and Training. By W. E. URWICK, University of Leeds. Crown 8vo., cloth, 45. 6d. net. LONDON : EDWARD ARNOLD, 41 & 43 MADDOX STREET, W. YU 284514 UNIVERSITY OF CALIFORNIA LIBRARY