LIBRARY OF THK UNIVERSITY OF CALIFORNIA. Class EXERCISES IN ELEMENTARY QUANTITATIVE CHEMICAL ANALYSIS THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO ATLANTA SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA , MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO EXERCISES IN ELEMENTARY QUANTITATIVE I CHEMICAL ANALYSIS FOR STUDENTS OF AGRICULTURE BY AZARIAH THOMAS LINCOLN, PH.D. ASSISTANT PROFESSOR OF CHEMISTRY, UNIVERSITY OF ILLINOIS AND JAMES HENRI WALTON, JR., PH.D. ASSISTANT PROFESSOR OF CHEMISTRY, UNIVERSITY OF WISCONSIN Nefo fforfc THE MACMILLAN COMPANY 1907 All rights reserved v COPYRIGHT, 1907, Set up and electrotyped. Published December, 1907. NortoooU J. 8. Cashing Co. Berwick & Smith Co. Norwood, Mass., U.S.A. PREFACE OWING to the growing demand for quantitative analytical chem- istry by those engaged in the study of agriculture, it seemed to the authors that the presentation of the fundamental methods of agricultural analysis as carried out in the laboratories of the American Experiment Stations would be desirable. While this book is designed primarily as an elementary quantitative guide for the use of agricultural students, it may also be used for the work in general elementary quantitative analysis. This text-book is the outgrowth of several years' experience in teaching quantitative analysis to students specializing in Agri- culture, Chemistry, Medicine, and Household Science. No attempt has been made to present a complete treatise on quantitative analysis ; but a few typical exercises have been chosen to illustrate the fundamental principles and the most important methods of manipulation. To further the interest in this work, the student should be encouraged to do considerable outside reading, and there should be available for his use a number of the best books of reference. In the Appendix will be found a list of some of the most important works having a bearing on this subject, while throughout the text reference is made to the original literature. The gravimetric exercises and the work outlined under Acidime- try and Alkalimetry, together with the analysis of Milk or Feeding Material and Fertilizer, comprise the work usually accomplished by the agricultural students in one semester. Those students who desire more quantitative analysis complete the remainder of the exercises in another semester. Owing to the importance of the calculation of analytical data, this subject has been treated in considerable detail in Part V (Stoichiometry). The matter presented is arranged to be studied in conjunction with the regular laboratory exercises. In addition to the methods of solving problems, a large number of problems is given for practice. The selection has been made with the idea of emphasizing the fundamental principles brought out in the 174976 vi PREFACE laboratory exercises, and many of the problems are taken from the experimental data of the students. Although it will be found convenient to have a certain amount of platinum ware available for these exercises, it is not necessary. Porcelain crucibles and dishes may be used for all the determina- tions, with the possible exception of the alkalies in soils. The notes which are introduced throughout the text emphasize the important points and may serve as the basis of the classroom work, which should be an important feature of instruction in quan- titative analysis. In preparing this manual, free use has been made of the various standard works on quantitative analysis, of the publications of the Association of Official Agricultural Chemists, of the Bulletins of the United States Department of Agriculture, Bureau of Chem- istry, and, particularly, of Leach's excellent treatise on Food Inspection and Analysis. The authors desire to express their gratitude to Mr. J. H. Pettit, Assistant Professor of Soil Fertility, University of Illinois, for many valuable suggestions on the determinations connected with Fertilizers and Soils ; to Mr. Cyril G. Hopkins, Professor of Agronomy, for his help in correcting the proofs of the Analysis of Fertilizers and of Soils ; and to Mr. D. L. Weatherhead, for assisting in solving the problems. A. T. L. J. H. W., JR. URBANA, ILLINOIS, August i, 1907. CONTENTS PART I INTRODUCTION PAGE GENERAL REMARKS i NOTEBOOKS 2 REAGENTS 4 SPECIAL APPARATUS 5 Desiccators 5 Wash Bottles 6 Stirring Rods 6 OPERATIONS OF QUANTITATIVE ANALYSIS 6 Sampling 6 The Weighing of Samples 7 Solution and Evaporation 8 Precipitation . . . . . . . . . . .10 Conditions . . . . . . . . . .10 Enlargement of the Grains of Crystalline Precipitates . . .11 Colloidal Precipitates 12 Filtration 12 Washing 13 The Drying and Ignition of Precipitates 14 Crucibles ............ 14 The Use and Care of Platinum . . . . . . . .15 THE BALANCE 16 The Construction of the Balance 17 Position of Center of Gravity . . . . . . . .17 Knife-edges 18 Beam 18 The Weights 19 Summary of Precautions to be observed in Weighing .... 20 PART II GRAVIMETRIC ANALYSIS EXERCISES WITH THE BALANCE 22 EXERCISE I Determination of the Time of Vibration 22 viii CONTENTS PAGE EXERCISE II Determination of the Zero Point 22 EXERCISE III Determination of the Sensitiveness .... 23 EXERCISE IV Weighing by the Usual Method .... 23 GRAVIMETRIC DETERMINATIONS 24 EXERCISE V The Determination of Chlorine 24 EXERCISE VI The Determination of Sulphur in a Soluble Sulphate . 29 EXERCISE VII Separation and Determination of Calcium and Mag- nesium in a Mixture of their Carbonates ...... 32 EXERCISE VIII The Determination of Aluminium in a Soluble Salt . 37 PART III VOLUMETRIC ANALYSIS GENERAL DISCUSSION 40 Volumetric Apparatus 40 Pipettes 40 Cylinders 41 Flasks 41 Burettes . . . . . 42 Calibration of Graduated Apparatus 43 EXERCISE IX The Calibration of a Burette .... 45 Standard and Normal Solutions ....... 49 ACIDIMETRY AND ALKALIMETRY 5! General 51 Indicators . . ......... 52 Litmus ........... 52 Phenolphthalein . . . . . . . . . .52 Methyl Orange .......... 52 Cochineal 52 Notebooks ............ 53 THE PREPARATION OF STANDARD AND NORMAL SOLUTIONS . . -54 Methods of Standardization ....... . . . . 54 a. By Precipitation . . . . . . . -54 b. By Titration . . . . .,-",.-. . . 54 c. By the Absorption Method . . * . . . -55 EXERCISE X Preparation of an Approximately Half-Normal Hydrochloric Acid Solution . . . . . . 55 EXERCISE XI Preparation of an Approximately Half-Normal Potassium Hydroxide Solution . .-..,... ,. . .. . 56 EXERCISE XII The Titration of the Acid against the Alkali . 56 CONTENTS ix PAGE STANDARDIZATION OF THESE SOLUTIONS . 57 EXERCISE XIII Standardization of the Hydrochloric Acid Solu- tion 57 a. By Precipitation of the Chlorine as Silver Chloride . . 57 b. Against Calcium Carbonate ...... 59 EXERCISE XIV Standardization of the Alkali Solution . . 59 a. Against Pure Chemicals -59 b. By the Absorption Method 60 EXERCISE XV Determination of the Percentage Strength of Acid Solutions .......... 62 EXERCISE XVI The Analysis of a Soluble Carbonate . . 63 EXERCISE XVII The Determination of Total and Caustic Alkali in a Mixture of Sodium Hydroxide and Sodium Carbonate . 63 OXIDATION AND REDUCTION 64 General . . .64 Available Oxygen 65 The Permanganate Method 67 EXERCISE XVIII Preparation of a Solution of Potassium Per- manganate . . . . . . . . .67 EXERCISE XIX Standardization of a Solution of Potassium Permanganate .......... 68 a. By Pure Iron dissolved out of Contact with the Air . . 68 b. By Pure Iron reduced by Means of the Jones Reductor . 69 Determination of the Blank 70 Reduction and Titration of the Iron .... 71 c. By Ferrous Ammonium Sulphate . . . . 71 d. By Means of Sodium Oxalate . . . . . .72 EXERCISE XX The Determination of the Percentage Purity of Oxalates 72 EXERCISE XXI The Determination of the Purity of Hydrogen Peroxide 73 EXERCISE XXII The Determination of Calcium 73 EXERCISE XXIII The Determination of Iron in Siderite . . 74 The Dichromate Method . . . . . . . . -75 Preparation of a Solution of Potassium Dichromate ... 76 Indicator 76 EXERCISE XXIV Standardization of a Solution of Potassium Dichromate 76 a. Against Ferrous Ammonium Sulphate .... 76 b. Against Pure Iron . . . . . . 77 EXERCISE XXV The Determination of Iron in Siderite . . 77 lODIMETRY 78 Methods of Determination . . 78 a. The Titration of Oxidizable Bodies 78 b. Bodies which contain Available Oxygen 78 CONTENTS c. Free Chlorine or Bodies which liberate Chlorine ... 78 EXERCISE XXVI Preparation of Solutions .... 79 a. Approximately N/io Iodine Solution . . .79 b. N/io Sodium Thiosulphate Solution .... 79 c. Starch Solution 80 EXERCISE XXVII Standardization of the Iodine Solution . So a. Against N/io Thiosulphate 80 b. Against N/io Arsenious Oxide 80 c. By Means of Standard Permanganate Solution . . .. 81 d. By Means of Standard Dichromate Solution ... 82 EXERCISE XXVIII Estimation of Available Chlorine in Bleach- ing Powder 82 EXERCISE XXIX The Determination of Available Oxygen in Pyrolusite 83 EXERCISE XXX The Determination of the Strength of Hydro- gen Peroxide 84 PART IV AGRICULTURAL ANALYSIS THE ANALYSIS OF MILK 85 General . . . . 85 Composition . . . . . . . . . . -85 Sampling ............ 86 Specific Gravity . . . . . . . . . . .86 Removal of Samples . . . . . . . . . .87 Total Solids 87 Ash 88 Fat 88 a. Adams' Paper Coil Method 88 b. Babcock Method 90 Total Proteids ........... 94 Kjeldahl Method 94 Determination of the Blank 97 Milk Sugar 99 Tabulation of Results .100 References . . . . . . . . . . . .100 THE ANALYSIS OF BUTTER 100 General 100 Sampling 101 Water 101 Fat 102 Casein . . . . 102 Ash 102 Salt 102 CONTENTS xi PAGE THE EXAMINATION OF BUTTER FAT 103 Composition 103 Differences 105 Chemical 105 Physical 105 Preparation of Pure Butter Fat 105 Physical Tests 106 Specific Gravity . . . . . . . . .106 Melting Point 107 Chemical Tests . . . . . . . . . .109 Volatile Fatty Acids no Reichert-Meissl Method . . . . . . 110 Soluble and Insoluble Fatty Acids 112 Saponification or Koettstorfer Number 114 Iodine Absorption Number, Hanus Method . . . .116 Household Tests 118 The Foam Test 118 Waterhouse or Milk Test 118 References . . . . . . . . . . .119 THE ANALYSIS OF CEREALS AND FEEDING MATERIALS . . . .119 Classification 119 Composition . . . . . . . . . . .119 Carbohydrates 120 Fats 121 Proteids 121 Preparation of the Sample 121 Dry Matter 121 Ether Extract 123 Separation of Carbohydrates, Stone^s Method . . . . .123 Reducing Sugars, Allihn's Method 124 Sucrose. Clergefs Inversion Method 124 Dextrin and Soluble Starch 125 Starch, Diastase Method 126 Starch, Saliva Method 127 Crude Fiber 128 Total Proteids 129 Ash 129 References 130 THE ANALYSIS OF FERTILIZERS 130 General 130 Sampling 131 Dry Matter 132 Phosphorus 132 Total Phosphorus 133 Water-soluble Phosphorus 136 xii CONTENTS PAGE Citrate-insoluble Phosphorus ... . . . .136 Citrate-soluble Phosphorus . . 137 Nitrogen I3 8 Total Nitrogen in Absence of Nitrates 138 Total Nitrogen when Nitrates are Present . . . . .138 Nitrogen Soluble in Water . - 139 Nitrogen as Ammonium Salts . 140 Potassium ... . j^o Potassium in Mixed Fertilizers 1-40 References . . . . . , I42 THE ANALYSIS OF SOIL, 142 Constituents of the Soil 142 Organic Constituents 143 Collection and Preparation of the Samples . . . . . .144 Moisture 146 Volatile Matter 147 The Extraction of the Acid-soluble Material . . . ... 147 Removal of Soluble Silica from Solution 148 Insoluble Matter and Soluble Silica 149 The Determination of the Acid-soluble Substances . . . .150 Iron, Aluminium, and Phosphorus, collectively . . . .150 Phosphorus 151 Manganese . . 151 Calcium 152 Magnesium . . .'"... . . . . . . .152 Sulphur . . . . . . . . . . .152 Iron 153 Potassium . . . . . . . . . . 153 Sodium . . . . . . . . . . . 153 Separation of Potassium from Sodium 153 ffumus . . . . . . . . . . . .154 Total Nitrogen in the Presence of not More than a Trace of Nitrates . 155 Carbon Dioxide . . . . . . . . . . .156 Statement of Results . . . . 159 References . . . . . . . . . . . 160 PART V STOICHIOMETRY EMPIRICAL FORMULAS . -. -. . -. -. . . . ~ . 161 Problems ' . . . . . ; . ; . . . .162 PERCENTAGE COMPOSITION . . -. > .- >. . ..y 162 Problems , ' . , .- ... ..,..'... * .. .'' . 163 CONTENTS xiii PAGE GRAVIMETRIC CALCULATIONS . . . . . . . . .163 Factors 165 Problems . . . 166 Indirect Methods .167 Problems . . . 168 The Volume of a Reagent Necessary for a Given Reaction . . .169 Problems . - 171 VOLUMETRIC CALCULATIONS . . .... 171 Acidimetry and Alkalimetry I7 1 Problems / . -^ . i?7 Oxidation and Reduction . . . . ^ .178 Balancing Equations 178 Oxidizing Agents . . . . . .180 Exercise in Balancing Equations . . . . . . .181 PERMANGANATE AND BICHROMATE METHODS 182 Numerical Relations . . . . . . . .182 Questions on Equations . . ,^ 183 Methods of Solving Problems . ... .184 Problems . .186 lODIMETRY 187 Method of Solving Problems . 187 Questions on Equations 188 Problems 188 FACTOR WEIGHTS 189 Miscellaneous Problems 190 APPENDIX BOOKS OF REFERENCE 195 TABLE I. Desk Reagents 196 TABLE II. Laboratory Reagents 196 TABLE III. Apparatus for Desk Equipment 202 TABLE IV. Specific Gravity of Hydrochloric, Nitric, and Sulphuric Acids 203 TABLE V. Specific Gravity of Ammonia Solutions .... 205 TABLE VI. Determination of Lactose by Soxhlefs Method . 206 TABLE VII. Determination of Dextrose by Allihn's Method . 207 TABLE VIII. Logarithms ......... 210 TABLE IX. Antilogarithms 212 TABLE X. Combining and Atomic Weights ..... 214 ANSWERS TO PROBLEMS 2I 5 INDEX 217 LIST OF ILLUSTRATIONS FIG. PACK 1 . Sample Pages of Notebook . . . . . . . . . 3 2. Desiccator 5 3. Wash Bottle 6 4. Cover-glasses and Clip 8 5 . Triangle for supporting Cover-glasses 9 6. Evaporation of Liquid from a Crucible ...... 27 7. Ignition of Precipitates 30 8. Half-form Filter 37 9. Pipettes 41 10. Graduated Cylinder 41 1 1 . Graduated Flask 42 12. Burettes and Holder 42 13. Reading Burettes .......... 43 14. Calibration Curves .......... 48 15. Recording Volumetric Data . 53 1 6. Gooch Apparatus 58 17. Absorption Flask 61 18. Dissolving Iron out of Contact with Air 69 19. Jones Reductor ........... 70 20. Apparatus for Determination of Available Oxygen ... 83 21. Muffle Furnace ........... 89 22. Extraction Apparatus . . . . . . . . . . 90 23. Extraction Battery, heated Electrically 91 24. Ether Distilling Apparatus 92 25. Centrifugal Machine 93 26. Digestion and Oxidation Battery 95 27. Apparatus for Distilling Ammonia in Kjeldahl Determination . . 96 28. Specific Gravity Flask 106 29. Weighing Tube for Butter 109 30. Reflux Hopkins Condenser and Flask 125 31. Copper Distilling Flask 156 32. Apparatus for Determination of Carbon Dioxide 157 xv OF THE f UNIVERSITY ) PART I INTRODUCTION GENERAL REMARKS THE knowledge of the amount of. a particular constituent in a substance is often of great importance from the commercial as well as from the scientific standpoint. The necessity of being able to answer the question " How much ?" with a high degree of accuracy has led to the development of the important branch of chemistry known as Quantitative Analysis. The methods of quantitative analysis may be classified according to the nature of the operations employed. The most important are the following : ~ , [Gravimetric General T\/T *.u j i Volumetric Methods [Electrolytic Special Methods Gasometric Colorimetric Photometric Attributive In the following pages the gravimetric and volumetric methods only will be discussed. For a description of the other methods the student is referred to the more comprehensive works on quantita- tive analysis, a list of which is given on page 195. In gravimetric methods the constituent is determined by trans- forming it into an insoluble compound, in which condition it can be separated by filtration from the other constituents which were orig- inally present in the substance. This insoluble compound either has a definite chemical composition or it may be changed into a sub- stance of known composition. It is weighed and the amount of the constituent sought calculated. The methods are based, therefore, upon the insolubility of some compound containing the constituent to be determined. No sub- stance is absolutely insoluble, however, and the amount that will dissolve depends upon the prevailing conditions. Consequently, it 2 QUANTITATIVE ANALYSIS is of fundamental importance to obtain and to maintain conditions of such a nature that the precipitate will always be under condi- tions of minimum solubility. The operations employed in gravimetric processes include pre- cipitation, filtration, and washing, and are very similar to those used in qualitative analysis. It is necessary, however, to perform them with much more care, neatness, and completeness, for in the quanti- tative work the entire amount of the constituent must be precipitated, separated from the other substances, and finally weighed. Not only are the operations similar to those employed in the qualitative work, but the methods of separation of the constituents invariably depend upon the same chemical facts. The relations existing between these two branches of analysis cannot be too strongly em- phasized. In order to become familiar with the fundamental clas- sifications, reactions, separations, and specific tests for the identifi- cation of the elements a careful and systematic review of qualitative analysis should be made. To successfully perform quantitative chemical analyses, one must learn to work carefully and intelligently and also to do more than one thing at a time. The student can work intelligently only when he has a clear idea of what is to be done and understands thor- oughly the chemistry of the process which he is carrying out. Fol- lowing the directions blindly always brings trouble. Plan the work so that several operations are going on at the same time ; for exam- ple, while the samples are being weighed, the crucibles may be heating to constant weight ; again, while a precipitate is being di- gested, the samples for the next determination may be weighed. Accuracy cannot be attained without neatness. Hence it is necessary to have the desk and apparatus neat and clean at all times and to exercise the greatest care to keep them in this condi- tion. Nothing makes a more unfavorable impression than dirty apparatus ; moreover, the effect on the student himself is often demoralizing. NOTEBOOKS Care and neatness are just as essential in recording data as in their collection. Record all of the data in a permanent form just as soon as they are obtained. Use the notebook provided for this pur- pose and make the entries in ink. Under no circumstances should records be placed on scraps of paper. If at any time the data INTR OD UCTION become valueless through accident, do not tear the leaves out of the notebook, but mark "discarded" and make new entries on another page. The student should learn to record his results in a systematic and orderly manner. The method of recording the data success- fully used in the authors' laboratories is illustrated in Fig. I, which represents two pages of the notebook employed. They are $" x 7f " and ruled in cross section by lines -J- of an inch apart. ?l * A IIUL A I I (} Nj S jia:^iu^K;iirim^!Rrif]:iH]:ii 1 ) > < ft Jj, 7/k,T ?' >d f= q p iL 1 f, I^fl6 3 i > .. . x E V w 1 ^,0 4 y f"> E QB VN t s g <-, 2 4f) D vy O-S "i '-> 5 2 j i ^J 'I H^ 4- X s F f=j ^j ^) i y ^S t ( , i 1 1 i P 4=i -7 i 62 y =. ( ( Ll ,- H L T q fi ^3 ^ pi! i! P i ES 3 ^ . " a 7 ul 6ft ( / 33 4 i j <, tb. ?9,^ 1 [ ) X ^ >- o r> 4 Uf '1 ( if- >lf b / 165 \ X = I/ ,c )C !' ?,( ( % !4- () I -) ""> 1 f\ t f\ f /j fl ( ;i ^' o If -> - u I , 1 l< M N ) <\ u -- A 9 N :) 5 A n f A p d 1 n n rf c ^ n ftf q f Iv M Ls 4d I,' u > )r *-J I i H i ;f H o r IP fr ,] ir c Kf - q ^ II ^ E = FIG. i The right-hand page is for the record of the experimental data and the report of the percentage of the constituent sought. On the left-hand page should be recorded : 1. The equations representing all of the chemical changes taking place in the process. 2. The calculation of the results from the data collected. 3. A record of any special difficulties encountered and the reme- dies employed. The use of logarithm tables will greatly facilitate the calculations. Too much importance should not be placed on the fact that du- plicates " check," because it sometimes happens that the same error 4 QUANTITATIVE ANALYSIS will be made in each determination, giving results which agree, but which may be several per cent from the true value. There is often a tendency for the student to " begin over " when some little irreg- ularity has been introduced into the procedure. This tendency is the cause of the loss of much time and also results in the student losing confidence in his work. By consulting the instructor and making a thorough study of the conditions, the difficulties may be overcome, the exercise carried out without loss of time and a certain amount of valuable experience gained. Each exercise should bring forth the best efforts of the student. As a last resort " begin over." REAGENTS One of the most important problems with which the analytical chemist has to deal is the purity of the reagents. It is obvious that no matter how good a manipulator the analyst may be, if im- pure reagents are employed, his results will be valueless. Young chemists are frequently deceived by reagents being marked "chemically pure," "for analysis," etc. For accurate work, how- ever, such labels cannot be considered as a guaranty of the purity of reagents. The analyst can be sure of his reagents only by sub- jecting them to thorough chemical tests, similar to those prescribed by Krauch. 1 Reagents are often tested by making a "blank" determination. This consists in carrying out the regular determination, omitting, however, the substances to be analyzed. The results of the blank are subtracted from those obtained in the regular determination. Attention should be called to the fact that solutions of ammo- nium hydroxide on standing in certain reagent bottles attack the glass, with the formation of flaky particles, which may result in spoiling an analysis. Distilled water, moreover, should be fre- quently tested, as certain forms of stills occasionally boil over, with the result that "distilled water" is sometimes more impure than the ordinary tap water. When removing the reagent from the bottle, always pour it out and discard the unused portion. In order to insure the purity of the reagents adopt the general principle of never introducing a pipette ', spatula, or other piece of apparatus into a reagent bottle and 1 The Testing of Chemical Reagents for Purity^ E. Krauch. Translated by Wil- liamson and Dupre. INTRODUCTION 5 never returning the unused portion of the reagent to the bottle. Be very careful when handling the stoppers of the reagent bottles ; do not put them in such a position that the part which fits into the neck of the bottle will touch the desk or anything else. Cultivate the habit of holding the top of the stopper between the fingers while removing the reagent. SPECIAL APPARATUS Desiccators For keeping crucibles, samples, etc., in a dry atmosphere an ap- paratus known as a desiccator is used. For quantitative work the form shown in Fig. 2 is very efficient. It is fitted with a porce- lain plate which is provided with holes for four crucibles. Granu- lar calcium chloride which has been sifted to remove the fine < particles is used as the desiccat- ing agent. When sulphuric acid is used for this purpose, the bottom of the desiccator should be covered with a half-inch layer of asbestos fiber, and this should be saturated with concentrated acid. This prevents the acid splashing upon the crucibles, with subsequent damage to the balances. To render the desic- cator tight, the ground part of the cover should be covered with a very thin coating of grease or vaseline. Trouble is often caused by the introduction of hot crucibles into the desiccator. This results in heating the air, which expands, and if the cover is then put into place, upon cooling a partial vacuum will be formed. Upon removing the cover the sudden rush of air will often blow the precipitate out of the crucible. It is advisable, therefore, to allow crucibles to cool for about a min- ute before placing them into the desiccator, and also to keep them covered. FIG. 2 QUANTITATIVE ANALYSIS At to be is in Wash Bottles least two wash bottles are necessary in analytical work, one used for hot and the other for cold water. A form which general use is shown in Fig. 3. A 500 or 750 c.c. plain flask makes a wash bottle of convenient size. To facilitate handling the hot water bottle, its neck should be wrapped with as- bestos paper. This is easily done by thor- oughly wetting a piece of asbestos paper and wrapping it about the neck of the flask. Upon boiling water in the flask, the asbes- tos paper will dry and adhere tightly to the neck. Stirring Rods FIG. 3 For the removal of precipitates from beakers a stirring rod provided with a rubber tip (a " policeman") is used. At least four stirring rods should be provided, two 13 cm. and two 18 cm. in length. The ends of these should be fused and rounded. THE OPERATIONS OF QUANTITATIVE ANALYSIS Sampling The analyst very seldom receives substances in a form ready for analysis. It is more often the case that they come to him in the form of tubs of butter, bags of fertilizers, car loads of ore, etc., and he must obtain a sample whose value shall be representative of the entire amount. At first sight this may not appear to present many difficulties, but when one considers the heterogeneous nature of the material, it is evident that the problem of obtaining a fair sample is one of the most difficult with which the analyst has to deal. The methods of sampling vary with many factors, the most important of which are : the nature and uniformity of the original material, the nature of the constituent to be determined, and the size of the original sample. Minerals are often sampled by crushing to a sufficient fineness, piling in a cone, and by means of a shovel removing the diagonally INTRODUCTION 7 opposite quarters of the cone. This removes one half of the ma- terial. The other half is again piled into the form of a cone and the process repeated. This is continued until only a pound or two of the sample is left, which is pulverized to the desired fine- ness and used for the analysis. At any desired stage the sam- ple may be ground. This process is known as sampling by " quartering." Metals such as pig iron are often nonhomogeneous, conse- quently great care must be exercised in obtaining samples. This is usually done by taking drillings from different parts of the bars by means of a clean steel drill, mixing these drillings, and using them for the analysis. Agricultural products are so diversified that no general method of sampling can be given. For certain substances like butter, flour, bags of ground fertilizers, etc., a long thin tube may be used, which permits the removal of samples from the various parts of the barrel or tub. Vegetables, such as beets and peas, are usu- ally reduced to a state suitable for chemical analysis by passing them through one of the ordinary kitchen grinding machines. Dry cereals like corn and wheat may be very satisfactorily ground in an ordinary coffee mill. Liquids should be thoroughly mixed by shaking before a sample is removed. REFERENCES ON SAMPLING LODGE, R. W., Notes on Assaying, p. 23. LORD, N. W., Notes on Metallurgical Analysis, p. 9. WILEY, H. W., Agricultural Analysis. Consult the chapters on the analysis of the different agricultural products. Weighing Samples The direct and the indirect methods are used in weighing sam- ples for analysis. Weighing by the direct method consists in placing the substance upon the pan of the balance, or upon a cover-glass or other ves- sel of known weight, and adding enough weights to balance the amount of substance taken, or placing the weight upon the pan and adding enough substance to the other pan to just balance it. This method is in general use in analytical chemistry, it being particularly adapted to weighing specified quantities of the sub- stance. Its application, however, depends to a certain extent on 8 QUANTITATIVE ANALYSIS the nature of the substance. Liquids and substances which absorb moisture from the air cannot be weighed in this manner. The indirect method, or weighing by difference, consists in plac- ing the substance into a stoppered tube or flask, weighing, remov- ing some of the substance, and weighing again, the difference between the two weights being the weight of substance taken. This indirect method is used for weighing substances which readily take up or lose moisture, for liquids, and in general when a speci- fied weight of the substance is not necessary. For weighing substances which absorb moisture readily, several devices may be employed. One of the most convenient is to use two cover glasses, the edges of which are ground to fit and held tightly together by a spring clip as illustrated in Fig. 4. The weight of the glasses and clip being known, the substance is placed upon one of the glasses, the other glass placed over this and held in position by the clip. The weight of the substance can then be obtained without danger of absorbing moisture. To determine the amount of substances to be taken for analysis requires considerable experience and no general rule can be given, as the quantity to be weighed out depends upon so many factors. The amount of the constituent to be deter- . , . , mined is of primary importance, as in some cases, where the percentage is small, 10 grams may be taken for the analysis, while in other cases 0.5 gram may be sufficient. The nature of the precipitate is also an important factor, a bulky gelatinous precipitate being hard to filter and wash. The quantity of the precipitate must not be too small, for a slight loss due to manipulation introduces a large error. Hence, as the beginner in quantitative analysis has not had the necessary experi- ence which will guide him in determining the amount of the sub- stance to be weighed for analysis, it is necessary to state the quantities to be used. Solution and Evaporation The samples for analysis are dissolved in distilled water whenever possible. If acid must be added to aid in the solution, a large excess INTRODUCTION 9 over the amount called for by the directions should be avoided. An excess of acid may dissolve some of the precipitate, or if it must be neutralized later, it increases the volume of the solution by using more ammonium hydroxide and also increases the amount of soluble salts present. In general the analyst should try to find the happy medium between working with a solution which is too concentrated and one which is too dilute. With concentrated solutions the quantitative separation of precipitates is frequently unsatisfactory, because of the occlusion of soluble salts; moreover, the loss of a drop of such a solution occasions a serious error. Ex- tremely dilute solutions, on the other hand, have the disadvantage of being difficult to handle, requiring considerable time for evapo- ration, and the large volume of liquid may dissolve an appreciable amount of the precipitate. Solutions should be kept covered as much as possible to protect them from contamination. It is frequently necessary to evaporate solutions over a flame or on a water bath, and here also the vessel should be kept covered. This is best done by placing a glass triangle, shown in Fig. 5, upon a beaker or casserole, and allowing a cover- glass with a diameter a little larger than that of the vessel to rest up- on the triangle. Small glass hooks which are hung over the side of the vessel may also be used to support the cover-glass. It should FlG be remembered that alkaline solutions attack glass appreciably, and therefore should not be allowed to stand for any length of time in contact with glass vessels, but whenever possible should first be made slightly acid. On boiling certain solutions, especially those which contain par- ticles of suspended matter, much trouble is often experienced by a violent agitation of the liquid which is called " bumping." This is caused by the incomplete diffusion of the heat applied to the solu- 10 QUANTITATIVE ANALYSIS tion. The liquid becomes locally superheated, a comparatively large amount of steam is given off at once, and this is attended by an explosion which may throw the liquid out of the vessel. This may be prevented in several ways. A stream of gas may be passed through the solution which keeps the heat diffused, so that superheating will not occur. If substances with sharp points, such as broken glass or pumice stone, are placed in the solution, the steam will be evolved gradually from these points. For dis- tilling solutions of this kind copper flasks are often used, the copper being such a good conductor that it permits the heat to be uniformly distributed throughout the solution. Precipitation Conditions The object of precipitation in quantitative analysis is to change the constituent which is being determined into such a form that it can be easily separated from the solution by mechanical means, or to remove from solution a substance whose presence would cause trouble in the subsequent procedure. The choice of the form in which the substance is precipitated depends upon the following factors : 1. Solubility. The necessity of the most complete separation possible is obvious. In general, it is customary to precipitate a substance in its least soluble form, and to maintain throughout the determination conditions under which the precipitate will remain insoluble. 2. Ease of filtration and washing. The importance of these factors from the standpoint of economy of time is apparent. 3. Stability on drying and ignition and the possibility of change to a more stable form are also important factors which must be taken into consideration. In general the precipitating reagent is added in the form of a solution. The method has several advantages, among which may be mentioned the ease of control of the quantity of the reagent, and also the possibility of detection of particles of insoluble foreign matter present in the solid reagent. In many cases, more- over, a quantitative separation can be obtained only by adding the precipitant in the form of a solution. Whenever it is possible, the INTR OD UCTION 1 1 quantity of reagent necessary to precipitate the substance should be calculated. This prevents the addition of an unnecessary ex- cess of the reagent and also permits a correction when a blank determination is made. The solution must always be tested for complete precipitation. This may be done by testing the super- natant liquid, or by filtering and testing a small portion of the filtrate. Many precipitates are less soluble in solutions which contain in common with them an element or radical (ion), therefore an excess of the precipitating reagent is often added. Thus barium sul- phate is more insoluble in barium chloride solution than in water, consequently in the determination of sulphuric acid, an excess of barium chloride is added to the solution. Precipitates often possess the power of carrying down or occlud- ing foreign substances. Even though the occluded substances are soluble in water, it is often practically impossible to remove them by washing; hence, conditions which favor occlusion should be carefully avoided. The occlusion of the precipitant is often caused by " dumping " a large quantity of the reagent into the solution. By stirring the solution while the precipitant is being slowly added from a pipette or dropper, this source of error may be avoided. Many substances when first precipitated exist in such a physical state that their separation from the solution by means of a filtering medium is almost impossible, owing to their tendency to run through the filter. Methods have been devised by which such precipitates can be changed to forms permitting their removal by filtration. The Enlargement of the Grains of a Crystalline Precipitate Barium sulphate is a crystalline precipitate whose grains are so small that they often run through the filter. The grains may be enlarged by allowing the precipitate to stand for some time in con- tact with the solution at a temperature close to the boiling point. This may also be accomplished by allowing the precipitate to re- main at the ordinary temperature in contact with the solution, but the length of time must be greatly extended. This process is termed digestion. Ostwald 1 gives the following explanation of this phenomenon : 1 W. Ostwald, The Scientific Foundations of Analytical Chemistry, p. 22 (1900). 12 QUANTITATIVE ANALYSIS Since every substance is slightly soluble, a certain amount of the precipitate always remains in solution. On heating, more of the precipitate dissolves and the smaller particles are the first to go into solution; the solution then becomes supersaturated with re- spect to the large particles and a precipitation on them takes place. As the heating continues, the small particles are dissolved, and the larger particles grow at their expense. This process goes on at the ordinary temperature, but much more slowly. The digestion must be carried on until the particles are so large that they will not pass through the pores of the filter. Colloidal Precipitates Many substances, such as aluminium hydroxide and the metallic sulphides, form gelatinous or flocculent precipitates and cause trouble by running through the filter. Precipitates of this kind, which are called "colloidal," are thrown down by heating the solu- tion, or by adding solutions of salts, acids, or bases. They are usually precipitated from hot solutions. The addition of salts to facilitate the precipitation is seldom necessary, as they are usually present in the solutions in sufficient amount. Filtration The process of filtration has as its object the separation of the precipitate from the liquid. For this purpose a special grade of filter paper is used which has been washed with acids, and which on burning leaves an ash whose weight may be neglected in ordi- nary quantitative work. The size of the filter should be adapted to the amount of precipitate. The larger the filter, the greater the quantity of wash water needed to remove impurities, consequently the filter should be kept as small as possible. The speed of filtration depends upon 1. The filtering medium. 2. The temperature of the solution. 3. The pressure. Paper is most commonly used for filtering, although in many cases asbestos may be used. Rapidity of filtration depends upon the size of the pores of the filter. Since the internal friction of water is less at high than at the INTR OD UCTION 1 3 ordinary temperatures, it is evident that hot solutions will filter more rapidly than those which are cold. Filtration is often accelerated by diminishing the pressure On one side of the filter. This is accomplished most frequently by the use of long narrow-stemmed funnels. The stem of the funnel becomes filled with a column of liquid, the weight of which draws the solution through the filter. It is apparent that if the filter does not fit the funnel, air will be drawn down between the filter and the funnel and the advantage of a long stem will be lost. Fil- tration may also be hastened by placing the funnel in the neck of a flask and diminishing the pressure in the flask by means of a suction pump. When this method is employed, care must be taken that the filter is not torn. Its point must be supported by means of a well-fitting platinum cone, or by a cone of hardened filter paper. A very serviceable form of filter paper used for this pur- pose is the half form hardened filter, the use of which is described in Part II, under the Determination of Aluminium, page 37. Washing In order to obtain a precipitate in the form of a definite chemi- cal compound, the impurities must be removed. These impurities are usually soluble salts which can be removed by washing. It sometimes happens, however, that a precipitate contains so much impurity that it must be dissolved and reprecipitated. In the second precipitation the greater part of the impurity remains in solution, while that remaining with the precipitate can easily be removed by washing. Whenever possible, precipitates should be washed several times by decantation, as impurities are much more rapidly removed in this way. When washing the precipitate on the filter, the water should be allowed to drain from the precipitate before the next portion of water is added, as the impurities are dis- solved more rapidly and with the use of the minimum quantity of wash water. The fact should be borne in mind that all precipitates are soluble to some extent, consequently a large amount of wash water may dissolve enough of the substance to introduce an appre- ciable error. Enough wash water should be used to remove the impurities, but no more. The washings are usually tested for some specific impurity, and when this is removed, it is assumed that the other substances have also been washed out. In the determina- 14 QUANTITATIVE ANALYSIS tion of chlorine, for example, the precipitate contains silver nitrate and sodium nitrate as impurities. It is washed until free from sil- ver nitrate on the assumption that by that time it will also be free from sodium nitrate. The wash water must always be tested to be sure that the impurities are removed and tinder no circum- stances may this be neglected. Colloidal precipitates on being washed frequently return to the finely divided state, and run through the filter. This may be pre- vented by using wash water which contains a salt which will vola- tilize when the precipitate is ignited. Ammonium nitrate is often used for this purpose. Drying and Igniting Precipitates For the removal of the last portion of wash water, the precipi- tate is usually dried in an air bath which is maintained at a tem- perature of 110. To prevent contamination from dust, the funnel should be covered with a wet qualitative filter the edges of which are folded down over the edge of the funnel. Gooch crucibles may be conveniently dried by placing them into small covered beakers, and then putting them into a hot closet. Filters are ignited by the following methods : 1. By placing them with the precipitate into a crucible, allow- ing access of air, and heating until the carbonaceous matter is con- sumed. This method is used when the burning filter paper has no action on the precipitate. 2. By removing the precipitate as completely as possible from the filter, igniting the filter paper upon a platinum wire, so that the ash will fall into a crucible, then adding the main part of the precipitate to the ash. This method is employed when the pre- cipitates are of such a nature that the burning filter paper will change their chemical composition. Crucibles For the ignition of many precipitates porcelain crucibles may be used. They have the disadvantage of being easily broken ; more- over, the thickness of the porcelain makes it impossible to heat the precipitate to a high temperature. On the other hand, they are cheap and are impervious to the reducing gases of the burner. For many purposes platinum crucibles are indispensable. Their INTR OD UCTION 1 5 advantages lie in their resistance to the ordinary reagents, also in the fact that they permit the precipitate to be heated to an ex- tremely high temperature. Their use is restricted by conditions described under the following paragraph. The Use and Care of Platinum 1 It is important to remember that, although platinum is not oxidized in the air at any temperature, nor attacked by any single acid, yet there are many substances that attack and combine with it at comparatively low temperatures. Platinum should never be used in solutions containing free chlorine, bromine, iodine, or ferric chloride, as it is attacked under these conditions. The caustic alkalies, the alkaline earths, nitrates and cyanides, and especially the hydrates of barium and lithium, attack platinum at a red heat, although the alkaline car- bonates have no effect at the highest temperatures. Sulphur, in the presence of alkalies, has no action, but phosphorus and arsenic attack platinum when heated with it. Organic matter containing phosphorus should not be ignited in platinum dishes, as it affects the platinum seriously. Direct contact of platinum with burning charcoal should be avoided, since the silicon reduced from the charcoal ashes unites with platinum, making it brittle and liable to fracture. Also contact with compounds of the easily reducible metals is especially dangerous at high tem- peratures, as alloys having a low fusing point are readily formed with platinum. This is especially true of lead. Moreover, the red-hot crucible should never be seized with brass crucible tongs, as hot platinum dissolves copper, and the cru- cible is often stained in this way. When gas is used, care should be taken to have the supply of air sufficient to insure complete combustion, since, with a flame containing free carbon, the plati- num suffers deterioration by the formation of a carbide of platinum, which, oxi- dizing later, blisters the metal. For this reason, also, the inner cone or reducing flame should not be in contact with the metal. The loosening effect of the Bun- sen flame upon the surface of platinum exposed to its action produces the familiar gray appearance which cannot be removed except by burnishing. Platinum tri- angles often become gray and very brittle from the same cause. Systematic application of moist sea sand to all articles affected in this way, after use, will keep them in prime condition and materially prolong their life, with but a trifling loss in weight. Hot crucibles should not be plunged into cold water to loosen fusions which they contain, nor should the platinum be worked between the fingers for the same purpose. If possible, each crucible should be provided with a wooden form which will aid materially in keeping it in the proper shape. Every careful analyst of necessity uses clean utensils. The habit of cleaning and polishing platinum dishes immediately after using them is easily formed, and repays the user with increased confidence in his work as well as in the prolonged life of the article. Rubbing the surface of platinum with moist sea sand (round 1 From directions furnished by Baker & Co. 1 6 QUANTITATIVE ANALYSIS grains only) applied with the finger, serves to remove most impurities and to pol- ish the metal without material loss. Fusing potassium bisulphate or borax in the platinum vessel and then boiling it in water and polishing it with sand, as above, is recommended by Gmelin. When it is desired to clean the outer surface of dishes in this manner, they must be placed in dishes of sufficient size to allow the fused flux to envelop completely the article to be cleaned. Sodium amalgam possesses the property of wetting platinum without amalgamating with it, even when other metals are purposely added to the amalgam. This substance, therefore, is useful for effecting a quick and thorough cleansing of platinum. The amalgam is gently rubbed upon the metal with a cloth and then moistened with water, which oxi- dizes the sodium and leaves the mercury free to alloy with foreign metals. The mercury is then wiped off, and the dish is cleaned and polished with sand. If the existence of a base metal alloyed with the platinum is suspected, immerse the article in question first in boiling hydrochloric acid for a few minutes, then, after a thorough rinsing with clean water, immerse it in boiling nitric acid free from chlorine. If the dish is unaffected in weight or appearance, and the acid baths fail to give reactions for the base metals, their absence in appreciable quantities is assured. The Balance Quantitative analysis may be said to have had its birth with the introduction of the balance into the chemical laboratory. The bal- ance is, therefore, one of the most important pieces of apparatus which 'the chemist uses, and in order to do intelligent work a thorough knowledge of the principles of construction and of its essential parts is necessary. The balance is used to determine the weight of substances, and this is accomplished by utilizing the force of gravity, which acts as parallel forces on the bodies to be weighed. When these forces are equal, the bodies are said to have equal weights. The weight of a body, i.e., the measure of the earth's attraction for it, bears a definite relation to the quantity of matter it contains, that is, to its mass. The process of weighing is, therefore, a determination of the relation between masses. The weights employed are standard masses, and the process of weighing consists in comparing the at- traction of the earth for the standard mass with its attraction for the mass of the substance whose weight is to be determined. The force of gravity is not the same at all places on the surface of the earth, but varies with the latitude and with the elevation above sea level. The mass of a body does not vary whatever its location on the surface of the earth, hence, the standard mass (weight) and INTRODUCTION 17 the body to be weighed will be affected alike by a change in location. The Construction of the Balance The usual analytical balance is essentially a lever supported at its middle point on a frictionless fulcrum and resting in a state of stable equilibrium. The lever, which is known as the beam of the balance, is, therefore, divided into two arms which have as nearly as possible the same length and weight. At the ends of the beam are suspended two pans by means of hooks or stirrups which rest on bearings similar to that on which the beam rests. The essential parts of the balance are : 1. The beam. This should be in a state of stable equilibrium and respond readily to small differences in load. 2. The bearings. Both the central and terminal bearings consist of a knife-edge and a plane or concave surface. They should be made of agate. 3. The pans and their supporting devices. They should be made of non-corroding metal and constructed as light as possible. To fulfill the requirements of the chemist, the balance should be accurate and sensitive. The construction of the essential parts of the balance determines its character. Position of the Center of Gravity The condition that the beam be in a position of stable equilib- rium is fulfilled when the center of gravity is below the axis, that is, below the line of contact between the central knife-edge and the plane on which it rests. For, if the center of gravity were in this axis, the condition of equilibrium would be indifferent, and the beam would not oscillate, but would remain in any position in which it was placed. If, on the other hand, the center of gravity were above the axis, the equilibrium would be unstable, and if the beam were once removed, it would not return to its original posi- tion. By sensitiveness is understood the ease with which the beam moves. The sensitiveness of a balance is usually defined as the angle through which the beam will turn for a given difference of load upon the two pans. It depends mainly upon the nearness of the center of gravity to the axis. Every balance is so constructed c i8 QUANTITATIVE ANALYSIS that the degree of sensitiveness can be regulated within certain limits by adjusting the distance between the two. This is accom- plished by raising or lowering a movable bob upon the pointer, or a nut upon the post above. The time of oscillation increases with the sensitiveness. It is possible for the oscillations to be so slow that a considerable amount of time will be lost in weighing. The time of an oscillation should be from ten to fifteen seconds. The Knife-edges The terminal knife-edges of a good balance should be parallel to each other and to the central knife-edge. They should lie in the same plane with the central knife-edge, or very slightly above it. By loading the pans of a balance there is a change in the po- sition of the center of gravity with respect to the axis, and it has been shown that a change in the relative position of the axis and the center of gravity affects the sensitiveness. If the terminal knife-edges are below the central one, loading the pans lowers the center of gravity still further and thereby decreases the sensitive- ness. The Beam The beam is one of the main factors in establishing the sensi- tiveness of a balance. The beam must be as rigid as possible, for by loading the balance the terminal knife-edges would be lowered if the beam should bend, and consequently the sensitiveness of the balance would be decreased. As no beam is absolutely rigid, it is practicable to place the terminal knife-edges slightly above the central one and so regulate their distance from the axis that the maximum load of the balance cannot produce indifferent or un- stable equilibrium. If the arms of the beam are heavy, it will re- quire a larger weight at one end (in one pan) to produce a given deflection than if the beam were lighter. Hence, it is apparent that the sensitiveness, which is the angle of deflection, depends upon the weight of the beam the lighter the beam, the greater the sensitiveness ; therefore, the beam should be constructed as light as possible. It is very evident, from the principles of the lever, that in the case of two levers (other things being equal), the one with the longer arms will be moved by a smaller weight than the one with short arms. The balance with the longer beam will INTRODUCTION 19 have a greater angle of deflection than the short-armed beam ; therefore, the longer the beam, the greater the sensitiveness. But here, too, there is a limit, for it is difficult to get a long beam that is sufficiently rigid without giving too much weight ; further, if it is too sensitive, there may be too much time lost in weighing. From these facts, there has grown up the rivalry between the long and short-armed balances. By the introduction of aluminium in the manufacture of balance beams and pans, we are enabled to get a medium length rigid beam that is very light, thus combining the strong points of the other two styles of balances. The pans are suspended from the ends of the beam upon the terminal knife-edges by means of hooks or stirrups, which permit them to hang perpendicularly and thus not increase the length of the beam. Friction at the terminal knife-edges affects very seri- ously the sensitiveness of the balance. The Weights The capacity of the analytical balances is usually 200 grams; i.e., the maximum weight which may be placed on each pan. It is very rarely, however, that the analyst weighs objects having a greater weight than 100 grams. Hence, sets of weights from 50 grams to 5 milligrams, having a total weight of about 100 grams, are usually provided with each balance. The weights from one gram up are made of brass and are often gold plated, while the fractional weights are of platinum made in the form of a square with one edge turned up to facilitate handling. Milligrams and fractions thereof are measured by a small weight called a rider. This is placed upon the beam, which is graduated from the point directly above the central knife-edge out to the point directly above the terminal knife-edge. The number of divisions depends upon the make of the balance, there usually being 50, 60, or 100. When 5, 6, and 10 milligram riders are used respectively, each di- vision will represent -fa of a milligram. By means of a rod carry- ing a finger the rider can be conveniently placed at will on any division on the beam. Owing to the different graduations on the beams of balances of different makes, much confusion may arise from use of riders obtained from the various manufacturers. Al- ways be sure that the rider employed when placed on the proper division will balance the 5 -milligram weight. 20 QUANTITATIVE ANALYSIS Summary of Precautions to be Observed in Weighing 1. Sit directly in front of the center of the balance so as to avoid parallax while observing the movements of the pointer. 2. See that the balance is level. 3. See that the rider will be free from the beam when it is swinging. 4. Release and arrest of the beam and pans. a. Release the beam before releasing the pans. b. Release and arrest the beam with a slow, steady move- ment, avoiding jerky movements which are sure to in- jure the knife-edges. c. The beam should be arrested only when it is in a hori- zontal position. d. Avoid giving the pans a rotatory motion in the horizon- tal direction, and all other motions which would cause the knife-edges to scrape on their bearings. e. If the beam does not begin swinging as soon as it is released, set it in motion by placing the rider on the four or five milligram division and raising it again. 5. Never place an object, not even the smallest weight, upon the pan, or remove one from it, unless the beam and pans are supported, i.e., arrested. 6. Always place the weights and objects to be weighed in the middle of the pans. Long tubes and other objects which cannot be easily centered on the pan, may be suspended from the hooks above the pans. 7. Handle all the weights with the tweezers provided for this purpose, and never use these tweezers for any other purpose. 8. Objects to be weighed must never be placed in direct con- tact with the pans unless they are metallic, glass, or porcelain. Hot objects cannot be accurately weighed, owing to the upward draughts they create about the pan on which they rest. They may also heat the beam and thus produce a change in the relative length of the arms. Hygroscopic and volatile substances, and those that absorb carbon dioxide from the air, should be weighed in closed vessels which must be opened a moment before weighing. 9. Weighing is an accurate operation : never do it when in a hurry. INTRODUCTION 21 10. Be sure that the reading of the weights is taken correctly. Check by two readings ; first, read the weights from the vacant spaces where they are kept, and, second, read again as the weights are returned to their places. 11. Never leave the beam resting on the knife-edge when not in use, and never leave the weights on the pan, but always return them to their places. PART II GRAVIMETRIC ANALYSIS EXERCISES WITH THE BALANCE EXERCISE I Determination of the Time of Vibration Procedure. Dust the beam and pans very carefully with a camel's-hair brush. Cautiously release the beam and then the pans. After the beam has oscillated long enough to recover from the effects of any jar it may have received when released, deter- mine the time required for the pointer to make ten excursions past the central or zero part of the ivory scale. One tenth of this is the Time of Vibration. Determine the time of vibration when the pointer makes long, short, and medium excursions. Note. Time of vibration varies with the load. It also varies with the length of the beam, the shorter the beam, other things being equal, the shorter the time. The time of vibration for a balance with a given load is a measure of the sensitiveness. Much can be learned concerning the quality and condition of a balance by simply determining the time of vibration under different loads. EXERCISE II Determination of the Zero Point Procedure. Release the beam and then the pans, and after a few excursions of the pointer, begin to note and record the num- ber of scale divisions the pointer passes over, estimating to tenths of a division. Place the readings to the right in a column headed R, and those to the left in one headed L. Take a number of observations, three or four on one side and a greater number by one on the other side. Add the two columns and divide each sum by the number of observations taken on that side. The re- sults represent the average excursion of the pointer. Now add these two and divide by two and subtract the quotient from the 22 GRA VIMETR1C ANAL YSIS 23 greater of the average excursions. The result gives the distance from the center of the scale, on the side of the longer swing at which the pointer would stop if the beam were to come to rest, i.e., the Zero Point. If the zero point is found to be more than half a division from the middle line of the scale, it should be brought nearer by adjusting the nut on the screw projecting from the end of the beam. Exact adjustment is not essential, as the relative length of the arms is constantly changing. Do not adjust the bal- ance, but ask the instructor to do so. Note. Lack of constancy of the zero point may be due to changes of temperature, defective condition of the knife-edges, or to jarring. EXERCISE III Determination of the Sensitiveness Procedure. Determine the zero point without a load. Now place the rider on the one milligram division (the first numbered division) of the arm and again determine the zero point. The dis- tance between these two zero points is usually designated the Sen- sitiveness of the balance. Note. A balance is sufficiently sensitive for ordinary quantita- tive work when a weight of one milligram changes the zero point three divisions. EXERCISE IV Weighing by the Usual Method Procedure. Obtain the object to be weighed and remove any moisture by means of a clean linen handkerchief. Determine the zero of the balance. Place the object in the center of the left pan and in the center of the right-hand pan a weight which is estimated to be approximately the weight of the object. Release the beam until it is evident which way it swings, then slowly sup- port it again. In case the weight added is nearly equal to the weight of the object, it may be necessary to release the pans in order to see which way the beam swings and which is the heavier, the weight or the object. If the weight is too heavy, remove it and add the next lighter weight, following the order in which the weights are placed in the box. When the beam shows that the 24 QUANTITATIVE ANALYSIS weight added is just too light, add to it the next smaller weight. If this is too heavy, remove it and make trials until one is found which again gives a total weight which is just too light. Continue this series of trials until all of the necessary weights from the box have been added, then place the rider at different points on the arm until one is reached at which the zero point is found to coin- cide with that previously found for the unloaded balance. Begin- ning with the largest weight, read them from the vacant spaces in the weight box and record the values, expressing them in grams and decimals thereof. Do not neglect to notice the position of the rider on the beam and include this value. Then check this by reading the values of the weights as they are removed from the balance pan. GRAVIMETRIC DETERMINATIONS EXERCISE V The Determination of Chlorine Procedure. Clean a weighing tube thoroughly, be sure that it is dry, and provide it with a well-fitting cork. Take the tube to the instructor's office and obtain the substance to be analyzed. With a clean linen handkerchief remove any particles of substance which adhere to the cork and the inside of the tube as far as the cork extends. Clean two No. 3 beakers, mark them I and 2 respectively, and take them and the weighing tube into the balance room. Be sure that the outside of the tube is clean, then weigh it on the balance which has been assigned, and record this weight in the notebook in the manner indicated on page 3. Hold the weighing tube over beaker No. I, carefully remove the cork by a rotary motion, and by rotating the tube introduce 0.2 to 0.4 gram of the substance into the beaker. Tap the tube gently to remove any loose particles, replace the cork, and weigh the tube and its contents. If much more than 0.4 gram has been taken, it will be necessary to weigh out another portion into a clean beaker. Weigh another portion of the substance into beaker No. 2. Be sure that the numbers on the beakers correspond with the proper weights of substances recorded in the notebook. Add to each portion of the substance about 100 c.c. of cold distilled water and a slight excess of dilute nitric acid. . This GRA VIMETRIC ANAL YSIS 2 5 should be done by making the solution just acid with dilute nitric acid. Use litmus paper to test the acidity of the solution and be sure to wash the liquid adhering to the paper back into the beaker by means of water from the wash bottle. Add to the beaker an excess of two or three cubic centimeters of dilute nitric acid. Now add a clear solution of silver nitrate, drop by drop, allowing it to run down the side of the beaker and stirring continuously with a glass rod. Continue this until no more precipitate is seen to form. Stir the solution vigorously until the particles of the precipitate collect in a curdy mass, then test for complete precipi- tation by adding a few drops of the silver nitrate to the solution. Heat the contents of the beaker until the temperature is near the boiling point, and continue the stirring until the liquid is practi- cally clear. Place a 9 cm. ashless filter paper into a funnel, folding it so that it will fit exactly. If the angle of the funnel is exactly 60, the filter will fit if it is carefully folded in the usual manner. If it does not fit, it will be necessary to adjust it to the funnel by allowing one edge to lap over the other. By holding the filter in place with the finger and wetting it, it will adhere to the side of the funnel. Be sure that the top edge fits snugly to the funnel. Now filter by pouring the liquid down a glass stirring rod, held tightly against the lip of the beaker and reaching nearly to the bottom of the filter. Wash the precipitate by decantation, using portions of about 20 c.c. distilled water acidified with nitric acid. This should be done by stirring the precipitate in order to disintegrate it, allowing it to settle and pouring off the super- natant liquid as described above. Repeat this process three or four times. Replace the beaker containing the filtrate with a clean beaker, and transfer the precipitate to the filter by aid of a stream from the wash bottle which should contain water acidi- fied with nitric acid. This may be accomplished by holding the beaker in an inclined position with the lip down, with stirring rod pressed firmly against the lip. By means of a jet of water from the wash bottle the precipitate may be washed down the rod and into the filter. If it cannot be entirely removed in this manner, then by means of a stirring rod provided with a policeman the precipitate can be loosened from the beaker and then removed. Be, sure that all of the precipitate is completely removed. This may be ascertained by cleaning the outside of the beaker and then 26 QUANTITATIVE ANALYSIS observing it when held toward the light. When the precipitate has been completely removed from the beaker, continue the washing by directing a stream of the cold acidified water from the wash bottle against the top of the filter. Conduct the stream around the edge of the filter until the water has filled it to within one quarter of an inch from the top. Add no more wash water until that in the filter has run through. Continue washing in this way until the impurities are all removed. This can best be ascer- tained by collecting about 3 c.c. of the wash water in a test tube, acidifying with nitric acid, and adding a drop of dilute hydro- chloric acid. If no turbidity results, the washing is complete. Allow the funnel to drain for a few minutes, cover the top with a piece of wet qualitative filter paper, label properly, and place it into a drying closet which is heated to 1 10. While carrying out the foregoing steps of precipitation and filtration, the student will find time to prepare in the following manner two porcelain crucibles in which to weigh the precipitates. Clean two porcelain crucibles and covers and mark them I and 2 respectively by means of a blue pencil. Place the crucibles on clean clay triangles which are resting on tripods, and heat them for fifteen minutes to the full heat of the adjustable burner. Remove the burners, allow the crucibles to cool for about a minute, place them into a desiccator, and weigh them after they have cooled to room temperature, which usually takes about fifteen minutes. Heat again and reweigh. Continue this until two consecutive weighings are not more than 0.2 milligram apart. The crucible has now a constant weight. When the contents of the funnels are dry, remove from the hot closet. Place side by side on the desk two pieces of glazed paper about six inches square, the edges of which should be smooth. Remove the filter from the funnel by inserting the small blade of a penknife between the paper and the funnel. Carefully invert the filter over one of the pieces of glazed paper. Loosen the precipitate by gently squeezing and rubbing between the fingers. When most of the precipitate is separated, reverse the filter, and loosen any portions of the silver chloride still remaining by carefully rubbing the sides of the filter together. Allow the portion that is thus detached to fall upon the glazed paper and cover with a cover-glass. Fold the filter so that it will form a half circle, place it upon the other sheet of glazed paper, and fold it into a narrow GRAVIMETRIC ANALYSIS 27 flattened roll, beginning with the straight edge. Now bring the two ends together and wrap a platinum wire securely around them. In this way the central parts of the filter, to which small particles of the precipitate still adhere, are thoroughly enveloped by the exterior parts so that in the subsequent burning nothing can be easily lost. By means of the wire hold the filter paper over the proper weighed crucible which has been placed upon the glazed paper, and ignite by means of a small Bunsen flame. Allow to burn quietly until the flame goes out and then use the burner to keep the residue red hot. Shake the ash into the crucible and remove the last portions from the wire with a small brush. Finally transfer any portions of the ash which have fallen upon the glazed paper into the crucible and heat with the free flame to remove the last trace of carbonaceous matter. As silver chloride is volatilized at a compara- tively low temperature the heating should be done very carefully. Hold the burner in the hand and heat only those parts of the crucible which show black particles of carbonaceous mat- ter. As soon as the carbon is all burned remove the burner at once, allow the crucible to cool, place it upon a sheet of glazed paper, and introduce the main portion of the precipitate. Use a small brush to transfer the last portion of the precipitate from the glazed paper to the crucible. At best some of the silver chloride precipitate remaining with the filter paper has been reduced to silver, and this must be changed to silver chloride by the following method. Add two or three drops of concentrated nitric acid to the crucible, warm, and, after allowing to cool a short time, add one or two drops of concentrated hydrochloric acid. The contents must be evaporated to complete dryness without loss by spattering. This is best accomplished by placing a small iron pan on a tripod, and supporting the crucible about one eighth of an inch above the bottom of the pan by means of a triangle resting on its edges. (See Fig. 6.) Place FIG. 6 28 QUANTITATIVE ANALYSIS under the pan a burner which is so regulated that it will not boil the contents of the crucible. When the contents of the crucible have evaporated, holding the burner in the hand, heat it with the small free flame until the precipitate just begins to fuse. Cool and weigh. Heat again and weigh as described above, until the weight of crucible and contents is constant. From the weight of the precipitate, calculate the weight of chlorine present and the percentage in the substance taken -for analysis. For the method of calculation see page 163. Notes. i. The presence of a slight excess of silver nitrate in the solution is advantageous because of the fact that silver chloride is more insoluble in water containing a small amount of silver nitrate ; moreover, it helps the particles of the precipitate to become coagulated. 2. Under the influence of light the silver chloride changes from white to a violet color. This is caused by a part of the precipitate changing to a lower chloride with the loss of an appreciable amount of chlorine. The chlorine is replaced, however, by the subsequent addition of nitric and hydrochloric acids to the precipitate. 3. Silver chloride is almost completely insoluble in water which contains a little silver nitrate. It is very slightly soluble in cold water and in cold dilute nitric acid. It is more soluble in concen- trated nitric acid ; hence, care should be taken that the precipita- tion does not take place in a solution which is strongly acid. The precipitate is also especially soluble in concentrated hydrochloric acid and hot concentrated solutions of chlorides. 4. Hot water dissolves too much silver chloride to permit its use in washing out the impurities. Cold water, on the other hand, causes the precipitate to return to the colloidal state and run through the filter. This is prevented by adding to the water a small amount of nitric acid. 5. Silver chloride fuses at about 460. At a temperature slightly higher than its fusing point the substance begins to vola- tilize. Considerable care should be exercised, therefore, in heating this substance. 6. The fused silver chloride may be removed from the crucible by placing a small piece of zinc upon the mass and adding very dilute hydrochloric acid. The chloride will be reduced and the metallic silver can then be easily removed. GRA VIMETRIC ANAL YSIS 29 7. The experiment just described is a type of a certain class of quantitative determinations. With certain modifications bromine and iodine may be determined by this method. It is obvious, moreover, that the method may be reversed and that a metal like silver may be determined by the addition of hydrochloric acid to a solution of its soluble salt. 8. The determination of the chlorine in the presence of a heavy metal is complicated by the fact that many metals, like iron, form basic salts under the condition of the precipitation, and these con- taminate the precipitate. In such cases it is best to first remove the metal by means of a suitable precipitant. 9. The filtrate and all silver residues should be placed into the bottles marked " Silver Residues." REFERENCE FRESENIUS (Cohn), Vol. I, par. 82 b, p. 198. EXERCISE VI The Determination of Sulphur in a Soluble Sulphate Procedure. Obtain the substance for analysis from the instructor and weigh two portions exactly as in Exercise V, but take a some- what larger amount, from 0.4 to I .o gram for each portion. Dissolve in 100 c.c. of distilled water, and acidify with 2 or 3 c.c. of dilute hydrochloric acid. Heat the solution to boiling and add, drop by drop, at a rate not exceeding 5 c.c. per minute, about ro.c.c. of a hot solution of barium chloride. The barium chloride is best added by means of a small medicine dropper similar to those used for filling fountain pens. Be sure that an excess of the precipitating reagent has been added to the solution. Keep the solution at a temperature near the boiling point for about an hour, then allow the'precipitate to settle. Prepare two filters in the usual way. If the precipitates have been properly digested, and a good grade of filter paper is used, no trouble should be caused by the particles running through the filter. As an extra precaution double filters may be used or a sin- gle filter may be saturated with a hot concentrated solution of ammonium chloride. Decant the hot supernatant liquid upon the filter. Watch the filtrate closely, and if it is turbid, replace the beaker containing the filtrate with a clean one, and pass the filtrate QUANTITATIVE ANALYSIS through the filter again. Do not proceed with the filtration until a clear filtrate is obtained. Wash the precipitate three or four times by decantation, using hot water containing a little hydrochloric acid. Replace the beaker containing the filtrate by a clean one, transfer the precipitate to the filter as in the determination of chlo- rine, and wash with hot water from the wash bottle until 3 c.c. of the filtrate give no test for chlorides. Place the funnel and con- tents into the drying closet. When dry, remove the filter from the funnel and fold it in such a way that it can be placed into a previously weighed porcelain crucible. Be sure that the part of the filter paper containing the main portion of the precipitate is placed in the bottom of the crucible. If any of the precipitate has crept over the edge of the filter and adheres to the funnel, remove FlG 7 it by means of a piece of moist ashless filter paper and place this into the crucible with the filter. Place the crucible in a reclining position on the triangle, and only partially cover with the crucible cover so that a current of air will pass over the filter. (See Fig. 7.) Place the burner under the crucible and heat gently with a low flame until volatile matter begins to come off. Do not allow the volatile gases to take fire, as this is attended by mechanical loss of the barium sulphate. If this should happen, extinguish the flame by means of the crucible cover. Gradually increase the flame until the volatile matter is expelled and nothing but a little carbonaceous matter is left with the precipitate. Heat to the full heat of the burner, directing the flame toward the base of the crucible. When the carbon is all oxidized, cool the crucible in the desiccator and weigh. Heat again and repeat until constant weight is obtained. From the weight of barium sulphate calculate the percentages of sulphuric anhydride and of sulphur present in the original sample. For the method of calculation see page 165. GRA VIMETRIC ANAL YSIS 3 1 Notes. i. The precipitate of barium sulphate possesses to a marked degree the power of dragging down or occluding other substances which cannot be easily removed by wash water. This may result in either high or low results. In the presence of iron, aluminium, or chromium the precipitate may be contaminated with the sulphates of these metals. On ignition, sulphur trioxide is given off, and the results obtained are low. In the presence of potassium salts low results are obtained owing to the fact that the precipitate is contaminated with potassium sulphate. When nitrates or chlorates are present, the precipitate will con- tain the barium salts of these acids, consequently high results will be obtained. The rapid addition of the precipitating reagent gives high results due to the occlusion of barium chloride. In general, the amount of occlusion is greater in concentrated solutions. From the above it is obvious that the solution from which the sulphate is to be precipitated must be as free as possible from iron, aluminium, chromium, and potassium salts. Moreover, nitric and chloric acids must be absent. 2. The addition of an excess of hydrochloric acid is to be avoided. Not only does it tend to dissolve the precipitate, but, as has been shown by Richards, it also increases the amount of barium chloride occluded. 3. If precipitated in a cold or very dilute solution, barium sul- phate will be found to be present in a very finely divided , state unless allowed to stand for several hours. If precipitated in a boiling solution, and then heated, the particles are larger. (See page n.) 4. The precipitate may be considered as insoluble in water and dilute acids. It is appreciably soluble, however, in concentrated hydrochloric acid and more soluble in either concentrated nitric or sulphuric acids. The presence of either a soluble barium salt or a soluble sulphate decreases the solubility of the barium sul- phate. In this determination, therefore, a small excess of the precipitating reagent is advantageous. (See page n.) 5. The filter containing the barium sulphate may also be ignited without first drying. f In this case extreme care must be used to heat slowly. The filter should be placed into the crucible, which is inclined on a triangle, as described above, and heated with a low flame which is directed towards the top of the crucible. This dries the precipitate from the top downwards, so that there is no danger 32 QUANTITATIVE ANALYSIS of particles being blown out of the crucible by the sudden forma- tion of steam. The final ignition is conducted in the manner already described. 6. If the precipitate is ignited slowly, the filter is easily oxidized. Rapid heating changes it to a form of carbon resembling graphite, which is oxidized with extreme difficulty. 7. By reversing this determination it is apparent that barium may be estimated as the sulphate. This is true of strontium ; and, with certain modifications of the method, lead may also be deter- mined in this way. REFERENCES FOLIN, Journal of Biological Chemistry, 1, 131 (1906). HULETT AND DusCHAK, Zeitschrift fur anorganische Chemie, 40, 196 (1904). RICHARDS AND PARKER, Proceedings of the American Academy of Arts and Sciences, 23, 67 (1895). EXERCISE VII Separation and Determination of Calcium and Magnesium in a Mixture of their Carbonates Calcium Procedure. Weigh out two portions of the sample of about i gram each into No. 3 beakers, add about 10 c.c. of water and cover with cover-glasses. By means of a stirring rod introduce through the opening between the lip of the beaker and the cover- glass about 20 c.c. of dilute hydrochloric acid. Heat the beaker on an asbestos gauze, and if any of the substance remains undis- solved, add more acid and warm again. Continue heating until all of the carbon dioxide gas is expelled ; wash the cover-glass with a little water in order to recover any of the solution that may have spattered upon it. Dilute the solution to approximately 200 c.c., make alkaline with ammonium hydroxide, and heat to boiling. To the hot solution add slowly 25 c.c. of a freshly prepared solution of ammonium oxalate, stirring well. Digest at a temperature near the boiling point for an hour, allow the precipitated calcium oxalate to settle, and decant the supernatant liquid through a filter, keep- ing as much of the precipitate as possible in the beaker. Wash the precipitate three times by decantation, using 20 c.c. of hot water each time. Test the filtrate for complete precipitation by GRA VIMETRIC ANAL YSIS 3 3 adding a few drops of the ammonium oxalate solution and allowing to stand. If no precipitate forms, make the nitrate slightly acid and evaporate it on the steam bath for the determination of magnesium. Place the beaker containing the calcium oxalate precipitate un- der the funnel, and dissolve the calcium oxalate by pouring suc- cessive portions of warm dilute hydrochloric acid through the filter, washing the filter this way three times. When the calcium oxalate is all dissolved, finally wash the filter with dilute ammonium hydroxide solution. Dilute the solution to about 200 c.c., add am- monium hydroxide in slight excess, then add 5 c.c. of the ammo- nium oxalate solution, and digest as before for about an hour. Filter the calcium oxalate upon the filter which was first used and wash the precipitate with hot water until it is free from chlorides. Add the first three washings to the filtrate, then use another beaker to collect the remainder of the washings. The filtrate should be made just slightly acid with hydrochloric acid, com- bined with the first filtrate, and used for the determination of mag- nesium. (See below.) Dry the precipitate of calcium oxalate in the drying closet and ignite as described in the determination of sulphur. By heating, the calcium oxalate is changed first to calcium carbonate and finally to calcium oxide. Allow the crucible to cool, and very carefully moisten the residue in the crucible after the carbon has all been consumed, first with one cubic centimeter of water, then with a few drops of dilute sulphuric acid. Heat very cautiously to evaporate the excess of acid. When the white fumes cease to be given off from the crucible, add a few drops more of the sulphuric acid and evaporate to dryness. Heat to redness by means of the free flame, cool, and weigh. Repeat the treatment with sulphuric acid until the weight is constant. All of the calcium is thus con- verted into calcium sulphate, in which form it is weighed. From the weight of the calcium sulphate calculate the weight of calcium oxide and the percentage present in the substance taken for analysis. Magnesium Concentrate the slightly acidified filtrate from the calcium deter- mination by heating on the water bath. When the volume is about 200 c.c., cool, add ammonium hydroxide until it is just neu- D 34 QUANTITATIVE ANALYSIS tral, or only very faintly alkaline. Add drop by drop 1 5 c.c. of a solution of sodium ammonium hydrogen phosphate (microcosmic salt). Add slowly to the solution one third its volume of ammo- nium hydroxide (sp. gr. 0.96) with constant stirring. Allow the solution to stand for several hours, then decant the supernatant liquid through a filter and wash the precipitate three times by decantation, using 2\ per cent ammonia solution and leaving as much of the precipitate as possible in the beaker. [Calculate the amount of desk reagent required to make 500 c.c. of the 2\ per cent ammonia solution and dilute this quantity to the required volume.] Dissolve the precipitate on the filter by pouring small quantities of warm hydrochloric acid through the filter, receiving the filtrate in the beaker in which the precipitation of the magne- sium ammonium phosphate took place. Wash the filter three times with warm, slightly acid water. Dilute the solution to about 200 c.c., and add ammonium hydroxide drop by drop until the solution is slightly alkaline, stirring vigorously meanwhile. Now add a few drops of the microcosmic salt solution to insure com- plete precipitation. Then add one third the volume of ammonium hydroxide with constant stirring, and allow to stand for several hours. Decant the supernatant liquid through a filter, wash the precipitate three times by decantation, using cold 2\ per cent ammonia solution, then transfer the precipitate to the filter, con- tinuing the washing with the dilute ammonium hydroxide until a few cubic centimeters of the filtrate give no test for chlorides. Dry the precipitate, transfer the main bulk to a glazed paper, and burn the filter separate from the precipitate as directed in the determi- nation of chlorine, but omit the treatment with acids. Transfer the precipitate to the crucible, bring gradually to the full heat of the Bunsen flame, and heat until the precipitate is white. Cool in the desiccator, weigh, and heat to constant weight. From the weight of the pyrophosphate calculate the weight of magnesium oxide, and the percentage of magnesium oxide in the substance taken for analysis. Notes. i. The separation of calcium and magnesium depends upon the different solubilities of the two oxalates. Calcium oxa- late is practically insoluble in hot water, whereas magnesium oxalate is relatively soluble. Magnesium oxalate is, however, much more soluble in water containing an excess of ammonium GRAVIMETRIC ANALYSIS 35 salts. If a large amount of magnesium is present, the precipitate of calcium will contain some magnesium oxalate, and a reprecipita- tion is necessary. 2. The solution should be well boiled to expel the carbon diox- ide. If this is not entirely removed, on adding ammonium hy- droxide and ammonium oxalate the precipitate will consist of calcium oxalate and calcium carbonate. As this latter compound is more soluble than the oxalate, it is well to avoid its formation. Ammonium oxalate solution should be freshly prepared. On standing it undergoes decomposition, ammonium carbonate being one of the products formed. 3. Calcium oxalate on gentle ignition below visible redness is changed to the carbonate and as such may be weighed. A tem- perature slightly too high, however, expels some carbon dioxide. The complete conversion to the oxide requires heating in a plati- num crucible at a high temperature. The action of the sulphuric acid on the calcium oxalate, oxide, and carbonate is to convert them into calcium sulphate. This compound will stand the cherry red heat of a Bunsen burner without alteration ; the higher heat of the blast will cause it to lose sulphuric anhydride. 4. On concentrating the filtrate from the calcium oxalate, a crystalline precipitate of magnesium oxalate will sometimes settle out. This may be dissolved in dilute hydrochloric acid and added to the solution. 5. The complete precipitation of magnesium as the salt MgNH 4 PO 4 takes place only under certain conditions which must be closely observed. Contamination of the precipitate may occur : l a. When the precipitation takes place in a strongly ammoniacal solution, particularly when the phosphate is slowly added, the pre- cipitate under these conditions always contains some of the normal magnesium phosphate. b. If the precipitation takes place in a neutral or slightly am- moniacal solution in the presence of ammonium salts and ammo- nium hydroxide is afterwards added, the precipitate then always contains some magnesium tetra ammonium phosphate. To insure a pure precipitate, the solution must -be neutral, as 1 This discussion of the determination of magnesium follows very closely Treadwell's (Treadwell-Hall, Vol. II, p. 62, ed. 1904) description of the experiments of Neubauer (Zeit. fur Angew. Chem. p. 439, 1896). 36 QUANTITATIVE ANALYSIS free as possible from ammonium salts, and the ammonium hydrox- ide must be added after the addition of microcosmic salt solution. 6. The solution in which precipitation takes place may be freed from ammonium salts : a. By evaporation of the solution and the ignition of the resi- due, or evaporation to dryness with an excess of nitric acid. b. By first precipitating the magnesium in the presence of the ammonium salts, then dissolving the impure precipitate in a small amount of acid, and reprecipitating. The second precipitation takes place under the specified conditions, and the precipitate is obtained pure. 7. On the addition of a microcosmic salt solution to the neutral solution containing magnesium, 90 per cent of the magnesium present is at once precipitated as magnesium hydrogen phosphate (MgHPO 4 ). When ammonium hydroxide is added to the cold solution, this precipitate is changed to the crystalline magnesium ammonium -phosphate. The 10 per cent of the magnesium hydro- gen phosphate which remained in the solution is also completely precipitated by this procedure as magnesium ammonium phos- phate. 8. Magnesium ammonium phosphate is appreciably soluble in hot water, but is much less soluble in cold water. It is least solu- ble in a cold dilute solution of ammonium hydroxide. 9. During ignition the magnesium ammonium phosphate loses water and ammonia, and is converted into magnesium pyrophos- phate. If the pyrophosphate appears gray, it may be whitened by moistening with a few drops of concentrated nitric acid and reigniting after expulsion of the excess of nitric acid by heating over a radiator. REFERENCES Calcium FRESENIUS, Quantitative Analysis (Cohn), Vol. I, par. 73, p. 173. Magnesium W. F. HILLEBRAND, The Analysis of Silicate and Carbonate Rocks, Bull. No. 305, U.S. Geol. Surv., p. 105. FRESENIUS, Quantitative Analysis (Cohn), Vol. I, par. 74, p. 176. GRAVIMETRIC ANALYSIS 37 EXERCISE VIII The Determination of Aluminium in a Soluble Salt Procedure. Obtain a sample containing aluminium and weigh out two portions of about one gram each. Dissolve in 100 c.c. of hot water, add about 5 c.c. of concentrated hydrochloric acid, and then enough of a clear solution of ammonium hydroxide to make the solution slightly alkaline. Test with litmus paper or by odor after stirring thoroughly. Be sure to avoid adding more than a slight excess of ammonium hydroxide. Boil gently until the liquid gives only a very slight odor of ammonia, or shows a slightly alkaline reaction. Allow the precipitate to settle, then filter at once. This nitration can best be accomplished by the use of suction. Obtain from the supply room the apparatus to be used for this purpose, which consists of the following : i filter pump ; 1 glass T-tube; 2 filter flasks (500 c.c.); 2 rubber stoppers (i hole) to fit the flasks; 2 hardened filter cones ; 2 ashless filter papers, 1 1 cm. Attach the filter pump to a water cock. Connect to this, by means of rubber tubing and the glass T-tube, the two filter flasks which carry by means of the rubber stoppers the two funnels. Fold the half form hardened filter into a cone by the method shown in Fig. 8, and place into the funnels. Upon these place the 1 1 cm. filter FIG papers folded in the usual way. Press the papers into position, be sure that the filter paper fits the funnel snugly at the upper edge, and moisten with a little distilled water. Pour the clear supernatant liquid through the filter and wash 38 QUANTITATIVE ANALYSIS the precipitate by decantation, using boiling water which contains a few drops of ammonium hydroxide and two or three grams of ammonium nitrate per liter. Use a gentle suction to accelerate the filtration and always keep some liquid in the funnel while suc- tion is being employed. Finally, transfer the precipitate to the filter, wash free from chlorides, dry the filter, and ignite as in the determination of sulphur. After burning the carbon of the filter, heat the precipitate in the flame of a blast lamp until the weight is constant. Calculate the percentage of aluminium oxide present in the sample taken for analysis. Notes. I. The complete precipitation of aluminium as the hydroxide takes place only in the presence of certain salts, in this case ammonium salts. The ammonium salts have a twofold function, they decrease the tendency of the excess of ammonium hydroxide to dissolve the precipitate, and they also prevent the aluminium hydroxide from running through the filter in a colloidal or semisoluble condition. The presence of the ammonium nitrate in the wash water has a similar effect. 2. Prolonged boiling to expel the excess of ammonia should be avoided, as it may result in the solution becoming acid, with the subsequent dissolving of a part of the precipitate. 3. The aluminium hydroxide should be filtered as soon as pos- sible after precipitation. On standing, it adheres to the beaker and is removed only with great difficulty. 4. The precipitate should not be allowed to stand in the funnel for any great length of time without washing, as it dries and cracks, and is then almost impossible to wash free from impurities. The washing should be continued until all chlorides are removed, as any ammonium chloride not washed out will form volatile aluminium chloride on igniting the precipitate. 5. When aluminium hydroxide is ignited, water is given off with the formation of AIO(OH), and on further ignition alu- minium oxide is formed. The aluminium oxide parts with the last trace of water with difficulty, so that the final heating must be done with the blast lamp. As the aluminium oxide also absorbs water easily, unless it is weighed quickly a considerable amount of water will be taken up. The weighing is best accomplished by obtaining an approximate weight of the crucible plus the precipi- tate, then making a second weighing by placing the necessary GRA VIMETRIC ANAL YSIS 39 weights upon the pan, removing the crucible from the desiccator and completing the weighing by means of the rider. 6. Many other metals, such as iron, chromium, nickel, and cop- per are determined by precipitating as the hydroxide in a manner similar to that just described. With the last two metals, potassium hydroxide is usually employed as the precipitating reagent. REFERENCE FRESENIUS, Quantitative Analysis (Cohn), Vol. I, par. 75, p. 179. PART III VOLUMETRIC ANALYSIS VOLUMETRIC analysis comprises those methods wherein the con- stituent of a sample is not isolated and weighed, but determined by allowing a solution of known composition to react with it, either directly or indirectly. From the volume of the solution used, the amount of the constituent can be computed by means of the laws of chemical equivalents. For example, in a solution containing sodium chloride, the amount present can be determined by pre- cipitating the chlorine as silver chloride, by the addition of a solu- tion of silver nitrate of known strength. In order to indicate the point at which all of the chlorine is precipitated, a little potassium chromate is added to the solution. When the silver nitrate has pre- cipitated all of the chlorine as silver chloride, the next drop of the solution added will react with the potassium chromate with the for- mation of a permanent reddish precipitate of the chromate of silver. A substance, such as potassium chromate, which is used to show when a reaction is complete is called an Indicator. It is very easy to detect this point at which all of the chlorine is precipitated, and from the amount of silver nitrate solution added the equivalent quantity of chlorine can be readily calculated. VOLUMETRIC APPARATUS 1 The ordinary methods of volumetric analysis require the employ- ment of vessels which will contain or deliver definite specified quantities of solutions. The vessels in general use are the follow- ing : Pipettes are used to deliver definite amounts of liquids. They are of two general kinds : Those provided with one mark deliver but one specified quantity of liquid. This form is illustrated by the 1 See report of the committee for cooperation with the National Bureau of Standards, Jour. Am. Chem. Soc. Proceedings, p. 17 (1904). 40 VOLUMETRIC ANALYSIS c.c. 40 =-20 25 c.c. pipette in Fig. 9. Those with two marks have the interven- ing space subdivided and permit the exact measurement of different quantities of liquid. This form is represented by the 10 c.c. pipette in Fig. 9. To fill the pipette the liquid is sucked above the upper mark and is then held in place by placing the index finger over the top. The liquid is lowered to the mark by slowly rotating the pipette between the thumb and middle finger, and is allowed to run out into the desired vessel by raising the index finger. The opening through which the liquid is delivered should be small, since the speed of outflow determines the amount of liquid remaining on the inner surface. In order to re- move a constant quantity of liquid, hold the point against the wall of the receiving vessel during the free outflow and for fifteen seconds thereafter. Graduated Cylinders are of vari- ous sizes, ranging from a few cubic centimeters to a liter or more in capacity. They are usually not graduated in small divisions and are, therefore, employed when liquids are to be measured only roughly. The usual form is rep- resented in Fig. 10. Graduated Flasks are made in sizes ranging from 25 c.c. to several liters in capacity. The general form is illustrated in Fig. ii. They are usually provided with two marks, the lower one in- dicating the point to which the flask is to be filled in order to have contained therein the des- ignated amount, while the upper mark indicates the amount which should be placed into the flask in order to remove from it the specified quantity, the difference in the two quantities being the amount of the liquid that will adhere to the inner surface of the flask. FIG. 9 FIG. 10 OF THE UNIVERSITY QUANTITATIVE ANALYSIS (_) Burettes are long tubes graduated in cubic centimeters and frac- tions thereof, from which liquids may be conveniently measured. They have capacities ranging as high as 100 c.c. In the authors' laboratories burettes of 30 c.c. capacity graduated to ^V f a cu i c centimeter have been found to be of convenient size. Two such burettes with a burette holder are represented in Fig. 12. Burettes should be read to hundredths of a cubic centi- meter, and in reading them the exact position of the curved surface of the liquid, termed the me- niscus, will depend upon the position of the eye. Hence, great care should be exercised to have the eye on a level with the meniscus. Many devices are employed to facilitate reading burettes. That represented in Fig. 13 shows a strip of paper wrapped around the bu- rette by means of which the position of the menis- cus can be accurately lo- cated. The paper should be held in such a position that the upper edge will be about one milli- meter below the lower surface of the menis- cus, and the eye on a level with the two upper edges of the paper. Parallax can also be avoided by providing burettes with marks which extend nearly or quite around them. A method of having burettes con- structed with a white back in the center of which is a blue stripe, has been devised by Shellbach. By this arrangement the menis- cus appears to be divided -into two parts which meet in a point in the center, thus giving a sharp definite point, which is very accurately located. FIG. ii mcolnsBuretteHo MH FIG. 13 VOLUMETRIC ANALYSIS 43 THE CALIBRATION OF GRADUATED APPARATUS In accurate chemical work the capacity of all graduated apparatus should be carefully tested. This process of testing is known as Calibration. The vessels to be used should all be calibrated among themselves, so that the relation is accurately known. The 25 c.c. pipette should deliver exactly the same amount of a solution as is delivered by the burette when it reads 25 c.c., and this quantity should be -^ the amount contained in the 250 c.c. flask, and -fa the capacity of the 1000 c.c. flask. It does not make any difference at what temperature these vessels are calibrated, because the meas- urements are only relative. Nor does it make any difference what unit is employed, provided the same one is used for all of the different measuring vessels. The Mohr cubic centimeter has been used ex- tensively as the unit of volume in volumetric work and is defined as the volume of one gram of water at 17.5 weighed in air with brass weights. This is not, however, a true cubic centimeter, which is defined as the volume of one gram of water in vacuum at its greatest density (4 C). The relation between the Mohr cubic centimeter and the true cubic centimeter is i Mohr c.c. = 1.0023 true c.c. 17 18 20 In other words, 1000 grams of water, weighed in air, would occupy a volume of 1002.3 c.c. at 17.5, or the Mohr liter would occupy a greater volume than the true liter. For the most accurate work, in which solutions of definite con- centrations are to be prepared, also for the calibration of burettes for measuring gases, the true cubic centimeter should be used as the standard of calibration. Suppose we desire to calibrate a liter flask in true cubic centi- meters. The dry flask is placed upon the balance pan and suffi- cient weights are added to counterpoise it. Now, as we desire to establish a mark on the flask which represents just one liter or 1000 true cubic centimeters which weigh 1000 grams in vacuum, the 44 QUANTITATIVE ANALYSIS question arises what difference would there be between the weight in air and in vacuum ? How much weight shall be placed upon the pan to represent the 1000 grams of water in vacuum ? One kilogram of water displaces approximately one liter of air, which under the ordinary conditions of temperature and pressure weighs about 1.2 grams. (One literate under a pressure of one atmos- phere weighs 1.293 grams.) Just as the weight of a body in a liquid is lighter than its weight in air by the amount of the liquid displaced, so the water is lighter in air than in a vacuum by the weight of the air it displaces. Therefore, one liter of water is lighter by 1.2 grams when weighed in air than when weighed in vacuum. But the brass weights with which it is weighed are also lighter than they would be were they weighed in vacuum ; hence, since brass has a specific gravity of 8.4 (i.e., 8.4 times as heavy as an equal volume of water), a kilogram of brass weights would occupy only - , or of the volume of the water. These brass 8.4 84 weights would displace of 1.2, or 0.14 gram of air. The 84 weight of the kilogram of water in air is then decreased 1.2 grams and that of the kilogram of brass weights, 0.14 gram ; hence, the total decrease of the weight of water due to the buoyant action of air will be the difference between 1.2 and 0.14, or 1.06 grams. A kilogram of water, i.e., exactly 1000 grams, weighed in vacuum, will weigh in air with brass weights 1000 1.06, or 998.94 grams, and will occupy at 4 C., 1000 true cubic centimeters, or one liter. But let us assume we desire to calibrate the flask at 20 C. At 20 C., 1000 true cubic centimeters of water weigh 998.26 grams in vacuum, and the correction for air displacement, as seen above, is 1.06 grams. Then 998.26 1.06 = 997.2 grams, and represents the weight that must be put upon the pan of the balance to be equal to the weight of the water that occupies the volume of 1000 true cubic centimeters, or one liter, at 20 C. When the calibration is expressed in true cubic centimeters, the weight of the water in vacuum must be calculated because the unit of volume is weighed under these conditions. The following table, which is given to facilitate the calculations involved, contains the weight in air of one true cubic centimeter of water, and the volume in true cubic centimeters corresponding to the weight in air of one cubic centimeter of water at temperatures from 10 to 30. VOLUMETRIC ANALYSIS 45 TEMPERATURE WEIGHT IN AIR OF i c.c. OF WATER VOLUME CORRESPONDING TO THE WEIGHT IN AIR OF i GRAM OF WATER 10 0.9986 gram 1.0014 c.c. 11 0.9985 I.OOI5 12 0.9984 1. 00l6 13 0.9983 I.OOI7 14 0.9982 I.OOlS 15 0.9981 I.OOI9 16 0.9979 1. 002 1 17 09977 1.0023 1 8 0.9976 1.0024 19 0.9974 1 .0026 20 0.9972 .0028 21 0.9970 .0030 22 0.9967 0033 . 23 09965 .0035 24 0.9963 .0037 25 0.9960 .0040 26 0.9958 .0042 27 0.9955 .0045 28 0.9952 .0048 2 9 0.9949 .0051 30 0.9946 .0054 EXERCISE IX _ The Calibration of a Burette Clean the burette thoroughly with the chromic acid cleaning mixture l and then with water, so that the water will not stand in drops on the inner surface, but runs down freely. Boil about 500 c.c. of distilled water, cool, and allow to stand until it has acquired the temperature of the laboratory. Take the temperature with an accurate thermometer, read to the closest degree, and record the same. Fill the glass-stoppered burette with this water and starting at the zero mark, run out a portion of about 5 c.c. into a previously weighed 50 c.c. glass-stoppered flask. Read the quantity of water taken to y^o" f a cubic centimeter and weigh it to one centi- 1 The chromic acid cleaning mixture is prepared by dissolving 25 grams of commercial sodium dichromate in 150 c.c. of water and adding 100 c.c. of concentrated commercial sulphuric acid. This solution should be placed into a glass-stoppered bottle and saved for future use, as it can be used many times. 4 6 QUANTITATIVE ANALYSIS gram. Introduce into the flask the second portion of approxi- mately 5 c.c., representing the amount of water between the five and ten cubic centimeter marks. Repeat this process by remov- ing and weighing the successive five cubic centimeter portions until the burette is emptied. Now, refill and repeat the calibration until the values are accurately known. From the values given in the table on page 45, calculate the volume in true cubic centimeters of these portions of liquid. Know- ing the volume as represented by the burette reading and the volume in true cubic centimeters as obtained from the weight, the correction is readily obtained by subtraction. Plot the cor- rection curves, using the abscissas for the burette readings and the ordinates for the corrections. Obtain the weight of the successive 5 c.c. portions taken from the pinchcock burette, calculate the volume in true cubic centi- meters, and plot the calibration curve as in the case of the glass- stoppered burette. The following table represents a method of recording the data for the calibration of a 30 c.c, burette. The headings of the columns are self-explanatory. CALIBRATION OF THE PINCHCOCK BURETTE Temperature of water 21 READINGS c.c. WEIGHT OF WATER VOLUME IN TRUE CUBIC CENTIMETERS CORRECTIONS ADDITIVE 0.00 21.375 weight of flask 5-00 26.410 weight of flask + water 5-035 5.05 + 0.05 10.00 31.395 weight of flask + water 4.985 5.00 0.05 15.00 36.410 weight of flask + water 5.015 5-03 0.08 20.00 41.415 weight of flask 4- water 5.005 5.02 0.10 25.00 46.430 weight of flask + water 5-0^5 5-03 0.13 30.00 51.435 weight of flask + water 5.005 5.02 0.15 The volume in true cubic centimeters occupied by the different weights of water may be readily calculated in the following man- ner. The weight of the first portion of water between the zero and the 5 c.c. mark was 5.035 grams. By consulting the table, page 45, it will be found that the weight in air of one true cubic centi- meter of water at 21 is 0.997 gram; 5.035 grams -i- 0.997 = 5-05, the number of true cubic centimeters in the first portion. The VOLUMETRIC ANALYSIS 47 weight of the second portion is 4.985 grams, and in a similar man- ner we find this equal to 5.00 c.c. Continuing this, we obtain the values for the various portions as given in next to the last column. The values given in the last column, representing the additive corrections for the successive 5 c.c. portions, are to be represented graphically by means of a curve known as the Calibration Curve. The calibration curve is to be drawn so that the corrections can be read to hundredths of a cubic centimeter and so that they are additive. That is, for any reading of the burette, the correction at that point is given for the total amount of liquid that has been re- moved. The curves given in Fig. 14 illustrate this method of drawing calibration curves. The abscissas represent the burette readings which can be read direct to 0.25, and the ordinates the corrections estimated to o.oi of a cubic centimeter. The data pre- sented in the above table and given in the last column are plotted as Curve i, which represents a convenient size and one which can be pasted upon the inside of the cover of the notebook. Notes. i. Be sure that all air bubbles are removed from the tips of the burettes. 2. From an inspection of the values given in the table, page 45, it will be observed that the temperature does not need to be read very closely. For example, the difference between 20 and 21 makes a difference in the volume corresponding to a weight in air of one gram of water, of 0.0002 c.c., and for 5 c.c. this would amount to o.ooi c.c., which is much beyond the accuracy with which the burette can be read. 3. In using a burette always run out the liquid slowly and allow a sufficient length of time to elapse to permit the liquid to run down from the sides before taking the reading. About one minute is sufficient when small quantities are delivered, and two minutes when about the total capacity of the burette is delivered. 4. Make the calibration curves of such size that they can be pasted upon the inside of the front cover of the notebook. This is done by using as the scale for the correction ten divisions of approximately one millimeter for o.i c.c., and the same for each 2.5 c.c. of the burette reading. 5. Burettes may be conveniently calibrated against a burette or vessel, the capacity of which has been accurately determined by VOLUMETRIC ANALYSIS 49 weighing. For this purpose, the Ostwald Calibrating Apparatus is frequently employed. 1 For the calibration of burettes and flasks the Morse-Blalock 2 Bulbs are often used, and are excellent when much of this work is to be done. STANDARD AND NORMAL SOLUTIONS A Standard Solution is one in which the contents of a definite volume are accurately known. The strength of a standard solution is expressed in various ways. If 58.5 grams, the molecular weight, of sodium chloride are dissolved and made up to a liter, one cubic centimeter will contain 0.0585 gram, which is ^he strength of the solution. Such a solution would contain 35.45 grams of chlorine per liter, i.e., 0.03545 gram per cubic centimeter. The strength may be stated either in terms of sodium chloride or of chlorine. The customary way of expressing the strength of a solution is to state it in terms of one of the constituents ; but it may also be stated in terms of the quantity of a substance to which it is chemi- cally equivalent and which is to be estimated by the use of the standard. Sodium chloride reacts with silver nitrate according to the following equation : NaCl + AgNO 3 = AgCl + NaNO 3 , i.e., one combining weight of chlorine is equivalent to one combin- ing weight of silver, or 35.45 grams of chlorine are equal to 107.93 grams of silver ; and 0.10793 grain of silver, which is contained in one cubic centimeter of the solution, is equivalent to 0.03545 gram of chlorine. We could state then that one cubic centimeter of the sodium chloride solution is equivalent to 0.10793 gram of silver. To a special kind of standard solution the term normal solution is applied. If the molecular weight of hydrochloric acid (36.458 grams) be dissolved in water and the solution made up to 1000 true cubic centimeters, we would have a liter of a hydrochloric acid solu- tion which would contain 1.008 grams of replaceable hydrogen, or one combining weight of hydrogen. One half the molecular weight in grams of sulphuric acid would also furnish one combining weight of hydrogen, or 1.008 grams. If this quantity of sulphuric acid were dissolved and made up to one liter, we would have an acid 1 Tread well- Hall, Analytical Chemistry, II, 417 (1906). 2 Morse, Exercises in Quantitative Chemistry, p. 85 (1905). E 50 QUANTITATIVE ANALYSIS solution of the same strength as the hydrochloric acid solution. These solutions would contain the same number of grams of the replaceable hydrogen per liter. Solutions which contain one com- bining weight of replaceable hydrogen per true liter are termed Normal Acid Solutions. The molecular weight of sodium hydrox- ide would neutralize the molecular weight of hydrochloric acid ; it follows, therefore, that if the gram molecular weight of sodium hydroxide were dissolved and made up to a liter, that these 1000 c.c. would neutralize loooc.c. of the normal hydrochloric acid solution, i.e., the two solutions would be equal chemically, cubic centimeter for cubic centimeter. The same may be stated concerning a solution looo c.c. of which contain the gram molecular weight of potassium hydroxide and the normal solution of sulphuric acid. It is custom- ary to designate alkali solutions which contain the equivalent of one combining weight of replaceable hydrogen per true liter, Normal Alkali Solutions. In solutions used for oxidation processes the oxygen furnished is the important factor, and since one combining weight of oxygen oxidizes two combining weights of hydrogen, these solutions can be conveniently expressed as normal solutions. A liter of a solu- tion of potassium permanganate which furnishes for oxidation purposes 8 grams of oxygen, i.e., 0.008 gram per cubic centime- ter, is equivalent to one combining weight of hydrogen, and, therefore, is a normal potassium permanganate solution. When the molecular weight of the substance is dissolved and made up to a true liter, the solution is a gram molecular solution. In many cases this is the same as a normal solution, as in the case of hydro- chloric acid, sodium hydroxide, acetic acid, and potassium chloride ; but in many other cases they are not the same, for example, sulphuric acid and potassium dichromate. As a result, consider- able confusion has arisen in the literature and unfortunately the terms normal and molecular are not distinguished ; but normal is sometimes used when gram molecular is meant. Normal solutions are usually too concentrated to be conveniently employed and fractional parts of the amount of the substance re- quired to make a normal solution are used instead. If one-half of the molecular weight of hydrochloric acid is contained in a liter, this is a half-normal solution and is expressed as N/2 HC1. If one-tenth the molecular weight is taken, the solution is tenth- normal, N/io, and so on. VOL UME TRIG ANAL YSIS 5 1 An error sometimes results from using these solutions at tem- peratures different from that at which they were prepared. The so- lutions are usually made up at a certain temperature (about 20 C), and then stored in bottles from which they are removed when de- sired. One such solution of hydrochloric acid was found to have a temperature of 33, or an increase of 13 over the temperature at which it was prepared. If we assume that the change between 20-30 is the same as that between 15-25, one liter of this acid would then occupy 1002.42 c.c. If the molecular weight (36.46 grams) of hydrochloric acid were contained in one liter at 20, at 30 it would be dissolved in 1002.42 c.c., or in the first case, one cubic centimeter would contain 0.03646 gram, and in the second =0.03637. Now, in titrating, if at 20, 25 c.c. of the solution 1002.42 would be required, at 30 it would take 25.06 c.c. to furnish the same quantity of acid. This difference is greater than the allowable experimental error, as the burette can be read direct to o.oi c.c. The following table 1 gives the expansion of 1000 c.c. of various solutions due to a change of temperature from 15 to 25: SOLUTION EXPANSION Water 2.OC N HC1 2.4.2 N H 2 SO 4 3.QC N 2.62 N NaOH J.I r N Na.COo O' 1 J N NaCl 2.12 N/io NaCl 2.06 N/io 2.l6 N/io KMnO 4 2.13 ACIDIMETRY AND ALKALIMETRY The processes of acidimetry and alkalimetry comprise the deter- minations of acids and alkalies (hydroxides and carbonates). When an acid is to be determined, a standard alkali solution is employed; and when the sample is analyzed for hydroxides or carbonates, a standard acid is used. The process of bringing the iSchultz, Zeit. fur Anal. Chem., 21, 167. 52 QUANTITATIVE ANALYSIS solutions of the reacting substances together is termed Titration. The neutral point, or, in general, the point which represents the completion of the reaction, is desigated as the End Point. INDICATORS The end of the reaction is made apparent to the eye by means of indicators whose colors in acid and in alkaline solutions are different. These indicators are usually solutions of organic com- pounds which are added directly to the solution to be titrated. There is no substance which can be used as a universal indicator, consequently, different indicators must be used for the titration of the various acids and alkalies. The following are the most impor- tant indicators used in the determinations of this kind. Litmtis. This is a vegetable coloring matter, usually employed in the form of the aqueous extract. It gives a red color with acids, while with alkalies a blue color is produced. Besides its applica- tion to the titration of the ordinary acids and alkalies, it may also be used for weak acids and in the presence of ammonium salts. Solutions containing carbon dioxide must be boiled, as litmus is not reliable when used in its presence. , , Phenolphthalein is an organic compound which is produced synthetically. It is used in the form of an alcoholic solution. In acid solutions this indicator forms a colorless compound, while in alkaline solutions the products are red. It finds special applica- tion with the weak acids, such as hydrogen sulphide and the organic acids. Carbon dioxide must be expelled from the solution by boiling, before the indicator can be used. It is not reliable when used for the titration of weak alkalies like ammonium hy- droxide. Methyl Orange is an organic substance which in aqueous solu- tion produces a red coloration with acids and a yellow coloration with alkalies. In 'neutral solution there is a rich golden brown tint which can be easily recognized. This indicator is very satis- factory for the titration of the inorganic acids. It is not affected by carbon dioxide nor hydrogen sulphide in cold solution, and con- sequently may be used in their presence. For the weaker organic acids, such as tartaric and oxalic, it is not reliable. It may also be used for the titration of solutions of ammonium hydroxide. Cochineal. This indicator is used in the form of an alcoholic VOLUMETRIC ANALYSIS 53 extract made from the cochineal insect. With acids the color of the solution is red. This turns to a violet color when the solution is made alkaline. It cannot be used in the presence of iron or aluminium or acetates. It is especially valuable for the titration of ammonium hydroxide. Note. Since the different indicators require different amounts of alkali or acid to produce the change in color, the same indicator should be used in the analysis as in the standardization ; moreover, an excess of the indicator should not be used. A few drops are usually sufficient. NOTEBOOKS The volumetric experimental data should be recorded in a system- atic manner. A satisfactory method of arrangement is represented in Fig. 15. On the right-hand page the readings of the burettes 3'3" 36 j A\ J J 5 1 ( i^ 7 {-] iBZt rr (- f f. t n of rs n X\ Ka [| H 1 -H ( B ^: H ( 1 H | s T nti Of i f) r) n n g p ~j- E || \- ion J i 4 - r f 4 ^ 1 08 3 T 1 E ( )( 1 o Hn rf= t "P -^ P n Hi n n <=j '- J , ,1 ^-HC1= | rc i T- K -| / \l 3 n i :K OH > H (/ ^1 1 L - If f a r< KqHs = c ST- (^ ( , t- |3 ^ 6 m ^1 E T, A-

-j Olive oil 43-3 84 6 Linseed oil 17 1 178 I/I 1/0 Household Tests Certain simple household tests for the identification of butter have been found after a little practice to give reliable results and have consequently been introduced into food laboratories. The Foam Test This is used to distinguish pure butter from process butter and oleomargarine. Procedure. Place from 3 to 5 grams of the sample into a test tube, or a large spoon, and heat over a low Bunsen flame, stir- ring constantly. If more convenient, the spoon may be held above the chimney of an ordinary kerosene lamp, or over an ordinary gas jet. If the sample is fresh butter, it will boil quietly with the evolution of many small bubbles throughout the mass, which pro- duce a large amount of foam. Oleomargarine and process butter foam either very slightly or not at all, and sputter and crackle like hot grease containing water. Another point of distinction is noted if a small portion of the sample be placed into a small bottle and set into a vessel of water sufficiently warm to melt the butter. The sample is kept melted from half an hour to an hour, and then examined. If renovated butter or oleomargarine, the fat will be turbid ; while if genuine fresh butter, the fat will almost certainly be clear. The Waterhouse or Milk Test This serves to distinguish oleomargarine from fresh and process butter. It is based on the fact that molten butter fat, if added to milk and cooled, will be found diffused with the milk fat, owing to AGRICULTURAL ANALYSIS . 119 its similarity to the latter. Oleomargarine, on the contrary, being made from foreign fats, will not diffuse under these conditions, but will remain in a mass. Procediire. Place about 50 c.c. of well-mixed sweet milk into a beaker, heat nearly to boiling, add 5 or 10 grams of the sample, and stir with a splinter of wood until the fat is melted. Place the beaker into a dish of ice water and begin stirring before the fat starts to solidify, which takes place in ten or fifteen minutes, and continue until the fat becomes solid. If the sample is butter, either fresh or renovated, it will be solidified in a granular condi- tion, and distributed through the milk in small particles. If the sample consists of oleomargarine, it solidifies practically in one piece, and may be lifted from the milk by means of the stirrer. The nature of the sample under examination may be deter- mined by these two tests. The first distinguishes fresh butter from renovated butter and oleomargarine, while the second dis- tinguishes oleomargarine from either fresh butter or renovated butter. REFERENCES LEACH, A., Food Inspection and Analysis, Chapter XII, p. 368. LEWKOWITSCH, J., Chemical Analysis of Oils, Fats, and Waxes. THE ANALYSIS OF CEREALS AND FEEDING MATERIALS These food stuffs may be conveniently classified as follows : 1. Cereals, occurring in the natural state, of which corn, oats, and wheat are types. 2. Cereal products, obtained from cereals by a certain amount of preparation. To this class belong flour, breakfast foods, etc. 3. Feeding materials, including such substances as hay, silage, also oil cake, dried sugar-beet pulp, and other industrial by- products. Composition Vegetable foods, in general, contain high percentages of car- bohydrates and comparatively low percentages of proteids and fats. There are certain exceptions, as in the case of leguminous foods such as peas and beans, which contain high percentages of proteid matter. Moreover, cotton, rape, and certain other seeds contain large amounts of fats and oils. I2O QUANTITATIVE ANALYSIS The following table shows the composition of some of the more common vegetable foods : WATER PROTEIDS FAT SUGAR GUM AND DEXIRIN STARCH CRUDE FIBER ASH Quaker Rolled Oats . . Oats 9.40 17-55 7.20 61.56! 2.40 1.89 Wheat ID 6^ 12 3^ o 2 1.91 1.79 o 54.08 f\A nft Corn . 9gt /a A 6'2 45 .2.30 o O 2 -53 Peas 12 4.O 20 68 4-u^s 3-3 62.57 C O rr> 1 2.49 i-S 1 r> 9,9. Beans 5-5 2 -f. - \ 4.21 Cotton-seed meal . Sugar-beet pulp 2 . . . 8.20 88-53 42.30 9-45 13.10 0.68 50-77 x 23.60! 62.62 1 3-54 5-60 22.40 3- 2 9 7-20 4-85 1 Nitrogen-free extract, obtained by difference. 2 Dry matter basis. Carbohydrates The food values of the carbohydrates present in vegetable foods depend to a great extent upon their solubilities or ease of con- version to soluble forms. The carbohydrates may be classified according to these properties : 1. Those soluble in water, of which the sugars and dextrin are the most important. 2. Those which are not easily soluble in water, but which are made soluble by the action of certain ferments or by hydrolysis with acid. Starch is the most important member of this class. 3. Carbohydrates which resist the action of the usual reagents. They are not hydrolyzed either by acid or alkali, but remain as fiber in the residue after treating the substance with these reagents. Cellulose is a type of this class. 4. Certain insoluble carbohydrates, which on being hydrolyzed with an acid yield sugars. The members of this class are often called "hemicellulose." The greater portion of these insoluble carbohydrates are pentosans. The class is of comparatively small importance. In the analysis of agricultural products the carbohydrates are often determined by difference, being included in what is known as the Nitrogen-free Extract. This is the residue left after the determination of proteids, ether extract, ash, moisture, and crude fiber. Since it contains such substances as gums, resins, etc., it approximates but roughly the total carbohydrates present. AGRICULTURAL ANALYSIS 121 The following table, containing the results of a series of analy- ses by Stone, shows the percentages of the various carbohydrates in certain of the more common cereals and cereal products : SUCROSE INVERT SUGAR DEX- TRIN SOLUBLE STARCH NORMAL STARCH PENTO- SANS CRUDE FIBER Wheat flour 0.18 O.OO O.OO O.OO 46.IQ O.OO O.2C Corn O.27 O.OO O.32 O.OO 42. CO c.14 I QQ i.yy Su"ar beet 8.^8 O.O7 o.^c O.OO O.OO 4.80 I OO Bread (wheat) .... 0.05 0.32 0.68 i-37 27-93 4.16 2.70 Corn cake (maize). . . 0.16 O.IQ 0.00 2.80 40.37 3-54 2.22 Fats. The fatty material present in vegetable foods is a complex mixture of glycerides. Olein, stearin, and palmitin are always present to a greater extent than the other glycerides. Proteids. The proteidsof the vegetable foods vary considerably both as to character and to the amount present. For the classifi- cation and general methods of separation of the various proteids, the student is referred to the more comprehensive works on the analysis of foods and to the original literature. Preparation of the Sample Grind the material in a coffee or spice mill until the powder will pass through a sieve with circular holes I mm. in diameter. Dry Matter Procedure. Weigh two samples of the substance of about 5 grams each into weighed cover-glasses which are provided with covers and spring clips as shown in Fig. 4, page 8. Heat for five hours in the water oven, place the covers on the cover- glasses, and weigh. Heat again for periods of one hour until the weight is constant to 2 mgms. From the loss of weight calcu- late the percentage of dry matter. Save the residue for the determination of the ether-soluble matter. 122 QUANTITATIVE ANALYSIS OUTLINE FOR THE ANALYSIS OF FEEDING MATERIALS. Determination of Dry Matter, Ash, Proteids, Ether Extract, Reducing Sugars, Sucrose (Dextrin -f Soluble Starch), Starch, and Crude Fiber. Determine proteids and ash in separate portions of the substance. The moisture, ether extract, and carbohydrates are determined as follows : Weigh out sample, dry at 1 10, reweigh. Calculate dry matter. RESIDUE A Extract with dry ether. RESIDUE B Extract with boiling alcohol. Ethereal solution (a) contains fats, oils, and various other substances. Evaporate the ether and weigh the crude fat. Alcoholic solution () contains sucrose and reducing sugars. Evaporate alcohol, make to known volume with water, remove two aliquot parts (i) and (2). Solution (i) Determine reducing sugars by Allihn's method. RESIDUE C Digest with cold water. Solution (2) Invert by heating with acid. Determine re- ducing sugars by Allihn's method. Subtract reducing sugars found in (i). Calculate sucrose present. Filter. I Solution (c} contains dextrin and soluble starch. Hydrolyze by boiling with HC1. Determine dextrose by Allihn's method. Calculate dextrin plus soluble starch. RESIDUE D Boil with water to gelatinize starch. Convert starch to dextrin and maltose by means of malt extract. Filter. RESIDUE E Boil with dilute H 2 SO 4 . Filter. Solution (lve in HC1. rmine Fe by ion with 2 7 . Filtrate. Ppt. MnO 2 . Add NH 4 OH and Ignite and weigh (NH 4 ) 2 C 2 4 . Mn 3 4 . Dissolve ppt. in HC1 and re-ppt. withNH 4 OH. Filter. Filtrate. Ppt. MgNH 4 P0 4 in the usual manner. Ignite and weigh Mg,P 2 7 . Ppt. CaC,0 4 . Ignite. Change to CaSO 4 and weigh. Ppt. ofMg(OH) 8 . ,OH+ Discard. 3 . Ppt. te to Disc expel m salts and aCl+ KCl. mixed in water. I 4 solution hoi. Filter ch crucible. ofBaCO 3 . ard. Ppt. K 2 PtCl 6 . '. Weigh and calculate NaCl by difference. 3 Determination of P 2 O 5 . Concentrate 200 c.c. of Solution A. Ppt. the P as (NH 4 ) 3 PO 4 . 12 MoO 3 . Dissolve and ppt. as MgNH 4 P0 4 . Weigh P as Mg 2 P 2 O 7 . 146 QUANTITATIVE ANALYSIS to the change between the surface soil and the subsoil, in case such change occurs between the depth of six and twelve inches. In no case should the sample be taken to a greater depth than twelve inches. If the surface soil extends to a greater depth, a separate sample below the depth of twelve inches should be taken if a thorough study of the soil is desired. If the surface soil ex- tends to a depth of less than six inches, and the difference between it and the subsoil is unusually great, a separate sample of the sur- face soil should be obtained besides the one to the depth of six inches. Mix all the samples of the surface soils thoroughly, remove all stones, shake out roots and foreign matter, and expose the soil in thin layers in a warm room until thoroughly air dry, or dry it in an air bath at 40. The soil should be dried rapidly, but it should not be heated above 40, because of the danger of breaking up the ammonium compounds or making some of the compounds present more insoluble. After drying, all lumps should be finely pulver- ized, the soil thoroughly mixed, spread out upon a clean paper and 200 grams taken from different parts of the sample and sifted through a sieve with circular openings \ mm. in diameter. If necessary, rub the soil gently in a mortar with a pestle until the fine earth has been separated as completely as possible from the particles that are too coarse to pass the sieve. Mix the fine soil which passes through the sieve, place in a tightly stoppered bot- tle, and use for the analysis. The coarse part should be weighed and bottled. Note. As a result of bacterial action certain constituents of the soil are constantly undergoing changes. The organic nitrogen, for example, is continually being oxidized to the more available forms, nitrates and nitrites. This change is termed nitrification. Because of these changes it is necessary to avoid prolonged dry- ing. Moisture Procedure. Place from two to four grams of the air-dried soil into a weighed porcelain dish and heat for five hours at 100. Cool in a desiccator and weigh rapidly to avoid absorption of mois- ture from the air. Repeat the heating, cooling, and weighing at intervals of two hours until constant weight is found, and estimate the moisture by loss of weight. AGRICULTURAL ANALYSIS 147 Volatile Matter Procedure. Heat the dish and dry soil from the above determi- nation to full redness, until all organic matter is burned. If the soil contains any carbonates, the contents of the dish, after cooling, should be moistened with a few drops of a saturated solution of ammonium carbonate, dried and heated to dull redness to expel ammonium salts, cooled in the desiccator, and weighed. Notes. i . The addition of ammonium carbonate changes any calcium oxide formed during the ignition back into the carbonate. 2. The loss in weight in the above determination is due to the following causes : (a) The ignition of the organic matter. (b) Volatilization of ammonium salts and of water of combina- tion. (c) The decomposition of magnesium carbonate with the forma- tion of magnesium oxide, which is not readily changed back to the carbonate, also the fact that the calcium originally present as the humate is changed to the carbonate. 3. A certain increase in weight is caused by the oxidation of any ferrous iron. This tends to counterbalance some of the above-mentioned losses. 4. Because of the variety of factors to which the loss on ignition is due, it is evident that this determination gives but an approxi- mate idea of the amount of organic matter present. The determina- tion of the total organic carbon has recently been used for the estimation of the organic matter in soils. The method is described by Pettit and Schaub, Jour. Am. Chem. Soc., 26, 1640 (1904), The Extraction of the Acid-soluble Material It is well known that the materials present in soils are not all available as plant food. Potassium, for example, may exist as the easily available carbonate, or it may be present as a feldspar which is of little immediate value in aiding the growth of plants. It is, therefore, the usual practice, when analyzing a soil, to deter- mine the amount of available plant food rather than its total quan- tity, although this latter determination is often of value. Numerous solvents have been suggested for the extraction of the plant food from the soil, but none of them imitates the extraction under 148 QUANTITATIVE ANALYSIS natural conditions. The following method, recommended by the Association of Official Agricultural Chemists, in which hydrochloric acid is used as a solvent, is of value in showing approximately the limit of the solvent action of the roots of plants. Procedure. Place ten grams of the air-dried soil into an Erlen- meyer flask of about 200 c.c. capacity, add 100 c.c. of pure hydrochloric acid of specific gravity 1.115, insert a rubber stopper carrying a hard-glass condensing tube about \ inch internal diameter and about 30 inches long. If sulphuric acid is to be determined in the solution, a flask with a ground-glass stopper carrying a con- densing tube must be used. Place the flask in a water bath, being sure that it is immersed in the water at least to the level of the acid and that the water is kept boiling during the digestion. Di- gest continuously for ten hours at the temperature of boiling water, shaking once each hour. Decant the clear liquid from the flask into a medium-sized casserole and wash the residue out of the flask with distilled water upon a filter, adding the washings to the acid liquid in the casserole. Thoroughly wash the residue free from acid and then dry it and save it for ignition as directed below. Notes. i . The amount of material dissolved by the acid varies with the length of time of heating, the temperature and the strength of the acid employed, and the fineness of the material. Conse- quently, the directions given above should be closely followed. 2. By the action of the hydrochloric acid solution on the soil, the following constituents are dissolved : ferrous and ferric oxides, ferrous carbonate, manganese oxides, calcium and magne- sium carbonates, calcium sulphate and phosphates, and certain silicates, such as those of aluminium, calcium, and potassium. Certain forms of organic matter are also dissolved. 3. The residue is composed for the greater part of crystallized and amorphous silica and silicates of Fe, Mn, Al, Ca, Mg, K, Na. Certain forms of organic matter are also present in the residue. Removal of Soluble Silica from Solution Principle. On evaporating a solution of silicic acid to dryness and heating at 100 it is dehydrated and rendered insoluble in dilute acids. AGRICULTURAL ANALYSIS 149 Procedure, Add about 5 c.c. of concentrated nitric acid to the filtrate from the insoluble matter in order to oxidize the organic matter present and evaporate to dryness on the steam bath until no more fumes of hydrochloric acid are given off, the residue being left in the form of a dry, dark-brown powder. Add 5 c.c. of con- centrated hydrochloric acid to the casserole, allow to stand for a few minutes to insure the solution of the basic salts, and add 100 c.c. of distilled water. Heat to boiling, filter through an ashless filter, wash with hot water containing a little hydrochloric acid, and wash finally with hot water alone until the residue is free from chlorides. Evaporate the filtrate to dryness and treat exactly as before, using, however, a new filter for the filtration. Cool the filtrate, make up to 500 c.c., and label the solution " A." Notes. i. For the complete removal of silica from solution, the following conditions should be closely observed: a. Two dehydrations of the silica should be made, since it has been found that only 95 per cent of the silica present is removed by one dehydration. An intermediate filtration between the two dehydrations has been found necessary. b. The silica may be completely dehydrated on the water bath, although many chemists prefer to heat finally at 110 or 120. Heating above 120 renders insoluble appreciable amounts of alumina and ferrie oxide which cannot be dissolved by long diges- tion with hydrochloric acid. Moreover, at higher temperatures magnesia recombines with silica with the formation of magnesium silicate, which is decomposed by hydrochloric acid with the for- mation of soluble silicic acid. 2. The precipitate should be first washed with hot water acidi- fied with a few cubic centimeters of hydrochloric acid. This will prevent the separation of insoluble iron salts, which would take place if hot water alone were used. Insoluble Matter and Soluble Silica Procedure. Add the silica residues from solution " A " to the main insoluble residue, ignite in the blast the combined residues together with the filters in a large weighed porcelain crucible and weigh. Heat to constant weight. From the weight of this resi- due calculate the percentage of insoluble matter plus the soluble silica. ISO QUANTITATIVE ANALYSIS The Determination of the Acid-soluble Substances Iron, Aluminium , and Phosphorus Collectively Procedure. To 100 c.c. of solution "A" add ammonium hy- droxide until the solution is slightly alkaline, observing the pre- cautions given under the determination of aluminium, page 37. Drive off the excess of ammonia by boiling, allow the precipitate to settle, and decant the clear solution through a filter. Add' 50 c.c. of hot distilled water, boil, allow to settle, and decant as before. After pouring off all the clear solution possible, dissolve the resi- due with a few drops of nitric acid, and precipitate again with ammonium hydroxide as before. Wash by decantation, transfer all the precipitate to the filter, and wash with hot distilled water containing a little ammonium nitrate, until the washings are free from chlorides. Dry the filter and precipitate, separate the pre- cipitate from the filter, burn the filter and add to the ash the precipitate, ignite the crucible to bright redness, cool in a desicca- tor, and weigh. The weight of the ignited precipitate minus the weight of the iron oxide and phosphorus pentoxide (found in separate determinations) represents the weight of the aluminium oxide. Notes. i. The separation of iron and aluminium from the divalent metals is not complete by one precipitation, a small amount of magnesium invariably precipitating at the same time. It is necessary, therefore, to make a second precipitation. 2. The ammonium hydroxide used must be free from the car- bonate, which would precipitate some of the calcium with the iron and aluminium. 3. If the precipitate is not washed completely free from chlo- rides, there is danger of volatilization of the chlorides of iron and aluminium upon ignition of the precipitate. To facilitate the removal of the chlorides, the precipitate is redissolved in nitric instead of hydrochloric acid. 4. In the presence of hot carbonaceous matter, ferric oxide is partially reduced to the magnetic oxide (Fe 3 O 4 ), which cannot be completely changed back to the ferric oxide, even by treatment with oxidizing agents. To avoid this reduction, it is necessary to ignite the filter separate from the precipitate. AGRICULTURAL ANALYSIS 151 Iron See the determination of sodium and potassium on page 1 54. Phosphorus Procedure. Evaporate 200 c.c. of solution " A " to about 75 c.c., nearly neutralize with ammonium hydroxide, and add about 10 grams of pure crystallized ammonium nitrate. Add gradually about 20 c.c. of ammonium molybdate solution and digest at 40. When the precipitate has settled, remove with a pipette about 5 c.c. of the clear liquid and test it by allowing it to run into 5 c.c. of warm molybdate solution. If any precipitate is produced, the test liquid should be returned to the main portion, more molybdate solution added, and the digestion continued. After standing from eight to twelve hours at a temperature not above 40, filter the ammonium phosphomolybdate and determine the phosphorus as magnesium pyrophosphate, as described under the determination of the total phosphorus in fertilizers, page 134. Express the re- sults as phosphorus and phosphorus pentoxide. Manganese Principle. When bromine water is added to an alkaline solution of a manganese salt, upon boiling, the manganese is precipitated as a hydrated manganese dioxide. Upon ignition the manganese dioxide is changed to Mn 3 O 4 . 3 Mn0 2 (ignited) = Mn 3 O 4 + O 2 . Procedure. Concentrate the filtrate from the determination of iron, aluminium, and phosphorus to about 75 c.c., make alkaline with ammonium hydroxide, add bromine water, and heat to boiling, keeping the beaker covered with a cover-glass. When most of the bromine has been driven off, allow the beaker to cool some- what, add more ammonium hydroxide and bromine water, and heat again. Continue this process until the manganese is completely precipitated, which requires from fifteen to thirty minutes. Acid- ify the solution with a few drops of acetic acid, filter while still hot, wash the precipitate with hot water, dry, ignite, and weigh as Mn 3 O 4 . Compute the percentage of manganese in the soil. Note. By strong ignition manganese dioxide is converted to mangano-manganic oxide Mn 3 O 4 . The exact composition of the 152 QUANTITATIVE ANALYSIS ignited precipitate varies with the conditions under which the igni- tion takes place. With small quantities of manganese the varia- tion is so small that it may be neglected. Large precipitates of manganese dioxide should be redissolved in a solution of sulphu- rous acid, precipitated from an ammoniacal solution as manganese ammonium phosphate and weighed as manganese pyrophosphate. Calcium Procedure. Evaporate the filtrate from the manganese deter- mination to about 50 c.c., make slightly alkaline with ammonium hydroxide, and precipitate with ammonium oxalate. Heat to boil- ing, digest, and decant the clear solution upon a filter. Pour from 15 to 20 c.c. of hot distilled water upon the precipitate, and again decant. Dissolve the precipitate in the beaker with a few drops of hydrochloric acid, add a little water, and reprecipitate. Filter through the same filter as before, wash the precipitate free from chlorides, dry, ignite, convert to calcium sulphate, and weigh. Calculate the percentage of calcium in the soil. Note. Read the notes on the separation of calcium and mag- nesium, page 34. Magnesium Procedure. Slightly acidify the filtrate and washings from the determination of calcium with hydrochloric acid, concentrate to about 50 c.c., and make slightly alkaline with ammonium hydrox- ide. Add 10 c.c. of microcosmic salt solution, allow to stand for a few minutes, then add one-third the volume of ammonium hydroxide solution. Allow to stand for twelve hours ; filter off the magnesium ammonium phosphate. Dissolve the precipitate in hydrochloric acid and reprecipitate. Ignite the precipitate and weigh as magnesium pyrophosphate. Express results as mag- nesium. Sulphur Procedure. Evaporate 100 to 150 c.c. of solution " A " nearly to dryness on a water bath, then add 50 c.c. of water and determine the sulphur by precipitating and weighing as barium sulphate as described under Exercise VI, page 29. Note. The precipitate is appreciably soluble in concentrated hydrochloric acid, hence the necessity of expelling the excess of acid by evaporation. AGRICULTURAL ANALYSIS 153 Iron, Potassium, Sodium Procedure. Add ammonium hydroxide to the filtrate from the determination of sulphur, and precipitate exactly as in the deter- mination of iron, aluminium, and phosphorus collectively. Wash the precipitate free from chlorides, dissolve it in hydro- chloric acid and estimate the iron present by titrating with standard dichromate solution. Calculate the percentage of iron in the soil. Evaporate the filtrate and washings from the precipitate to dryness on the water bath in a small casserole, heat cautiously for an hour at 110, to avoid decrepitation due to incomplete drying, then heat at a low red heat until the ammonium salts are expelled, holding the casserole in the hand. Dissolve the residue in about 25 c.c. of hot water, add 5 c.c. of a saturated barium hydroxide solution and heat to boiling. Allow the precipitate to settle and test the supernatant liquid for complete precipitation with a few drops of barium hydroxide. When no further precipitate is pro- duced, filter, and wash thoroughly with hot water. Add ammonium hydroxide and ammonium carbonate, to precipitate the barium. Allow to stand a short time on the water bath, filter, wash the precipitate with hot water, and evaporate the filtrate and washings to dryness in a casserole. Expel the ammonium salts as before by first heating at no , then over the flame at a low red heat, dissolve the residue in a little water, add a few drops of ammonium hydroxide and a drop or two of ammonium carbonate solution, let stand on the water bath for a few minutes, and filter into a weighed platinum dish. Evaporate to dryness on the water bath (heat at iio-i2O for half an hour) and heat with a free flame at a dull red heat until the ammonium salts are expelled and the residue just begins to fuse. This part of the procedure must be carried out with extreme care. The burner should be held in the hand, the flame continually moved about the bottom of the plati- num dish in order to prevent the volatilization of the alkali chlorides. The weight of the residue represents potassium and sodium chlo- rides. Separation of Potassium from Sodium Principle. If an excess of a solution of platinic chloride is added to a solution of sodium and potassium chlorides and alcohol then added, potassium chlorplatinate is precipitated, while sodium 154 QUANTITATIVE ANALYSIS chlorplatinate remains in solution. Since sodium chloride is insol- uble in alcohol, it is necessary to add enough of the platinic chloride to change both the sodium and the potassium chlorides to the chlorplatinates. Procedure. Dissolve the combined weighed chlorides in about 10 c.c. of water. If they do not go completely into solution, filter, wash, evaporate the filtrate in a platinum dish as before, and weigh again. The solution in water must be complete. When the com- bined chlorides dissolve completely, transfer the solution to a small porcelain dish. Add enough platinic chloride solution (containing o.i gram of platinum per cubic centimeter) to combine with the residue to form the chlorplatinate, assuming that this residue is composed entirely of sodium chloride. Evaporate to a pasty consistency on a water bath, then pour into the dish about 50 c.c. of 80 per cent alcohol and heat the dish and contents for two or three minutes upon the water bath. Stir well and then allow to stand for at least two hours in a cool place, inverting a beaker over the dish, or by some other means protecting it from possible access of ammonia vapors. Pour off the clear liquid through a weighed Gooch crucible, filter and wash the precipitate by decantation, using small quantities of 80 per cent alcohol. Bring the potassium chlorplatinate upon the filter and wash completely by applying repeatedly small quantities of the alcohol. Dry the filter and con- tents to constant weight at 1 3 5. Calculate the weight of the potas- sium chlorplatinate to potassium chloride. Deduct the weight of the potassium chloride from the weight of the mixed chlorides. From the weights of the chlorides calculate the percentages of potassium oxide and sodium oxide in the soil, also the percentages of potassium and sodium. Humus Principle. The soil is leached with cold dilute hydrochloric acid, which dissolves calcium and magnesium salts. By the re- moval of these substances, the humus is left in a form which is easily changed to a soluble ammonium compound. It is washed out of the soil by means of dilute ammonium hydroxide, the solution is evaporated to dryness, weighed, ignited, and the loss of weight calculated as humus. Procedure. Place ten grams of the sample in a prepared Gooch crucible, extract with one per cent hydrochloric acid until the AGRICULTURAL ANALYSIS 155 filtrate gives no test for calcium, and remove the acid by washing with water. Wash the contents of the crucible (including the asbestos filter) with four per cent ammonium hydroxide into a 500 c.c. glass-stoppered cylinder, make up to the mark with the ammonium hydroxide and allow to remain, with occasional shaking, for twenty-four hours. During this time the cylinder should be inclined as much as possible without bringing the contents in con- tact with the stopper, thus allowing the soil to settle upon the side of the cylinder and exposing a large surface to the action of the ammonium hydroxide. Place in a vertical position for twelve hours to allow the sediment to settle, then filter the supernatant liquid through a dry filter. Evaporate 100 c.c. of the filtrate to dryness, dry to constant weight at 100, ignite in the ash muffle, and weigh. The difference in weight between the dried and the ignited residues is humus. Notes. i. The chemical nature of humus is very imperfectly known. Several distinct bodies having acid characters have been obtained from the humus, but very little is known of their compo- sitions or properties. 2. The ammonium compound of humic acid is very soluble in water, while the calcium compound is insoluble. Total Nitrogen in the Presence of not More than a Trace of Nitrates Procedure. Place from 7 to 14 grams of the soil in a 500 c.c. Kjeldahl digestion flask, add 30 c.c. of strong sulphuric acid or more if necessary, and about 0.65 gram of mercury. Digest for an hour and if necessary oxidize the residue with potassium per- manganate in the usual way. Cool, add to the flask about 100 c.c. of nitrogen-free water, shake vigorously, allow the sediment to subside, and filter through ignited asbestos into an 800 c.c. Kjeldahl flask, or proceed according to Note 2. The filter is easily prepared by placing a few short pieces of glass tube into the bottom of a Gooch funnel and covering them with a thin layer of the ignited asbestos. The filtration may be accelerated by fitting the funnel by means of a two-hole cork in the neck of a Kjeldahl flask and connecting with the suction. Wash the residue in the flask at least a dozen times with portions of 25 c.c. of hot nitrogen-free water, and determine the ammonia by distilling in the usual manner. Calculate the percentage of nitrogen in the soil. 156 QUANTITATIVE ANALYSIS Notes. i. If the soil contains more than a trace of nitrates, the modified Kjeldahl process described under the determination of the total nitrogen in fertilizers, page 138, must be used. 2. If the solid residue left after digesting the soil is not removed, on distilling the ammonia violent explosions will be caused by " bumping." The bumping may also be prevented by transferring the entire contents of the digestion flask to a copper distilling flask (see Fig. 31) and proceeding as usual. Carbon Dioxide The Apparatus. For this determination the apparatus shown in Fig. 32 has been found to give satisfactory results. It consists essentially of a flask C, into which the sample is placed. This is provided with a two-hole rubber stopper which carries a Hopkins condenser D, and a dropping funnel B by means of which dilute acid can be introduced into the flask. The carbon dioxide gas evolved first passes through the condenser, then through the U-tube E which contains glass beads and a few cubic centimeters of sul- phuric acid (sp. gr. 1.4) saturated with silver sulphate, the function of which is to remove hydrochloric acid gas. It is dried by passing I j into the U-tube /''which is filled with calcium ^*- S chloride, and is finally absorbed in the weighed Geissler bulb G which is filled with potassium hydroxide solution. The last traces of carbon dioxide are expelled from the apparatus by replacing it with air which has been freed from carbon dioxide by passing it through the soda-lime tube A. To draw the air through the apparatus, water is allowed to run from the bottle K into L, which should be placed about five feet lower than K. This process is termed Aspiration. Procedure. Weigh out two samples of from five to ten grams of the soil into clean dry flasks of 250 c.c. capacity. Fill two Geissler potash bulbs with a solution of potassium hydroxide (350 grams per liter) so that the bulbs are two-thirds full, and fill the drying tubes with fresh granular calcium chloride. Provide the open ends of the bulbs with caps made of short pieces of rubber tubing about I \ inches long, closed with a short piece of glass rod. Put these caps in place, wipe the bulbs with a clean cloth, and allow them to stand AGRICULTURAL ANALYSIS 157 158 QUANTITATIVE ANALYSIS in the balance case for twenty minutes. Remove the caps to equalize any pressure on the inside of the bulbs, replace them and weigh accurately. Attach the potash bulb to the apparatus as shown in the figure, then place the soda-lime tube H between the absorption bulbs and the aspirator, which should be full of water. Be sure that all rubber connections are tight. Examine the stem of the dropping funnel for drops of acid which might fall into the flask, wipe it dry if necessary, and attach the flask. Test the apparatus for tightness by closing the cock in the drop- ping funnel and opening the pinchcocky which connects with the aspirator. If the apparatus has no leaks, bubbles will pass through the absorption bulb for a minute or two and then cease. When it is evident that the apparatus is tight, close the pinchcock on the aspirator tube and equalize the pressure in the flask by carefully opening the cock in the funnel. Disconnect the aspirator from the guard tube. Close the funnel cock, place into the funnel 50 c.c. of hydrochloric acid (sp. gr. 1.12), put the guard tube A in place, and allow two or three drops of hydrochloric acid to run into the flask. Carbon dioxide gas will be evolved and bubbles will be forced through the absorption bulbs. The bubbles should pass through the bulbs at a rate not greater than three per second. When the evo- lution of gas slackens, add a few more drops of acid, but not enough to cause a rapid evolution of the gas. Proceed in this way until all of the acid has been added, then close the cock in the dropping funnel. Be sure that the water is running through the condenser, then heat the flask with a low flame, regulating the heat so that there will be no rapid evolution of gas. Finally heat to boiling and boil for three minutes. Remove the burner and immediately open the stopcock carefully to admit air and prevent the potash solution from being drawn back. Allow the apparatus to cool for two or three minutes, then connect with the aspirator and draw air through for thirty minutes. Detach the absorption apparatus, place the caps on the ends, allow it to stand in the balance case for twenty minutes, and weigh as before. From the increase in weight calculate the per- centage of carbon dioxide in the sample. Notes. i. The U-tube for drying the gas should be filled with the granular and not the fused calcium chloride, which contains calcium oxide and consequently absorbs carbon dioxide. Even with the granular calcium chloride when the tube is first filled, a stream of AGRICULTURAL ANALYSIS 159 carbon dioxide should be passed through it for half an hour to neutralize any lime which might be present. The excess of car- bon dioxide must be removed by a current of air. 2. Sulphuric acid should not be used to dry the carbon dioxide passing into the absorption bulbs, because it dries gases more thor- oughly than calcium chloride. On leaving the bulb, the gas passes over calcium chloride, therefore, if it were first dried by means of sulphuric acid, it would leave the absorption apparatus carrying more moisture than when it entered. The result would be a loss of water from the absorption bulb. 3. The Geissler potash bulb may be used until a white precipi- tate of potassium bicarbonate in the first bulb shows that the liquid is saturated. 4. The guard tube .//prevents carbon dioxide or moisture passing back into the absorption apparatus. It can be used for a large number of determinations without refilling. 5. The above apparatus may be used for the determination of carbon dioxide in carbonates, baking powder, etc. Statement of Results as Oxides All results of the soil analysis should be calculated as per cent of the soil dried to constant weight in the water oven, and stated in the following order : Insoluble matter ... Soluble Silica Potash (K. 2 O) Soda (Na 2 O) Lime (CaO) Magnesia (MgO) ... Manganese Oxide (MnO) Ferric Oxide (Fe 2 Oa) . Alumina (Al 2 Os) ... Phosphorus Pentoxide Sulphur Trioxide (SO 3 ) . Carbon Dioxide (CO 2 ) . Volatile matter ... Total. Humus . Also calculate the following statement of results 160 QUANTITATIVE ANALYSIS Statement of Results as Elements Insoluble matter ) Soluble Silica > Nitrogen Phosphorus Potassium Calcium Magnesium Iron Sulphur Sodium Aluminium Manganese Inorganic Carbon Oxygen equivalent of above elements (except ) Nitrogen) Volatile matter (less Nitrogen) Total . . Humus NOTE. If the organic carbon is added to the above list of determined elements, the remaining " volatile matter " consists chiefly of organic hydrogen and oxygen, combined water (as in hydrated silicates), and errors due to unavoidable changes in mineral com- pounds during ignition. REFERENCES SNYDER, Soils and Fertilizers. WILEY, Agricultural Analysis, Vol. I, Soils (1906). PART V STOICHIOMETRY EMPIRICAL FORMULAS THE Law of Definite Proportions states that chemically homo- geneous substances chemical compounds always have the same composition. Common salt, the chloride of sodium, is always found upon analysis to contain chlorine and sodium in the same proportions by weight. The elements in any chemical compound are always found in a certain definite ratio, and it is by means of this ratio that we are often able to identify a compound. In the case of silver chloride it has been found by analysis that there is 24.74 per cent of chlorine and 75.26 per cent of silver ; that is, in 100 grams of silver chloride there are 24.74 grams of chlorine and 75.26 grams of silver. If the combining weight of chlorine is 35.45 grams, there will be as many combining weights of chlorine in 24.74 grams of chlorine as 35.45 is contained in 24.74 which is 0.69. Similarly, if the combining weight of silver is 107.93 grams, in 75.26 grams of silver there are 0.69 combining weights. Hence, in 100 grams of silver chloride there are 0.69 combining weights of chlorine and 0.69 combining weights of silver ; that is, they are present in the ratio of 0.69 Ag to 0.69 Cl, or i : i. The simplest formula for silver chloride, therefore, is AgCl, and is known as the Empirical Formula. In a similar manner, the empirical formulas of more complex compounds may be calculated. A substance on analysis gave the following percentage composition : Pb, 68.31; S, 10.54; O, 21.15. What is the empirical formula ? Pb= = -330, -*- 0.330 =1.00. S = 3^06 = ' 329 ' "*" ' 330 = 0<997 ' 21.15 = x - 320, *-(>. 3 30 =4.00. 161 1 62 QUANTITATIVE ANALYSIS The ratio of the combining weights as found above is 0.330 : 0.329 : 1.32. Dividing by the greatest common divisor gives the ratio in whole numbers, as I : 1:4. The empirical formula, therefore, is PbSO 4 . Because of unavoidable errors in the analysis, the values of the percentages almost always vary from the theo- retical value. Although this makes a slight variation in the ratio as seen in the case of sulphur in the problem above, the value is so close that it may be taken as unity. PROBLEMS Calculate the empirical formula from the percentage composition of each of the following compounds : 1. Na, 34.38^ C, 14.89; O, 47.73. 2. K, 16.12; Pt, 40.10; Cl, 43.78. 3. K, 26.58; Cr, 35.37; O, 38.02. 4. N, 14.32; H, 4.11; Mo, 32.63; 0,48.95. 5. C, 31.99; H, 4.03; O, 63.98. Percentage Composition The calculation of the percentage composition of a substance from its empirical formula is the reverse of the foregoing. In magnesium sulphate (MgSO 4 ), the molecule is composed of com- bining weights of magnesium, sulphur, and oxygen in the ratio 1:1:4. The molecular weight will then be the sum of these com- bining weights. Mg= 24.36 S = 32.06 4 O = 64.00 120.42 In one gram molecule of magnesium sulphate (120.42 grams) there are 24.36 grams of magnesium, 32.06 grams of sulphur, and 4 x 1 6 (64) grams of oxygen. Therefore, Per cent = o .2023 x 100= 20.23 120.42 S = 32>o6 = 0.2662 x ioo = 26.62 120.42 = 0.5315 x 100= 53.15 I20 ' 42 100.00 STOICHIOMETRY 163 In a similar manner the percentage of any combination of ele- ments may be calculated, as, for example, MgO and SO 3 in magne- sium sulphate. Per cent = 33 - 52 = 0.6648 X 100 = MgSO 4 120.42 PROBLEMS Calculate the percentages of the constituents from the empirical formulas in the following problems : 6. The empirical formula of zinc sulphate is ZnSO 4 . Calculate the percentages of Zn and ZnO. 7. The empirical formula of ferrous ammonium sulphate is FeS0 4 (NH 4 ) 2 S0 4 6 H 2 O. Calculate the percentages of Fe, FeO, S, SO 3 , and H 2 O. 8. The empirical formula of zinc pyrophosphate is Zn 2 P 2 O 7 . Calculate the percentages of ZnO and P 2 O 5 . 9. The empirical formula of calcium silicate is CaSiO 3 . Calcu- late the percentages of CaO and SiO 2 . GRAVIMETRIC CALCULATIONS There are a few isolated cases in gravimetric analysis in which the substance to be determined is weighed in the form in which the result is to be expressed. This is true in the determination of nickel, which is sometimes weighed as the metal, in which case the percentage is easily calculated. Weight of constituent sought x 100 = ent of constituent Weight of substance taken In the majority of cases the compound weighed contains other elements besides the one to be determined, as in the determination of silver, in which case the substance is weighed as silver chloride. The amount of silver present is calculated from the percentage composition of silver chloride. One gram molecule of silver chloride (143.38 grams) contains 164 QUANTITATIVE ANALYSIS one combining weight of silver (107.93 grams). If the precipitate weighs 0.2 gram, then letting x equal the weight of silver, AgCl Ag wt. of ppt. 143.38 : 107.93 : : 0.2 gram : x. x = o. 1 506 gram of silver. When barium, barium oxide, or sulphur are to be determined, they can be weighed in the form of barium sulphate and the con- stituents calculated in a manner similar to that given above. In each case, let x equal weight of constituent sought. (a) BaSO 4 : Ba : : (wt. of ppt.) : x; (b) BaSO 4 : BaO : : (wt. of ppt) : x\ (c) BaSO 4 : S : : (wt of ppt.) : x. If we wish to calculate the potassium chloride in a precipitate of potassium chlorplatinate (K 2 PtCl 6 ), it is evident that two mole- cules of KC1 will be formed from one molecule of the precipitate. K 2 PtCl 6 : 2 KC1 : : (wt. of ppt) : x. Potassium is often calculated as the oxide, and it is then necessary to express the K 2 PtCl 6 in terms of this compound. It is evident that for potassium the following relation holds true: K 2 PtCl 6 : 2 K : : (wt of ppt.) : x (wt. of K). Now, two combining weights of potassium (2 K) form one mole- cule of potassium oxide (K 2 O). Consequently, 2 K : K 2 O : : x \y (wt of K 2 O). Expressing these proportions in the form of equations, we have: K 2 PtCl fi = wt. of ppt. . 2 K x (wt of K) ' 2K ^(wt. of K) K 2 y (wt of K 2 0) Multiplying the two equations, K 2 PtCl 6 2K = wt. of ppt. x (wt. of K) 2 K K 2 O x (wt. of K) y (wt. of K 2 O)* STO1CH1OMETRY 165 Canceling, we have, K 2 PtCl 6 = wt. of ppt. K 2 O ~^/(wt. of K 2 O)' Expressing as a proportion, K 2 PtCl 6 : K 2 O : : wt. of ppt. : y (wt. of K 2 O). Or, since in K 2 PtCl 6 there are two combining weights of potas- sium, K, we have enough to make two molecules of KC1 or one molecule of K 2 O. Therefore K 2 PtCl 6 =K 2 0. Hence K 2 PtCl 6 : K 2 O : : wt. of ppt. : wt. of K 2 O. Factors The amount of the constituent in the substance weighed is often determined by means of factors. In the foregoing examples the sulphur in barium sulphate was calculated by the expression BaSO 4 : S : : (wt. of ppt.) : x (wt. of S present). 233.5 : 32-06 : : (wt of ppt.) : x Solving for x we have : 12 O6 x == -^ - x (wt. of the precipitate). 233-5 It is evident that the value -^ = 0.1373, which represents the amount of sulphur equivalent to one gram of barium sulphate, is a constant quantity. Therefore, the sulphur in any quantity of barium sulphate may be determined by multiplying its weight by this value, which is called the factor for the conversion of barium sulphate to sulphur. Other factors may be similarly calculated. Barium oxide in barium sulphate : BaSO 4 : BaO : : wt. of ppt. : x. BaO x(wt of ppt j B BaSO 4 1 66 QUANTITATIVE ANALYSIS Potassium in potassium chlorplatinate : K 2 PtCl 6 : 2 K : : wt. of ppt. : x. Potassium oxide from the potassium chlorplatinate : K 2 PtCl 6 : K 2 O : : wt. of ppt. : x. 1941, factor. K 2 PtCl 6 485.8 From these calculations it will be readily seen that the factor may be considered as the weight of the constituent sought in one gram of the substance. PROBLEMS 10. Calculate the factors for the following substances: a. FeO in Fe 2 O 3 . b. P 2 O 5 and P in Mg 2 P 2 O 7 . c. ZnO in ZnNH 4 PO 4 . d. SO 2 in PbSO 4 . e. PbO in PbSO 4 . f. MnO 2 from Mn 3 O 4 . 11. What is the weight of calcium oxide in 1.25 grams of CaC 2 4 ? 12. What weight of pyrite (FeS 2 ) must be taken to furnish enough sulphur to make 1.6 grams of barium sulphate ? 13. A substance containing 15 per cent MgO, on being analyzed gave 0.2240 gram of magnesium pyrophosphate. How much of the sample was weighed out for the analysis ? 14. What weight of magnesium ammonium phosphate will yield on ignition 0.5 gram of magnesium pyrophosphate? 2 MgNH 4 PO 4 = Mg 2 P 2 O 7 + 2 NH 3 + H 2 O. 15. 1.2 grams of an alloy containing 80 per cent silver and 20 per cent copper are dissolved in nitric acid. To the solution 0.3 STOICHIOMETRY 167 gram of pure dry potassium chloride is added. What percentage of the silver remains in solution ? 1 6. A sample of 0.3 gram of bauxite (AIO(OH)) gave a precipi- tate equivalent to 0.25 gram of aluminium oxide. Calculate the percentage purity of the bauxite. 1 7. The zinc in 2.5 grams of a sample of zinc ore was precipitated as the carbonate. On being ignited to constant weight the precipi- tate lost 0.2 gram of CO 2 . ZnCO 3 = ZnO + CO 2 . Calculate the percentage of zinc in the sample. 1 8. One gram of a sample of rock on analysis gave 0.15 gram of the mixed chlorides of sodium and potassium. The potassium was precipitated as the potassium chlorplatinate (K 2 PtCl 6 ), a pre- cipitate of 0.120 gram being obtained. Calculate the percentages of sodium and potassium in the sample. Indirect Methods In a solution containing the chlorides of sodium and potassium the amount of each salt may be determined by evaporating the solution to dryness, weighing the mixed chlorides, dissolving them in water, and determining the total chlorine present as silver chlo- ride. This is a type of the class of indirect methods. The data are best calculated algebraically, the method being illustrated by the following example. The weight of the mixed chlorides of sodium and potassium is 0.3 gram, and the weight of the silver chloride is 0.6323 gram. Cal- culate the weights of sodium chloride and potassium chloride in the mixture. Let x = wt. of KC1 ; Then, (0.3 -x) = wt. of NaCl. (The weight of AgCl from x) -f (weight of AgCl from (0.3 x)) = 0.6323 gram. AgCl : KC1 : : (AgCl from x) : x. Therefore, (AgCl from x) = 4^r x 168 QUANTITATIVE ANALYSIS AgCl : NaCl : : (AgCl from (0.3-*)) : (0.3-*). Therefore, AgCl from (0.3 - x) = A |g| (0.3 -x). .3-*)= 0.6323 gram. 1.922 x + 2.451 (0.3 - x} = 0.6323. 0.529^- = 0.1030. x = 0.1946, wt. of KC1. (0.3 x) = 0.1054, wt. of NaCl. A mixture of BaCO 3 and CaCO 3 weighed a grams. On conver- sion to the sulphates a weight of b grams was obtained. Calculate the weights of BaO and CaO in the original mixture. Let x = wt. of BaO. y = wt. of CaO. BaCO 3 CaCO 3 -B^^-CEO 8 '-" BaSO 4 CaSO 4 --- 19740 100.10 153.40 56.10 * 3346 . 153.40 56.10 ' The equations are then solved for the values of x and y as shown in the last problem. PROBLEMS 19. A mixture of the carbonates of calcium and magnesium weighs 1.2 grams. The carbon dioxide obtained from this mixture weighs 0.58 gram. Calculate the weights of calcium and magne- sium. 20. In a mixture of 2.3 grams of the sulphates of lead and barium there is 0.675 gram of SO 3 . Calculate the weights of PbO and BaO present. STOICHIOMETRY 169 21. A mixture of bromide and chloride of silver weighs 4 grams. The bromine is replaced by chlorine, and the mixture then weighs 3.8 grams. What is the percentage of bromine present? The Volume of a Reagent Necessary for a Given Reaction The amount of a reagent necessary to bring about a given reaction must often be calculated. The following examples are types of this class of calculations. How many cubic centimeters of a barium chloride solution con- taining 50 grams of the crystallized salt (BaCl 2 2H 2 O) per liter will be necessary to completely precipitate the sulphuric acid in a solution containing 0.25 gram of potassium sulphate ? From the equation, K 2 SO 4 + BaCl 2 - 2 H 2 O = BaSO 4 + 2 KC1 + 2 H 2 O, it is evident that one gram molecule of barium chloride (244.3 grams) is equivalent to one gram molecule of potassium sulphate (174.4 grams). Then, K 2 SO 4 BaCl 2 2H 2 O wt. of K 2 SO 4 wt. of BaCl 2 * 2 H 2 O 174.4 : 244.3 '>'. 0.25 : x. ^=0.3501 gram of BaCl 2 2 H 2 O necessary to precipitate the sulphate. i c.c. barium chloride solution = 0.05 gram BaCl 2 - 2 H 2 O. 0.3501 0.05 = 7 c.c. of the solution. The other type of problem involves the use of the specific gravity of the solution used. c .,, .,. Weight of volume of liquid Specific gravity = , . , s ^ - - Weight of same volume of standard This ratio gives the number of times the liquid is heavier than the same volume of the standard. The standard which is used is the weight of one cubic centimeter of water at its greatest density, 4 C. Therefore, .,, Weight of I c.c. liquid Specific gravity = ... . , . J Weight of i c.c. water I/O QUANTITATIVE ANALYSIS And since the weight of one cubic centimeter of water is one gram, we have c .,, Weight of i c.c. liquid Specific gravity = , i gram or Specific gravity = Weight of i c.c. of the liquid. In determining the specific gravity it is not always convenient to measure the volume of substances at 4 C., but at more conven- ient temperatures, such as 15 or 20. The value of the specific gravity is expressed in terms of the standard at 4 C. and is written i5/4, which signifies that the substance was measured at 1 5 and compared with water at 4, i.e., the ratio of weights of equal volumes of the liquid at 15 and of the standard at 4; 4/4 signifies that the weight of equal volumes are compared at the same tem- perature, < ; likewise, 2O/2O signifies the temperature was 20 when the ^eights were compared. How many cubic centimeters of hydrochloric acid (sp. gr. 1.04) containing 8.16 per cent of HC1 are necessary to completely pre- cipitate the silver from i . 5 grams of silver sulphate ? Ag 2 S0 4 + 2 HC1 = 2 AgCl + H 2 S0 4 . From this equation it is evident that one gram molecule(3 1 1 .9 grams) of silver sulphate is precipitated by two gram molecules (72.92 grams) of hydrochloric acid, and the amount of the acid necessary to precipitate the silver in 1.5 grams of silver sulphate would be Ag 2 SO 4 2HC1 wt. of AgSO 4 wt. of HC1 311.9 : 72.92 :: 1.5 : x. #=0.3506 gram HC1 necessary to precipitate the silver. i c.c. of HC1 (sp. gr. i. 04) = 1.04 grams. It contains 8.16 per cent HC1 by weight. Therefore, i c.c. of HC1 =(0.0816 x 1.04) gram HC1 =0.0849 gram HC1. To furnish 0.3506 gram HC1, 0-35Q6 STOICHIOMETRY 171 Therefore, 4.13 c.c. of the solution will be required to precipitate the silver. PROBLEMS 22. How many cubic centimeters of silver nitrate solution (100 grams of AgNO 3 per liter) will be necessary to completely pre- cipitate the chlorine from 0.22 gram of BaCl 2 2H 2 O? 23. How many cubic centimeters of sodium ammonium hydrogen phosphate solution (microcosmic salt, NaNH 4 HPO 4 4 H 2 O) con- taining 1 5 grams of the salt per liter will be necessary to precipitate the magnesium from 1.2 grams of a substance containing 40 per cent magnesium oxide? 24. A sample of i gram of barium carbonate, the only impurity in which is 3.5 per cent SiO 2 , is dissolved in hydrochloric acid. How many cubic centimeters of sulphuric acid solution (sp. gr. 1. 1 o) containing 14.35 percent H 2 SO 4 by weight v M be neces- sary to completely precipitate the barium as barium sulphate ? 25. How many cubic centimeters of ammonium hydroxide (sp- gr. 0.96), containing 9.91 per cent NH 3 , would be necessary to completely precipitate the iron in a solution containing 1.3 grams of ferric chloride ? VOLUMETRIC CALCULATIONS ACIDIMETRY AND ALKALIMETRY A normal acid solution contains one combining weight, or 1.008 grams of replaceable hydrogen, in one true liter. One combining weight of hydrogen is furnished by one gram molecule of hydro- chloric acid ; hence, it is necessary to have one gram molecule of hydrochloric acid, i.e., the molecular weight in grams (36.46) dis- solved in one liter, to have contained therein 1.008 grams of hydrogen. One gram molecule of sulphuric acid, H 2 SO 4 , contains two combining weights of hydrogen, or 2.016 grams. Hence, to obtain 1.008 grams per liter, one gram molecule of sulphuric acid would have to be contained in two liters, or one-half of it in one liter ; therefore, two liters of a normal solution can be made from one gram molecule of sulphuric acid. According to the equation HC1 + KOH = KC1 + H 2 O, I gram mol. of HC1 (36.46 grams) = I gram mol. of KOH (56.16 grams). 172 QUANTITATIVE ANALYSIS Since, 1000 c.c. normal hydrochloric acid solution = 36.46 grams HC1, 1000 c.c. normal HC1 = 56.16 grams of KOH. If 56.16 grams of potassium hydroxide are dissolved and made up to one liter, we have one liter of a normal potassium hydroxide solution. Hence, 1000 c.c. N. KOH = 56.16 grams of KOH. Therefore, 1000 c.c. N. HC1= 1000 c.c. N. KOH, or, i c.c. N. HC1= i c.c. N. KOH. From the equation H 2 SO 4 + 2 NaOH = Na 2 SO 4 + 2 H 2 O, one gram molecule of sulphuric acid neutralizes two gram molecules of sodium hydroxide. That is, i gram molecule of H 2 SO 4 = 2 gram molecules of sodium hydroxide, (98.08 grams) (2 x 40.06 grams) but, i gram molecule of H 2 SO 4 = 2000 c.c. N. H 2 SO 4 , (98.08 grams) hence, 2000 c.c. N. H 2 SO 4 = 2 gram molecules of NaOH, (2 x 40.06 grams) or, looo c.c. N. H 2 SO 4 = i gram molecule of NaOH. (40.06 grams) If 40.06 grams of sodium hydroxide are dissolved and made up to 1000 c.c., we shall have one liter of a normal sodium hydroxide solution. Hence, 1000 c.c. N. NaOH = 40.06 grams NaOH. Therefore, 1000 c.c. N. NaOH = 1000 c.c. N. H 2 SO 4 , or, i c.c. N. NaOH = i c.c. N. H 2 SO 4 . It, therefore, follows that i c.c. N. HC1 = i c.c. N. H 2 SO 4 , i c.c. N. KOH = i c.c. N. NaOH, i c.c. N. HC1 = i c.c. N. NaOH, i c.c. N. H 2 SO 4 = i c.c. N. KOH, STOICHIOMETRY 173 or, in general, one cubic centimeter of any normal acid solution is equivalent to one cubic centimeter of any normal alkali solution, or normal solutions of acids and alkalies are equal, cubic centimeter for cubic centimeter. The following typical exercises will emphasize these fundamen- tal principles and illustrate the relations between the volumetric solutions employed in acidimetry and alkalimetry, as well as the methods of calculation : 9.2637 grams of a sample of KOH were dissolved in 250 c.c. of water; of this solution 25.45 c - c - were equivalent to 14.90 c.c. of N. acid. Calculate the percentage of KOH. Since, 25.45 c.c. KOH solution = 14.90 c.c. N. acid, i c.c. KOH solution =14^.= 0.5855 c.c. N.acid, 2 5-45 and 250 c.c. KOH solution = 250 x 0.5855 = 146.37 c.c. N.acid. HC1 + KOH = KC1 + H 2 O. From which it follows that 1000 c.c. N. HC1 = 56.16 grams KOH. Hence, looo c.c. N. HC1: 56.16 grams KOH : : 146.37 c.c. N. acid \x grams KOH. Solving, x = 56.16 x 146.37 = 8 220 grams IOOO Hence, 8.220 grams of KOH were furnished by 9.2637 grams of the sample. What percentage of the sample is pure potassium hydroxide ? grams sample grams KOH 9.2637 : 8.220 :: 100 per cent : x per cent. Solving, 8.220 x loo 9.2637 = gg Therefore, 88.73 per cent. This same result may be obtained by rinding the relation of the alkali in terms of the normal acid. It is sometimes preferable to 174 QUANTITATIVE ANALYSIS express the relation of the solutions in terms of the standard solution. 14.90 c.c. N. acid = 25.45 c - c - KOH solution. i c.c. N. acid = 1.708 c.c. KOH solution. Since 1000 c.c. N. acid = 56.16 grams KOH, i c.c. N. acid = 0.05616 gram KOH, then, 1.708 c.c. KOH solution = 0.05616 gram KOH. Hence, 1.708 c.c. KOH solution : 0.05616 gram KOH : : 250 c.c. KOH solution : x grams KOH. Solving, x = -56i6 x 250 = ^ 2Q gmms KQH 1.708 The percentage is found as above. 50 c.c. of a sample of nitric acid of a specific gravity 1.176 were diluted to 250 c.c. Of this solution 33.10 c.c. were neutralized by 35.55 c.c. of N. KOH. Calculate the percentage of nitric acid in the sample. 33.10 c.c. HNO 3 solution = 35.55 c.c. N. KOH, i c.c. HNO 3 solution = 1.074 c.c. N. KOH, then, 250 c.c. HNO 3 solution = 268.50 c.c. N. KOH. Since, HNO 3 + KOH = KNO 3 + H 2 O, 1000 c.c. N.KOH = 1000 c.c. N.HNO 3 = 63.02 grams HNO 3 . Therefore, looo c.c. N.KOH : 63.02 grams HNO 3 : : 268.50 c.c. N.KOH \x grams HNO 3 . Solving, * = 63.02 x 268.50 = I6 grams HNQ IOOO The specific gravity of the nitric acid is 1.176, i.e., i c.c. weighs 1.176 grams, then 50 c.c. will weigh 50 x 1.176 or 58.80 grams, which is the weight of the sample employed in the analysis. STOICHIOMETRY 175 Therefore, 58.80 grams sample : 16.92 grams HNO 3 : : loo per cent \x per cent HNO 3 . Therefore, 28.78 per cent of HNO 3 in the sample. A sample of corn weighing 2.0894 grams was taken for analysis and the nitrogen determined by the Kjeldahl process with the following results : 30.00 C:C. of N/3 acid (HC1) were placed in the receiving flask and after distillation 22.39 c - c - of a standard am- monium hydroxide solution (i.o c.c. = 1.004 c>c - N/3 acid) were required to neutralize the excess of acid. Calculate the percent- age of nitrogen and the percentage of total proteids. Proteids are 6.25 times the nitrogen. If i.o c.c. NH 4 OH solution = 1.004 c ' c - N/3 acid, then, 22.39 c.c. NH 4 OH solution = 22.39 x 1.004 = 22.48 c.c. N/3 acid; therefore, there were 22.48 c.c. of the standard N/3 acid not neu- tralized by the ammonia distilled over. 30.00 c.c. N/3 acid introduced into the flask, 22.48 c.c. N/3 acid in excess in the flask, 7.52 c.c. N/3 acid is amount neutralized by the am- monia distilled over. HC1 + NH 4 OH = NH 4 C1 + H 2 O, then, 1000 c.c. N. HC1 = i gram molecule of NH 4 OH. But, I gram molecule NH 4 OH NH 3 = N, 35.05 grams = 17.03 grams = 14.01 grams, therefore, 1000 c.c. N. HC1 = 14.01 grams nitrogen, 1000 c.c. N/3 HC1 = lA^l. = 4.670 grams nitrogen, and i c.c. N/3 HC1 = 0.004670 gram nitrogen. J 1 76 QUANTITATIVE ANALYSIS Then, 7.52 c.c. N/3 acid = 0.004670 x 7.52 = 0.03512 gram nitrogen, and the percentage this is of the original sample is found by the following proportion : 2.0894 grams sample : 0.03512 gram nitrogen : : 100 per cent : x per cent. Solving, ^0.03512 x ioo = l6S cent 2.0894 Therefore, 1.68 per cent of nitrogen in the sample, and 6.25 x 1.68 = 10.50 per cent of total proteids. . A sample of calcium carbonate weighing 0.6759 gram was dis- solved in 44.50 c.c. of 1.005 N/2 acid (HC1), and the excess of acid neutralized by 18.21 c.c. of a standard alkali, i.oo c.c. of the acid being equal to 1.031 c.c. of the alkali. Calculate the purity of the calcium carbonate. 1.031 c.c. of the alkali = i c.c. of acid, T Q o r and 1 8. 2 1 c.c. of the alkali = - = 17.66 c.c. acid. 1.031 44.50 c.c. of 1.005 N/2 acid used 17.66 c.c. of 1.005 N/2 acid remaining 26.84 c - c - of i -5 N/2 acid used in neutralizing the CaCO 3 . Since the acid is 1.005 times as strong as N/2 acid, 26.84 c - c will equal 26.84 x 1-005 = 26.97 c - c - N/2 acid. CaCO 3 + 2 HC1 = CaCl 2 + CO 2 + H 2 O. i gram molecule of CaCO 3 , i.e. (100.1 grams) = 2000 c.c. N. HC1 = 4000 c.c. N/2 HC1. Therefore, 4000 c.c. N/2 HC1 : 100.1 grams CaCO 3 : : 26.97 c.c. N/2 HC1 \x grams CaCO 3 . Solving, x = IQ Q.i x 26.97 = 0>6750 gram CaC0 3 . 4000 Then, 0.6759 gram of sample : 0.6750 gram CaCO 3 : : 100 per cent : x per cent. UNIVERSITY ) STOICHIOMETR Y 1 77 Solving, ^ = 0.6750x100 0.6759 Therefore, 99.87 per cent of the sample is CaCO 3 . PROBLEMS 26. 11.2798 grams of NaOH were dissolved and diluted to 250 c.c., 36.15 c.c. of which were equivalent to 37.40 c.c. N. acid. Calculate the percentage purity. 27. 6.5563 grams of NaKCO 3 were dissolved and diluted to 250 c.c., 42.88 c.c. of which were equivalent to 17.71 c.c. of N. acid. Calculate the percentage purity. 28. 0.7752 gram of calcium carbonate was dissolved in 32.00 c.c. N. acid; the excess of acid required 16.52 c.c. N. KOH for neutralization. Calculate the percentage purity of the calcium carbonate. 29. 9.4116 grams of a mixture of sodium hydroxide and sodium carbonate were dissolved and made up_to 250 c.c. ; 40.85 c.c. of this solution required 24.32 c.c. N. acid when phenolphthalein was used as an indicator, and 30.56 c.c. when methyl orange was used. Calculate the percentages of sodium carbonate and sodium hydrox- ide. Calculate the percentage of total alkalinity expressed as sodium oxide. 30. 24.84 c.c. NH 4 OH, the specific gravity of which was 0.944, were diluted to 250 c.c., and 28.50 c.c. were equivalent to 22.71 c.c. N. acid. Calculate the percentage of ammonia in the sample. 31. 15.00 c.c. of H 2 SO 4 solution, the specific gravity of which was 1.624, were diluted to 250 c.c., and 25.55 c.c. of this solution were equivalent to 35.25 c.c. of N. KOH. Calculate the percent- age of acid in the sample. 32. 25 c.c. of a sample of HC1, the specific gravity of which was 1.116, were diluted to 250 c.c. ; 20.54 c - c - f this solution were equivalent to 14.30 c.c. N. KOH. Calculate the percentage of HC1 in the sample. 33. 23.12 c.c. of HNO 3 solution, specific gravity 1.19, were diluted to 250 c.c. ; 25.00 c.c. of this solution were equivalent to 12.92 c.c. N. KOH. Calculate the percentage of nitric acid in the sample. QUANTITATIVE ANALYSIS 34. How many cubic centimeters of 0.9 N. H 2 SO 4 solution are required to precipitate the barium from 0.25 gram BaCl 2 H 2 O ? 35. In the absorption method for standardizing the KOH solu- tion 7.9284 grams HC1 gas were absorbed and diluted to 250 c.c. ; 24.89 c.c. of this solution were equivalent to 21.65 c - c - of the KOH solution. Calculate the normality of the KOH solution. 36. 25.00 c.c. of a standard acid were diluted to 250 c.c. and 25 c.c. of this solution were treated with AgNO 3 . The silver chloride from the same weighed 0.3505 gram. What was the normality of the standard acid ? 37. A solution of KOH requires 27.00 c.c. of a standard HC1 (i c.c. of which = 0.022 gram CaCO 3 ) for neutralization. What is the weight of potassium hydroxide in the solution ? 38. One gram of silver is dissolved in nitric acid. To the solu- tion 8 c.c. of N. HC1 are added. What percentage of the silver remains in solution ? OXIDATION AND REDUCTION Balancing Equations In writing the equations representing oxidations and reductions, considerable difficulty is experienced owing largely to the fact that the elements undergo a change of valency. These equations can be balanced only when all of the reacting substances and products are known. The numerical values can be readily obtained and the reactions more easily understood if they are represented as taking place by stages, the final result being expressed as the sum of the various steps. A few specific examples will illustrate the method by means of which the equation may be readily balanced. If the reacting substances are nitric acid and metallic copper, the products of the reaction will be copper nitrate, nitric oxide, and water. The usual action of an acid on a metal is attended with the evolution of hydrogen, Cu + 2 HNO 3 = Cu(NO 3 ) 2 + H 2 , which in the presence of nitric acid will be oxidized. The nitric acid may be assumed to break up as follows : 2 HNO 3 = H 2 + 2 NO + 3 O, STOICHIOMETRY 179 and the hydrogen oxidized by the oxygen, 3 H 2 + 3 O = 3 H 2 0. The first equation must be multiplied by three in order to provide enough hydrogen to combine with the oxygen from two molecules of nitric acid. Multiplying by three and collecting the equations we have, 3 Cu + 6 HN0 3 = 3 Cu(N0 3 ) 2 + 2 HNO 3 = H 2 O + 2 NO + 3 Cu + 8 HN0 3 = 3 Cu(N0 3 ) 2 + 2 NO + 4 H 2 O. Adding and simplifying gives the above. In the oxidation of ferrous chloride by potassium dichromate in the presence of hydrochloric acid, the products of the reaction are ferric chloride, chromic chloride, potassium chloride, and water. The potassium dichromate may be conceived as splitting up in the following manner : K 2 Cr 2 7 = K 2 O + Cr 2 3 + 30. The oxides react with hydrochloric acid, K 2 + 2 HC1 = 2 KC1 + H 2 0, Cr 2 3 + 6 HC1 = 2 CrCl 3 + 3 H 2 O. The oxygen and hydrochloric acid react with the liberation of chlorine, The chlorine reacts with ferrous chloride, oxidizing it to ferric chloride, 6FeCl 2 + 6Cl = 6FeCl 3 . Adding and simplifying we have : K 2 Cr 2 7 = j^O + <>atf 8 + 2 HC1 = 2 KC1 + H 2 + 6 HC1 = 2 CrCl 3 + 3 H 2 O 6 FeCl 2 + 1 = 6 FeCl 3 K 2 Cr 2 7 + 14 HC1 + 6 FeCl 2 = 2 KC1 + 2 CrCl 3 + 6 FeCl 3 + 7 H 2 O, i8o QUANTITATIVE ANALYSIS The reduction of potassium permanganate by potassium iodide (hydriodic acid) in the presence of sulphuric acid may be illus- trated in a similar manner. The potassium permanganate may be conceived as breaking down in the following manner : 2 KMnO 4 = K 2 O + 2 MnO + 5 O. The oxides react with sulphuric acid, forming salts, K 2 O + H 2 SO 4 = K 2 SO 4 + H 2 O ; 2 MnO + 2 H 2 SO 4 = 2 MnSO 4 + 2 H 2 O. , The oxygen reacts with the hydriodic acid, 10 KI + 5 H 2 SO 4 = 10 HI + 5 K 2 SO 4 ; Adding and simplifying we have : 2 KMnO 4 + 10 KI + 8 H 2 SO 4 = 2 MnSO 4 -f 6 K 2 SO 4 + 5 1 2 4- 8 H 2 O. The oxidation of arsenious oxide by chlorine (iodine or bromine) is another example. As 2 O 3 + 2 C1 2 + 2 H 2 O = As 2 O 5 + 4 HC1. Oxidizing Agents The following compounds are some of the more important oxi- dizing agents from the standpoint of analytical chemistry. Their method of breaking up when acting as oxidizing agents is illus- trated. 12 KMnO 4 = K 2 O + 2 MnO + 5 O (in acid solution). T^TI/T r\ ir r\ , n/r r\ r\ 2 KMnO 4 = K 2 O + 2 MnO 2 -f 3 O (in alkaline solution). Potassium dichromate. K 2 Cr 2 O 7 = K 2 O -f Cr 2 O 3 + 3 O. Potassium chlorate. KC1O 3 = KC1 +30 Nitric acid. 2 HNO 3 = H 2 O + 2 NO + 3 O. STOICHIOMETRY 181 Sulphuric acid H 2 SO 4 = H 2 O + SO 2 + O. (hot concentrated). Manganese dioxide. MnO 2 = MnO + O. (in acid solution). Sodium peroxide Na 2 O 2 = Na 2 O + O. (fusion). Hydrogen peroxide. H 2 O 2 = H 2 O + O. The halogens oxidize by decomposing water with the Bromine. [ liberation of oxy g e n. H 2 O + C1 2 = 2 HC1 + O. Iodine. J It should not be forgotten that oxidizing agents are reduced to dif- ferent compounds under different conditions, as may be seen in the case of potassium permanganate in acid and alkaline solutions. Balance the following equations : 1 . Fe 2 (SO 4 ) 3 + H 2 SO 4 + Zn = FeSO 4 + ZnSO 4 + H 2 O. 2. KN0 3 + FeCl 2 + HC1 = KC1 + NO + FeCl 3 + H 2 O. 3. KC1O 3 + FeSO 4 + H 2 SO 4 = KC1 + Fe 2 (SO 4 ) 3 + H 2 O. 4. K 2 Cr 2 O 7 + H 2 SO 4 + Zn = Cr 2 (S0 4 ) 3 + K 2 S0 4 + ZnS0 4 + H 2 O. 5. Mn0 2 + H 2 S0 4 + H 2 C 2 4 = MnSO 4 + CO 2 + H 2 O. 6. As 2 O 3 +HNO 3 +H 2 O = H 3 AsO 4 +NO. 7. K 4 Fe(CN) 6 + H 2 S0 4 + KMn0 4 = K 2 SO 4 + MnSO 4 + K 3 Fe(CN) 6 '+ H 2 O. 8. MnO 2 + KOH + KC1O 3 (fusion) = K 2 MnO 4 + KC1 + H 2 O. 9. Cr 2 Cl 6 + NaOH + NaClO 3 (fusion) = NaCl + Na 2 CrO 4 + H 2 O. 10. Cr 2 (OH) 6 + Na 2 O 2 (fusion) = Na 2 CrO 4 + Na 2 O + H 2 O. n. K 2 Cr 2 7 + HCl+C 2 H 5 OH = CrCl 3 -hKCH-C 2 H 4 12. H 2 S0 4 + C 12 H 22 O n = S0 2 + C0 2 13. KIO 3 + KI + H 2 SO 4 =K 2 SO 4 +I 2 14. KC1O + HI = KC1 + H 2 O + I 2 . 15. 182 QUANTITATIVE ANALYSIS 16. PbO 2 + HI = PbI 2 + H 2 + I 2 . 17. KBr0 3 + KI + H 2 S0 4 = KBr + K 2 SO 4 + I 2 + H 2 O. 18. KC1O 3 + KI + HC1=KC1 + H 2 O + I 2 . 19- K 3 Fe(CN) 6 + KI = K 4 Fe(CN) 6 + I 2 . 20. Ca(OCl) 2 CaCl 2 + HC1 + KI = CaClg + KC1 + I 2 + H 2 O. PERMANGANATE AND BICHROMATE METHODS Numerical Relations The quantitative relations between certain oxidizable substances can be determined by rinding their values in terms of oxygen. Potassium permanganate oxidizes ferrous sulphate to ferric sul- phate. It also oxidizes oxalic acid to carbon dioxide and water. What is the relation between these two reducing agents and what are their values in terms of oxygen ? The ferrous sulphate is oxidized to ferric sulphate, this being equivalent to oxidizing ferrous oxide to ferric oxide. That is, one combining weight of oxygen will oxidize two mole- cules of ferrous oxide, which is equivalent to 2 FeSO 4 or 2 Fe. Similarly, oxalic acid is oxidized by one combining weight of oxygen to carbon dioxide and water, H 2 C 2 O 4 + O = 2 CO 2 + H 2 O. Therefore, H 2 C 2 4 {2 Fe H 2 C 2 O 4 -2H 2 O [2FeSO 4 or expressing the relation in grams: 1 6 g. of oxygen: 90.03 g. oxalic acid = 126.06 g. crystallized oxalic acid = 1 1 1.8 g. of Fe 143.8 g. of FeO 303.9 g. of FeS0 4 If the strength of a solution is given in terms of either of these substances, it stands in a simple ratio to the other substances. STOICHIOMETRY 183 If i c.c. of KMnO 4 = o.O3 gram of oxalic acid, what is its strength in terms of FeO and oxygen? H 2 C 2 O 4 2 FeO 90.03 : 148.08 :: 0.03 : x. x = 0.0496 gram, the value of i c.c. in terms of FeO. H 2 C 2 4 O 90.03 : 1 6 : : 0.03 \x. ^ = 0.005331 gram, the value of i c.c. of the permanganate in terms of oxygen. In the case of potassium dichromate, since, K 2 Cr 2 7 = 3O and O =2 FeO = 2FeSO 4 =2Fe K 2 Cr 2 O 7 =3O =6 FeO =6FeSO 4 =6Fe 294.5 grams =48 grams = 43 1.4 grams = 91 1.7 grams =33 5. 4 grams. QUESTIONS ON EQUATIONS Equation I, page 181. How many gram molecules of ferric sulphate take part in the reaction ? When ferric sulphate acts as an oxidizing agent, how many grams of available oxygen are contained in one gram mole- cule ? How many gram molecules of ferrous sulphate can be ob- tained by the action of one combining weight of zinc? How many grams, by one gram of zinc ? Equation 3. One gram molecule of potassium chlorate contains how many grams of available oxygen? One gram molecule of potas- sium chlorate will oxidize how many grams of FeSO 4 ? Of FeS0 4 (NH 4 ) 2 S0 4 -6H 2 O. Equation 5. How many gram molecules of manganese dioxide and oxalic acid take part in the reaction ? Considering the oxalic acid as crystalline, how many grams are equivalent to one gram of man- ganese dioxide ? Equation 7. How many grams of potassium ferrocyanide will reduce the 1 84 QUANTITATIVE ANALYSIS same amount of permanganate as one gram of hydrogen ? As one gram of ferrous sulphate ? Equation n. Calculate the weight of alcohol necessary to reduce two grams of K 2 Cr 2 O 7 . If the specific gravity of the alcohol used is 0.8043, how many cubic centimeters will be required ? Methods of Solving Problems A solution of potassium permanganate was standardized by (a) pure iron, (b) ferrous ammonium sulphate, and (c) sodium oxalate. In each case calculate the number of grams of oxygen in one cubic centimeter of the permanganate and also the amount of iron equivalent to one cubic centimeter of the solution. a. 0.1104 gram of electrolytic iron was dissolved, out of contact with air, and required 22.30 c.c. of the permanganate solution to oxidize the ferrous iron to the ferric condition. We saw above that 1 6 grams of oxygen are equal to in. 8 grams of iron, then i gram oxygen = 6.988 grams of iron; therefore, 0.1104 gram of iron will require 1104 = 0.01580 gram of oxygen. 6.988 Since this quantity of oxygen is furnished by 22.30 c.c. of per- manganate, then, 22.30 c.c. KMnO 4 = 0.01580 gram oxygen. I c.c. KMnO 4 = = 0.0007085 gram oxygen. Therefore, i c.c. KMnO 4 furnishes 0.0007085 gram of oxygen for oxidation. Since 22.30 c.c. KMnO 4 = o. 1 104 gram iron, 1 c.c. KMnO 4 = 0.004950 gram iron. b. 0.8350 gram of ferrous ammonium sulphate was dissolved and oxidized by 24.01 c.c. of the permanganate solution. Since, FeSO 4 (NH 4 ) 2 SO 4 6 H 2 O Fe wt. of sample wt. of Fe. 392.26 grams : 55.9 :: 0.8350 : x. STOICHIOMETRY 185 Solving, fof iron equivalent to this x _. 55-9 x - 35 = o. 1 190 gram J quantity of ferrous ammo- Inium sulphate. Now, knowing the grams of the iron and the amount of perman- ganate solution required to oxidize it from the ferrous to the ferric condition, the results can be calculated in the manner illustrated in the preceding example. c. 1.401 grams of sodium oxalate were dissolved and made up to 250 c.c. ; 26.50 c.c. of this solution were oxidized by 25.08 c.c. of the potassium permanganate solution. 5 Na 2 C 2 O 4 + 2 KMnO 4 + 8 H 2 SO 4 = 2 MnSO 4 + 5 Na 2 SO 4 4- K 2 SO 4 + 10 CO 2 + 8 H 2 O. 26.50 c.c. oxalate solution = 25.08 c.c. KMnO 4 , i c.c. oxalate solution = 0.9464 c.c. KMnO 4 , 250 c.c. oxalate solution = 236.61 c.c. KMnO 4 . From the above equation 5Na 2 C 2 4 =2KMn0 4 =50, or, Na 2 C 2 O 4 = O, i.e., 134.1 grams = 16 grams of oxygen. Hence, 134.1 grams Na 2 C 2 O 4 : 16 grams oxygen : : 1.401 grams Na 2 C 2 O 4 \x grams oxygen. Solving, x=- - " =0.16716 gram oxygen. Since 236.61 c.c. of KMnO 4 furnished 0.16716 gram of oxygen, one cubic centimeter would furnish '* ' l = 0.0007065 gram of oxy- 236.61 gen for oxidizing purposes. Since, i gram oxygen = 6.988 grams iron, 0.0007065 gram oxygen = 0.0007065 x 6.988 = 0.004937 gram iron. Therefore, I c.c. KMnO 4 = 0.004937 gram iron. 1 86 QUANTITATIVE ANALYSIS PROBLEMS 39. From the following data calculate the number of grams of available oxygen in one cubic centimeter of a potassium perman- ganate solution and also the number of cubic centimeters of this solution required to oxidize o.io gram of iron. a. 0.0946 gram of metallic iron required 10.78 c.c. KMnO 4 solution. b. 1. 145 grams of ferrous ammonium sulphate required 18.70 c.c. of the permanganate solution. c. 1.5477 grams of crystallized oxalic acid were dissolved and made up to 250 c.c. ; 25.25 c.c. of this solution were equivalent to 15.76 c.c. of the permanganate solution. Write the equations representing the reactions in each case. 40. 3.7613 grams of ammonium oxalate((NH 4 ) 2 C 2 O 4 H 2 O) were dissolved in water and made up to 250 c.c. ; 10.00 c.c. of which were equal to 20.33 c - c - of KMnO 4 solution. If i c.c. of the KMnO 4 is equivalent to 0.000830 gram of oxygen, calculate the percentage purity of the sample. 41. Calculate the percentage purity of KH 3 (C 2 O 4 ) 2 2H 2 O, if 1.1881 grams were dissolved and made up to 250 c.c., and 25.10 c.c. of this solution were equivalent to 17.58 c.c. of KMnO 4 , I c.c. of which is equivalent to 0.000851 gram of oxygen. 42. 1.6124 grams of a substance containing calcium were dis- solved and made up to 250 c.c. The calcium was precipitated from 50 c.c. of this solution as calcium oxalate, washed thoroughly, and then dissolved in dilute sulphuric acid. This solution was then titrated with a KMnO 4 solution, I c.c. of which furnished 0.000830 gram of oxygen. 55-88 c.c. of this KMnO 4 were re- quired to oxidize the oxalic acid liberated. Write equations repre- senting all of the reactions and calculate the percentage of calcium oxide in the sample. 43. A solution of K 2 Cr 2 O 7 was standardized with the following results : (a) 0.771 gram of ferrous ammonium sulphate required 19.80 c.c. of the K 2 Cr 2 O 7 solution. (b) 0.430 gram of metallic iron was dissolved and made up to 250 c.c.; 50 c.c. of this solution required 15.45 c.c. of the K 2 Cr 2 O 7 solution. STOICHIOMETRY 187 Write the equations representing all of the chemical changes. Calculate the number of grams of available oxygen in each cubic centimeter of the dichromate solution and the number of cubic centimeters of the solution equivalent to o. i gram of iron. 44. 10.00 c.c. of hydrogen peroxide solution were diluted to 250 c.c., and titrated against a potassium permanganate solution. 25.00 c.c. of the diluted peroxide were equivalent to 19.71 c.c. of the permanganate, i c.c. of which contained 0.00070 gram of oxy- gen. Calculate the number of grams of oxygen furnished by each cubic centimeter of the original peroxide solution. Calculate the percentage purity of the hydrogen peroxide, assuming the spe- cific gravity to be one. lODIMETRY Method of Solving Problems. In the solution of problems in which a number of equations are involved, short cuts in the calculations are often made possible by equating the values in such a way that the intermediate calcula- tions may be omitted. If 25 c.c. of a solution of potassium permanganate (i c.c. = 0.004 gram Fe) are added to an acid solution of potassium iodide, how many grams of sodium thiosulphate (Na 2 S 2 O 3 5 H 2 O) will be oxidized by the iodine liberated ? Since i c.c. KMnO 4 solution = 0.004 gram Fe, 25 c.c. KMnO 4 solution = o.ioo gram Fe. Two combining weights of iron are equivalent to one combining weight of oxygen, or 2 Fe = O, and one of oxygen is equivalent to two combining weights of iodine, O = 2 I. Two combining weights of iodine will oxidize two gram mole- cules of sodium thiosulphate, 2 1 = 2Na 2 S 2 O 3 - 5H 2 O; therefore, 2 Fe = 2 Na 2 S 2 O 3 - 5 H 2 O. That is, 55.9 grams Fe = 248.3 grams Na 2 S 2 O 3 5 H 2 O. 188 QUANTITATIVE ANALYSIS It follows then that 55.9 grams Fe : 248.3 grams Na 2 S 2 O 3 5H 2 O : : o. 100 gram Fe : x grams Na 2 S 2 O 3 5 H 2 O. Solving, 248.3 xo. i _ 55.9 Therefore, 0.4442 gram of sodium thiosulphate will be oxidized by the iodine liberated. This exercise illustrates the common method employed in the solution of problems in iodimetry. It is obvious that the method may be applied to the solution of other classes of problems of oxi- dation and reduction. QUESTIONS ON EQUATIONS Equation 13, page 181. How many grams of potassium iodate will be required to furnish one combining weight of iodine ? One gram of iodine ? Equation 15. How many gram molecules of chlorine are liberated? How many grams of iodine are equivalent to the available oxygen in one gram molecule of MnO 2 ? To one gram of chlorine ? Equation 17. How many grams of iodine are equivalent to the available oxy- gen in 50 c.c. of a solution containing one gram molecule of KBrO 3 in a liter ? How many grams of KBrO 3 should be dis- solved in a liter to make a half-normal solution ? Equation 19. How many grams of potassium ferricyanide are necessary to liberate one combining weight of iodine ? How many grams of the ferricyanide should be dissolved in a liter of water to make a normal solution ? PROBLEMS 45- 3-35 grams of arsenious oxide were dissolved and made up to 500 c.c. ; 25.70 c.c. of this solution were equivalent to 37.70 c.c. of an iodine solution. Calculate the grams of iodine in one cubic centimeter of the iodine solution. 46. An iodine solution was found by titration to be exactly equivalent to a thiosulphate solution which was standardized by a standard potassium permanganate solution, according to Exercise STOICHIOMETRY 189 XXVII, c. If one cubic centimeter of the permanganate solution was equivalent to 0.000707 gram of oxygen and 28.50 c.c. were equivalent to 26.00 c.c. of the thiosulphate solution, calculate the number of grams of iodine in one cubic centimeter of the iodine solution. Express the normality factor of. the iodine solution. 47. 7.0799 grams of bleaching powder were taken for analysis, dissolved and diluted to 1000 c.c. 50 c.c. of this solution were treated with potassium iodide and acetic acid and the iodine liber- ated, titrated against N/io thiosulphate solution, of which 24.45 c.c. were required. Calculate the percentage of available chlorine in the sample. 48. 0.7697 gram of pyrolusite was treated, as described in Exercise XXIX, with concentrated hydrochloric acid, and the lib- erated chlorine passed into a solution of potassium iodide. This solution was diluted to 500 c.c., and 50 c.c. of it titrated against N/io thiosulphate solution of which 11.90 c.c. were required. Calculate the percentage purity of the pyrolusite. 49. An iodine solution was standardized by means of a standard dichromate solution (i c.c. =0.000848 gram oxygen) according to the method described in Exercise XXVII, d. 28.29 c.c. K 2 Cr 2 O 7 liberated enough iodine to oxidize 30.05 c.c. sodium thio- sulphate, i c.c. of which = 1.206 c.c. of the iodine solution. Cal- culate the normality of the iodine solution. Factor Weights In order to facilitate the calculations, -it is frequently of value in volumetric determinations to so adjust the weight of the sample to the strength of the solution that each cubic centimeter used in the titration will represent a definite amount of the constituent. Suppose a permanganate solution is standardized and each cubic centimeter found to be equivalent to 0.0045 gram of iron. If in the analysis 0.45 gram of the sample is weighed out and 22.30 c.c. used in the titration, the percentage of iron found would be 22.30x0.0045 x I00 = 22.3 per cent. 0.45 For this particular weight of substance, therefore, each cubic centimeter of the solution used would indicate one per cent of the constituent sought. 190 QUANTITATIVE ANALYSIS If 0.90 gram of the sample were taken, each cubic centimeter would read 0.50 per cent; if 0.2250 gram, 2 per cent; and so on. In gravimetric processes, the weight of the sample may also be so selected that each milligram of the precipitate will represent a definite amount of the substance sought. How much pyrite must be taken for analysis in order that each milligram of BaSO 4 shall represent o. i per cent of S ? i mg. of BaSO 4 = 0.1373 mg. of S. 0.1373 mg. of S is o.i per cent of 0.1373 gram. If 0.1373 gram of sample is taken, therefore, each milligram of the precipitate will represent o. i per cent of sulphur. PROBLEMS 50. How much limestone must be taken for analysis for each milligram of calcium sulphate to represent o. i per cent of calcium oxide ? 51. How much barite must be taken for analysis in order that each milligram of barium sulphate shall represent 0.20 per cent of BaO? 52. One cubic centimeter of a solution of KMnO 4 = 0.0075 gram of oxygen. How many grams of limestone should be weighed out in order that when titrating the calcium as the oxa- late each cubic centimeter of the permanganate solution used cor- responds to 0.5 per cent CaO ? 53. How much of a feeding material must be taken for analysis by the Kjeldahl method in order that each cubic centimeter of N/4 HC1 used to titrate the ammonia distilled over shall represent 0.5 per cent of proteid matter. Use 6.25 for conversion of nitro- gen to proteid matter. MISCELLANEOUS PROBLEMS 54. A mixture of the sulphates of sodium and potassium weighs i.i grams. It is dissolved in water and barium chloride solution added, a precipitate of BaSO 4 weighing 1.699 grams being obtained. Calculate the weight of each sulphate in the original mixture. 55. How many grams of a sample of fertilizer should be taken for analysis in order that each milligram of Mg 2 P 2 O 7 shall repre- sent o. i per cent of P ? 0.2 per cent of P 2 O 5 ? STOICHIOMETRY 191 56. A mixture of equal parts of sodium chloride and potassium chloride weighs 0.30 gram. How many cubic centimeters of platinic chloride solution containing o.i gram platinum per cubic centimeter will be necessary to completely change the sodium and potassium chlorides to the chlorplatinates ? 2KCl+PtCl 4 =K 2 PtCl 6 . 57. 10 grams of a sample of soil were fused with sodium car- bonate, dissolved in hydrochloric acid after the removal of the silica, and the solution made up to 500 c.c. The phosphorus in 200 c.c. of the sample was precipitated and gave on ignition 0.072 gram of Mg 2 P 2 O 7 . 100 c.c. of the solution were titrated with dichromate solution for iron, 8.23 c.c. of the dichromate solution being used, (i c.c. K 2 Cr 2 O 7 = 0.00072 gram oxygen.) The iron, aluminium, and phosphorus in 100 c.c. of the solution were precipi- tated with ammonium hydroxide, and on ignition weighed 0.380 gram. Calculate the percentages of Fe 2 O 3 , A1 2 O 3 , and P in the soil. 58. 1.2 grams of a silver coin were dissolved in nitric acid, and the silver precipitated with normal hydrochloric acid, 9.10 c.c. being used. What percentage of silver was in the coin ? 59. To a solution of Glauber's salt N/io BaCl 2 solution was added until no more precipitate was formed, 14.70 c.c. of the solu- tion being used. Calculate the number of grams of anhydrous sodium sulphate in the solution. 60. 13.48 c.c. of a solution of standard hydrochloric acid were necessary to dissolve one gram of pure calcium carbonate. How many cubic centimeters of this solution must be taken to make a liter of normal acid ? 61. How many cubic centimeters of N/2 HC1 would be neces- sary to dissolve 0.3 gram of witherite (BaCO 3 ) which contains as an impurity 7 per cent of quartz ? 62. How many cubic centimeters of 5.5 normal ammonium hydroxide solution would be required to precipitate the aluminium in one gram of potassium alum ? 63. How much NaOH, 85 per cent pure, must be added to 2 liters of a NaOH solution, i c.c. of which is equivalent to 0.041 gram H 2 SO 4 , in order to make the solution normal? How much water should be added to make it N/3 ? 192 QUANTITATIVE ANALYSIS 64. 1.2 grams of pure ammonium chloride were dissolved in water and heated with an excess of sodium hydroxide solution. The ammonia gas was conducted into water and neutralized with standard sulphuric acid, 18.30 c.c. being used. What was the normality of the sulphuric acid ? 65. A standard solution of HC1 is analyzed by precipitating with AgNO 3 ; 10 c.c. of the acid solution gave 0.22 gram AgCl. What is the normality of the acid ? What weight of calcite con- taining 0.3 per cent SiO 2 as an impurity will be dissolved by 50 c.c. of the acid ? 66. The total phosphorus in a sample of 0.22 gram of fertilizer was precipitated as ammonium phosphomolybdate. The precipi- tate was dissolved in 40 c.c. of N/3 potassium hydroxide solution and the excess of alkali titrated with standard nitric acid (i c.c. = 1.021 c.c. of N/3 KOH), 14.20 c.c. being used. Calculate the percentage of phosphorus in the sample. 2(NH 4 ) 3 PO 4 - i2MoO 3 +46KOH = 2 (NH 4 ) 2 HPO 4 + (NH 4 ) 2 MoO 4 + 23 K 2 MoO 4 + 22 H 2 O. 67. A sample of 1.5 grams of feeding material was weighed out for the determination of total proteids by the Kjeldahl method. The ammonia was absorbed in 25.00 c.c. of N/2 HC1. The excess of acid in the absorption flask was neutralized with 12.00 c.c. of standard ammonium hydroxide solution (21.20 c.c. = 18.00 c.c. N/2 HC1). Calculate the percentage of total proteids in the sample. Use 6.25 as the factor for the conversion of nitrogen to proteids. 68. In the determination of the Reichert-Meissl number for butter fat as described on page no, a sample of 5.023 grams was taken for analysis. The total distillate containing the volatile acids was no c.c.; 100 c.c. of this solution required 12.50 c.c. of KOH (i c.c. = 1.092 c.c. N/io KOH) for neutralization. Calculate the Reichert-Meissl number. 69. In the determination of the saponification number of butter fat, as described on page 115, 1.740 grams of the sample were taken for analysis. On titrating the blank, 69.70 c.c. of HC1 were used, while the sample required 46.75 c.c. HC1. i c.c. HC1 = 0.01014 gram of HC1. Calculate the saponification number. 70. A sample of 9.200 grams of butter fat was used for the de- termination of salt, which was extracted with water (see page 102) STOICHIOMETRY 193 and the solution made up to 200 c.c. 50 c.c. of the salt solution re- quired 14.40 c.c. of N/20 AgNOg solution for titration. Calculate the percentage of salt in the butter. 71. A sample of 0.5 gram of siderite (FeCO 3 ), the only impurity in which is 3.5 per cent quartz, is dissolved out of contact with the air. How many cubic centimeters of permanganate solution (i c.c. = 0.008 gram of H 2 C 2 O 4 2 H 2 O) will be required to oxidize the iron ? 72. 0.5 gram of a sample of ferrous ammonium sulphate which had been heated, was dissolved and titrated with N/io KMnO 4 , 16.80 c.c. being required. What percentage of the water of crystallization had been lost ? 73. A sample of 0.5 gram of an iron ore was titrated for iron with N/io KMnO 4 solution, 27.80 c.c. being used. If the student neglected to apply the calibration correction of +0.14 c.c., what would be the error in the percentage of iron as reported ? 74. One cubic centimeter of a solution of KMnO 4 contains 0.00042 gram of available oxygen. How much oxygen will be available when the permanganate is used for titration in a neutral solution ? 2 KMnO 4 = K 2 O + MnO 2 +30. 75. What weight of iron wire 99.7 per cent pure will be oxi- dized by the potassium dichromate formed from 0.35 gram of chrome iron (FeO Cr 2 O 3 ) the only impurity in which is 4.5 per cent silica ? 76. 25.00 c.c. of a solution of potassium permanganate, on being added to a solution of potassium iodide in sulphuric acid, liberated 0.33 gram of iodine. To what volume should one liter of the solu- tion be diluted to make it exactly tenth normal ? 77. Some crystallized sodium thiosulphate (Na 2 S 2 O 3 5 H 2 O) was exposed to the air and lost water of crystallization. A sample of 0.62 gram was dissolved in water and titrated with an iodine solution (i c.c. = 0.0049 gram As 2 O 3 ), 28.10 c.c. being used in the titration. What percentage of the water of crystallization had been lost? How many grams of the sodium thiosulphate should be weighed out for a liter of N/io solution? 78. A sample of 0.5347 gram of pyrolusite was weighed out for analysis, into a retort. It was heated with hydrochloric acid and 194 QUANTITATIVE ANALYSIS the chlorine evolved passed into a solution of potassium iodide. The iodine solution was diluted to 250 c.c., and 100 c.c. titrated with N/io Na 2 S 2 O 3 solution of which 21.90 c.c. were used. Cal- culate (a) the purity of the pyrolusite ; (b) the oxidizing power of one gram in terms of iron and crystallized oxalic acid. 79. In the determination of the iodine absorption number by the Hanus method described on page 117, 0.7380 gram of butter fat was taken for analysis. On titrating Blank required 32.40 c.c. Na 2 S 2 O 3 solution, Sample required 11.30 c.c. Na 2 S 2 O 3 solution. 2O c.c. K 2 Cr 2 O 7 solution are equivalent to 16.20 c.c. Na 2 S 2 O 3 . i c.c. of the K 2 Cr 2 O 7 contains 0.00387 gram of the dichromate. Calculate the iodine absorption number. 80. Cupric salts in a solution of potassium iodide containing acetic acid are reduced to cuprous salts with the liberation of iodine. The iodine can then be titrated in the usual way with sodium thiosulphate solution. 2 Cu(C 2 H 3 2 ) 2 4- 4 KI = Cu 2 I 2 + 4 KC 2 H 3 O 2 + I 2 . How many grams of copper will furnish the iodine necessary to react with 18.00 c.c. of N/io Na2S 2 O 3 solution ? APPENDIX BOOKS OF REFERENCE Agricultural Analysis ALLEN, A. H. Commercial Organic Analysis. 4 Vols. BLYTHE, A. W. Foods, Their Composition and Analysis. 5th Edition (1903). INGLE, H. Manual of Agricultural Chemistry (1902). JAGO, W. The Science and Art of Bread Making. Chemistry and Analysis of Wheat, Flour, etc. (1895). KONIG, J. Untersuchung Landwirtschaftlich und Gewerblich Wichtiger Stoffe (1906). LEACH, A. E. Food Inspection and Analysis (1904). LEFFMAN AND BEAM. Select Methods of Food Analysis (1905). RICHMOND, H. D. Dairy Chemistry. SHERMAN, H. C. Organic Analysis (1905). SNYDER, H. Dairy Chemistry (1906). Contains an excellent Bibliography, page 161. Soils and Fertilizers (1905). United States Department of Agriculture, Division of Chemistry, Bulletin No. 46 (1898), Methods of Analysis adopted by the Association of Official Agricultural Chemists. United States Department of Agriculture, Bureau of Chemistry, Bulletin No. 65 (1902), Provisional Methods for the Analysis of Foods adopted by the Association of Official Agricultural Chemists. WILEY, H. W. Foods and their Adulteration (1907). Principles and Practice of Agricultural Analysis. Vol. i. Soils (1906). Vol. 2. Fertilizers (New Edition in Press). Vol. 3. Agricultural Products (1897). General Quantitative Chemical Analysis CLASSEN, A. Ausgewahlte Methoden der Analytischen Chemie. 2 Vols. (1901). COHN. Indicators and Test Papers (1899). FRESENIUS. Quantitative Chemical Analysis. 2 Vols. Translated by Cohn (1904). HILLEBRAND, W. F. The Analysis of Silicate and Carbonate Rocks. United States Geological Survey, Bulletin No. 305. JULIAN, F. Quantitative Chemical Analysis (1902). OLSEN, J. C. Quantitative Chemical Analysis (1904). SUTTON, F. Volumetric Analysis, 9th edition. TREADWELL-HALL. Analytical Chemistry, Vol. II, Quantitative Analysis. 195 196 QUANTITATIVE ANALYSIS The Application of the Modern Theories of Chemistry to Quantitative Analysis ABEGG, A. The Electrolytic Dissociation Theory. Translated by von Ende. BOTTGER, W. The Principles of Qualitative Analysis from the Standpoint of the Theory of Electrolytic Dissociation and the Law of Mass Action. Translated by Smeaton. OSTWALD, W. The Scientific Foundations of Analytical Chemistry. Translated by McGowan. TALBOT AND BLANCHARD. The Electrolytic Dissociation Theory. TABLE I DESK REAGENTS The reagents placed on the students 1 desks have the following concentrations. When concentrated and dilute acids are referred to in the procedure, these acids should be used. HC1 concentrated sp. gr. 1. 12 contains 23.82 per cent HC1. HC1 dilute sp. gr. I.O4 contains 8.16 per cent HC1. HNO 3 concentrated sp. gr. 1.42 contains 69.80 per cent HNO 3 . HNO 8 dilute sp. gr. 1.20 contains 32 36 per cent HNO 3 . H 2 SO 4 dilute sp. gr. I. II contains 15.71 per cent H 2 SO 4 . NH 4 OH sp. gr. 0.96 contains 9.91 per cent NH 3 . TABLE II LABORATORY REAGENTS Name Descrip- tion Formula Molecu- lar Weight Grams per Liter Specific Gravity at 15 C. Remarks, Preparation, etc. Acid, acetic HC 2 H 3 2 60.03 99.5 per cent. (Glacial) Acid, acetic Solution 1.0412 30 per cent. Acid, hydro- Solution HC1 36-46 469.00 1.20 39.11 per cent. chloric Acid, hydro- 267.00 1. 12 23.82 per cent. 3 vols. chloric of acid sp. gr. 1.20 to 2 vols. water. Acid, hydro- Solution 255-00 I.IX5 22.86 per cent. chloric . Acid, hydro- Solution 85.00 1.04 8.16 per cent. chloric Acid, hydro- Solution 18.23 N/2 chloric Acid, hydro- Solution 9.12 N/ 4 chloric APPENDIX 197 TABLE II Continued Name Descrip- tion Formula Molecu- lar Weight Grams per Liter Specific Gravity at 15 C. Remarks, Preparation, etc. Acid, nitric HN0 8 63.02 991.00 1.42 69.8 per cent Acid, nitric Solution 388.00 1.20 32.36 per cent. Made by diluting 2 vols. of sp. gr. 1.42 with 3 vols. of water Acid, oxalic [H 2 C 2 4 126.05 2H 2 0] Acid, salicylic [C 6 H 4 (OH) 138-05 COOH] Acid, sulphuric H 2 S0 4 98.08 1759.00 1.8 4 95.6 per cent H 2 SO 4 Acid, sulphuric 1.82 Commercial for Babcock test Acid, sulphuric Solution 702.00 1.40 50.11 per cent H 2 SO 4 Acid, sulphuric Solution 175.00 I. II 15.71 per cent H 2 SO 4 Acid, sulphuric Solution 12-5 1.25 per cent for crude fiber Acid, tartaric H 2 C 4 H 4 6 150.05 Alcohol C 2 H 6 OH 46.05 0.8164 95 per cent by volume Alcohol Solution 0.8639 80 per cent by volume Ammonium car- [(NH 4 ) 2 C0 3 - 114.1 bonate H 2 O] Ammonium NH 4 C1 53-49 chloride Ammonium Solution 200.00 Saturated with chloride K 2 PtCl 6 . See page 201 Ammonium Solution [(NH 4 ) 3 C 6 243- J 7 1.00-20 For preparation of citrate H 5 7 ] solution see page 201 Ammonium Solution NH 4 OH 35-05 0.96 9.91 per cent NH 3 hydroxide Ammonium Solution [(NH 4 ) 2 Mo 196.08 6ogrs. For preparation of molybdate 4 ] Mo0 3 solution see page 201 Ammonium NH 4 NO 3 80.05 nitrate Ammonium Solution 100.0 nitrate Ammonium Solution [(NH 4 ) 2 C 2 142.1 42.00 Saturated solution at oxalate 4 -H 2 0] 15 Arseaious oxide As. 2 3 198.00 Asbestos For Gooch crucibles. For preparation see page 201 Barium chloride Solution [BaCl 2 244-33 I22.OO 2H 2 0] Barium hydrox- Solution [Ba(OH) 2 . 3I5-5 50 Saturated solution ide 8H 2 0] at 20 198 QUANTITATIVE ANALYSIS TABLE II Continued Name Descrip- tion Formula Molecu- lar Weight Grams per Liter Specific Gravity at 15 C- Remarks, Preparation, etc. Bromine water Solution Br 2 IS9-92 Water at room tem- perature saturated with liquid bromine with a few drops of bromine in the bot- tom of the bottle. Calcium carbon- CaCO 3 IOO.I For standardising so- ate lutions. Iceland spar, or the pure precipitated sub- stance Calcium chlo- CaCl 2 III.OO Granular. For ab- ride sorbing moisture Chloroform CHC1 3 119.36 Copper sulphate [CuS0 4 249.74 5H 2 0] Ether, ethyl (C 2 H 6 ) 2 74.08 For extracting fats. Dry. Distilled from sodium Fehling's copper Solution 69.27 grams CuSO 4 solution 5 H 2 O per liter Fehling's alkali Solution 356 grams Rochelle solution, for salts and 100 grams lactose, by NaOH in one liter S o x h 1 e t's method Fehling's alkali Solution 356 grams Rochelle solution for salts and 250 grams use in Allihn's KOH in one liter method for dextrose Ferrous ammo- [FeSO 4 392.20 . nium sulphate (NH 4 ) 2 S0 4 - 6H 2 0] Iodine Is 253-94 Iodine mono- Solution IBr 206.93 For preparation of so- bromide lution see page 116 Iron Fe 55-9 Pure, electrolytic Litmus paper Magnesite MgCOg 84-36 Magnesium mix- Solution [MgCl a + Dissolve no grams ture NH 4 C1+ of crystallized mag- NH 4 OH] nesium chloride (MgCl 2 .6H 2 O)and 40 grams of am- monium chloride in 1300 c.c. of water and make up to two liters with ammonium hy- droxide (sp. gr. 0.96) APPENDIX 199 TABLE II Continued Name Descrip- tion Formula Molecu- lar Weight Grams per Liter Specific Gravity at 15 C. Remarks, Preparation, etc. Magnesium ox- MgO 40.36 ide Malt extract Solution For preparation, see page 127 Mercury Hg 200.00 Mercuric chlo- Solution HgCl 2 270.9 50.0 ride Methyl orange Solution I. CO Dissolve i gram in (orange No. one liter of water Ill) Molybdic oxide MoO 3 144.00 Paraffine Phenolphthalein Solution 5.00 Dissolve 5 grams in one liter of 60 per cent alcohol. Filter Platinic chloride Solution PtCl 4 336.6 172.8 I c.c. of solution con- tains o.i gram of platinum Potassium chro- Solution K 2 CrO 4 194.4 100.00 Indicator for determi- mate nation of chlorine Potassium di- K 2 Cr 2 7 294-5 chromate Potassium ferri- K 8 Fe(CN) 6 329.42 cyanide Potassium hy- KOH 56.16 droxide Potassium hy- Solution KOH 40.00 Dissolve in one liter droxide of redistilled 95 per cent alcohol Potassium io- KI 166.12 dide Potassium io- Solution KI 150.00 dide Potassium per- KMnO 4 158.15 manganate Potassium sul- Solution K 2 S 110.36 40.00 phide Pumice Ignited at red heat and plunged into cold water. Kept under water Rochelle salt [KNaC 4 H 4 282.3 6 . 4 H 2 0] Silver nitrate Solution AgN0 3 169.94 ICO.OO Silver nitrate Solution 8.499 N/20 for determina- tion of salt in butter Sodium acid NaHCO 8 84.06 carbonate 20O QUANTITATIVE ANALYSIS TABLE II Continued Name Descrip- tion Formula Molecu- lar Weight Grams per Liter Specific gravity at 15 C. Remarks, Preparation, etc. Sodium "ammo- Solution [NaNH 4 209.16 100.00 nium hydro- HP0 4 gen phosphate 4 H 2 0] (microcosmic '" salt) Sodium carbon- Na 2 CO 3 106.10 ate Sodium dichro- [NasCr s Or 298.33 Commercial. For mate 2H 2 0] cleaning solution. See page 45 Sodium hydrox- NaOH 40.06 ide Sodium hydrox- Solution One part sodium hy- ide droxide to one part of water Sodium hydrox- Solution 600.00 600 grams of commer- ide cial (Greenbank) alkali dissolved in one liter of water Sodium hydrox- Solution 20.03 N/2 ide Sodium hydrox- Solution 4.006 N/io ide Sodium hydrox- Solution 12.5 1.25 per cent. For ide crude fiber deter- minations Sodium oxalate Na 2 C 2 4 134.10 For preparation, see page 72 Sodium thiosul- [Na^CV 248.30 phate 5H 2 0] Stannous chlor- Solution SnCl 2 189.9 Dissolve 30 grams of ide tin in 125 c.c. of HC1 (sp. gr. 1. 20). Dilute to 250 c.c. and filter. Add 250 cc. HC1 (sp. gr. 1.12) and make up to i liter with water. Add a few pieces of granulated tin Starch (C 6 H 10 6 ) For indicator, see page 80 Sugar (sucrose) C 12 H 22 O n 342.18 Water nitro- H 2 O 18.016 See page 201 gen-free Wool, glass Zinc Zn 654 Dust Zinc Granulated Zinc For Jones Reductor APPENDIX 201 Ammonium Citrate Solution Dissolve 370 grams of commercial citric acid in 1 500 c.c. of water ; nearly neu- tralize with ammonium hydroxide ; cool, add ammonium hydroxide until exactly neutral (tested with a saturated alcoholic solution of corallin) and dilute the vol- ume to 2 liters. Determine the specific gravity, which should be 1.09 at 20. For another method of preparing this solution, see U.S. Department of Agricul- ture, Bull. No. 46, page n. Asbestos for Gooch Crucibles Select a grade of asbestos having long fibers, soak it with water, shred it in a porcelain mortar. Treat it with hydrochloric acid (sp. gr. 1.12) for twelve hours, wash it by decanting with distilled water several times, allowing the fine particles of fiber to be decanted with the distilled water. Filter, wash well, dry, and ignite in a platinum dish with the blast lamp. I. Ammonium Chloride Solution saturated with Potassium Chlorplatinate Dissolve 100 grams of ammonium chloride in 500 c.c. of water, add from 5 to 10 grams of pulverized potassium chlorplatinate, allow to stand for six or eight hours, shaking at intervals. Allow the mixture to settle overnight, then filter. The residue may be used for the preparation of a fresh supply. Ammonium Molybdate Solution Dissolve 100 grams of molybdic acid (MoO 3 ) in 417 c.c. of ammonium hydrox- ide (sp. gr. 0.96) and slowly pour the solution thus obtained into 1250 c.c. of nitric acid of specific gravity i .20. Keep the mixture in a warm place for several days or until a portion heated to 40 deposits no yellow precipitate of ammonium phosphomolybdate. Preparation of Nitrogen-free Water Add to a carboy of ordinary distilled water enough bromine water to give it a distinct color. Allow to stand for a day or two, then add an excess of sodium carbonate and distill in a room free from ammonia fumes. The distillate will be ammonia-free. 2O2 QUANTITATIVE ANALYSIS TABLE III APPARATUS FOR DESK EQUIPMENT Beakers, nests 0-6 2 Bottles, glass-stoppered, i\ liter . 2 Brush, camePs-hair I Burette, glass stopcock, 30 c.c. . I Burette, pinchcock, 30 c.c. . . I Burette holder i Burners, adjustable 2 Casseroles, 250 c.c 2 Cover-glasses, 50 mm 2 Cover-glasses, 75 mm 2 Cover-glasses, 125 mm 2 Crucibles, porcelain, No. oo . . 4 Cylinder, graduated, 50 c.c. . . I Desiccator, for four crucibles . . I Dishes, porcelain evaporating, 5 cm. diam 2 File i Filter papers, ashless gem. . 50 Filter papers, ashless n cm. . 10 Filter papers, qualitative, 9 cm. . 25 Filter papers, hardened, half form 4 Flasks, Erlenmeyer, 250 c.c. . . 4 Flasks, Jena Erlenmeyer, 125 c.c. 2 Flasks, Kjeldahl, 500 c.c. ... 2 Flasks, plain, 250 c.c. ..... 2 Flasks, plain, 500 c.c 2 Flasks, volumetric, glass-stoppered, 250 c.c 2 Flasks, volumetric, glass-stoppered, 500 c.c i Flasks, volumetric, glass-stoppered, 1000 c.c i Forceps, steel, 130 mm. ... i Funnels, 75 mm., stem 200 mm. . 4 Funnels, 25 mm., stem 50 mm. . 2 Indicators, 50 c.c. flasks of ... 2 Lock and key . Matches boxes . Notebook .... Pan, 15 cm. diameter Paper, sheets of glazed Pinchcock .... Pipettes, 5 c.c 10 c.c 10 c.c. graduated . 25 c.c 50 c.c 100 c.c Policemen, rubber Reagent bottles, 30 c.c., for silver nitrate I Rod, glass, feet of 2 Sponge i Stand, filter i Stands, iron, with two rings each 2 Stopper, rubber, No. 5 .... i Tongs, brass .... . . i Towel i Triangles, pipe stem, new form . 2 Tripods 2 Tubes, inner extraction, length 85 mm., diam. 25 mm 2 Tubes, inner extraction, length 70 mm., diam. 18 mm 2 Tubes, weighing, with corks . . 3 Tubing, glass, i" diam., feet 3 Tubing, rubber, J" diam., feet 6 Tubing, " T y diam., foot i Wire gauze, asbestos center . . 2 Wire, platinum, inches .... 3 APPENDIX 203 TABLE IV SPECIFIC GRAVITY OF HYDROCHLORIC, NITRIC, AND SULPHURIC ACIDS G. Lunge Specific Gravity 3 (Vacuo) Per Cent by Weight Specific Gravity f (Vacuo) Per Cent by Weight HCl HNO, H 2 S0 4 HN0 3 H 2 S0 4 .OOO 0.16 O.IO 0.09 1.205 33.09 27.95 .005 I.I5 1. 00 0.83 1. 210 33.82 28.58 .OIO 2.14 1.90 1-57 I.2I5 34.55 29.21 .015 3.12 2.80 2.30 I.22O 35.28 29.84 .020 4-13 3.70 3-03 1.225 36.03 30.48 .025 5-15 4.60 3.76 1.230 36.78 3 I.II .030 6.1 5 5.50 4.49 1.235 37-53 31.70 035 7.15 6.38 5.23 1.240 38.29 32.28 .040 8.16 7.26 5.96 1.245 39.05 32.86 .045 9.16 8.13 6.67 1.250 39.82 33-43 .050 10.17 8.99 7-37 1.255 40.58 34.00 .055 II.I8 9.84 8.07 1.260 41-34 34-57 .060 12.19 10.68 8.77 1.265 42.10 35.H .065 I3-I9 11.51 9-47 1.270 42.87 35-71 .070 14.17 12.33 10.19 1.275 43-64 36-29 .075 15.16 13-15 10.90 1.280 44.41 36.87 .080 I6.I5 13-95 ii. 60 1.285 45.18 37-45 .085 17.13 14.74 12.30 1.2 9 45-95 38.03 .090 18.11 15-53 12.99 1.2 9 5 46.72 38.61 .095 19.06 16.32 13.67 1.300 47-49 39-19 .100 20.01 17.11 14-35 1.305 48.26 39-77 .105 20-97 17.89 15-03 I.3IO 49.07 40.35 .110 21.92 18.67 15.71 L3I5 49.89 40.93 .115 22.86 J 9-45 16.36 1.320 50.71 41.50 .120 23.82 20.23 17.01 L325 5L53 42.08 .125 24.78 21.00 17.66 1-330 52-37 42.66 .130 25-75 21.77 18.31 1-335 53-22 43.20 135 26.70 22.54 1 8.. 96 1.340 54.07 43-74 .140 27.66 23.31 19.61 1-345 54-93 44.28 .145 28.61 24.08 20.26 1-350 55-79 44.82 .150 29.57 24.84 20.91 1-355 56.66 45-35 155 30-55 25.60 21.55 1.360 57-57 45.88 .I60 31.52 26.36 22.19 1-365 58.48 46.41 .165 32.49 27.12 22.83 1.370 59-39 46.94 .170 33-46 27.88 2347 1-375 60.30 47-47 175 34.42 28.63 24.12 1.380 61.27 48.00 .180 35.39 29.38 24.76 1-385 62.24 48.53 .185 36.31 30.I3 25.40 1.390 63-23 49.06 .190 37.23 30.88 26.04 1-395 64.25 49-59 .195 38.16 31.62 26.68 1.400 65.30 50.11 .200 39. II 32.36 27.32 1.405 66.40 50.63 2O4 QUANTITATIVE ANALYSIS TABLE IV Continued Specific Gravity at 15! 4 (Vacuo) Per Cent by Weight Specific Gravity 15 at t (Vacuo) Per Cent by Weight Specific Gravity -* (Vacuo) Per Cent by Weight HNO 3 H 2 S0 4 H 2 SO 4 H 2 S0 4 1.405 66.40 50.63 1.570 65.90 730 79.80 I.4IO 67.50 51.15 1-575 66.30 735 80.24 I.4I5 68.63 51.66 1.580 66.71 .740 80.68 I.42O 69.80 52.15 1.585 67.13 745 8I.I2 1.425 70.98 52.63 1.590 67.59 .750 81.56 1.430 72.17 53-11 J -595 68.05 755 82.00 1-435 73.39 53-59 i. 600 68.51 .760 82.44 1.440 74.68 54.07 1.605 68.97 .765 82.88 1.445 75.98 54.55 1.610 6943 770 83-32 1.450 77.28 55'3 1.615 69.89 775 83.90 M55 78.60 55.50 1.620 70.32 .780 84.50 1.460 79.98 55-97 1.625 70.74 .785 85.10 1.465 81.42 56.43 1.630 7I.l6 .790 85.70 1.470 82.90 56.90 1-635 7L57 795 86.30 1-475 84.45 57-37 1.640 71.99 .800 86.90 1.480 86.05 57-83 1.645 72.40 .805 87.60 1.485 87.70 58.28 1.650 72.82 .810 88.30 1.490 89.60 58.74 1.655 73-23 .815 89.05 1.495 91.60 59.22 i. 660 73-64 .820 90.05 1.500 94.09 59.70 1.665 74.07 .825 91.00 1.505 96.39 60.18 1.670 74.51 .830 92.10 1.510 98.10 60.65 1.675 7497 -835 93-43 1-515 99.07 61.12 i. 680 75 42 .840 95.60 1.520 99.67 61.59 1.685 75.86 .8405 95-95 1.525 62.06 1.690 76.30 .8410 97.00 1-530 62.53 1.695 76.73 .8415 97-70 1-535 63.00 1.700 77.17 .8410 98.20 1.540 63-43 1.705 77.60 .8405 98.70 1-545 63.85 1.710 78.04 .8400 99.20 1.550 64.26 1.715 78.48 8395 99-45 1-555 64.67 1.720 78.92 .8390 99-70 1.560 65.08 1.725 79.36 .8385 99-95 1.565 65.49 APPENDIX 205 TABLE V SPECIFIC GRAVITY OF AMMONIA SOLUTIONS AT 15 C. Lunge and Wiernik Specific Gravity Per Cent NH 3 Specific Gravity Per Cent NH 3 1. 000 0.00 0.940 I5-63 0.998 0.45 0.938 16.22 0.996 0.91 0.936 16.82 0.994 i-37 0-934 17.42 0.992 1.84 0. 9 32 18.03 0.990 2.31 0.930 18.64 0.988 2.80 0.928 19.25 0.986 3-30 0.926 19.87 0.984 3.80 0.924 20.49 0.982 4-30 0.922 21.12 0.980 4.80 0.920 21.75 0.978 5-30 0.918 22.3 9 0.976 5.80 0.916 23.03 0.974 6.30 0.914 23.68 0.972 6.80 0.912 24.33 0.970 7-3i 0.910 24-99 0.968 7.82 0.908 25.65 0.966 8.33 0.906 26.31 0.964 8.84 0.904 26.98 0.962 9-35 0.902 27.65 0.960 9.91 0.900 28.33 0.958 10.47 0.898 29.01 0.956 11.03 0.896 29.69 0.954 1 1. 60 0.894 30.37 0.952 12.17 0.892 3L05 0. 9 50 12.74 0.890 31-75 0.948 I3-3I 0.888 32.50 0.946 13.88 0.886 33-25 0.944 14.46 0.884 34.10 0.942 15.04 0.882 34-95 206 QUANTITATIVE ANALYSIS TABLE VI DETERMINATION OF LACTOSE BY SOXHLET'S METHOD 1 Milli- grams of copper Milli- grams of lactose Milli- grams of copper Milli- grams of lactose Milli- grams of copper Milli- grams of lactose Milli- grams of copper Milli- grams ol lactose Milli- grams of copper Milli- grams of lactose 100 7 1.6 138 99-8 I 7 6 128.5 214 157-5 252 186.3 101 72.4 139 100.5 177 129.3 2I 5 158.2 253 187.1 102 73-i 140 101.3 I 7 8 I 3 O.I 216 159.0 254 187.9 103 73-8 141 102.0 I 79 130.8 217 J 59-7 255 188.7 104 74.6 142 102.8 1 80 I3I.6 218 160.4 2 5 6 189.4 105 75-3 143 103-5 181 132.4 2I 9 161.2 257 190.2 1 06 76.1 144 104.3 182 I33-I 220 161.9 2 5 8 I9I.O 107 76.8 145 105.1 183 133-9 221 162.7 259 I9I.8 108 77.6 146 105.8 184 134-7 222 163.4 260 192.5 109 78.3 147 106.6 185 135-4 223 164.2 26l J 93-3 IIO 79.0 148 107.3 186 136.2 224 164.9 262 194.1 in 79-8 149 108.1 187 137.0 22 5 165.7 263 194.9 112 80.5 150 108.8 1 88 137-7 226 166.4 264 195-7 H3 81.3 151 109.6 189 138.5 227 167.2 265 196.4 114 82.0 I 5 2 110.3 190 J39-3 228 167.9 266 197.2 II 5 82.7 153 in. i 191 140.0 22 9 1 68. 6 267 198.0 116 83-5 154 111.9 192 140.8 2 3 169.4 268 198.8 117 84.2 155 112. 6 193 141.6 231 170.1 269 199.5 118 85.0 I 5 6 ii3-4 194 142.3 232 170.9 270 200.3 119 85.7 157 114.1 195 I43-I 233 171.6 271 20 1. 1 120 86.4 I 5 8 114.9 196 H3-9 234 172.4 272 201.9 121 87.2 J 59 115.6 197 144.6 235 I73-I 273 202.7 122 87.9 1 60 116.4 198 145.4 2 3 6 173-9 274 203.5 I2 3 88.7 161 117.1 199 146.2 237 174.6 275 204.3 124 89.4 162 117.9 200 146.9 238 175-4 2 7 6 205.1 I2 5 90.1 163 118.6 201 147-7 239 176.2 277 205.9 126 90.9 164 119.4 202 148.5 240 176.9 2 7 8 206.7 127 91.6 165 I2O.2 203 149.2 241 177.7 279 207.5 128 92.4 166 120-9 204 150.0 242 178.5 280 208.3 I2 9 93-i 167 I2I.7 205 150.7 243 179-3 28l 209.1 I 3 93-8 1 68 122-4 206 151.5 244 180.1 282 209.9 131 94.6 169 123.2 207 152.2 245 180.8 283 210.7 I 3 2 95-3 170 123.9 208 i53-o 2 4 6 181.6 284 211.5 133 96.! 171 124.7 209 153-7 247 182.4 285 212.3 134 96.9 172 125.5 210 154-5 2 4 8 183.2 286 213.1 !35 97.6 173 126.2 211 155.2 249 184.0 287 213.9 136 98.3 174 127.0 212 156.0 250 184.8 288 214.7 137 99.1 175 127.8 213 156.7 2 5 I 185.5 289 215.5 1 Principles and Practice of Agricultural Analysis, Vol. Ill, pp. 163-165. APPENDIX 207 TABLE VI Continued Milli- grams of copper Milli- grams ol lactose Milli- grams of copper Milli- grams of lactose Milli- grams of copper Milli- grams of lactose Milli- grams of copper Milli- grams of lactose Milli- grams of copper Milli- grams of lactose 2 9 216.3 312 233-7 334 250.8 356 268.8 378 287.4 2 9 I 2I7.I 313 234-5 335 251.6 357 269.6 379 288.2 2 9 2 217.9 314 235-3 336 252.5 358 270.4 380 289.1 293 218.7 315 236.1 337 253-3 359 271.2 381 289.9 294 219.5 316 236.8 338 254.1 360 272.1 382 290.8 295 220-3 317 237.6 339 254.9 361 272.9 383 291.7 296 221. 1 318 238.4 340 255-7 362 273-7 384 292.5 297 221.9 319 239.2 34i 256.5 363 274.5 385 293-4 298 222.7 320 240.0 342 257.4 3 6 4 275-3 386 294.2 299 223.5 3 2I 240.7 343 258.2 365 276.2 387 295.1 300 301 224.4 225.2 3 22 323 241.5 242.3 344 345 259.0 259.8 366 367 277.1 277.9 388 389 296.0 296.8 302 225.9 324 243.1 346 260.6 368 278.8 39 297.7 o/^Q r 303 226.7 325 243-9 347 261.4 369 279.6 39 l 295.5 34 227.5 326 244.6 348 262.3 370 280.5 VM 300 \ 305 228.3 327 245.4 349 263.1 37i 281.4 394 301.1 306 229.1 328 246.2 350 263.9 372 282.2 395 302.0 307 229.8 329 247.0 351 264.7 373 283.1 39 6 302.8 308 230.6 330 247.7 352 265.5 374 283.9 397 303-7 309 231.4 331 248.5 353 266.3 375 284.8 398 304.6 3 IO 232.2 332 249.2 354 267.2 376 285.7 399 305-4 3" 232.9 333 250.0 355 268.0 377 286.5 400 306.3 TABLE VII DETERMINATION OF DEXTROSE BY ALLIHN'S METHOD 1 Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose 10 6.1 19 10.5 28 15.0 37 19.4 4 6 23-9 II 6.6 20 II.O 29 15-5 38 I 9 . 9 47 24.4 12 7-i 21 II.5 30 16.0 39 20-4 48 24. 9 13 7.6 22 12.0 31 16.5 40 20.9 49 25.4 H 8.1 23 12.5 32 17.0 4i 21.4 50 25.9 15 8.6 24 13-0 33 17-5 42 21.9 5i 26. 4 16 9.0 25 13-5 34 18.0 43 22.4 52 26.9 17 9-5 26 14.0 35 18.5 44 22. 9 53 27-4 18 IO.O 27 14.5 36 18.9 45 23.4 54 27-9 1 Principles and Practice of Agricultural Analysis^ Vol. Ill, pp. 156-158. 208 QUANTITATIVE ANALYSIS TABLE VII Continued Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose 55 28.4 9 6 48.9 137 69.8 I 7 8 9 I.I 2I 9 II2.7 56 28.8 97 49-4 138 70.3 179 91.6 220 II3.2 57 29-3 98 49.9 139 70.8 1 80 9 2.1 221 II3-7 58 29.8 99 50.4 140 71-3 181 92.6 222 II4-3 59 30-3 100 50.9 141 7 1.8 182 93-i 22 3 II4.8 60 30.8 101 51.4 142 72-3 183 93-7 224 H5.3 61 31-3 102 51.9 143 72.9 184 94-2 225 II5. 9 62 31-8 103 52.4 144 73-4 185 94-7 226 Il6.4 63 32.3 104 52.9 145 73-9 1 86 95.2 227 116.9 64 32-8 I0 5 53-5 146 74-4 187 95-7 228 H74 65 33-3 1 06 54.0 147 74-9 188 96-3 22 9 II8.0 66 33-8 107 54-5 148 75-5 189 96.8 2 3 II8.5 67 34-3 108 55.0 149 76.0 190 97-3 231 Iig.O 68 34-8 109 55-5 I 5 76.5 191 97.8 232 II9.6 69 35-3 no 56.0 151 77.0 192 98-4 233 120. 1 70 35-8 III 56.5 I 5 2 77-5 193 98.9 234 120-7 7i 36.3 112 57.0 153 78.1 194 99-4 235 121. 2 72 36.8 H3 57-5 154 78.6 195 100. 2 3 6 I2I.7 73 37-3 114 58.0 155 79.1 196 100.5 237 122.3 74 37-8 II 5 58.6. I 5 6 79.6 197 IOI.O 238 122.8 75 38.3 116 59.1 157 80. i 198 101.5 239 123.4 76 38.8 117 59.6 I 5 8 80.7 199 102.0 240 123.9 77 39-3 118 60. i J 59 81.2 200 102.6 241 1244 78 39-8 119 60.6 1 60 81.7 201 103.1 242 125.0 79 40-3 120 61.1 161 82.2 2O2 103.7 243 125.5 80 40.8 121 61.6 162 82.7 203 104.2 244 126.0 81 41-3 122 62.1 163 83-3 204 104.7 245 126.6 82 41.8 123 62.6 164 83.8 205 105-3 246 I27.I 83 42.3 124 63.1 165 84-3 206 105.8 247 127.6 84 42.8 I2 5 63-7 1 66 84.8 207 106.3 248 I28.I 85 43-4 126 64.2 167 85-3 208 106.8 249 128.7 86 43-9 127 64.7 1 68 85.9 20 9 107.4 250 129.2 87 44-4 128 65.2 169 86.4 210 107.9 251 129.7 88 449 I2 9 65.7 170 86.9 211 108.4 252 130.3 89 45-4 1.30 66.2 171 87.4 212 109.0 253 130.8 90 45-9 131 66.7 172 87.9 213 109.5 254 I3I-4 9i 46.4 132 67.2 173 88.5 214 IIO.O 255 I31'9 92 46.9 133 67.7 174 89.0 215 no. 6 2 5 6 132.4 93 47-4 134 68.2 r 75 89.5 216 in. i 257 133-0 94 47-9 135 68.8 176 90.0 217 in. 6 258 133-5 95 48.4 136 69.3 177 90.5 218 112. 1 259 I34-I APPENDIX 209 TABLE VII Continued Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams of dextrose Milli- grams of copper Milli- grams ol dextrose Milli- grams of copper Milli- grams of dextrose 260 134.6 301 I57.I 342 I7 9 .8 383 203.1 424 226.9 26l I35-I 302 157.6 343 180.4 384 203.7 425 227.5 262 135-7 303 158.2 344 180.9 385 204.3 426 228.0 263 136.2 304 158.7 345 I8I.5 386 204-8 427 228.6 264 136.8 305 159.3 346 I82.I 387 205.4 428 229.2 265 137-3 306 159.8 347 182.6 388 206.0 429 229.8 266 137-8 37 160.4 348 183.2 389 206.5 43 230.4 267 138.4 3 08 160.9 349 183.7 390 207.1 43i 231.0 268 138.9 39 161.5 350 184.3 391 207.7 432 231.6 269 : 39-5 3 IO 162.0 35i 184.9 392 208.3 433 232.2 270 140.0 311 162.6 352 185.4 393 208.8 434 232.8 271 140.6 3 I2 I6 3 .I 353 186.0 394 209.4 435 233.4 272 141.1 313 163.7 354 186.6 395 210.0 436 233-9 273 141.7 3H 164.2 355 187.2 396 210.6 437 234-5 274 142.2 315 164.8 356 187.7 397 211. 2 438 235-1 275 142.8 316 165.3 357 188.3 398 2II-7 439 2357 2 7 6 H3-3 317 165.9 358 188.9 399 212.3 440 236.3 277 143-9 318 166.4 359 189.4 400 212.9 441 236.9 2 7 8 144.4 319 167.0 360 190.0 401 213.5 442 237.5 279 145.0 320 167.5 36i 190.6 402 2I4.I 443 238.1 280 145-5 3 2I I68.I 362 191.1 403 214.6 444 238.7 28l 146.1 322 168.6 363 191.7 404 215.2 445 239-3 282 146.6 .323 169.2 364 192.3 405 215.8 446 239.8 283 147.2 324 169.7 365 192.9 406 2l6.4 447 240.4 284 147-7 325 170.3 366 193-4 407 217.0 448 241.0 285 148.3 326 170.9 367 194.0 408 217.5 449 241.6 286 148.8 327 I7I.4 368 194.6 409 2I8.I 450 242.2 287 149.4 328 172.0 369 195.1 410 218.7 45i 242.8 288 149.9 329 172.5 370 195-7 411 219.3 452 2434 289 I50-5 330 I73-I 37i 196.3 412 219.9 453 244.0 2 9 151.0 331 1737 372 196.8 4i3 220-4 454 244.6 2 9 I 151.6 332 174.2 373 197.4 414 221.0 455 245.2 2 9 2 152.1 333 174.8 374 198.0 4i5 221.6 456 245.7 293 152.7 334 175-3 375 198.6 416 222.2 457 246.3 294 153-2 335 '75-9 376 199.1 4i7 222.8 458 246.9 295 153.8 336 176.5 377 199.7 418 223.3 459 247.5 2 9 6 154.3 337 177.0 378 200.3 419 223.9 460 248.1 297 154.9 338 177.6 379 200.8 420 224.5 461 248.7 298 1554 339 178.1 380 201.4 421 225.1 462 249-3 299 156.0 340 178.7 38i 202.0 422 225.7 463 249.9 300 156.5 34i 179-3 382 202.5 423 226.3 2IO QUANTITATIVE ANALYSIS TABLE VIII LOGARITHMS NATURAL NUMBERS 1 2 8 4 5 6 7 8 9 PROPORTIONAL PART 1 -5 4 r> 7 8 IO 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 4 8 12 17 21 25 2933 II 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 4 8 XX 15 19 23 26 30 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 3 7 IO 14 I 7 21 24 28 13 1139 1173 1206 1239 1271 1335 1367 1399 1430 3 6 IO 1 6 19 2326 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 3 6 9 2 15 18 21 24 15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 3 6 8 I 14 I 7 20 22 16 2041 2068 2095 2122 2148 2175 22OI 2227 2253 2279 3 5 8 I 13 x6 l82I 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2 5 7 O 12 15 17 20 18 2553 2577 2601 2625 2648 2b72 2695 2718 2742 2765 2 5 7 9 12 14 16 19 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 2 4 7 9 II 3 16 18 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 2 4 6 8 II 13 15 17 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 2 4 6 8 IO 12 14 16 22 3424 3444 3464 3483 3502 3522 354i 35 6 3579 3598 2 4 6 8 ro xa 14 15 23 3617 3636 3655 3674 3692 37 11 3729 3747 3766 3784 2 4 6 7 9 XX 13 T 5 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 2 4 5 7 9 ii 12 14 2 5 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 2 3 5 7 9 xo 12 14 26 415 4166 4183 42OO 4216 4232 4249 4265 4281 4298 2 3 5 7 8 xo II 13 27 43H 4330 4346 4362 4378 4393 4409 4425 444 445 6 2 3 5 6 8 9 II 13 28 4472 4487 4502 4518 4533 4548 45 6 4 4579 4594 4609 2 3 5 6 8 9 II 12' 29 4624 4639 4654 4669 4683 4698 47*3 4728 4742 4757 I 3 4 6 7 9 j 10 12 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 I 3 4 6 7 9 10 11 31 4914 4928 4942 4955 4969 4983 4997 5011 5 02 4 5038 I 3 4 6 7 8 10 x" 32 505 1 5065 579 5092 5105 5119 5132 5*45 5159 5172 I 3 4 5 7 8 33 5185 5198 5211 5224 5237 525 5263 5276 5289 53 2 I 3 4 5 6 8 9 10 34 5315 5328 5340 5353 5366 5378 5391 5403 5428 I 3 4 5 6 8 910 35 5441 5453 5465 5478 5490 5502 55'4 5527 5539 5551 I a 4 5 6 7 9 10 36 55 6 3 5575 5587 5599 561 1 5623 5635 5 6 47 5658 5670 X .a 4 5 6 7 8 10 37 5682 5 6 94 5705 5717 5729 5740 5752 57 6 3 5775 5786 I a 3 5 6 7 8 9 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 I a 3 5 6 7 8 9 39 59" 5922 5933 5944 5955 5966 5977 5988 5999 6010 I 2 3 4 5 7 8 9 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 X 2 3 4 5 6 8 9 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 x 2 3 4 5 6 7 8 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 X 2 ;; 4 5 6 7 8 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 I 2 3 4 5 6 7 8 44 6435 6444 6454 6464 6474 6484 6493 6503 65 J 3 6522 I 2 3 4 5 6 7 8 45 6532 6542 6551 6561 657 1 6580 6590 6599 6609 6618 X 2 3 4 5 6 7 8 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 I 2 3 4 3 6 7 7 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 x 2 3 4 5 5 6 7 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 x 2 3 4 4 5 6 7 49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 I 2 3 4 4 5 6 7 50 6990 6998 7007 7016 7024 733 7042 7050 759 7067 I 2 3 3 4 5 6 7 5 1 7076 7084 793 7101 7110 7118 7126 7 J 35 7*43 7152 x 2 3 3 4 5 6 7 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 X 2 2 3 4 5 6 7 53 7243 725 1 7259 7267 7275 7284 7292 7300 7308 73'6 t 3 a 3 4 5 6 6 54 7324 7332 7340 7348 735 6 7364 7372 7380 7388 7396 X 3 2 3 4 5 6 6 APPENDIX 211 TABLE Mill Continued NATURAL NUMBERS 1 2 8 4 5 6 7 8 9 PROPORTIONAL PARTS 1 3 3 4 5 6 7 8 55 7404 7412 74i9 7427 7435 7443 745 i 7459 7466 7474 3 4 5 5 6 56 57 7482 7559 74 ?A 7566 7497 7574 755 7582 75*3 7589 7520 7597 7528 7604 7536 7612 7543 7619 7551 7627 3 3 4 4 5 5 5 6 5 6 58 ' **.*> * 7 6 34 7642 7649 7657 7664 7672 7679 7686 7694 7701 3 4 4 5 6 59 7709 77 l6 7723 773i 7738 7745 775 2 7760 7767 7774 3 4 4 5 6 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 3 4 4 5 6 61 7 8 53 7860 7868 7875 7882 7889 7896 7903 7910 7917 3 4 4 5 6 62 7924 793 * 7938 7945 7952 7959 7966 7973 7980 7987 3 3 4 5 6 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 3 3 4 5 5 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 3 3 4 5 5 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 3 3 4 5 5 66 8i95 8202 8209 8215 8222 8228 8235 8241 8248 8254 3 3 4 5 5 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 3 3 4 5 5 68 8325 8331 8338 8344 835 i 8357 8363 8370 8376 8382 3 3 4 4 5 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 2 3 4 4 5 70 845 r 8457 8463 8470 8476 8482 8488 8494 8500 8506 2 3 4 4 5 7 1 85U 8519 8525 8531 8537 8543 8549 8555 8561 8567 2 3 4 4 5 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 2 3 4 4 5 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 2 3 4 4 5 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 9 3 4 4 5 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 2 3 3 4 5 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 a 3 3 4 5 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 2 3 3 4 4 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 2 3 3 4 4 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 2 3 3 4 4 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 2 3 3 4 4 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 2 3 3 4 4 82 9138 9H3 9149 9*54 9i59 9165 9170 9175 9180 9186 2 3 3 4 4 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 2 3 3 4 4 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 2 3 3 4 4 85 9294 9299 9304 9309 93i5 9320 9325 9330 9335 9340 2 3 3 4 4 86 9345 9350 9355 9360 9365 937 9375 9380 9385 9390 2 3 3 4 4 87 9395 9400 9405 9410 94i5 9420 9425 943 9435 9440 a 2 3 3 4 88 9445 945 9455 9460 9465 9469 9474 9479 9484 9489 2 2 3 3 4 89 9494 9499 954 959 95 J 3 95i8 9523 9528 9533 9538 o 2 2 3 3 4 90 9542 9547 9552 9557 9^62 9S66 9571 957 6 958i 9586 o 2 2 3 3 4 9i 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 2 2 3 3 4 92 (\1 9638 068 c 9643 0680 9647 f\f\c\A 9652 (\f\f\C\ 9657 9*-r\i 9661 CtTlR 9666 r\t-i T -> 9671 f\hj T *7 9675 9680 .-. ^ -, >, o 2 2 3 3 4 yj 94 y u 3 973i yuoy 973 6 yuy4 9741 yyy 9745 7 U O 975 9/ uo 9754 97 J 3 9759 9717 97 6 3 9722 9768 9727 9773 2 2 3 3 4 95 9777 9782 97 86 9791 9795 9800 9805 9809 9814 9818 2 2 3 3 4 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 o 2 2 3 3 4 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 o 2 2 3 3 4 98 9912 9917 9921 9926 993 9934 9939 9943 9948 9952 o 2 2 3 3 4 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 2 2 3 3 3 i ! 212 QUANTITATIVE ANALYSIS TABLE IX ANTILOGARITHMS LOGARITHMS 1 2 3 4 5 6 7 8 9 PROPORTIONAL PART 1 8 3 4 r> (> 7 8 .00 IOOO 1 002 IOOs 1007 1009 IOI 2 1014 1016 IOIQ IO2I .01 1023 1026 *-^ nj j 1028 1030 1033 !035 1038 1040 IO42 1045 o o i i 2 2 .02 1047 1050 1052 1054 1057 1059 1062 1064 1067 1069 O i i 2 2 03 1072 1074 1076 1079 1081 1084 1086 1089 1091 I0 94 o i i 2 2 .04 1096 1099 1 102 1104 1107 1109 III2 1114 III 7 III9 X X 2 2 2 5 1 122 1125 II2 7 1130 1132 "35 1138 1140 H43 1146 o x 2 2 2 .06 i ij.8 iim II r ? ii c6 1 1 cq 1161 1164 1 167 1 169 1 1 72 .07 * **^*-' "75 D* 1178 * j J 1180 j. i^u 1183 * * jy 1186 1189 II9I 1194 1197 11 /* 1199 o X 2 2 2 .08 1202 1205 1208 I2II 1213 1216 1219 1222 I22 5 I22 7 o I a 2 2 .09 1230 1233 1236 1239 1242 1245 1247 1250 1253 1256 X 2 2 2 .10 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 o I 2 2 2 .11 1288 1291 1294 1297 1300 1303 1306 1309 I 3 I2 1315 o 2 2 2 2 .12 I3l8 1321 1324 1327 1330 1334 1337 1340 J 343 J 346 o 2 2 2 2 13 1349 1352 1355 1358 1361 1365 1368 1371 '374 !377 a 2 2 3 .14 1380 i34 1387 1390 1393 1396 1400 1403 1406 1409 2 2 2 3 .15 1413 1416 1419 1422 1426 1429 1432 H35 *439 1442 o 2 2 2 3 .16 1445 1449 H5 2 H55 1459 1462 1466 1469 1472 1476 o 2 2 2 3 .17 H79 1483 1486 1489 H93 1496 1500 I53 i57 1510 2 2 2 3 .18 I5H i5'7 1521 1524 1528 i53i 1535 1538 1542 J 545 2 2 2 3 .19 1549 1552 1556 1560 1563 1567 I S7 1574 1578 1581 2 2 3 3 .20 1585 1589 1592 1596 1600 1603 1607 1611 1614 1618 2 a 3 3 .21 1622 1626 1629 1633 1637 1641 1644 1648 1652 1656 2 2 3 3 .22 1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 2 2 3 3 23 1698 1702 1706 1710 1714 1718 1722 1726 1730 1734 o 2 a 3 3 .24 1738 1742 1746 175 *754 1758 1762 1766 1770 *774 o 2 a 3 3 2 5 1778 1782 1786 1791 !795 1799 1803 1807 1811 1816 2 a 3 3 .26 1820 1824 1828 1832 1837 1841 1845 1849 1854 1858 o 2 3 3 3 .27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 o 2 3 3 3 .28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 o 2 3 3 4 .29 195 1954 1959 1963 1968 1972 1977 1982 1986 1991 o a 3 3 4 30 1995 2OOO 2004 2OO9 2014 2018 2023 2028 2032 2037 2 3 3 4 3 1 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 o a 3 3 4 32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 o 2 3 3 4 33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 o 2 3 3 4 34 2188 2193 2198 22O3 2208 2213 2218 2223 2228 2234 x 3 3 4 4 35 2239 2244 2249 2254 2259 2265 2270 2275 2280 2286 ,x 3 3 4 4 36 2291 2296 2301 2307 2312 2317 2323 2328 2333 2339 I 3 3 4 4 37 2344 2350 2355 2360 2366 2371 2377 2382 2388 2393 X 3 3 4 4 38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 X 3 3 4 4 39 2 455 2460 2466 2472 2477 2483 2489 2495 2500 2506 X 3 3 4 5 .40 2512 2518 2523 2529 2535 2541 2547 2553 2559 2564 X 3 4 4 5 .41 2570 2576 2582 2588 2594 2600 2606 2612 2618 2624 X 3 4 4 5 .42 2630 2636 2642 2649 2655 2661 2667 2673 2679 2685 I 3 4 4 5 43 2692 2698 2704 2710 2716 2723 2729 2 735 2742 2748 I 3 3 4 4 5 44 2754 2761 2767 2 773 2780 2786 2793 2799 2805 2812 I 3 3 4 4 5 45 2818 2825 2831 2838 2844 2851 2858 2864 2871 2877 I 3 3 4 5 5 .46 2884 2891 2897 2904 2911 2917 2924 2931 2938 2944 I 3 3 4 5 5 47 295 * 2958 2965 2972 2979 2985 2992 2999 3006 3013 I 3 3 4 5 5 .48 3020 3027 3034 3041 3048 3055 3062 3069 3076 3083 I 3 4 4 5 6 49 3090 397 3 I0 5 3112 3H9 3126 3133 3*41 3H8 3155 I 3 4 4 5 U APPENDIX 213 TABLE IX Continued LOGARITHMS 1 2 3 4 5 6 7 8 9 PROPORTIONAL PARTS 1 2 3 4 5 G 7 8 5 3162 3*7 377 3184 3192 3199 3206 3214 3221 3228 3 4 4 5 6 5 1 3236 3243 3251 3258 3266 3273 3281 3289 3296 334 3 4 5 5 6 5 2 33ii 33'9 3327 3334 3342 335 3357 33 6 5 3373 338i 3 4 5 5 6 53 3388 3396 344 3412 3420 3428 3436 3443 345 J 3459 3 4 5 6 6 54 3467 3475 3483 3491 3499 3508 35'6 3524 3532 3540 3 4 5 6 6 Ji 3548 3631 355 6 3639 3648 3573 3656 358i 3664 3589 3673 3597 3681 3606 3690 3 6 H 3698 3622 3707 2 3 3 3 4 4 5 5 6 6 7 7 57 37 J 5 3724 3733 374i 375 3758 37 6 7 3776 3784 3793 3 3 4 5 6 7 58 3802 3n 3819 3828 3837 3846 3855 3864 3873 3882 3 4 4 5 6 7 59 3890 3899 3908 3917 3926 3936 3945 3954 3963 3972 3 4 5 5 6 7 .60 398i 3990 3999 4009 4018 4027 4036 4046 4055 4064 3 4 5 6 6 7 *.6i 4074 4083 4093 4102 4111 4121 4130 4140 4 I 5 4159 3 4 5 6 7 8 .62 4169 4178 4188 4198 4207 4217 4227 4236 4246 4256 3 4 5 6 7 8 63 4266 4276 4285 4295 435 4315 4325 4335 4345 4355 3 4 5 6 7 8 1 .64 4365 4375 4385 4395 4406 4416 4426 4436 4446 4457 3 4 5 6 7 8 65 4467 4477 4487 4498 4508 45 T 9 4529 4539 4550 4S6o 3 4 5 6 7 8 .66 457 1 458i 4592 4603 4613 4624 4634 4645 4656 4667 3 4 5 6 7 9 .67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 3 4 5 7 8 9, .68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 3 4 6 7 8 .*! .69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 3 5 6 7 8 9 .70 5012 5023 5035 547 5058 5070 5082 593 5 I0 5 5"7 4 5 6 7 8 9 7i 5129 5 HO 5152 5 l6 4 5*7 6 5188 5200 5212 5224 5236 4 5 6 7 8 10 .72 5248 5260 5272 5284 5297 5309 532i 5333 5346 5358 4 5 6 7 9 10 73 5370 5383 5395 5408 5420 5433 5445 5458 547 5483 3 4 5 6 8 g 10 74 5495 5508 552i 5534 5546 5559 5572 5585 5598 5610 3 4 5 6 8 9 10 75 5623 5636 5 6 49 5662 5 6 75 5689 5702 5715 5728 574i 3 4 5 7 8 9 to .76 5754 5768 578i 5794 5808 5821 5834 5848 5861 5875 3 4 5 7 8 s XX 77 5888 5902 59i6 5929 5943 5957 597 5984 5998 6012 3 4 5 7 8 1C ii .78 6026 6039 6053 6067 6081 6095 6109 6124 6138 6152 3 4 6 7 8 10 ii 79 6166 6180 6194 6209 6223 6237 6252 6266 6281 6295 3 4 6 7 9 10 ii .80 6310 6324 6339 6353 6368 6383 6397 6412 6427 6442 3 4 6 7 9 10 12 .81 6457 6471 6486 6501 6516 6531 6546 6561 6577 6592 3 3 6 8 9 II 12 .82 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 3 5 6 8 9 II xa 83 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 3 5 6 8 9 II 13 .84 6918 6934 6950 6966 6982 6998 7015 73i 7047 7063 3 5 6 8 10 II 13 .85 7079 7096 7112 7129 7H5 7161 7178 7194 7211 7228 3 5 7 8 IO 12 X 3 .86 7244 7261 7278 7295 73ii 7328 7345 7362 7379 7396 3 5 7 8 10 12 13 .87 7413 7430 7447 7464 7482 7499 75i6 7534 755i 7568 3 5 7 9 IO 12 M .88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 4 5 7 9 II 12 J 4 .89 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 4 5 7 g II 13 14 .90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 4 6 7 9 II 13 *5 .91 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 4 6 8 g II 13 s .92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 4 6 8 10 12 *4 15 93 8511 8531 855i 8570 8590 8610 8630 8650 8670 8690 4 6 8 10 12 M 16 94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 4 6 8 10 12 14 16 95 8913 8933 8954 8974 8995 9016 9036 9057 9078 9099 4 6 8 10 12 5 i? .96 9120 9141 9162 9183 9204 9226 9247 9268 9290 93" 4 6 8 II 13 5 7 97 9333 9354 9376 9397 9419 9441 9462 9484 9506 9528 4 7 9 II 13 5 17 .98 9550 9572 9594 9616 9638 9661 9683 9705 9727 9750 4 7 9 II 13 6 18 99 9772 9795 9817 9840 | 9863 9886 9908 993i 9944 9977 5 7 9 11 14 6 18 214 QUANTITATIVE ANALYSIS TABLE X COMBINING AND ATOMIC WEIGHTS 1907 Aluminium . . . . Al . . . Sb = 16. 27.1 I2O 2 Neodymium . . Neon . . Nd Ne 0=16. 143.6 Argon . ... A Nickel Ni Arsenic ... As 7C.O Nitrogen . . . N l2t oi Barium . . Ba 1 77 4. Osmium Os . . . Bi 2O8.O Oxvsren . . O 1 6 oo Boron . . . . B I I.O Palladium . . . Pd 1 06 c Bromine . . . . Br 7Q.O.6 Phosphorus . . P Cadmium . . . . Cd 1 12.4. Platinum . . . . Pt TQ/1 8 Caesium . . . . Cs Potassium K Calcium . . . . . Ca 4.O I Praseodymium . . Pr I4.O C Carbon . . . . . C 12 OO Radium Rd 22C Cerium . . . . . Ce I4O 2C Rhodium . Rh IO7 O Chlorine . . Cl Rubidium Rb Chromium Cobalt . . . Cr ... Co 52.1 Ruthenium . . Samarium . . Ru Sa IOI-7 Columbium . . Cb 59 Scandium Sc 4.4. I Copper . Cu 67 6 Selenium Se Erbium Er 1 66 Silicon Si 28 4 Europium . . . . . Eu I C2 Silver . . . Ag IO7. Q7 Fluorine . .. . . . F IQ.O Sodium "& . . Na Gadolinium . . . . Gd u6 Strontium . . . . . Sr 87.6 Gallium . . . . Ga 2^1 7O Sulphur . . . . . S 72.O6 Germanium . Glucinum . . . Ge . . . Gl 72.5 9 * Tantalum . . . Tellurium . . Ta . . Te 181 127.6 Gold Au I Q7 2 Terbium . . Tb I CQ-2 Helium . . He 4. O Thallium . . . . . Tl 2O4.. I Hydrogen . . H I OO8 Thorium . . . . . Th 272. C Indium In IIC Thulium . . . . Tm 171 Iodine I ii J 126 Q7 Tin . . . Sn I IQ.O Iridium Ir Titanium . . Ti 4.8.1 Iron Fe 93 Tungsten . . . W 184. Krypton Kr 81 8 Uranium . . U 278. c Lanthanum . Lead ... La Pb 138.9 206 9 Vanadium . . Xenon . . . V . . Xe 51.2 128 Lithium Li 7 07 Ytterbium . . . . . Yb 177.0 Magnesium . Manganese . . . Mg . . Mn 24.36 p p O Yttrium . . . . . Yt . . Zn 89.0 6c.4 Mercury . . HP 2OO O Zirconium . . . . Zr QO.6 Molybdenum . iA & . . .Mo 96.0 ANSWERS TO PROBLEMS 1. Na 2 CO 3 . 2. K 2 PtCl 6 . 3. K 2 CrO 4 . 4. (NH 4 ) 2 MoO 4 . 5. C 4 H 6 6 . 6. Zn 40.51 per cent. ZnO 50.41 per cent. 7. Fe 14.25 per cent. FeO 18.33 P er cen t- S 16.35 P er cen t- SO 3 40.83 per cent. H 2 O 27.56 per cent. 8. ZnO 53.41 per cent. P 2 O 5 46.59 per cent. 9. CaO 48.15 per cent. SiO 2 51.85 per cent. 10. a. 0.8999 gram. b. 0.2784 gram. 0.6376 gram. c. 0.4562 gram. d. 0.2 1 14 gram. ' -7357 g ram / I-I397 g rams - 11. 0.5475 gram. 12. 0.4113 gram. 13. 0.5412 gram. 14. 0.6169 gram. 15. 54.79 per cent. 16. 98.02 per cent. 17. 11.90 per cent. 18. K 1.93 per cent. Na 4.46 per cent. 19. Ca 0.2257 gram. Mg 0.1840 gram. 20. PbO 1.0637 grams. BaO 0.5613 gram. 21. 8.98 per cent. 22. 3.06 c.c. 23. 165.83 c.c. 24. 3.04 c.c. 25. 4.30 c.c. 26. 91.87 per cent. 27. 96.23 per cent. 28. 99.93 per cent. 29. Na 2 O 61.70 per cent. NaOH 47.07 per cent. Na 2 COs 43.06 per cent. 30. 14.47 per cent. 31. 69.43 per cent. 32. 22.74 per cent. 33. 29.59 per cent. 34. 2.27 c.c. 35. Normal. 36. 0.9778 Normal. 37. 666.5 grams. 38. 13.66 per cent. 39. a. 0.001256 gram; 11.370.0. b. 0.001249 g ram > 11.46 c.c. c. 0.001259 gram; 11.370.0. 40. 99.61 per cent. 41. 99.63 per cent. 42. CaO 50.43 per cent. 43. a. 0.0007943 gram; 18.02 c.c. b. 0.0007966 gram; 17.97 c.c. 44. a. 0.0138 gram of Oxygen per c.c. b. 2.93 per cent H 2 O 2 . 45. 0.01061 gram. 46. a. 0.01230 gram. b. 0.09687 Normality Factor. 47. 24.48 per cent. 2I 5 216 ANSWERS 48. 67.25 per cent. 49. 0.01051 gram. 0.08275 Normality Factor. 50. 0.4120 gram. 51. 0.3285 gram. 52. 0.5259 gram. 53. 0.4378 gram. 54. K 2 SO 4 0.3543 gram. Na2SC>4 0.7457 gram. 55. For o.i per centP, 0.2784 gram. For 0.2 per cent P2Os, 0.3195 gram. 56. 4.46 c.c. 57. FeO 2.66 per cent. A1 2 O 3 14.89 per cent. P 0.501 per cent. 58. 81.85 per cent. 59. 0.1045 g ram - 60. 674.7 c.c. 61. 5.65 c.c. 62. 1.15 c.c. 63. a. 15.45 grams. b. 3016.5 c.c. 64. 1.226 Normality Factor. 65. a. 0.1534 Normality Factor. b. 0.3851 gram. 66. 5.21 per cent. 67. 43.23 per cent. 68. 14.95 Reichert-Meissl Number. 69. 206.0 Saponification Number. 70. 1.83 per cent. 71. 26.05 P er cent . 72. 87.50 per cent. 73. o.i 6 per cent too low. 74. 0.000252 gram per c.c. 75. 0.5018 gram. 76. 1039.6 c.c. 77. a. 28.21 per cent. b. 22.289 grams. 78. a. 44.54 per cent. b. 0.5724 gram Fe. 0.6453 gram Oxalic Acid. 79. 35-35 Iodine Absorption Number. 80. 0.1145 gram. INDEX Acidimetry, 51. Acids, specific gravity, tables of, 203. Adams paper coil method for fat in milk, 88. Alkalimetry, 51. Allihn's method for carbohydrates, 124. Aluminium, determination of, 37. in soils, 150. Ammonia, specific gravity, tables of, 205. Answers to problems, 215-216. Antilogarithms, table of, 212-213. Available oxygen, 65. Babcock method for fat in milk, 90. Balance, 16-20. exercises with, 22-23. Balancing equations, 178. Bleaching powder, estimation of available chlorine in, 82. Books of reference, 195. Bumping, 9, 156. Butter, analysis of, 100-118. Calcium, determination of, 32, 73, 152. separation from magnesium, 33. Calibration, of burettes, 45. curve, 48. Carbohydrates in cereals, 120, 123. Carbon dioxide, determination of, 156. Caustic alkali, determination of, 66. Cereals, 119. Chlorine, determination of, 24/82, 102. Clerget's inversion method for sucrose, 124. Crucibles, 14. Gooch, 57, 58. Desiccators, 5. Desk, equipment, 202. reagents, concentration of, 196. Dextrin, determination of, 125. Dextrose, determination of, 124, tables for 207, 209. Diastase method for starch, 126. Empirical formula, 162. End point, 52. Factor weights, calculation of, 189. Factors, 165. Fat, in milk, 88, 92. in butter, composition of, 103. Fatty acids, determination of, no, 112, "3- Feeding materials, analysis of, 119, 122. Fertilizers, analysis of, 130. Filtration, 12. by means of suction, 37. Gravimetric analysis, 22. calculations for, 163. Humus, 154. Hydrogen peroxide, purity of, 73, 84. Indicators, 32. Indirect methods, calculation for, 167. lodimetry, 78. calculations for, 187. Iodine absorption number, determination of, 1 1 6. Iron, determination of, 74, 77, 150, 153. Jones reductor, 70. Kjeldahl method for nitrogen, 94, 129, 138. Lactometers, 87. Lactose, by Soxhlet's method, table for, 206. Logarithms, table of, 210-211. Magnesium, determination of, 33, 152. Manganese, determination of, 151. Milk, analysis of, 85. Nitrogen, determination of, 138, 155. Normal solutions, 49, 50. 217 218 INDEX Normality factor, 59. Notebooks, 2, 53. Oleomargarine, 105, 115, 118. Operations of quantitative analysis, 6-14. Oxalates, determination of purity of, 72. Oxidation and reduction, calculations for, 178-185. Oxidation processes, 64. Percentage composition, calculation of, 162. Phosphorus, determination of, 132, 136, 15, 151- Platinum, care of, 15. Potassium, determination of, 140, 153. Precipitates, colloidal, 12. crystalline, n. drying and ignition of, 14. Precipitation, 10. Problems, 162, 163, 166, 168, 171, 177, 1 86, 1 88, 190. Proteids, 94, 129. Pyrolusite, determination of available oxy- gen in, 83. Questions on equations, 183, 188. Reagents, 4. laboratory, table of, 196-201. Saliva method for starch, 127. Sampling, 6, 86, 101, 121, 131, 145. Saponification numbers, 114. Siderite, determination of iron in, 74, 77. Silica, 148. Sodium, determination of, 153. Soil, analysis of, 142. constituents of, 142, 145. Solutions, normal, 49. preparation for iodimetry, 79. for oxidation and reduction, 67, 79. standard, 49. Specific gravity, 170. of butter fat, 106. Standardization of solutions, acid, 57, 62. alkali, 59. iodine, 80. methods of, 54. potassium dichromate, 76. potassium permanganate, 68. Starch, 125, 127. Stirring rods, 6. Stoichiometry, 161. Stone's method for carbohydrates, 123. Sucrose, 124. Sulphur, determination of, 29, 152. Titration, 52. of acid against the alkali, 56. Volumetric analysis, 40. apparatus, 40, 41. calibration of, 42. calculations, 171. Wash bottles, 6. Washing of precipitates, 13. Weighing, precautions in, 20. STANDARD BOOKS ON CHEMISTRY PUBLISHED BY THE MACMILLAN COMPANY ABEGG AND HERZ. Practical Chemistry : An Experimental Introduction to Labo- ratory Practice and Qualitative Analysis from a Physico-Chemical Standpoint. By R. ABEGG and W. HERZ, of the University of Breslau. Authorized translation by H. B. Calvert, B.Sc. (Vic.), A.I.C. With Three Tables. 12 + 118 pages, I2mo, cl., $1.50 net ARRHENIUS. Immunochemistry. 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