IPRARY NIVERSITY OF CAUfOtNIA/ ARTHUR 8. EAfiULfi PRINCIPLES OF QUANTITATIVE ANALYSIS AN INTRODUCTORY OOU.KSE . .V BY WALTER C. BLASDALE, PH.D. Associate Professor of Chemistry in the University of California SECOND EDITION REVISED AND ENLARGED THIRD THOUSAND 70 ILLUSTRATIONS NEW YOKK D. VAN NOSTRAND COMPANY 25 PARK PLACE 1918 Geoi. dept. COPYRIGHT, 1914, 1917, BY D. VAN NOSTRAND COMPANY Stanbope flbreas F. H. GILSON COMPANT BOSTON, U.S.A. PREFACE TO THE SECOND EDITION THE changes which have been made in preparing the second edition of this book, aside from the rectification of the typographi- cal errors which crept into the first edition, are relatively few. Certain sections, which experience in the use of the book had shown to be too condensed, have been expanded and the material in certain other sections has been rearranged or entirely rewritten. Many of the problems have been modified or others believed to be more instructive have been substituted. The suggestions made by a number of instructors who have used the book that answers to the problems be given, has been acted upon and answers to many of the more complex numerical problems are now included. The results obtained in the use of the book have confirmed the author in his belief that the statements made in the preface to the first edition are correct and that the method of presenting the subject of quantitative analysis which has been adopted is an improvement over that heretofore in general use, at least where students of a sufficient degree of maturity are concerned and where the training which it is desired to give them is not of a specialized character. W. C. B. BERKELEY, CALIFORNIA October, 1916. 819468 iii PREFACE TO FIRST EDITION THE introductory course in quantitative analysis is expected to meet a variety of needs. For a limited number of students it represents the beginning of a course of training which ultimately leads to the ability to do effective work as a professional analyst. For others it represents merely one of the necessary features of the training, which every student who aspires to the title of chemist must complete. For still others < the object to be gained is a general survey of the methods of quantitative analysis, and the ability to comprehend and make intelligent use of the results obtained by it, especially as applied to the various branches of both pure and applied science. Some of the other difficulties which arise in presenting the sub- ject are, the limited amount of time which can be devoted to it; the large amount of personal supervision and assistance which should be given each student, if he is to acquire the necessary manipulative skill with the least expenditure of time and effort; and the inability of the instructor to furnish the student with an adequate supply of platinum ware and of many of the conven- iences and special forms of apparatus, with which it is desirable the student should become acquainted. In this book the attempt has been made to meet these difficulties by outlining the entire field covered by the subject; that is, by presenting it from the standpoint of a comprehensive scheme of classification, which is based upon the different types of chemical and physical equilibrium. By adopting this method of presentation it becomes readily possible to discuss the theory of all classes of quantitative processes from the point of view of modern theoretical chemistry, which forms the only logical basis for effective work in analytical chemistry, and incidentally to vi PREFACE add to the student's experience in dealing with the factors which affect equilibrium. After the general theory underlying each type of process has been presented, a number of examples designed to illustrate it are discussed and described in detail. The number outlined is larger than can be made use of in the introductory course usually given, but can be reduced to a single illustration from each class if necessary. Altho especial emphasis has been placed upon its theoretical features, the fact that the subject is essentially a practical one, and that the student's interest is most easily main- tained when he is required to solve practical problems, the results of which cannot be foretold, has not been lost sight of. Hence a large number of the illustrations chosen are practical problems, which have been selected from a variety of fields and which are solved by the use of methods employed in practical work. It is assumed that as far as possible, individual samples, whose compo- sition is known only to the instructor, will be given out for these determinations. In the development of these illustrations, the attempt is made to make use of as great a variety of principles and methods of procedure as possible, and to develop the student's ability to make use of them by assigning for solution a series of questions and problems; those outlined are offered as suggestions only, and should be modified from year to year. It is scarcely necessary to add that most of the ideas which have been made use of are not new. Especial acknowledgment should be made to Ostwald, whose "Grundlagen der analytischen Chemie" represents the first attempt to summarize those features of theoretical chemistry which can be most profitably applied to analytical chemistry. Acknowledgment of some of the other sources of information will be found in the text, but the limitation imposed on the size of the book has made it impossible to ac- knowledge all of them. ^ Q g BERKELEY, CAL. July 1, 1914. TABLE OF CONTENTS PAGE PREFACE TO THE SECOND EDITION iii PREFACE TO THE FIRST EDITION V CHAPTER I. INTRODUCTORY STATEMENTS AND DEFINITIONS 1 Section One. General Features of Gravimetric Processes II. THE METHOD OF WEIGHING 9 I. Theory of the Use of the Balance. II. Rules for the v / Use of the Balance. III. Details of Procedure for Determina- tion of Point of Rest. IV. Details of Procedure for Determina- tion of Weight of a Watch Glass. V. Details of Procedure for Calibration of a Set of Weights. VI. Questions and Problems, Series 1. III. PREPARATION OF THE SUBSTANCE FOR ANALYSIS 26 IV. THE NATURE AND PROPERTIES OF SOLUTIONS 31 V. THE FACTORS WHICH DETERMINE EQUILIBRIUM 42 VI. THE CHEMICAL ACTIVITY OF ELECTROLYTES 49 VII. METHODS OF PRODUCING AND APPLYING HEAT 61 VIII. THE REMOVAL OF UNDESIRABLE CONSTITUENTS BY EVAPO- RATION 68 IX. THE CALCULATION OF RESULTS 74 Section Two. Gravimetric Gas-evolution Processes X. GENERAL FEATURES OF GAS-EVOLUTION PROCESSES 81 XI. DETERMINATION OF WATER IN GYPSUM 90 I. Facts upon Which the Determination Is Based. II. Details of the Method of Procedure. III. Further Details Re- garding the Determination. IV. Questions and Problems, Series 2. vii Viii TABLE OF CONTENTS CHAPTER P AGE XII. DETERMINATION OF WATER IN CRYSTALLIZED COPPER SUL- FATE 96 I. Facts Upon Which the Determination Is Based. II. Construction of the Apparatus. III. Details of the Method of Procedure. IV. Questions and Problems, Series 3. XIII. DETERMINATION OF CARBON DIOXIDE IN LIMESTONE 103 I. Facts Upon Which the Determination Is Based. II. Preparation of the Apparatus. III. Details of Method of Pro- cedure. IV. Questions and Problems, Series 4. XIV. DETERMINATION OF CARBON DIOXIDE IN BAKING POWDER. 107 I. Facts Upon Which the Determination Is Based. II. Construction of the Apparatus. III. Outline of Method of Pro- cedure. IV. Questions and Problems, Series 5. XV. DETERMINATION OF MERCURY IN AN ORE Ill I. Facts Upon Which the Method Is Based. II. Outline of Method of Procedure. III. Questions and Problems, Series 6. Section Three. Gravimetric Precipitation Processes XVI. GENERAL THEORY OF PRECIPITATION PROCESSES 115 XVII FILTERING, WASHING AND IGNITING PRECIPITATES 122 XVIII. THE PHENOMENA OF OCCLUSION 133 XIX. GENERAL THEORY OF ELECTROYLTIC SEPARATIONS 141 XX. DETERMINATION OF CHLORINE IN SODIUM CHLORIDE 154 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. III. Questions and Problems, Series 7. XXI. DETERMINATION OF MAGNESIUM IN MAGNESIUM SULPHATE. 159 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. III. Questions and Problems, Series 8. XXII. DETERMINATION OF IRON IN FERROUS AMMONIUM SULPHATE. 163 I. Facts Upon Which the Determination Is Based. II. Details of Method of Procedure. III. Questions and Problems, Series 9. TABLE OF CONTENTS ix CHAPTER PAGE XXIII. DETERMINATION OF SULFUR IN PYRITES 168 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. III. Additional Notes on the Determination. IV. Questions and Problems, Series 10. XXIV. SEPARATION OF CALCIUM FROM MAGNESIUM AND PARTIAL ANALYSIS OF LIMESTONE 175 I. Preliminary Statements, Facts Upon Which the Analysis Is Based. III. Outline of Method of Procedure. IV. Questions and Problems, Series 11. XXV. ANALYSIS OF ALLOYS CONTAINING TIN AND LEAD 184 I. Facts Upon Which the Analysis Is Based. II. Outline of the Method of Procedure. III. Questions and Problems, Series 12. XXVI. THE ANALYSIS OF BRASS 189 I. Facts Upon Which the Analysis Is Based. II. Out- line of Method of Procedure. III. Questions and Problems, Series 13. XXVII. DETERMINATION OF SILICA IN A HORNBLENDE 194 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. Section Four. Gravimetric Solution and Extraction Processes XXVIII. GENERAL FEATURES OF SOLUTION AND EXTRACTION PROC- ESSES 199 XXIX. DETERMINATION OF POTASSIUM IN CRUDE POTASSIUM SUL- FATE 209 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. III. Questions and Problems, Series 14. XXX. DETERMINATION OF CRUDE FAT IN PEANUTS 214 I. Facts Upon Which the Method Is Based. II. Out- line of Method of Procedure. XXXI. ANALYSIS OF BLACK POWDER 218 I. Facts Upon Which the Analysis Is Based. II. Out- line of Method of Procedure. X TABLE OF CONTENTS Section Five. Partition Processes CHAPTER PAGE XXXII. GENERAL FEATURES OF PARTITION PROCESSES 220 XXXIII. DETERMINATION OF NICKEL IN NICKEL STEEL 225 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. III. Questions and Problems, Series 15. XXXIV. DETERMINATION OF CAFFEINE IN TEA 230 I. Facts Upon Which the Determination Is Based. II. Outline of Method of Procedure. III. Questions and Problems, Series 16. Section Six. General Features of Volumetric Processes XXXV. THEORY OF VOLUMETRIC PROCESSES 234 XXXVI. MEASUREMENT OF SOLUTIONS USED 240 I. Sources and Methods of Avoiding Errors. II. Details of Method for Calibration of Volumetric Apparatus. III. Ques- tions and Problems, Series 17. XXXVII. SYSTEMS USED IN THE PREPARATION OF STANDARD SOLU- TIONS 251 Section Seven. Volumetric Processes Involving Precipitation XXXVIII. DETERMINATION WHICH DEPEND UPON THE USE OF A STANDARD SOLUTION OF SILVER NITRATE 256 I. Theory Upon Which the Methods Depend. II. Prep- aration and Standardization of a One-tenth Normal Solution of Silver Nitrate. III. Determination of Chlorine in Kainite. IV. Determination of Chlorine in Tap Water. V. Determination of Potassium Cyanide in Commercial Cyanide. VI. Questions and Problems, Series 18. XXXIX. DETERMINATION OF ZINC BY MEANS OF A SOLUTION OF POTASSIUM FERROCYANIDE 268 I. Theory Upon Which the Method Depends. II. Ap- plication of the Method to the Analysis of Zinc Ores. III. Out- line of Method for the Preparation and Standardization of the Ferrocyanide Solution. IV. Outline of Method for Determina- tion of Zinc in an Ore. V. Questions and Problems, Series 19. TABLE OF CONTENTS XI Section Eight. Volumetric Processes Involving Neutralization CHAPTER PAGE XL. GENERAL THEORY OF NEUTRALIZATION PROCESS 278 XLI. APPLICATIONS OF THE METHODS OF ACIDIMETRY AND ALKA- LIMETRY 292 I. Determination of Acids and Acid Salts. II. Deter- mination of Bases and Basic Salts. III. Determination of Salts of Weak Acids and Bases. IV. Indirect Determinations. V. Questions and Problems, Series 20. XLII. THE PREPARATION OF STANDARD SOLUTIONS OF ACIDS AND BASES 300 I. Factors to be Considered. II. Outline of Method for Preparation of Semi-normal Acid and Alkali. III. Experiments with Indicators. IV. Questions and Problems, Series 21. XLIII. DETERMINATIONS WITH A STANDARD ACID AND BASE 306 I. Determination of the Strength 'of Concentrated Sul- furic Acid. II. Determination of the Acidity of Vinegar. III. Determination of Potassium Bitartrate in Argol. IV. Deter- mination of Boric Anhydride in a Natural Borate. V. The Analysis of Commercial Alkalies. VI. Determination of Crude Protein in Flour. VII. Questions and Problems, Series 22. Section Nine. Volumetric Processes Involving Oxidation XLIV. GENERAL FEATURES OF PROCESSES INVOLVING OXIDATION 314 XLV. DETERMINATIONS WITH POTASSIUM PERMANGANATE 322 I. Potassium Permanganate as an Oxidizing Agent. II. Preparation and Standardization of a Permanganate Solution. III. Determination of Iron in Cast Iron. IV. Determination of Potassium Nitrite in the Commercial Salt. V. Determination of Calcium in Limestone. VI. Questions and Problems, Series 23. XL VI. DETERMINATIONS WITH POTASSIUM DICHROMATE 336 I. Potassium Dichromate as an Oxidizing Agent. II. Preparation and Standardization of a Dichromate Solution. III. Determination of Iron in an Ore. VI. Determination of Chrom- ium in Chromite. V. Questions and Problems, Series 24. Xll TABLE OF CONTENTS CHAPTER PAGE XLVII. DETERMINATIONS WITH IODINE AND SODIUM THIOSUL- FATE 347 I. General Features of lodometric Processes. II. Clas- sifications of lodometric Processes. III. Outline of Method for Preparation of Solutions. IV. Determination of Arsenic in Paris Green. V. Determination of Copper in Brass. VI. Determina- tion of Copper in a Cholcopyrite Ore. VII. Questions and Prob- lems, Series 25. Section Ten. Physico-chemical Processes XLVIII. THEORY OF PHYSICO-CHEMICAL METHODS 358 XLIX. PROCESSES BASED UPON THE DETERMINATION OF THE SPECIFIC GRAVITY OR SPECIFIC VOLUME OF SOLIDS OR LIQUIDS 365 I. General Features of the Method. II. Analysis of a Lead-tin Alloy. III. Determination of Sulfuric Acid in a Com- mercial Sample. IV. Determination of the Specific Gravity of Crude Petroleum. V. Questions and Problems, Series 26. L. COLORIMETRIC PROCESSES 378 I. General Features of Colorimetric Processes. II. De- termination of Manganese in Cast Iron or Steel. III. Deter- mination of Copper in a Copper Slag. APPENDICES 389 I. Table of Logarithms. II. Table of Specific Gravities of Sulfuric Acid. III. List of Apparatus Needed. QUANTITATIVE CHEMICAL ANALYSIS CHAPTER I INTRODUCTORY STATEMENTS AND DEFINITIONS Importance of Quantitative Analysis. Quantitative analysis has for its object the determination of the quantity of some element or compound present in a particular substance. The result of the determination is usually expressed as a percentage, ordinarily by weight, but sometimes by volume, of the substance concerned. The subject is of importance from a number of standpoints. An accurate evaluation of most of the important objects of com- merce, and determination of their fitness for certain purposes, cannot be made until their quantitative composition has been determined. In many manufacturing industries the raw products used are purchased, and the finished products obtained are sold, on the basis of the results shown by their analysis; further, the entire process of manufacture is often controlled by means of analyses of the various products, for such analyses enable the manufacturer to determine whether each of the various stages of the process have been properly carried out, and to reduce wastes and losses to a minimum. In the study of many branches of natural science the investiga- tor is often obliged to depend upon quantitative analyses for the identification and comparison of the substances with which he is concerned, and is frequently enabled to trace the laws which govern the changes taking place in these substances thru the study of the results of their analysis. The present science of chemistry 1 2 QUANTITATIVE CHEMICAL ANALYSIS is based very largely upon the employment of quantitative methods in the study of chemical changes; the sciences of geology and physiology have been very largely developed by the use of data gathered thru the employment of quantitative methods. The subject has also a certain educational value, in that it concentrates the attention of the student upon a limited number of chemical transformations; teaches him to observe critically all of the changes which take place in the material with which he is dealing, and to devise methods of avoiding certain undesirable effects and take advantage of others which are desirable. Range of the Subject. It is evident from the preceding para- graphs that the field of quantitative analysis extends over an extremely wide range of subjects, for the analyst may be called upon to determine the quantitative composition of any material object whatever. The analysis of substances containing a number of constituents often presents a problem of much complexity, and much ingenuity has been used in devising methods, which can be employed to determine those elements and compounds, that are of importance from either a practical or scientific standpoint, with the requisite accuracy and with the minimum expenditure of time and effort. The acquirement of a working knowledge of even the more important of these methods is a task of considerable mag- nitude, and the subject forms one of the most comprehensive branches of the science of chemistry. Types -of Quantitative Processes. A sufficiently comprehen- sive and entirely satisfactory classification of all the methods included under the general head of quantitative analysis is not easily formulated. All of the more important methods in general use may be grouped under four classes, which differ so fundamen- tally in method of procedure that it is desirable to discuss them separately. Gravimetric methods are those in which the determination is effected by the actual separation of the desired constituent, or some product which bears a definite quantitative relation to it, INTRODUCTORY STATEMENTS AND DEFINITIONS 3 and the determination of the weight of the product thus separated. Thus the silver can be determined in an alloy by dissolving a definite weight of the alloy in nitric acid, separating the silver present as insoluble silver chloride, weighing the latter, and calcu- lating the weight of silver present from the factor representing the ratio of the atomic weight of silver to the molecular weight of silver chloride. The distinguishing feature of all gravimetric processes is the mechanical separation of a product, the weight of which bears a known relation to the weight of the substance which is being determined, from the substance being analyzed. Such separations are possible only when there are definite surfaces, which represent the limits of the spaces occupied by the separated substance on the one hand, and the residual mixture on the other. Expressed in the language of modern theoretical chemistry every gravimetric process involves a series of chemical and physical operations, which bring about such changes in the original substance that a new " phase" separates, the term phase being used to designate a mass of matter which is physically and chemically homogeneous. In the illustration cited the separated phase took the form of a solid ; it might have taken the form of a gas, or of a second liquid, which does not mix with the first, and a logical and convenient basis for the classification of gravimetric processes is found in the type of " phase-transf ormation " which they represent. Such a scheme has been adopted in this book, and separate sections are devoted to "gas evolution processes," in which a new gas phase is made to separate from a solid or liquid; " precipitation processes," in which a new solid phase is made to separate from a liquid; "solution and extraction processes," in which a new liquid phase is made to separate from a solid; and "partition processes," in which a new liquid phase is made to separate from a liquid phase. Volumetric methods are those in which the amount of substance to be determined is estimated by measuring the volume of some reagent of known concentration, which must be used to completely 4 QUANTITATIVE CHEMICAL ANALYSIS transform the constituent being determined into some other form. The actual separation of a particular product is thereby avoided. Thus the silver can also be determined in the alloy by measuring the amount of sodium chloride solution of known strength which must be added to a solution containing a known weight of the alloy to precipitate all of the silver as chloride. Volumetric processes are conveniently classified with respect to the type of reaction upon which they are based; the three important classes are made the subject of separate sections of this book. Physico-chemical methods are those in which the unknown substance is determined by measuring some one of the various physical properties of a solution containing a known concentration of the sample under investigation, and comparing with the corre- sponding properties of solutions containing known concentrations of the substance to be determined. They are of rather restricted application, and are not strictly speaking chemical processes, but they are so frequently used by the analytical chemist that it is customary to group them with these. Gas-analysis methods which are based upon the direct measure- ment of gas volumes form still a fourth group. They are used not only for the analysis of gaseous mixtures but also for the deter- mination of a large number of substances which yield gaseous products when submitted to the action of certain reagents. The successful use of these methods demands the employment of a large amount of specialized forms of apparatus; it has not been thought desirable to consider them in this book. The Training and Skill Required. Success in quantitative work demands first of all a certain amount of dexterity in perform- ing the mechanical operations involved. Training of the hand and eye, which results in the formation of habits of deftness and precision in manipulation is an essential prerequisite to work in this field. Certain individuals are able to acquire this skill with comparative ease, but, unfortunately, by far the great majority of persons can acquire it only thru patient and persistent appli- INTRODUCTORY STATEMENTS AND DEFINITIONS 5 cation. The beginner cannot be expected to do as rapid or as accurate work as the trained analyst, and only actual experience with a great variety of quantitative processes will teach the most effective methods of dealing with the problems which constantly arise in the execution of quantitative work and enable him to reduce to a minimum those errors of the process which depend upon manipulative skill. Absolute Honesty Demanded. Of the many qualifications which the successful analyst must possess none equals in impor- tance that of unimpeachable honesty. It is unnecessary to con- demn or to point out the ultimate effect of the intentional falsifi- cation of the results obtained in any line of scientific work to any intelligent student; but even when there is no desire to misrepre- sent, care must be taken to overcome any temptation which may arise to pick and choose results on the basis of some preconceived notion of their comparative accuracy. If, for example, a number of results have been obtained with the same process, the fact that some one of these agrees most nearly with what is supposed to be the correct result does not justify suppressing the -others, unless there is positive evidence of the fact that they involve errors which do not appear in the one which it is proposed to accept. If the student finds himself unable to do as good work as a more experi- enced or more fortunately endowed neighbor he should not hesitate to frankly acknowledge the fact, and should devote his efforts to increasing his proficiency rather than to concealing his lack of it. Deficiencies of this kind can be overcome thru intelligent and well-directed effort, and the satisfaction which results from over- coming them is well worth the effort which it may cost. The ability to do good analytical work represents a non-transferable asset of no small commercial value. Theoretical Knowledge Necessary. Altho any person who has acquired the necessary manipulative skill may be able to execute the details of a carefully described quantitative process, his ability to make effective use of the process will be decidedly 6 QUANTITATIVE CHEMICAL ANALYSIS limited, owing to the fact that unforeseen contingencies, which his carefully worded description did not allow for, constantly arise. It is only thru a definite knowledge of the theory of each step of the process that the analyst can work intelligently and effec- tively; the mechanical performance of such operations without understanding the reason for each step is not worthy of being dignified by the term " quantitative analysis." It should also be noted that the method employed must be adapted to the purpose for which the desired result is to be used. Frequently the rapidity with which a result can be obtained is of greater importance than extreme accuracy, and in such cases time and labor can be saved by neglecting certain of the details com- monly used or by employing certain " short-cut " methods. Every quantitative determination is, therefore, a specific problem in itself, and an analysis of the various factors concerned in every detail of the proposed method may render it possible to increase either the accuracy of the work, or the productive capacity of the analyst. An accurate sense of proportion and judgment, as to the importance and necessity of the details of quantitative work must be developed if the greatest efficiency is to be attained. The Literature of the Subject. A vast amount of experi- mental work having for its object the development of new, or perfection of old, methods of analysis is being carried out con- tinually. The results are published either in certain special journals devoted to this branch of chemistry, such as the Zeit- schrift fur analytische Chemie (Wiesbaden) and the Analyst (London) or in the more numerous chemical periodicals of a more general character. Especial importance should be attached to the reports of Committees and Associations, who cooperate in making tests of analytical methods under as nearly identical conditions as possible. Such, for instance, is the work of the Official Association of Agricultural Chemists or of the various Committees of the American Chemical Society. The progressive analyst will find it necessary to keep in touch with the newer INTRODUCTORY STATEMENTS AND DEFINITIONS 7 developments of the subject, and even the beginner will derive much profit and inspiration from consulting the original sources of information upon which the methods he uses are based ; hence, references to a limited number of important articles are added to some of the processes described in this book. Altho a number of works which attempt to summarize all of the more important quantitative methods are available, more comprehensive and usually more up-to-date information can be found in the numerous manuals devoted to the elaboration of the methods which are especially adapted to the analysis of particular classes of materials, such as ores and metallurgical products, alloys, rocks, soils and fertilizers, foods, etc. Proposed Plan of Work. The object of this book is to present the fundamental principles used in the general subject of quanti- tative analysis, and outline a method by which a working knowl- edge of the subject can be attained. In the plan of work here adopted the theory of each of the larger groups of quantitative processes is first discussed, then a limited number of typical illustrations are described in detail and the various sources of error and further applications of the method suggested. A series of questions and problems designed to point out the reasons for certain features of the methods and emphasize the general prin- ciples used are appended to most of these descriptions. In the elaboration of each of the different classes of processes much matter of a more general character finds constant use; this has been presented in brief form in the series of chapters forming the first section of the book. Familiarity with all of the facts there pre- sented is not an essential prerequisite to actual work with the methods described in the subsequent sections; all of it is necessary to a comprehensive knowledge of the principles of quantitative analysis, and these chapters should be carefully read and digested as progress is made in the practical part of the work. Strength of Reagents Used. A large number of the reagents used in quantitative analysis are prepared for one specific purpose 8 QUANTITATIVE CHEMICAL ANALYSIS only; the method of preparing such reagents will be given in the descriptions of the processes in which they are used. The strength of certain reagents which are used in a great variety of processes are given below. Dilute ammonium hydroxide, made by adding one and one-half volumes of water to one of concentrated ammonium hydroxide (sp. gr. 0.9). One cc. of the diluted reagent contains 0.102 gm. NHs. It is 6-normal. Dilute acetic acid, made by adding one and four-tenths volumes of water to one of 80 per cent acid. One cc. contains 0.36 gm. C2H 4 02- It is 6-normal. Concentrated hydrochloric acid. One cc. contains 0.44 gm. HC1. Its specific gravity is 1.19. It is 12-normal. Dilute hydrochloric acid, made by adding one volume of water to one of the concentrated acid. One cc. contains 0.22 gm. HC1. Its specific gravity is 1.10. It is 6-normal. Concentrated nitric acid. One cc. contains 0.99 gm. HNOs. Its specific gravity is 1.42. It is 15-normal. Dilute nitric acid, made by adding one and six-tenths volumes of water to one of concentrated acid. One cc. contains 0.38 gm. HNOs. Its specific gravity is 1.2. It is 6-normal. Concentrated sulfuric acid. One cc. contains 1.77 gm. Its specific gravity is 1.84. It is 36-normal. Dilute sulfuric acid. Made by adding one volume of the con- centrated acid to five of water. One cc. = 0.30 gm. H 2 S0 4 . Its specific gravity is 1.19. It is 6-normal. SECTION I GENERAL FEATURES OF GRAVIMETRIC PROCESSES CHAPTER II THE METHOD OF WEIGHING I. THEORY OF THE USE OF THE BALANCE Construction. Quantitative processes involve determinations of the relations existing between two masses of matter, but since both masses are determined by means of a beam balance under identical conditions the distinction between mass and weight can be disregarded. The accuracy of such processes must depend in part upon the accuracy with which the two weighings are made, and instrument makers have developed certain forms of balances known as " analytical balances" the use of which makes it possible to reduce the errors from this source to insignificant proportions. The details of the mechanism used by different makers for the adjustment and protection of such balances vary, but since all are based upon the use of essentially the same principles, only one type will be described here. The beam of such a balance is represented in Fig. 1. It is con- structed of such material, and in such a form, as to combine the maximum degree of rigidity and strength, with the minimum weight. It is suspended at its center on a horizontal axis, which is made of agate and accurately ground to a knife-blade edge, as shown at A of the figure. This axis rests upon a strip of polished agate supported upon the top of a pillar, and the beam is free to turn in a vertical plane about this axis. Two other knife-blade 9 10 QUANTITATIVE CHEMICAL ANALYSIS edges B and B f , which are of a similar construction, but with edges turned upwards instead of downwards, are fixed at the two ends and equidistant from the center. These edges sustain specially constructed stirrups, which are also provided with strips of agate, 15 Fig. 1. Beam of an Analytical Balance C and C" of the figure, at the points of contact; from them are suspended two pans, one of which supports the substance being weighed, and the other the weights used. The beam may be regarded as a compound lever in which the fulcrum is at the axis of suspension. If the two arms are of equal length, and if the pans and the loads which they contain are of equal weight, the effect of the force of gravity upon the two ends of the beam is identical, and a depression of one end of the beam will produce a series of vibra- tions similar to those of a pendulum. The process of weighing consists in plac- ing the substance whose weight is to be Fig. 2. Scale of Balance , . .. . , , determined in one pan, and adding weights to the other until the two counterbalance each other. This point can be recognized by observing the movements of the beam, and a pointer, the upper part of which is shown at D, is attached to it for the purpose of magnifying these movements; a small ivory scale, represented by Fig. 2, is placed just back of the end of the pointer, in order to make it possible to measure and record the magnitude of these movements with respect to the central axis. THE METHOD OF WEIGHING 11 The center of this scale, which is directly below the axis of sus- pension, should be marked 10, the tenth division to the left zero, and the tenth to the right twenty; this method of marking the scale at once indicates whether the numbers recorded are to the left or the right of the center. As the movement of the beam is greatly retarded by friction, and as the friction losses increase very rapidly as the knife-blade edges lose their sharpness, it is necessary to protect these bearings against needless wear; hence, analytical balances are often pro- vided with two sets of rests, known as " beam-rests " and " pan- rests" respectively. The beam-rests are controlled by a milled button, placed at the center and on a level with the floor of the balance case. When rotated it turns an eccentric, which raises a rod passing thru the center of the pillar of the balance, and this in turn raises two hinged arms E and E', which lift the knife- blade edge A from the agate plate, and also the stirrups sustaining the pans from the knife-blade edges B and B' on which they rest. The hinged arms are also provided with two studs F andF', which fit into a cup and a trough terminating the two studs G and G f , fastened to the beam. The effect of raising and lowering the beam-rests is to bring the beam into exactly the same position with re- spect to the agate plate upon which Fig 3> _ Bafle of BaIajlce Case it rests. The pan-rests are controlled by a small knob placed at the left of the center, as shown at / of Fig. 3. When a slight pressure is applied to this button, the rod to which it is attached moves the lever J which carries two arms K and K f and cause these to drop. Ordinarily these arms impinge upon the bottom of the pans L and L' and prevent needless vibration and wear of the bearings B and B' y but when they drop the beam is free to vibrate. As a protection 12 QUANTITATIVE CHEMICAL ANALYSIS against dust, moisture and air currents, the entire apparatus is enclosed in a glass case, one side of which consists of a movable slide of the same material. Conditions which Determine Accuracy. An accurate com- parison of the relative magnitudes of two masses cannot be made with such a balance unless certain essential conditions are complied with. First, the point of suspension of the beam should be equidistant from the points of suspension of the two pans, for if these distances differ the loads sustained by the two arms act with unequal lever- ages. If the total length of the beam is known the difference in the lengths of the two arms can be calculated from the weights found to be necessary to counterbalance the same object, when placed first on one pan and then on the other. If we represent the length of the right arm by r, that of the left arm by I, the true weight of the object by W, the apparent weight when placed in the left pan by A, and when placed in the right pan by A + a, we have, Ar = Wl, also Wr = (A + a) I If we multiply these two equations together and simplify the resulting expression we can obtain the relation (r) 2 : (Z) 2 : : A + a : A. It is also easy to show that the true weight of the object corre- sponds to the square root of the product of the two apparent weights, or since the two differ but slightly, it is represented with sufficient accuracy by the average of the apparent weights. Since it is not possible to make a balance whose two arms are absolutely equal, this method of "double weighing" is always used where extreme accuracy is demanded. The error which might result from this defect in the construction of the balance can usually be neglected if the same pan, usually the left-hand one, is used for all the weighings concerned in the analyses. Second, the center of gravity of the entire system, that is, of the beam and the two loads which it sustains, must be slightly below THE METHOD OF WEIGHING 13 the point of suspension of the beam. If the reverse relation holds, the system is in unstable equilibrium; if the two points fall to- gether, the system is in neutral equilibrium, and vibration of the beam even with equal weights is impossible. If the center of gravity of the system is too far below the point of suspension, the deflection produced by a slight excess of weight in either pan is but slight, and the balance is not sufficiently sensitive. By means of a small weight, which slides up and down the pointer, but which can be fixed by means of a set screw, see H of Fig. 1, the center of gravity can be lowered or raised. If, however, this distance is made too small the retarding effect of friction is relatively greater, and the movements of the beam are slow and uncertain. Third, the point of suspension of the beam and of the two pans must be very nearly on the same horizontal line; otherwise, changes in the loads carried by the pans change the position of the center of gravity, and hence the sensitiveness. Since all balance beams yield slightly to heavy loads it is impossible to comply with this condition in all cases. Manufacturers usually endeavor to make A stand as much below the line joining B and B f , when the balance is empty as it stands above this line when the pans sustain the maximum permissible load; the balance should then show the minimum change in sensitiveness with an average load. Sensitiveness. The sensitiveness of a balance is measured by the magnitude of the angle, corresponding to the change in the position of the pointer, produced by a slight excess of weight in either pan. Evidently this angle must increase as the length of the beam is increased, but it is undesirable to increase the length of the beam beyond a certain maximum, as the movements of the pointer then become correspondingly slow (and in this respect the behavior of the beam differs from that of a pendulum), and the time occupied in making a weighing is materially increased. The sensitiveness decreases as the weight of the beam and the other factors which produce friction increase. The third, and perhaps most important, factor is the adjustment of the center of 14 QUANTITATIVE CHEMICAL ANALYSIS with respect to the point of suspension. The quantitative ex- pression which represents the relation between these factors is given by the equation: LXW in which L is the length of the arm, W the excess of weight in the pan, D the distance referred to above, and Q the weight of the beam. As ordinarily used the term sensitiveness represents the number of scale divisions thru which the pointer is deflected by one milli- gram. Altho it is desirable to make the sensitiveness large by reducing the value of D, it cannot be reduced below a certain limit, which depends largely upon the skill used in the construction of the balance and the weight of the beam, or the movements of the pointer become so variable and uncertain that the point of rest cannot be determined with certainty. It should be possible to so adjust the balance that it has a sensitiveness of from 1.5 to 2 divisions. The Point of Rest. If we have an ideal balance, that is, one which has been perfectly constructed, which moves without friction, and which is loaded with equivalent weights, a slight depression of one end of the beam will cause the beam to vibrate back and forth and the pointer to move an equal number of divisions to the right and to the left of the central point of the ivory scale for an indefinite length of time. Owing to friction, and various faults of construction, there is a constant decrease in the amplitude of these vibrations, and the beam finally comes to rest. This posi- tion, as indicated by the position of the pointer with reference to the divisions of the ivory scale, is called the "point of rest" of the balance, and is constant for any given set of conditions. Owing to slight variations in these conditions, accumulation of dust on the pans, temperature changes, etc., this point may vary slightly from day to day, and rarely corresponds exactly with the center of the ivory scale. If it differs from it greatly the balance should THE METHOD OF WEIGHING 15 be readjusted by movement of one of the two buttons, and 0' of Fig. 1, at the end of the beam, toward or away from the point of suspension as the case may require. The exact position of the point of rest C is most rapidly and accurately determined by noting the limits of a series of vibrations, and averaging the results. If there were no decrease in the amplitude of these vibrations, one-half the sum of the aver- ages of the positions reached by the pointer on the right and left respectively would give the correct position of the point. Fi S- 4. Diagram Representing Move- ^ , ,, . , , , ment of Pointer Owing to this decrement, how- ever, this is strictly true only when an even number of readings is made on one side and an odd number on the other, as considera- tion of the accompanying diagram, Fig. 4, will show. In this dia- gram the successive positions reached are designated by the letters of the alphabet. If there were no decrement due to friction the expression n a + c + e} = ~~~ would give the correct position of the point of rest. The positions actually reached differ from those to which the above formula would apply by multiples of the decrement k which is approxi- mately constant. If a be taken as the starting point the position b differs from that which would be attained if there were no friction by the constant fc, the position c by twice that constant, the posi- tion d by three times the constant, etc. If now we average the two series, the one to the right, the other to the left, for five vibra- tions, we obtain as the expression for the point of rest, using the corrected values: r r(a + c + e-6fc) , (b + d + 4/b)1 m TT "2~ h2> 16 QUANTITATIVE CHEMICAL ANALYSIS In solving this expression the value of the constant k is eliminated while if an equal number of readings be taken for the two series this is no longer true. 'The Accurate Method of Weighing. Having determined in the manner described the point of rest of the empty balance, the weight of any substance can be determined by placing it on one pan of the balance, and adding weights to the other until the point of rest corresponds to that originally found. If accurately carried out the process is a slow one, and may be abbreviated by an equally exact interpolation process, which depends upon the fact that the change in the point of rest is directly proportional to the weight by which it is produced. In using this method the unknown substance is placed on the left pan and weights added, using milligrams only, until the point of rest is not far from that of the empty balance. If this point of rest is to the right of C another milligram is added to the weights in the pan, and the point of rest again determined, or if it is to the left, one milligram is removed and the point of rest determined. The difference A B, in which A and B represent the points of rest corresponding to the lesser and the greater weights respectively, gives the deflection produced by one milligram. In order to change the point of rest to that of the empty balance ( A C) -r- ( A B) mg. must be added to the lesser weight. The interpolation method is represented graphi- cally on Fig. 2, which shows the actual positions of A } B and C, on the ivory scale in a specific case. It is obvious that (12 9) -r- (12 6) or 0.5 mg. must be added to the weight which gave the point of rest A in order to counterbalance the unknown substance in the left pan. The value of (A B) is not constant unless the load sustained is constant but where these differences are small the changes in this value can be neglected, hence, it is often possible to omit the determination of either A or B if the proper constant has been previously determined. The value of C does not usually cfiffer greatly during the course of a laboratory period, and need only be determined once. This method of weighing is the most THE METHOD OF WEIGHING 17 accurate in use and with experience is rapidly executed. Under favorable conditions it should be possible to reduce the error involved in weighing by this process to one-tenth of a milligram, but this represents the extreme limit of accuracy which can be attained with the ordinary analytical balance. If a greater degree of accuracy is demanded a more carefully constructed "assay balance" must be used, but this cannot be employed for weights which exceed 5 grams. Abbreviations of Accurate Method. In all kinds of quantita- tive work it is the percentage rather than the absolute error which has to be considered, and where large amounts of material are to be weighed the above method may be shortened. If we are to weigh a precipitate of about the magnitude of one gram, and weigh to within one-tenth of a milligram, the percentage error involved will be one-hundredth, which is insignificant, as compared with the other unavoidable errors of most quantitative processes, and even if the error involved is a half milligram the percentage error is not excessive. If, however, our precipitate weighs two-tenths of a gram an absolute error of a half milligram cannot be safely disregarded. The abbreviation referred to above consists in making a rough mental calculation of the point of rest from a mere inspection of the movement of the pointer. It may be further noted that most of the weighings made actually involve the differ- ence between two weights, namely, the weight of the empty vessel and that of the vessel and substance. If the same point of rest is assumed for both weighings, the same error will appear jn both and the difference will give the correct value of the magnitude desired. The point usually assumed is the center of the scale. Hence the process of weighing which may be used in such cases consists in manipulating the weights till the pointer swings to approximately an equal number of divisions on both sides of the center of the scale, making the proper allowance for the decre- ment in the amplitude of each vibration. The error involved in this method should riot exceed three-tenths of a milligram. 18 QUANTITATIVE CHEMICAL ANALYSIS Some judgment must be used as to which of these methods of weighing should be employed, but a fairly satisfactory general rule is to use the more accurate method when the quantity weighed is less than three-tenths of a gram. The Weights Used. Since the results of quantitative proc- esses are usually expressed in terms of the ratio of the substance found to the substance used, and since the same set of weights is used to determine the value of both of these magnitudes, the abso- lute value of the standard or -unit mass employed is of no signifi- cance. If the weights used are consistent between themselves, that is, if the different pieces bear to each other the exact relation for which they are used, no error will appear in the final result. If, however, as in the assay of gold and silver ores, the result is to be reported in terms of the money value per ton, the absolute value of the unit of weight employed is of the greatest importance. The sets of weights sold by firms of established reputation are frequently sufficiently accurate for most kinds of work, but the results obtained with them will always be subject to some uncer- tainty until they have been accurately tested. Such weights should be handled with ivory-tipped pincers and kept in a closed box when not in use. Platinum weights should not change in value even after years of constant use, but aluminum weights are subject to slight corrosion and must be more carefully pro- tected. The manipulation of very small weights, especially those below 5 mg. in value, is troublesome and is usually avoided by the use of a " rider." This is a piece of platinum or aluminum wire bent in such form as to hang on the beam of the balance, and easily movable from place to place on the beam by means of a rod. If such a rider, whose weight is exactly 5 mg., is placed on the beam of the balance exactly above the point of suspension of the pan containing the weights it would have the same effect as the addition of 5 mg. to that pan, or if placed in any position between this point and the point of suspension of the beam it would THE METHOD OF WEIGHING 19 have an effect proportional to its distance from the point of sus- pension of the beam. If the beam is divided into five equal parts each division would be equivalent to 1 mg. Further sub- division of these large divisions enables one to add tenths of a milligram as desired. The Calibration of Weights. It is often necessary to accu- rately calibrate a set of weights. This involves first a determina- tion of the exact relations between the different pieces composing the set, and second a reduction of the values thus obtained to the absolute metric unit or some other convenient standard. The method can be readily illustrated by a concrete example. In this work the 5 mg. weight was temporarily adopted as a standard of reference and was found to agree absolutely with the rider of the balance. By comparing systematically the different pieces of the set on an assay balance the results recorded in the accompanying table were obtained. In this table the first column represents the marks on the weight placed in the left pan of the balance, the second column the weights added to the right pan, and the third the position of the rider on the beam of the balance. The figures 5 5 5 5 10 5 5 10 10 10' 10 10 10 20 10+10* 20 20 50 20+10+10* +5 5.08 50.08 50 100 50+20+ 10+ 10* +5 5.08 100.16 100 100* 100 0.05 100.21 100.1 200 100+100* 0.05 200.42 200.2 500 200+100+100'+50+20+10+10*+5 5.08 500.95 500.3 1000 500+200+ 100+ 100* +50+20+ 10+ 10* +5 5.12 1001.94 1000.7 in the fourth column represent a summation of those in the second and third plus the corrections previously found, and hence the values of the different weights in terms of the 5 mg. weight. The 1 gm. weight was next compared with a standard metric gram on an assay balance and found to bave the value 1.00075. 20 QUANTITATIVE CHEMICAL ANALYSIS Multiplying the series of figures in the fourth column by the factor (1.00075 -r- 1.0019), that is, 0.9988, they were reduced to the corre- sponding values in terms of the absolute metric units and the results which appear in the last column of the table obtained. The figures which appear in the second decimal place have no significance in analytical work and are therefore neglected. Correction for Buoyancy. The apparent effect of gravity upon any object which is surrounded by the atmosphere is less than the true effect by an amount corresponding to the weight of the volume of air which it displaces. If the loads sustained by the two pans of the balance displace the same volume of air, buoyancy affects both equally, but where the object being weighed, and the weights used to counterbalance it differ in volume, buoyancy affects the load displacing the greater volume of air to a greater extent than the other, and causes a corresponding error. The magnitude of this error can be calculated from the weight of a unit volume of air, and the difference between the specific gravities of the weights and object weighed. If the specific gravity of the sample weighed out for an analysis equals that of the substance separated, buoyancy causes the same proportionate error in the two weighings upon which the final result depends. The Error Resulting from Hygroscopic Water. Any solid object, which has not been especially dried and maintained in an atmosphere which is free from water vapor, retains a film of hygro- scopic water upon its surface. If the surface presented is large the true weight of such an object may differ from the apparent weight, that is, the weight determined under ordinary atmospheric conditions, by several milligrams; and further, the difference varies with the amount of water in the atmosphere. Altho this film of water can be expelled by heating the object to 100 for a few minutes, it is not readily possible to entirely prevent the re- absorption of hygroscopic water while it is being cooled and weighed. A 15-gm. crucible, for example, which has been allowed to cool in a desiccator, and which is weighed in a balance, the case THE METHOD OF WEIGHING 21 of which contains a jar of calcium chloride, will frequently show a gain of from one to three-tenths of a milligram on long standing on the balance pan. When it is necessary to weigh accurately to one-tenth of a milligram this becomes one of the most trouble- some difficulties to avoid. Since most weighings are made in some form of a container, such as a crucible or bottle, the weight actually used in the final calculation represents the difference between the weight of the container plus substance and the container, and the error resulting from the absorption of hygroscopic water can often be reduced to negligible proportions by submitting both to exactly the same conditions before weighing. If, for example, the empty crucible and the crucible plus the substance to be weighed are ignited, placed in a desiccator while still warm, allowed to stand for an hour and then weighed at once, the amount of hygroscopic water absorbed by the crucible in the two cases is practically the same, but not exactly so unless the percentage of water vapor in the atmosphere has remained constant. The only error to be con- sidered in such a case is that due to the absorption of water by the substance itself, which can usually be neglected unless it is decidedly hygroscopic. If it is decidedly hygroscopic it becomes necessary to use a closed container. When the container cannot be heated to a temperature necessary to drive off all hygroscopic water, wiping with a dry cloth has to be substituted. When the surface presented by the container is very large, variations in the moisture content of the air may lead to errors which cannot be neglected. In such cases it is desirable to prepare a counterpoise of about the same surface area as the vessel to be weighed, to submit both vessels to the same treatment before both weighings and to substitute the counterpoise for some of the weights employed in both cases. It may be assumed that variations in the atmos- pheric conditions will affect the amount of water retained by the two vessels to the same extent, and that no error from this source will appear in the difference finally found. 22 QUANTITATIVE CHEMICAL ANALYSIS II. RULES FOR THE USE OF THE BALANCE Altho the general facts and principles upon which the use of the balance is based have been presented in the preceding section, there are a number of details of a purely practical nature which must be observed if the balance is to be maintained in good work- ing order. These are elaborated in the form of the series of rules given below. First, in order to prevent wear of the bearings, and consequent rapid decrease in the sensitiveness of the balance, large weights should never be placed on or removed from the balance pans, unless the beam- and pan-rests are in position; if the weight being added or removed does not exceed 100 mg. the pan-rests alone will suffice. Both rests should always be left in position before leaving the balance. Second, the floor of the balance case and the pans should be kept perfectly clean. If substances are spilled within the case they should be brushed up at once with a fine brush or cloth. Third, no solid substances except certain metals and alloys should be placed in contact with the balance pans. No liquids of any description should be brought into the balance case unless retained in tightly stoppered bottles. Fourth, hot objects should be allowed to cool to a temperature not greatly in excess of the normal temperature of the balance room before being weighed. If this precaution is not taken dis- turbing air currents are set up within the balance case. For a like reason the slide of the balance case should be kept closed while the movements of the beam are being observed. Fifth, the weights should always be handled with bone-tipped forceps and should be carefully protected from dust and fumes. Sixth, if the point of rest of the empty balance differs from ten by more than one unit, or if the balance fails to behave properly, ask the instructor in charge to make whatever adjustments may be necessary. THE METHOD OF WEIGHING 23 III. DETAILS OF PROCEDURE FOR DETERMINATION OF POINT OF REST Seat yourself squarely in front of the balance case so that your line of vision is directly opposite the center of the balance. Re- lease the beam-rests by turning the button at the center of the case, then the pan-rests by pressing the small knob to the left, next gently lower the rider till it rests on the end of the beam and allow it to remain just long enough to displace the pointer about ten divisions on the ivory scale, and finally remove the rider and permit the beam to swing freely. Take an odd number of con- secutive readings (five are sufficient) corresponding to the extreme positions reached by the pointer. Add together the averages of the two sets of readings, one set representing all the readings taken on the right of the center, the other all the readings taken on the left of the center, and divide the sum by two. This gives the point of rest of the empty balance. Repeat the determinations till results are obtained whose extreme differences do not exceed two-tenths of a division. IV. DETAILS OF PROCEDURE FOR THE DETERMINATION OF THE WEIGHT OF A WATCH GLASS Elaborate Method. Hold a clean watch glass over a gauze heated by the flame of a burner until it is decidedly hot to the touch, then place on a clean support inside a desiccator and allow to cool for twenty minutes. Transfer the glass by means of clean dry pincers to the left pan of the balance and add in regular succession weights of decreasing value to the right pan until the correct weight is determined to within 10 mg. if the balance is provided with a 10-mg. rider, and to within 5 mg. if it is provided with a 5-mg. rider. Next vary the position of the rider on the right arm, placing it at points corresponding to entire milligrams, until the weight is found to within 1 mg. Finally determine accurately the point of rest, first, with the rider in the position 24 QUANTITATIVE CHEMICAL ANALYSIS which makes the total weights used slightly less, and second that which makes the total weights used slightly greater than that of the watch glass. These relations can be determined by noting whether the pointer swings decidedly to the right or the left as the changes are made. Let A represent the point of rest found with the lesser weight, B that found with the greater weight, and C the point of rest of the empty balance. Calculate the correction, expressed in milli- grams, to be added to the lesser weight necessary to shift the point of rest from A to C by dividing (A C) by (A B), and add this correction to the lesser weight. Verify the accuracy of the result by adding, by means of the rider, the fraction of a milligram calculated to be necessary and again determine the point of rest. If the work has been accurately carried out, and if the balance is properly constructed and ad- justed, the points of rest obtained should not differ from that of the empty balance by more than two-tenths of a division of the ivory scale. Make a permanent record of the weight thus obtained in the laboratory notebook, in which all weighings and the data upon which they are based should be recorded when obtained. Dis- regard all figures beyond the fourth decimal place. Abbreviation of the Method Outlined. In subsequent work this method of weighing may often be abbreviated. Where the weight actually determined is the difference between the weight of the containing vessel and the weight of that vessel plus another substance, the point of rest of the empty balance may be assumed to be ten. Where the magnitude of the mass weighed is not less than 0.3 gm. the accurate determination of the points of rest may be omitted and the weight determined with sufficient accuracy by changing the position of the rider on the beam until the pointer swings to approximately the same distance on either side of the point of rest of the empty balance, making a slight allowance for the decrease in the value of each successive vibration. THE METHOD OF WEIGHING 25 V. DETAILS OF PROCEDURE FOR CALIBRATION OF A SET OF WEIGHTS Determine the relations between the different pieces composing the set, using the procedure outlined on page 19. It is not neces- sary to reduce the results to the absolute metric standard. VI. QUESTIONS AND PROBLEMS. SERIES 1 1. The right arm of a balance has a length of 150.1 mm., the left arm 150 mm. ; the apparent weight of a crucible placed in the left pan is 10.032 gm., what is its true weight? 2. What error would result in weighing a 0.3 gm. precipitate in the crucible referred to above if, first, both empty crucible and crucible plus precipitate are weighed on the left pan, and second, if the crucible is weighed on the right pan and the crucible plus precipitate on the left pan? 3. Show that no error is involved in weighing a precipitate if the point of rest of the empty balance is not actually determined, provided the same value is assumed in weighing both empty crucible and the crucible plus pre- cipitate. 4. A crucible placed on the left pan of a balance is exactly counterbalanced when a weight of 10.05 gm. is placed on the right pan and the rider is at the point marked 8.2 on the right arm; if the right arm is divided into 12 equal divisions and the rider weighs 10 mg., what is the weight of the crucible? 5. The weight of a balance beam is 350 gm., its total length 200 mm., and the pointer attached to it has a length of 180 mm. ; if one milligram causes a deflection of 2 mm. at the end of this pointer, what is the position of the center of gravity with respect to the point of suspension? Am. 0.026 mm. 6. What error results from failure to correct for buoyancy in weighing a 10-gm. porcelain crucible, assuming that brass weights with a specific gravity of 8.33 are used, that the specific gravity of porcelain is 2.14 and that one liter of air weighs 1.2 gm.? 7. A crucible is found to weigh 10.0542 gm. when placed on the right-hand pan of a balance and 10.058 gm. when placed on the left-hand pan; what is the true weight of the crucible? If the total length of the beam is 180 mm., what is the difference in the lengths of the two arms? Arts. 0.02 mm. CHAPTER III PREPARATION OF THE SUBSTANCE FOR ANALYSIS Theory of Sampling. The amount of substance actually em- ployed in making a quantitative analysis is comparatively small, and the result obtained is of but little value unless the portion actually used accurately represents the average composition of the entire mixture. In the analysis of gases and liquids homo- geneous mixtures are very easily obtained by a slight amount of stirring, but in the analysis of solid mixtures it is usually neces- sary to prepare a "sample." The difficulties which arise in preparing a representative sample of a solid mixture result from differences in size and lack of uniformity in the distribution of the different constituents, and from differences in the hardness and the specific gravity of these constituents. The general method of procedure in sampling a non-homogeneous solid, whether it represents a carload or a few pounds is essentially the same. It involves removing and setting aside according to a uniform plan a fractional part of the total amount, reducing the portion set aside to a finer state of division, mixing thoroughly, and repeating this cycle of operations until a sample of such fineness is obtained that the small amount actually weighed out represents the entire original mass. The fundamental principle which must be kept in mind is that the fineness to which the sample is crushed at each cycle must be such that the ratio between the size of the sample and the size of the largest particle is sufficiently large. The size of the largest particle must be so small that the addition of one such particle to the portion which has been selected does not change the average composition of the mixture by an appreciable amount. 26 PREPARATION OF THE SUBSTANCE FOR ANALYSIS 27 Calculation of the Maximum Size of Particle. The maximum size of particle which is permissible depends upon a number of factors, and can be calculated if certain assumptions are made. The method is most conveniently outlined by the consideration of a specific case. Let it be assumed that a lump of iron ore, which weighs 1000 gm., consists of 200 gm. of quartz, which has a specific gravity of 2.5 and contains no iron, and 800 gm. of hematite, which has a specific gravity of 4.5 and contains 60 per cent of iron. Let it be assumed further that it is desired to crush this lump to such a degree of fineness that when one-fourth of the well-mixed mass is selected the addition of a further particle of quartz will not reduce the percentage of iron, or of a further particle of hematite will not increase the percentage of iron, by more than one-tenth of one per cent. The correct percentage of iron in the lump is evi- dently 48, and if x and x' represent the respective weights of quartz and hematite whose size is just sufficient to meet the requirements named, the following expressions are true: (250 X 48) + (x X 0) 250 + z a1 ' (250 X 48) + (x' X 60) _ 250 + x' When these expressions are solved x will be found to have the value 0.52 gm. and x' 2.1 gm. The volume of a quartz particle which weighs 0.52 gm. is evidently 0.208 cc. and if it is assumed to have the form of a perfect cube its length would be approx- imately 0.6 cm. The volume of a hematite particle which weighs 2.1 gm. is evidently 0.46 cc. and if it is also assumed to be a cube, its length would be 0.77 cm. Hence the sample should be crushed fine enough to pass thru a sieve which has open- ings not exceeding 0.6 cm. in diameter, and since the assumptions here made are not actually realized, a sieve with still smaller openings should be used if the specified degree of accuracy in the preparation of the sample is to be assured. 28 QUANTITATIVE CHEMICAL ANALYSIS Methods of Selection. The simplest method of selecting a fractional part of the mixture is to turn over the entire mass with a shovel or spoon, and set aside every tenth, fifth, or second shovel or spoonful. Another method is to distribute the entire mass in the form of a cone-shaped pile, flatten the pile slightly, and remove a sector representing one-quarter or one-half of the pile; it can be assumed that the large and small particles and the light and heavy particles are distributed symmetrically with respect to the central axis of such a cone. A large number of mechanical devices, which automatically separate a fractional part of all the material passed through them, are used where the sample is large. Methods of Powdering. A great variety of grinding or shred- ding machines, which are especially adapted to the nature of different classes of materials, are in use. Altho the grinding parts of such machines are made of hardened steel, appreciable amounts of iron are added to the sample during the grinding process if the sample contains constituents whose hardness ap- proaches that of steel. This is usually neglected in commercial work, but cannot be tolerated in many lines of scientific work. In such cases the sample must be pulverized by hand by means of a mortar and pestle which are made of agate. It is sometimes advantageous to separate out the coarse from the fine particles during the grinding process; but since certain constituents of the mixture may be more easily reduced than others, none of the sample can be rejected, that is, the entire sample must be made to pass thru the sieve used. Methods of Mixing. Mixing is best performed by placing the mass in a cylindrical vessel, which is then carefully corked and rotated by means of a motor. The same result can be obtained more slowly by hand rotation. Another method consists in plac- ing the sample on a large piece of rubber " sampling-cloth " and rolling the contents toward the center by raising successively the opposite corners of the cloth. Mixing and grinding can be ef- fected simultaneously by means of the small "ball mill" repre- PREPARATION OF THE SUBSTANCE FOR ANALYSIS 29 sented in Fig. 5. It consists of a porcelain jar, which contains in addition to the sample a large number of porcelain balls. When closed and rotated these rapidly reduce the sample to a fine homogeneous mixture. The Moisture Content of the Sample. All solid substances contain at least appreciable amounts of hygroscopic water unless previously dried. If the percentage is large the fine par- ticles tend to stick together and may make it impossible to powder and mix the sample properly. Frequently a mass which seems to be fairly dry becomes moist and sticky as soon as it is roughly powdered, since water is sometimes held within the interior of the larger masses. The chemist is usually expected to report results on the basis of the mixture actually received. If he dries the mixture sub- mitted to him in order to make it possible to prepare a representa- tive sample the results obtained will not represent the composition of the original mixture. In such cases it becomes necessary to save out a sufficient amount of the original mixture to permit of an accurate determination of the water present, and to multiply the results of the analysis by a factor, which can be calculated from the percentage of water found, in order to report the percentages present in the original mixture. If the sample contains a small amount of hygroscopic water only it is preferable not to dry it, for since all finely divided substances are at least appreciably hygroscopic it is often difficult to preserve such samples and to weigh them out accurately. Methods of Drying. Hygroscopic water is usually determined by drying the sample in an oven (see Chapter IX) which is kept at a temperature of 105. This method cannot be used where the sample loses chemically combined water, or undergoes other 30 QUANTITATIVE CHEMICAL ANALYSIS changes at this temperature. In such cases, dehydration can be effected by the use of a desiccator similar to the one represented in Fig. 6. It consists of a glass vessel provided with a tightly fitting cover, and containing some substance, such as strong sulfuric acid or calcium chloride, which is a good absorbent of water. The general theory of its use will be discussed in Chapter X. Still another device which some- times becomes necessary is to absorb the water by means of a filter paper or a porous plate. The finely pow- dered substance is manipulated by means of a spa.tula in such a manner that fresh portions of the mass are Fig. 6. Desiccator constantly brought into contact with the plate or paper; the capillary action of these agents gradually absorbs the adhering water. CHAPTER IV THE PROPERTIES OF SOLUTIONS AND THE ELECTROLYTIC DISSOCIATION THEORY The Possible Kinds of Solutions. Solutions are defined as homogeneous mixtures whose composition can undergo continuous variation between certain definite limits. Such mixtures repre- senting all three states of aggregation are known. All substances in the gaseous state are miscible with each other in any proportions whatever. In the liquid state the possibilities are limited; certain pairs of liquids, such as alcohol and water, are capable of forming a continuous series of homogeneous mixtures; others, such as ether and water, are mutually miscible to a limited extent only. In the solid state the possibilities are still more limited and it was only comparatively recently that the existence of " solid solutions" was recognized. Instances in which two solids are miscible in any proportions whatever are known, but usually solids are soluble in each other to a limited extent only. Solids which are closely related to each other crystal lographically, that is, which are iso- morphous, usually form solid solutions with one another. Many solid mixtures which appear to be homogeneous can be shown by examination with a microscope to be very finely-grained conglom- erates of the constituent solids, and, therefore, are not true solutions. Substances existing in different states of aggregation are often able to form solutions with each other. Gases are frequently soluble in both liquids and solids up to a certain extent; liquids sometimes dissolve in solids to a limited extent, and solids are often soluble in liquids. In dealing with solutions of all classes it is customary to designate the substance present in relatively large amount as the ''solvent" and the substance present in relatively 31 32 QUANTITATIVE CHEMICAL ANALYSIS small amount as the dissolved substance or " solute." If the two constituents of the solution are miscible in all proportions either may be the solvent or the solute according to the proportions represented in the mixture concerned. Solutions of Gases in Liquids. The solubility of a gas in a liquid is usually expressed in terms of the volume of gas, measured under standard conditions of temperature and pressure, dissolved by a unit volume of the liquid. The gases which are most fre- quently dealt with in quantitative work are, with the exception of ammonia and the halogen acids, but slightly soluble in water, or aqueous solutions which do not act upon the gas chemically. With one or two exceptions only, the solubility of a gas in a liquid is decreased by increasing the temperature. The amount of gas dissolved by a liquid increases in direct proportion to the pressure of that gas in contact with the liquid except in those cases in which the solubility is very great. The complete saturation of a liquid with a gas requires intimate contact of the two components for some time, and is not usually attained unless a stream of gas is permitted to pass through the liquid, or unless the liquid is shaken with an excess of the gas in a closed vessel. Solutions of Solids in Liquids. The solubility of a solid in a liquid is expressed either in terms of the number of grams of solid which can be dissolved in a liter of the pure liquid, or of the number of grams of solute present in a liter of the saturated solution. The weight of solute present in a unit volume of any solution, whether saturated or not, is known as the " concent ration." Increasing the temperature usually increases the solubility of solids in liquids, altho the increment per degree is often small; a relatively small number of cases are known in which the solubility decreases with increasing temperature. The effect of pressure upon the solu- bility of solids is small and unless the differences concerned amount to a hundred atmospheres can be neglected. The Speed of Solution of Solids in Liquids. The rate at which a solid dissolves in a liquid depends primarily upon the rate PROPERTIES OF SOLUTIONS 33 at which the particles of solid are taken up by the liquid, and the rate at which the dissolved particles pass away from the immediate neighborhood of the solid and diffuse into the surrounding liquid. Both of these factors depend upon the specific natures of the solid and liquid concerned, and upon the temperature and concentra- tion of the solution with respect to the dissolved salt. Increasing the temperature increases both the rate at which the solid body is taken up and the rate at which the dissolved particles diffuse into the surrounding liquid. The rate of diffusion is further directly proportional to the difference between the concentration of the solution with respect to the dissolved salt at any two points in the solution. Further, the amount of surface of the solid as compared with the volume of liquid to be saturated and the rate at which the concentrations of different portions of the solution are equalized thru mechanical agencies greatly affect the rate at which saturation of the solution is effected. It is apparent that wherever it is desired to dissolve a given amount of solid rapidly the latter should be reduced to a fine state of division in order that the extent of surface presented shall be as large as possible, that the temperature be as high as the other conditions of the experiment permit, and that the solid and liquid be agitated violently. Supersaturated Solutions. Altho the rate at which a solid is dissolved by a liquid decreases as the concentration of the resulting solution increases, and becomes zero as soon as the solution has attained a certain maximum concentration, it is possible, under certain conditions, to prepare solutions which contain more than the normal quantity of dissolved solute; such solutions are then designated as " supersaturated." Supersatu- rated solutions usually result when a solvent is saturated with a solute at a temperature at which the solubility is greater and the temperature slowly changed to that at which the solubility is less; or, where the solid is generated in the solvent as the result of changes in the composition of the liquid. The excess of dissolved 34 QUANTITATIVE CHEMICAL ANALYSIS solute usually separates out from such solutions on standing, especially if the mixture is agitated. Effect of Size of Particles on Solubility of Solids. The size of the solid particles in contact with the solvent affects not only the rate at which the solid dissolves but, in some cases at least, affects the actual value of the solubility constant. This was clearly shown through a series of experiments* on the solubility of gypsum (CaS04 2 H 2 0) and barium sulphate in water. Solutions which had been thoroughly saturated thru long contact with particles of gypsum of moderate size were found to show a decided increase in concentration as soon as a small amount of more finely divided particles were added; on long standing, however, the very fine particles all disappeared, and the solubility constant attained its former magnitude. Solutions saturated with particles whose average diameter was 0.002 mm. were found to contain 2.085 gm. of calcium sulfate per liter; if saturated with particles whose average diameter was 0.0003 mm. the concentration corresponded to 2.476 gm. per liter, that is, decreasing the size of the solid particles from 0.002 to 0.0003 mm. increased the solubility by about nineteen per cent. Further experiments showed that with solid particles whose average diameters equaled or exceeded 0.002 mm. the solubility value remained constant and was there- fore designated as the " normal solubility"; if the particles con- cerned were less than 0.002 mm. in diameter the solubility value exceeded the normal but gradually attained the normal value, and the very fine particles gradually disappeared. Experiments with barium sulfate gave still more striking results. When precipitated from a boiling solution the particles of salt showed an average diameter of 0.0018 mm. and gave a normal solubility of 0.0023 gm. per liter; when the particles of precipitate were reduced to 0.0001 mm. the solubility was increased to 0.00415 gm. per liter and with the naturally occurring salt, reduced to a still finer state of division, the solubility reached 0.00618 gm. per liter. * Hulett, Zeitschrift fiir physikalische Chemie, 37, 385 (1901). PROPERTIES OF SOLUTIONS 35 These facts explain the well-known phenomenon that particles of a precipitate which are too small to be retained by a filter are often retained on the same filter after they have been allowed to remain in contact with the solution for some time. It is probable that there is a tendency for all finely divided substances in contact with their saturated solutions to increase the size of their particles up to a certain maximum, and for the resulting saturated solutions to attain a certain normal solubility. If this is generally true all solutions which have been saturated with a solid, some of the particles of which are below the normal size, are supersaturated with respect to the particles which exceed the normal size, and on standing some of the dissolved substance should be deposited upon these large particles; further, since the solution would then be undersaturated with respect to those particles which are smaller than the normal size, these should pass into solution. The total effect should be the gradual disappearance of all particles whose size is below the normal. Changes of this kind are found to take place much more rapidly as the temperature of the mixture is increased. The Molecular Weights of Dissolved Substances. It was first shown by Van't Hoff in 1886 that a remarkable analogy exists between dissolved and gaseous substances: He was able to show from the data available at that time that the "osmotic pressure"* exerted by a substance dissolved in a liquid was directly propor- tional to the concentration and to the absolute temperature; further, that the osmotic pressure of such a solution was exactly equal to the gaseous pressure which the solute should exert, if it was vaporized, and if the vapor occupied a space equal to the volume of the solution concerned. The validity of these con- clusions has been tested by more recent investigators, and so far * The student should consult some modem book on Theoretical Chemis- try, or the first volume of Stieglitz' " Qualitative Analysis," for an explana- tion of this term and for a further elaboration of much of the matter which follows. 36 QUANTITATIVE CHEMICAL ANALYSIS as solutions of small concentration are concerned, sufficiently con- firmed. They render it almost necessary to assume that the hypothesis of Avogadro is as valid for dissolved substances as for gases, and hence Van't Hoff was led finally to the conclusion that equal volumes of solutions of different substances, which give equal osmotic pressures, at the same temperature, contain the same number of molecules. The most important application of these conclusions was the calculation of the molecular weights of dissolved substances from determinations of the osmotic pressures of solutions containing them. Owing to the practical difficulties which arise in the deter- mination of osmotic pressures, certain physical properties which are related to osmotic pressure, such as the changes in the vapor pressure of the solvent, and in the boiling or freezing point of the solution, have been more generally used for the determination of the molecular weights of dissolved substances. When these methods were applied to certain classes of solutions, especially to dilute aqueous solutions of strong acids, of strong bases, and of salts in general, the molecular weights obtained were less than the values usually assigned to these substances, in many cases ap- proximately one-half or one-third of these values. Van't Hoff was unable to explain these discrepancies. Development of the Electrolytic Dissociation Theory. In 1887 Arrhenius noted the fact that when osmotic pressure methods were used for the determination of molecular weights, normal values were obtained for those solutions which did not conduct electricity, whereas abnormally low results were obtained with all solutions which were good conductors. It had been already shown by Faraday that the passage of an electric current through a solution was always associated with the decomposition of the solute into two products, one of which separated at the negative pole or cathode, and the other at the positive pole or anode; and further, that the amount of electricity transmitted was directly proportional to the weights of either of the decomposition products PROPERTIES OF SOLUTIONS 37 formed. These facts suggested to Arrhenius the " Electrolytic Dissociation Theory." According to this theory all substances which form solutions capable of conducting an electric current, and, therefore, desig- nated as " electrolytes," do not exist in such solutions in the form of the original molecules, but in part at least as " dissociation products." These products are designated as "ions," or more specifically as "cations" or "anions," according to whether they separate at the cathode or anode during the passage of an electric current through the solution. The ions are either simple elements or combinations of elements charged with large amounts of elec- tricity, each cation with a definite amount of positive electricity, and each anion with an equal amount of negative electricity, or with some simple multiple of that amount. According to these assumptions the abnormally low results obtained for the molecular weights of electrolytes is a necessary consequence of the fact that such solutions contain a greater number of ultimate particles, that is ions, capable of affecting the osmotic pressure of the solution than would be present if the solu- tion was undissociated. Such solutions are conductors because the positively charged cations are attracted by the negatively charged cathode and repelled by the positively charged anode, while the negatively charged anions are attracted by the positively charged anode and repelled by the negatively charged cathode. These attractions and repulsions cause the cations to migrate toward the cathode, and the anions toward the anode, that is, cause a flow of electricity through the solution. When the ions reach the surfaces of the electrodes they lose their charges, which change materially affects their chemical and physical properties, and is the cause of the phenomenon of "electrolysis." Composition of the Ions. The probable composition of the ions which are present in a solution of an electrolyte can usually be inferred from the composition of the substances which separate at the electrodes during electrolysis. When a solution of hydro- 38 QUANTITATIVE CHEMICAL ANALYSIS chloric acid is electrolyzed gaseous hydrogen separates at the cathode and chlorine at the anode. The simplest assumption which can be made is that such a solution contains positively charged hydrogen ions and negatively charged chlorine ions; the hydrogen atoms, which result from the loss of positive charges by two hydrogen ions, unite to form a molecule of hydrogen, and the chlorine atoms, which result from the loss of negative charges by two chlorine ions, unite to form a molecule of chlorine. Since solutions of all soluble chlorides yield chlorine during electrolysis it is probable that all such solutions contain simple chlorine ions. When a solution of a strong base, such as potassium hydroxide, is electrolyzed hydrogen is liberated at the cathode and oxygen at the anode. It is probable that the solution contains positively charged potassium ions and negatively charged ions having the formula HO. The metallic potassium which first separates at the cathode at once reacts with water to form hydrogen and more potassium hydroxide; the negatively charged HO ions cannot exist independent of this charge, and unite to form water and molecular oxygen. All hydroxides yield solutions containing these ions. When a solution of copper sulfate is electrolyzed, metallic copper separates at the cathode, and oxygen at the anode and the solution becomes acid. It seems probable that the solution con- tains positively charged copper ions and negatively charged ions of the formula S04; the former yield metallic copper at the cathode, but as the latter cannot exist independent of their negative charge they decompose and unite with water, forming oxygen and sulfuric acid, which in turn gives hydrogen ions and S0 4 ions. A more careful study of the subject, by methods which need not be considered here, shows that the dissociation of even simple electrolytes may be a more complex process than the foregoing statements suggest. It is known, for example, that solutions of sulfates contain ions of the formula HSO4, in addition to S0 4 ions, also that phosphates yield ions of the formula H 2 P04, HP0 4 and P0 4 . Further, certain metallic ions show a decided tendency to PROPERTIES OF SOLUTIONS 39 unite with other groups of elements such as H 2 0, NHa, C1 2 and (CN) 2 . In order to designate the various ions, symbols which represent not only their chemical composition but also the number and character of the charges which they carry are used. The charge carried by the hydrogen ion is chosen as the standard of comparison and represented by a single + sign written above the symbol, ions which carry double this amount of positive charge are represented by the proper symbol with the + sign written twice. Similarly, ions which carry negative charges equal to the positive charge of the hydrogen ion are represented by the proper symbol with a single sign written above it, those which carry twice this amount of charge show the sign written twice. Factors Affecting the Dissociation of Electrolytes. Since elec- tricity is carried through a solution by the ions, not by the un- dissociated molecules which it contains, its " conductivity," that is its efficiency as a conductor, is a measure of the extent to which the electrolyte is dissociated. In comparing the conductivities of solutions, the relations are greatly simplified if concentrations are expressed in terms of gram molecules or " moles" per liter, that is, if the weight of solute per liter is divided by the molecular weight of the solute concerned. When the conductivities of solutions, which contain the same number of moles of various electrolytes per liter, are measured in the same apparatus and under identical conditions very different values are obtained. These differences have been shown to be due in part to variations in the speed with which the different ions travel when attracted by a charge of the same intensity, and in part to the fact that the different electrolytes are not dissociated to the same extent. When the conductivities of solutions containing different con- centrations of the same electrolyte are measured under identical conditions, and the results are divided by the respective concentra- tions it is found that the quotients obtained for the weaker solu- 40 QUANTITATIVE CHEMICAL ANALYSIS tions exceed those obtained for the stronger solutions. This seems to mean that the percentage of electrolyte which exists hi the dissociated condition is greater in dilute than in concentrated solutions. It has been shown, however, that altho the conductivi- ties of all electrolytes increase as the concentration of the solution decreases, the conductivity attains a definite limiting value at a certain concentration which is not changed by further dilution. It seems probable that this limit, corresponding to the so-called "maximum conductivity," represents the conductivity of the completely dissociated electrolyte. If this conclusion is accepted the ratio between the conductivity of a solution of any electrolyte and the maximum conductivity of that electrolyte is a measure of the " degree of dissociation" of the electrolyte in the solution concerned. Extent to Which Different Electrolytes are Dissociated. Some of the results, showing the extent to which solutions contain- ing different concentrations of a number of electrolytes are dis- sociated, which were obtained by the method just outlined, are given in the accompanying table.* The first column gives the concentrations in moles per liter, the remaining columns the per- centage of dissociation of the given reagents at different con- centrations. It is now known that the method here used gives results which are only rough approximations of the correct values for solutions whose concentrations exceed molar, prob- ably owing to the resistance offered by large concentrations of non-ionized molecules. The differences between the percentages given for strong acids like nitric, hydrochloric, and sulfuric and a weak acid like acetic are striking, even where the concentrations are below molar. Simi- lar differences are shown between the figures for a strong base like potassium hydroxide, and a weak base like ammonium hydroxide. They are found to be characteristic of all acids and bases and there is abundant evidence for the statement that what is com- * From data of Kohlrausch and Holborn, Leitvermogen der Electrolyte, 160. PROPERTIES OF SOLUTIONS 41 Cone. HC1 HNO, H 2 S0 4 H(C 2 H 3 2 ) NaCl KOH (NH 4 )OH 10 17 08 17 44 19 02 05 19 14 08 7 28 17 28 53 28 67 14 33 00 17 5 4 3 2 1 0.5 0,1 40.37 48.14 57.03 67.37 79.84 86.74 93.10 40.16 49.60 58.66 68.80 82.66 86.40 93.33 36.68 41.14 45.32 49.73 53.00 55.71 61.14 0.27 0.36 0.50 0.75 1.23 1.87 4.30 38.92 44.84 51.50 59.07 67.82 73.74 84.32 45.21 52.22 60.08 68.72 78.63 84.19 91.02 0.31 0.40 0.55 0.80 1.35 2.06 5 monly known as the "strength" of an acid or base depends upon the extent to which it is dissociated at different concentrations. The table shows further, that sodium chloride resembles the strong acids and bases rather than weak ones, and a large amount of experimental work is available which shows that most salts, with the exception of mercuric cyanide and certain other salts of mercury and cadmium, are largely dissociated. It has also been shown that water possesses the property of causing solutes to dissociate to a greater extent than any other solvent; alcohol possesses this property to some extent, but the re- maining organic solvents yield solutions which are non-conductors. Importance of the Electrolytic Dissociation Theory. This theory is of especial importance in the study of quantitative analysis owing to the fact that many of the chemical reactions upon which quantitative processes are based are reactions between electrolytes, and there are decided differences between reactions of this type and those in which electrolytic dissociation plays no part. In general, the ions possess a much greater chemical activity than undissociated molecules, and the extent to which two reagents react with each other, and the speed with which they react is often largely determined by the extent to which these reagents or the products which result from their interaction are dissociated. The theory enables us to understand a large number of facts which are difficult to explain on any other basis, and to predict with a fair degree of certainty many effects which can be used to advantage in analytical chemistry. CHAPTER V THE FACTORS WHICH DETERMINE CHEMICAL EQUILIBRIUM Equilibrium and Reaction Velocity. When two substances react chemically they are in a condition of unstable equilibrium with respect to each other; when no further changes in the relative masses of these substances are taking place, ''equilibrium' 7 has been reached. This condition is also defined by the statement that the "reaction velocity" is zero, where the term reaction velocity is defined as the mass of one or both of the original sub- stances transformed into new substances during some unit of time. The velocity of many chemical reactions, especially those desig- nated as "explosive" must be expressed by very large numbers, even when the unit of time adopted is the second; that of other reactions is so small that the day is the more convenient unit to employ. Most of the reactions which are of importance in quan- titative analysis have velocities which are too great to be deter- mined with even approximate accuracy. Homogeneous and Heterogeneous Equilibrium. In discuss- ing the subject of chemical equilibrium and reaction velocity a very important factor to be considered is whether all the reacting substances, and all of the products of the reaction, exist in the same phase and the nature of this phase. (For a definition of the term phase see page 3.) If all the substances concerned are gases, or if all remain dissolved in the same liquid phase thruout the reaction period, their respective concentrations remain uni- formly distributed thruout the entire mass, and the resulting equilibrium is called "homogeneous." If the reacting substances exist as two distinct phases, or if two distinct phases result as the reaction progresses, the resulting equilibrium is called "hetero- 42 FACTORS WHICH DETERMINE CHEMICAL EQUILIBRIUM 43 geneous." In homogeneous equilibrium the reaction velocity is uniform at all points thruout the reacting mass; in heterogeneous equilibrium the reaction velocity may differ in the different phases, and may be reduced to practically zero except at the surfaces of contact between the different phases. A condition of perfect equilibrium between the different phases of a heterogeneous system must result if they are allowed to remain in contact for a sufficient length of time, but the extent of the surfaces of contact between these phases and the rates at which the products of the reaction diffuse away from the immediate neighborhood of these surfaces materially affect the time needed for the establishment of this equilibrium. Factors Affecting Chemical Equilibrium. There are four fac- tors which materially affect the direction and rate of progress of chemical reactions: first, the chemical properties of the reacting substances; second, the concentrations of the substances taking part in the reaction; third, the temperature; and fourth, the pressure. As regards the first of these factors our present knowledge suggests the theory that among the other specific properties with which every substance is endowed is a certain intensity of chemical energy or chemical potential, and in general, any two substances tend to react with each other to an extent directly dependent upon the difference between the intensity of the chemical energy asso- ciated with them. In other words, there is a universal tendency for the equalization of chemical intensities just as there is a uni- versal tendency for the equalization of heat intensities, and no reaction takes place which does not involve a reduction hi the chemical potential of the mixture. The action of the second factor is expressed in the "Law of Mass Action," which states that the speed of the reaction between any two substances in a mixture is proportional to the product of the concentrations of these substances in that mixture, where the concentrations are expressed in moles per unit volume. According 44 QUANTITATIVE CHEMICAL ANALYSIS to this law the expression for a reaction between the substances A and B which unite to form the substances P and Q is (C A Y (C B y>- k ='(C P )". (C ). A/. In this expression (C^), etc., represent the concentrations of these molecules; a, b, etc., the number of molecules of these substances concerned in the reaction; k a constant representing the speed of the reaction between A and B; and k' a constant representing the speed of the reaction between P and Q. Since k and k' are both constants the expression can be simplified by dividing by k' and substituting K for k -5- &'; it then becomes ~ It might have been simplified by dividing by k, in which case k' + k QT K would have a value represented by the reciprocal of that given in the above expression. Thruout this book the former procedure will be employed, that is, where K is referred to, it should be understood to represent the constant obtained when K appears on the left of the sign of equality in the mass law expression. It is evident that K represents a ratio, whose value depends on the specific properties of the four substances A, B, P and Q, and not upon the concentration in which any one or two of them exist in the mixture. If a mixture is made in which (C P ) P (C Q ) -5- (C A ) a (C B ) b exceeds K, (C A ) and (C B ) must increase, and (C P ) and (C Q ) must decrease until the mass law expression is satisfied, that is, the reaction must progress from right to left. If this quotient is less than K the reaction must progress from left to right. In general, if the value of K is large the predominating tendency is for the reaction to proceed from left to right; if it is a small fraction of unity the predominating tendency is for it to progress from right to left. Since the value of K determines to a large extent the direction in which reactions progress it is called the "reaction constant" or " equilibrium constant." FACTORS WHICH DETERMINE CHEMICAL EQUILIBRIUM 45 The effect of temperature upon a reaction depends upon whether it absorbs or liberates heat. Increasing the temperature displaces the equilibrium in the direction of that reaction which absorbs heat, that is, it increases K if heat is absorbed when the reaction progresses from left to right; it displaces equilibrium in the reverse direction if heat is given out, that is, it decreases K if heat is liberated when the reaction progresses from left to right. The effect of pressure upon a reaction depends upon whether the volume of the reacting mass is increased or decreased as the reaction progresses. If it is decreased, increasing the pressure favors the reaction, and increases the value of K', if it is increased it inhibits the reaction and decreases the value of K. The volume changes in reactions in which only solid and liquid phases are concerned are so small that they have an inappreciable effect upon the value of K. When gases are produced or absorbed as the reaction progresses pressure has a large effect upon the value of K. An Illustration of Homogeneous Equilibrium. The manner in which the factors named in the preceding section affect a simple reaction involving homogeneous equilibrium can be most easily comprehended by considering a specific case, such as the action between acetic acid and ethyl alcohol. These substances as well as the products of their interaction are soluble in each other to an unlimited extent. When acetic acid is added to alcohol the result- ing reaction is represented by (C 2 H 5 )HO + (CH 3 )COOH- (C 2 H 5 )COO(CH 3 ) + H 2 0. If water is added to ethyl acetate, alcohol and acetic acid are produced, that is, the reaction progresses in the reverse direction when the concentrations of water and ethyl acetate are large. If either of the two mixtures are allowed to stand until equilibrium has been attained the concentrations of the four substances in the mixture must be in accord with the expression (C 4 H 8 2 ) (H 2 0) (C 2 H 4 2 ) . (C 2 H 6 0) ' 46 QUANTITATIVE CHEMICAL ANALYSIS in which, and in all of the subsequent pages of this book, a chemical formula enclosed in brackets designates concentrations of the corresponding substance expressed in moles per liter. The value of K in this expression has been found to be 4 and it is easy to calculate the composition of the mixture which results when known quantities of alcohol and acetic acid or of ethyl acetate and water are mixed. Suppose we make a mixture of 240 gm. of acetic acid, 138 of alcohol and 54 of water. If we represent the volume of the mixture before any action takes place by V then (C^EUC^) in that mixture is 240 -*- 60 V or 4 ^ 7, (C 2 H 6 0) is 138 -^ 46 F or 3 ^ F and (H 2 0) is 54 -5- 18 V or 3 -s- V. If x represents the moles of ethyl acetate present after equilib- rium has been attained, x also represents the moles of water pro- duced by the reaction, also (4 x) the moles of acetic acid and (3 x) the moles of alcohol left uncombined. If we represent the final volume of the mixture by V the mass law expression becomes 4 x 3 x . _ x_ 3 + x ~ y y ~ y y ' from which 48 - 28 x + 4 x 2 = 3 x + z 2 . When solved for x the latter is found to have the value 1.9 which means that the final mixture contains 1.9 X 88 or 167.2 gm. of ethyl acetate and 54 + (1.9 X 18) or 88.2 gm. of water. Since the formation of ethyl acetate and water liberates heat, increasing the temperature decreases the value of K and decreases the amount of ethyl acetate and water produced. Since no gases are either produced or absorbed, pressure has no appreciable effect upon the value of K and does not affect the amount of ethyl acetate and water formed. Reversible and Irreversible Reactions. In the reaction dis- cussed in the previous section the constant K has a moderately large value; this means that altho the tendency for the reaction to progress in one direction preponderates over its tendency to progress in the reverse direction, both tendencies are recognizable, FACTORS WHICH DETERMINE CHEMICAL EQUILIBRIUM 47 and where equivalent concentrations of the reacting substances are used, large concentrations of all four substances are present in the resulting mixture. Such reactions are spoken of as " rever- sible." In many reactions, however, the value of the constant K is either very large or small; this means that the tendency for the reaction to progress in one direction greatly preponderates over the reverse tendency, and with equivalent concentrations of the reacting constituents, conversion into the resulting products is practically complete. Such reactions are spoken of as " irre- versible/' altho strictly speaking, all reactions are to be regarded as reversible to some degree even tho it may be difficult to recognize the fact experimentally. Most quantitative processes which depend upon the employment of chemical reactions are inaccurate unless the substance under treatment is almost com- pletely transformed into the desired compound, and reactions whose constants are large are the only ones which can be em- ployed to advantage in such processes. The factors already dis- cussed may be used to assist in displacing the equilibrium of reversible reactions in the desired direction. Reactions Involving Heterogeneous Equilibrium. The factors which affect chemical reactions also affect the processes of evapora- tion and solution, and the simplest illustrations of heterogeneous equilibrium are those in which two- phases containing different concentrations of the same substance are in equilibrium with each other. This is true of a solid or liquid which is in equilibrium with its vapor, or of a solid which is in equilibrium with a solution. All such systems conform to a very simple law, namely, that the ratio between the concentrations of the substance concerned in the two phases is constant for any given temperature. When, for example, a solid substance is brought into contact with a liquid it continues to dissolve until the solution is saturated, that is, when equilibrium between the two phases has been attained the solution contains a fixed concentration of the dissolved substance, and since the 48 QUANTITATIVE CHEMICAL ANALYSIS solid phase represents the pure substance its concentration does not vary, but depends only upon its specific gravity. Hence the general expression for the equilibrium condition becomes K = C, in which C represents the concentration of the saturated solution. The more complex examples of heterogeneous equilibrium will be discussed in Chapters X, XVI and XXXII. Reaction Velocity and Catalysis. The speed with which a reaction progresses depends upon the specific properties of the reacting substances and their concentrations; in general, it is more than doubled for every increase of 10 in the temperature of the reacting mass. The reaction velocity of certain processes is increased in an abnormal manner by certain substances and decreased by others. The former class of substances are known as positive and the latter as negative catalyzers. Very small concentrations of a catalyzer may produce very marked effects, and as they do not suffer an appreciable change in concentration they must act indirectly, that is, form one or more intermediate compounds with the reacting substances which at once decompose into the original catalyzer and the desired end product. According to this theory the velocity of the reaction is increased because the velocities of the intermediate reactions greatly exceed that of the direct reaction between the original substances. They have no effect upon the value of the equilibrium constant, but increase the speed at which a condition of equilibrium is attained. CHAPTER VI THE CHEMICAL ACTIVITY OF ELECTROLYTES Preliminary Statements. In outlining the general principles which determine reaction velocity and equilibrium in the previous chapter the possibility of electrolytic dissociation was not consid- ered. The principles there set forth are universally valid, and if the dissociation theory is also accepted it becomes necessary to point out how these principles should be applied to the study of reactions between electrolytes. Since, according to this theory, the ions possess a greater chemical activity "than the original molecules, the concentrations of the ions should determine the reaction velocity and the resulting equilibrium, to a greater extent than the concentration of the original molecules. Experience confirms this suggestion, for a great variety of well-established facts show that the chemical properties of solutions of largely dissociated electrolytes can be most easily understood by assuming that these properties depend upon the concentrations of the ions which they contain. The Law of Electro-neutrality. Whenever a compound un- dergoes electrolytic dissociation the quantity of positive electricity, which is associated with the resulting cations, exactly equals the quantity of negative electricity, which is associated with the resulting anions, and the solution obtained is, therefore, electri- cally neutral. The quantity of positive charge which is associated with the hydrogen ion is fixed and invariable; all other cations bear positive charges, which are either equal to, or simple multiples of, this charge; all anions bear negative charges which are either equivalent to the positive charge associated with the hydrogen ion, 49 50 QUANTITATIVE CHEMICAL ANALYSIS or to simple multiples of it. The value of these multiples is determined in all cases by the valence of the element, or the com- bination of elements representing the composition of the ion, in the undissociated molecule. Those elements which form com- pounds representing different degrees of oxidation also form ions associated with different amounts of electrical charge, and the properties of such ions depend upon the charges with which they are associated. Thus the cation which results from the dissocia- tion of a ferrous salt differs from the cation resulting from the dissociation of a ferric salt, in that the former consists of an iron atom associated with two positive charges, the latter of an iron atom associated with three positive charges. When solutions containing different electrolytes are brought together various changes may take place. Certain ions which possess but slight affinity for their charges may give them up to other elements or groups of elements and form more stable ions. Certain di- or tri-valent ions may lose a half or a third of their charges, or certain uni- or di-valent ions may take up charges and become di- or tri-valent. In other instances certain charges may disappear entirely from the solution. The law of electro-neutrality requires that, whatever the character or complexity of these changes, the solutions must remain electrically neutral; that is, wherever positive charges disappear, an equivalent number of negative charges must disappear simultaneously; and wherever positive charges are added to the solution, equivalent amounts of negative charges must be added to it at the same time. The Chemical Activity of Acids. All acids which dissociate to an appreciable extent, produce corresponding concentrations of hydrogen ions, and the characteristic properties of aqueous solutions of this class of substances are dependent upon this fact. In so far as these general properties are concerned, the element or combination of elements with which the hydrogen is combined in the undissociated molecule is of importance mainly in that it determines the extent to which the acid undergoes dissociation THE CHEMICAL ACTIVITY OF ELECTROLYTES 51 when dissolved in water. Thus the chlorine atom possesses a greater affinity for a negative charge than the CzH^Oz group, hence the sum of the forces which tend to bring about dissociation of the hydrochloric acid molecule will exceed the sum of the forces which tend to bring about dissociation of the acetic acid molecule; since solutions of both acids must remain electrically neutral, the con- centration of the hydrogen ions in a solution of hydrochloric acid must exceed the concentration of the hydrogen ions in solutions of acetic acid of equivalent concentration. The chemical activity of an acid can be measured by determining the rate at which solutions containing known concentrations of the acid in question affect certain chemical transformations. The chemical activities of solutions containing equivalent amounts of some of the more important acids have been determined by a variety of methods, and the differences in the values thus obtained are found to agree at least approximately with the corresponding variations in the concentrations of the hydrogen ion present, as calculated by the method described on page 40. The conduc- tivity of an aqueous solution of an acid containing one equivalent in grams per liter is, therefore, a measure of its " strength." The comparative conductivities of some of the more important acids are given in the following table in which the conductivity of hydrochlooc acid has been arbitrarily given the value of 100. Hydrochloric acid 100 Hydrobromic acid 104 Nitric acid 99.6 Sulfuric acid 66.4 Oxalic acid 19 . 7 Phosphoric acid 7.27 Arsenic acid 5 . 38 Formic acid 1 . 68 Acetic acid 0.42 Succinic acid 0. 58 Tri-chlor acetic acid 62.3 These numbers relate to normal concentrations only, and increas- ing or decreasing the concentration does not increase or decrease the conductivity, and, therefore, the strength of the solution to 52 QUANTITATIVE CHEMICAL ANALYSIS a corresponding degree. The concentration of the hydrogen ion present in any solution of an acid equals the product of the numbers representing the concentration of the acid, hi gram equivalents per liter, and the degree of dissociation of the acid at that concen- tration. Since the degree of dissociation increases with the dilu- tion the series of numbers given in the table should become more nearly equal with decreasing concentration. The highest attain- able concentration of hydrogen ion is found in a solution of nitric acid having a specific gravity of 1.19; this solution contains about 31 per cent of HNOs, of which about 35 per cent is dissociated, hence the concentration of hydrogen ion represented by such a solution is about 2 gm. per liter. The non-acidic properties of solutions of acids are determined by the concentrations of the anions present, and, also, especially with those acids which are but slightly dissociated, upon the un- dissociated molecules, whose chemical activity cannot be entirely disregarded. The Chemical Activity of Bases. All bases which dissociate to an appreciable extent produce corresponding concentrations of the hydroxyl (HO) ion, and this fact determines the characteristic properties of aqueous solutions of this class of substances. The extent to which different bases dissociate depends upon the nature of the cation to which they give rise, or more specifically upon the strength of the affinity of the cation for its positive charge. The chemical activities of solutions containing equivalent concentra- tions of different bases have been determined by methods similar to those used in the study of acids. The results show a substantial agreement between the chemical activity and the degree of dis- sociation, that is the " strength " of a base is determined by the concentration of the hydroxyl ion which results when it is dissolved in water. The comparative conductivities of fortieth normal solu- tions of some of the more common bases are represented by the numbers of the following table, in which the number 100 has been arbitrarily assigned to potassium hydroxide. THE CHEMICAL ACTIVITY OF ELECTROLYTES 53 Potassium hydroxide 100 Sodium hydroxide 92 Lithium hydroxide 88 . 2 Ethyl amine 12.46 Ammonium hydroxide 2 . 53 The Chemical Activity of Salts. The salts of most acids and bases are largely dissociated in aqueous solutions of moderate concentration, hence the concentrations of the anions or cations present in solutions containing equivalent concentrations of salts of the same' acid or base are more nearly equal, and the chemical properties of such solutions are more nearly uniform. Certain salts, especially certain salts of mercury and cadmium are peculiar in that they ionize to a slight extent only, and as a consequence the reactions of these salts are somewhat anomalous. The phe- nomenon of " hydrolysis," which will be discussed in a succeeding section, is the cause of marked peculiarities in the chemical prop- erties of certain salts. Dissociation in Solutions Containing a Single Electrolyte. The dissociation of an electrolyte should obey the law of mass action. The general expression representing the dissociation of a molecule AB, which yields two ions A + and B~~, is: (A+) (B-) (AB) k = (A+) (B-), or k = (AB) The value of k in this expression depends upon the specific prop- erties of the electrolyte and the temperature; it expresses the tendency of the electrolyte to undergo dissociation, and is generally known as the "dissociation constant." It was noted in Chapter IV that the degree of dissociation of an electrolyte increases with the dilution, and an expression which represents the effect of dilution on dissociation can be derived from the mass law. If we represent the concentration of an electrolyte which dissociates into two ions by a and the fraction of it which is dissociated by x, ax must represent the concentration of both anion and cation and (a ax) that of the undissociated electrolyte. If 54 QUANTITATIVE CHEMICAL ANALYSIS the volume of solution be represented by V the mass law expression is a- ax (ax) (ax) _ a(x) 2 v ~ W 00 ' " (T^W This formula, which was first proposed by Ostwald, has been tested by determining the effect of dilution on the conductivity of a long series of electrolytes. When the value of k was calculated from these determinations it was found to be nearly constant for all the weaker acids and bases, but was found to decrease decidedly with dilution for the strong acid and bases, and for most salts. This means that the dissociation of those electrolytes which are largely dissociated does not increase with the dilution as much as the law of mass action demands. Several modifications of the expression designed to more accurately represent the effect of dilution on the dissociation of these electrolytes have been sug- gested; they all contain one or more empirically determined constants and need not be considered here. The use of the expression given can be shown by a simple illus- tration. Let us suppose that we have two liters of a solution which contains 20 gm. of acetic acid and let us represent the fraction dissociated by x. Then the number of moles present if there were no dissociation would be 20 -f- 60, or 0.333, and both H+ and C2H 3 02~ are represented by 0.333 x, while C2H 4 02 is represented by 0.333 0.333 x. The dissociation constant of acetic acid has the value 1.8 X 10~ 5 ; by making the proper substitutions in the general equation we get 2 _ i 8xl(> -5 (0.333- 0.333 x)2 or 0.333 x 2 + 3.6 X 10- 5 z = 3.6 X 10~ 5 , from which we obtain x = 0.0108. Hence the degree of dissociation and the concentration of the ions in any solution of such electrolytes can be calculated if the con- centration and dissociation constant are known. It might be THE CHEMICAL ACTIVITY OF ELECTROLYTES 55 noted that when the total concentration of the electrolyte is 1, and k has a small value the value of x is approximately equal to the square root of k. For instance, the concentration of H+ in a normal solution of acetic acid is 1 X (1.8 X 10- 5 )s, or 0.00425. Dissociations in Solutions Containing Two Electrolytes Which Yield a Common Ion. It can be shown that when two solutions which contain equal concentrations of the same ion are mixed in any proportions whatever, the dissociation of the two electrolytes in the resulting mixture satisfies the law of mass action if the con- centration of the common ion remains unchanged. Such solutions are designated as "isohydric." Solutions of the two electrolytes are isohydric when the product of the concentration of the elec- trolyte and its degree of dissociation at this concentration is the same for both solutions. When both electrolytes are but slightly dissociated solutions of them are approximately isohydric when their concentrations are inversely proportional to their dissocia- tion constants. When solutions which are not isohydric are mixed, changes in the dissociation of both electrolytes are inevitable. In such mixtures the concentration of the common ion represents the sum of the concentrations due to the dissociation of both electrolytes. If C represents the total concentration of one electrolyte and C' that of the other, and X and Y their respective degrees of dissociation, the concentration of the common ion is (CX + C'F), and assuming that they are both weak electrolytes the following expressions are true. /o\ r. _ (CX + CiY) X (r , Y i si - (CX ~ (4) V = l c _' = pT (CX + C.Y). If we divide (3) by (4) we obtain X Y . 56 QUANTITATIVE CHEMICAL ANALYSIS that is, the ratio of the dissociated to the undissociated molecules of one electrolyte bears the same relation to the corresponding ratio for the other, as the dissociation constants of the respective electrolytes bear to each other. If it is assumed that the second electrolyte is added as a solid, so that the change in volume is eliminated, a reduction in the degree of dissociation of the first electrolyte must take place; this change will be large in proportion as the dissociation constant of the added electrolyte is large as compared with that of the original electrolyte. The degree of dissociation of the added electrolyte must be less than it would have been if added to the same volume of water, and the reduction will be large in proportion as the dissociation constant of the original electrolyte exceeds that of the added electrolyte. If the second electrolyte is added in the form of a solution the effect of dilution on the dissociation of both electrolytes must also be considered. The action of either electrolyte upon the dissocia- tion of the other is large in proportion as the composition of the two solutions differ from that of isohydric solutions. The " Repression of lonization." The most important prac- tical result of the above discussion is to give a better under- standing of the phenomenon now known as the "repression of ionization." The chemical activity of certain reagents is greatly diminished by the addition of certain electrolytes which yield a common ion. The addition of potassium acetate to a solution of acetic acid greatly reduces the acidic properties of the latter; the addition of ammonium chloride to a solution of ammonium hy- droxide also reduces the basic properties of this reagent. In both cases the reagents added have large dissociation constants, and those originally present have small ones. If the solution of potas- sium acetate added contains a greater concentration of C 2 H 3 2 ion than the acetic acid solution, the degree of ionization of the latter must be reduced, and the concentration of the hydrogen ion in the resulting mixture must be less than that of the original THE CHEMICAL ACTIVITY OF ELECTROLYTES 57 solution. Similarly, if the solution of ammonium chloride added is sufficiently concentrated to yield a greater concentration of NKU ion than the ammonium hydroxide solution, the degree of ioniza- tion of the latter, and hence the concentration of the hydroxyl ion, must be reduced. Reactions Between Electrolytes Which Do Not Yield a Com- mon Ion. The most important effects to be considered here result from the formation of entirely new compounds. If both electrolytes yield one anion and one cation at least two undis- sociated molecules, in addition to the two undissociated molecules present in the original solutions, should exist in the resulting mixture. The concentrations of these molecules will depend for the most part upon their respective dissociation constants. If these constants are large their concentrations will be very small, and the resulting mixture will retain for the most part the com- bined properties of the two constituent solutions. If, however, one of these constants is small this favors the formation of the new molecule at the expense of the ions concerned. Reactions which Involve the Formation of Water. Pure water dissociates into hydrogen and hydroxyl ions to a very slight extent only; the value of its dissociation constant is 1 X 10~ 14 . When an acid is added to a base, water and a salt are formed. If both acid and base are strong, and the concentration of the resulting mixture is small, their dissociation may be considered complete, and with but few exceptions the dissociation of the resulting salt can also be considered complete. The essential feature of the reaction therefore is the disappearance of hydrogen and hydroxyl ions and the formation of water; the concentrations of the anion of the acid and the cation of the base remains practically constant. Hence the reaction is expressed by H+ + HO--HA and K = Since (H 2 0) -f- (H+) (H0~) is the reciprocal of the expression representing the dissociation constant of water, K has the value 58 QUANTITATIVE CHEMICAL ANALYSIS 1 -T- 1 X 10~ 14 and therefore all reactions of this type are very nearly complete. If both acid and base are but partly dissociated the reaction con- stant may have a small value only. The most important equilib- rium concerned in such reactions is expressed by ROH + HA->H 2 + R+ + A- in which ROH represents a weak base and HA a weak acid. Three other relations must also exist in the final solution, namely : (R+KHO-) (H+XA-) (H+KHO-) (ROH) (HA) H 2 If we multiply (a) by (b) and divide by (c) we obtain the expression ) (H 2 0) k a -k b (ROH) (HA) k w This expression shows that the value of the constant for this class of reactions depends upon, and can be calculated from, the disso- ciation constants of the acid and base and of water. If the acid is strong its dissociation constant can be represented with ap- proximate accuracy by one, and the general expression becomes zr_ kb IT' tvw If the base is strong its dissociation constant can be represented with approximate accuracy by one, and the general expression be- comes Hydrolysis. This represents the converse of the class of reac- tions just considered. It is expressed by (R+) + (A-) + H 2 -> (ROH) + (HA). THE CHEMICAL ACTIVITY OF ELECTROLYTES 59 The value of K for such reactions is evidently the reciprocal of that representing the formation of a salt and water from a weak acid and a weak base, namely, ivy) K= k a k b Evidently K has a maximum value when k a and k b are both very small, but it may be moderately large when either of them has a value which approaches that of k w . The effect of hydrolysis is most striking when the salt yields either a strong acid and a very weak base, or a strong base and a very weak acid. In the former case the solution contains a con- centration of hydrogen, and in the latter case of hydroxyl ion, which is directly proportional to the extent to which the salt is hydrolyzed, and for this reason solutions of salts representing combinations of strong acids and weak bases show acidic properties and solutions of salts representing combinations of strong bases and weak acids show basic properties. If the dissociation con- stants of the acid and base formed have the same value the solution will contain equivalent concentrations of hydrogen and hydroxyl ions and hence, such solutions are neutral even though the salt is hydrolyzed to a much greater extent than when one dissociation constant is large and the other small. Reactions Involving the Displacement of One Acid or Base by Another. When a salt which represents the result of the combination of a base with a weak acid is treated with a second acid a reaction becomes possible which is represented by (R+) (A-) + (HA 2 ) - (R+) + (A.-) + (HA) (Ar) (HA) (A-)(HA 2 )' Two other equilibria must exist in the resulting solution, namely, (H+)(Ar) (HA 2 ) n " (HA) 60 QUANTITATIVE CHEMICAL ANALYSIS If we divide (a) by (b) and eliminate (H) we obtain (A 2 -)(HA) k^ (A-)(HA 2 ) /CHA " Hence the completeness of such reactions increases in proportion as the dissociation constant of the added acid exceeds that of the acid from which the original salt was formed. If the dissociation constant of the added acid can be represented with approximate accuracy by one, the value of K becomes the reciprocal of the dissociation constant of the acid from which the salt was formed. Similarly it can be shown that the reaction constants of those processes which involve the displacement of one base from a salt by a second base depend upon the ratio of the dissociation constant of the second base to that of the base from which the original salt was formed. Reactions Involving the Formation of Complex Ions. Certain reactions depend upon the tendency which certain ions possess of combining with other ions or non-ionized molecules to form com- plex ions. For example, when a soluble silver salt is added to a soluble cyanide a reaction takes place which is represented by Ag+ + N0 3 - + 2 K+ + 2 CN- - Ag(CN) 2 - + K+ + NOr. The essential feature of this process is the formation of AgCN 2 ~ from Ag + and 2CN~, a process which involves the loss of one positive and one negative charge. The mass law requires that (Ag(CN) 2 )- (Ag+)(CN) 2 - K is here a constant which is a numerical expression for the tendency of the complex ion to form and may be designated as the " complex ion constant." In this example it has a very large value, namely, 1 X 10 21 , and hence the reaction is practically a complete one. CHAPTER VII METHODS OF PRODUCING AND APPLYING HEAT Sources of Heat Used. Many quantitative operations depend for their success Upon the maintenance of definite temperatures for either long or short time intervals. The range of temperatures used is wide, and a great number of devices become desirable or necessary if efficiency and speed are to be attained. Altho it costs less under normal conditions to produce heat by the consumption of gas than of electrical energy, the latter method is more directly and easily controlled, and frequently the difference in cost is more than offset by the greater certainty with which it can be used, and the absence of undesirable products of combustion. Heating with an Electric Current. The amount of heat pro- duced by the passage of a current through a resistor varies with the product of the resistance offered and the square of the current transmitted, and, therefore, depends upon the current strength to a greater extent than the resistance. Various materials are used as resistors in constructing devices for this purpose; the most convenient are certain alloys, such as German silver, monel metal, and nichrome, which possess a high specific resistance, a high melting point and ability to resist oxidation at high tempera- tures. The alloy last named possesses all of these properties to a maximum degree and can be obtained at small cost in wire or ribbon of any desired size. In constructing an electric heating device the factors of greatest importance are the voltage of the current available, which may be either direct or alternating, the masses and specific heats of the substances used hi its construction, the losses from radiation, and 61 62 QUANTITATIVE CHEMICAL ANALYSIS the temperature which it is desired to attain. If the voltage is fixed the length and size of the wire used as a resistor are the essential features to be decided on, and, owing to the large number of variables concerned, this must be determined by experiment rather than by calculation. It may be noted, however, that a long piece of coarse wire forms a more durable resistor than a short piece of fine wire which has an equal resistance. The temperature attained with such devices is fairly constant so long as the voltage and radiation losses are constant. It can be reduced by reducing the voltage, and is therefore easily regulated, that is for tempera- tures attained with the maximum voltage, by introducing a rheo- stat in the circuit. Devices Used for Evaporation, The evaporation of solutions rarely necessitates the use of temperatures greatly in excess of 100. Temperatures somewhat below this point, but sufficient for the evaporation of most aqueous solutions, are conveniently attained by the use of a "steam bath," that is, a vessel in which water is made to boil vigorously, either by a coil of steam pipes or by the flame of a gas burner, and which has a cover provided with openings for the receptions of the vessels containing the solutions to be evaporated. A bath of a sufficient size to accommodate a large number of such vessels is an essential part of the equipment of a quantitative laboratory. It has the great advantage of keeping the solutions at a uniform temperature well below the point at which mechan- ical losses are to be anticipated. Direct heating of the vessel contain- ing the solution by a flame is usually avoided by interposing a plate of metal, forming a "hot-plate," or a tray filled with sand, forming a " sand A sand bath of this character is represented in Fig. 7. It gives a higher temperature, Fig. 7. Sand Bath bath," between the flame and the vessel. METHODS OF PRODUCING AND APPLYING HEAT 63 and, therefore, more rapid evaporation than the steam bath, and can be controlled by varying the gas supplied to the burner or the thickness of the layer of sand used. It is especially useful where the liquid is retained in a flask and gentle ebullition is not objectionable. When it becomes necessary to attain still higher tempera- tures, as in the evaporation of sulfuric acid, the vessel contain- ing the substance to be evapo- Fig. 8. Asbestos Muffle Fig. 9. Air Bath rated may be placed inside a " muffle," that is, an outer shell which protects the inner vessel from the flame and permits it to be heated by radiation only. A large nickel or iron crucible can be used as a muffle for this purpose, but the device represented in Fig. 8, which is made of heavy asbestos board and bound with sheet iron, is more durable. Devices for Drying Solids. The amount of vapor to be ex- pelled in drying solids is usually small, as compared with that expelled in evaporating liquids, and the apparatus used may take the form of a rectangular oven, such as is represented in Fig. 9. 64 QUANTITATIVE CHEMICAL ANALYSIS Its temperature can be roughly regulated by varying the height of the flame or the size of the burner by which it is heated; if greater refinement is necessary an automatic gas-regulator, which increases or decreases the gas supply as the temperature falls below or exceeds that for which the regulator is set, can be used. Ovens of larger size which are used for cooking and can be obtained from hardware dealers can often be used to advantage. Still another device, represented in Fig. 10, consists of a double- walled oven, in which the intervening space is filled with a liquid whose boiling point is slightly above the temperature desired. This liquid is kept at the boiling point by means of a burner, and the vaporized liquid is condensed + and returned to the oven as fast as produced. The liquids most frequently used are water, which gives a temperature of about 96, and toluene which gives a temperature of nearly 105. In all devices of the oven type the water vapor which is generated escapes but slowly and their effi- ciency, that is, the rate at which Fig. lO.-Constant-temperature Oven drying ig affected) j g ^ great A further objection to ovens heated by gas is that some of the combustion products may enter the oven and produce objection- able effects upon the substance being dried. For this reason the electrically heated ovens, which can now be purchased from dealers in chemical apparatus, are to be preferred to all others; their cost, however, is somewhat large. Temperatures Attainable by the Use of Gas Burners. Direct heating of the substance in a crucible is always to be preferred where there is no danger of exceeding the maximum permissible METHODS OF PRODUCING AND APPLYING HEAT 65 temperature. The temperature actually attained inside of the crucible depends upon the type of burner used, the calorific value of the gas burned, and the masses and specific heats of the sub- stances heated, that is, the crucible used, the triangle used to support it, and the substance which it contains. The Bunsen burner is decidedly inferior to the more recently devised Meker burner, a vertical projection of which is represented in Fig. 11. In the former the air supplied at the base is not sufficient for the gas burned and a long cone-shaped flame results; the area over which active combustion takes place is comparatively large, and the highest temperature is attained at the apex of the inner blue cone. In the Meker burner the air supplied at the base is sufficient, but "striking back" is prevented by the grid and enlargement at the outlet; the entire combustion takes place within a few millimeters of the top of the grid, and the heating effect is therefore concentrated in a single horizontal plane. The temperatures actually attained in the in- Fig. 11. M^ker terior of uncovered crucibles of different sizes and materials, which were heated on triangles of nichrome wire by the two forms of burners, are given in the following table: Berlin Berlin Berlin Crucible heated porcelain porcelain porcelain Platinum 00 1 Capacity 10 CC. 15 CC. 23 cc. 14 cc. 29 cc. Temperature with Bun- sen burner .... 820 780 720 840 780 Temperature with Meker burner 880 840 770 890 805 66 QUANTITATIVE CHEMICAL ANALYSIS Somewhat higher temperatures are attained by using covers on the crucibles, but this prevents the circulation of air within the crucible and the escape of gases which may be liberated by the substance heated in the crucible, both of which effects are unde- sirable. Still higher and more uniform temperatures can be reached by surrounding the burner and crucible with a shield, which cuts off air-currents and greatly reduces the radiation losses. This device is utilized in the burner devised by Chaddock, a vertical projection of which is repre- sented in Fig. 12. Combustion of the gas used is effected exactly as in the Bunsen burner, but the entire burner is made of porcelain, and a fire-clay chimney which fits upon it loosely both reduces the losses from radiation and forms a support for a triangle over which a crucible can be heated. Where still higher temperatures are needed a " blast lamp," that is, a burner which is supplied with a blast Fig. 12. -Chaddock Burner of air > or an electric furnace can be used. An effective blast lamp is ca- pable of producing a temperature of 1100 in a platinum crucible of moderate size. Construction of an Electric Furnace. Small electric furnaces designed to heat crucibles of moderate size, which can be pur- chased from dealers, are extremely advantageous. The plan of an inexpensive and easily constructed furnace is represented in vertical and horizontal projection in Fig. 13. The heating unit consists of an alundum core (A) two inches in diameter, around which is wound 15 feet of No. 23 nichrome wire coiled in the form of a helix four feet long and one-eighth of an inch in diameter. METHODS OF PRODUCING AND APPLYING HEAT 67 The core and helix rest upon a piece of asbestos board supported by a ring of porcelain (B); it is placed in the center of a cylinder of sheet copper some four inches in diameter, which is supported in a vertical position by means of a wooden base (C); but is insulated from the base by strips of thick asbestos. The entire space between the core and cyl- inder is filled with a compact mass of asbestos. The ends of the helix are brought thru but insulated from the copper cylin- der and attached to binding posts screwed into the base. When this furnace is attached to a 110-volt circuit it consumes about 3 amperes of current. When a crucible is placed in- side the core and the furnace is covered, the temperature inside the crucible rapidly rises to 1000. A lower temperature can be attained by placing a rheo- stat in series with it, but it is more economical to construct Fig. 13. -Plan of an Electric Funw* other furnaces which offer a greater resistance where lower tem- peratures are desired. CHAPTER VIII THE REMOVAL OF UNDESIRABLE CONSTITUENTS BY EVAPORATION Factors to be Considered. It is frequently necessary to re- duce the volume of the solution containing the substance being 'analyzed or to eliminate certain volatile constituents by evapora- tion. The factors which determine the rate at which evaporation takes place are the vapor pressure of the solution at different temperatures, the rate at which the vapor formed is carried away from the surface of the liquid, the extent of this surface and, where the temperature used is that of the boiling point, upon the efficiency of the heating device employed. The phenomenon of boiling is due to the fact that bubbles of vaporized liquid are constantly forming at the bottom or in the interior of the mass of liquid and passing to its surface; these bubbles are often pro- jected above the surface of the liquid with considerable violence, and may carry with them small quantities of the solution being evaporated. Hence, unless a special form of apparatus is used, which prevents the escape of these particles, appreciable losses of the non-volatile constituents of the solution may occur. This difficulty is somewhat intensified by the phenomenon of " super- heating," in which portions of the liquid which are in immediate contact with the bottom of the containing vessel are temporarily heated above the normal boiling point and then suddenly vapor- ized, it can be avoided by agitating the liquid, or by adding to it a small piece of platinum wire or some other good conductor of heat. If a mixture of a solid and a liquid is being evaporated the phenomenon known as "bumping" may occur. It is due to the 68 REMOVAL OF UNDESIRABLE CONSTITUENTS 69 fact that the solid, especially when it has a high specific gravity, packs together on the bottom of the containing vessel, and bubbles of vapor accumulate between this layer and the bottom of the vessel. Their pressure finally overcomes that of the layer and in escaping they throw masses of the mixture out of the vessel with considerable violence. This difficulty does not arise if the tem- perature is kept somewhat below the boiling point, or if the mixture is stirred vigorously. Evaporation can be greatly hastened by sucking the vapor formed from the containing vessel by means of a suction pump, or by directing a current of air against the surface of the liquid by means of a force pump. Either device cools the surface appreci- ably, but as a more efficient heating device can then be used, the rate of evaporation can be greatly increased. Methods of Effecting Evaporation. Two extremes are repre- sented in the methods used to effect rapid evaporations. Either the liquid is placed in a shallow evaporating dish and heated to a temperature somewhat below its boiling point, or it is placed in a flask or narrow beaker and boiled violently. The latter method is somewhat more rapid but requires care and watchfulness on the part of the analyst, and is always subject to the possibility of small mechanical losses. Where the former method is used, a heating device which permits of a rapid and constant control of the temperature is necessary. Direct heating over a flame, even though the vessel is protected from it by a piece of wire gauze, is not to be recommended. The use of a water or " steam bath," which insures a temperature somewhat below 100, is usually very satisfactory. A sand bath, or a hot plate give higher temperatures and more rapid evaporation but involve possibilities of mechanical losses. Evaporation of Mixtures of Two Volatile Substances. When two substances, which possess appreciable vapor pressures and form homogeneous solutions, are mixed together a reduction in the vapor pressures of both constituents takes place, and the sum 70 QUANTITATIVE CHEMICAL ANALYSIS of the vapor pressures of the two constituents in the mixed vapor phase is less than the sum of the vapor pressures of the pure sub- stances at the same temperature. The extent to which one con- stituent of such a mixture lowers the vapor pressure of the other, varies with different pairs of liquids, but all known examples be- long to one of three types. These types can be differentiated most readily by plotting the curves representing the total vapor pres- sures of the two constituents in the mixed phase corresponding to all possible mixtures of these constituents. Such curves are repre- sented in Fig. 14, in which the ordinates represent vapor pressures, A 10 20 30 40 50 60 70 80 90 B Fig. 14. Curves Representing Vapor Pressures of Mixed Liquids and the abscissas the comparative amounts of the two constituents A and B. In type I the total vapor pressure of the mixture in- creases continuously from a, corresponding to the pure constituent A, to 6, corresponding to the pure constituent B. In type II the total vapor pressure attains a minimum value at p, that is, it is reduced by adding B to pure A or A to pure B up to the concentra- tion which yields the minimum value p. In type III the total pressure attains a maximum value at q, that is, it is increased by adding B to pure A or A to pure B up to the concentration which REMOVAL OF UNDESIRABLE CONSTITUENTS 71 gives the maximum value q. Since the boiling points of such mix- tures depend directly upon the sum of vapor pressures of the two constituents the boiling points of mixtures representing type I decrease continuously as the percentage of that constituent which has the greater vapor pressure increases; whereas the boiling points of mixtures representing type II attain a maximum and those of type III attain a minimum at certain concentrations of the two constituents. If then mixtures belonging to type II are continuously evaporated the composition of the mixture changes up to the point at which it has the maximum boiling point; those representing type III must change up to the point at which it has the minimum boiling point. Mixtures which are characterized by constant boiling points yield mixed vapor phases in which the relative amounts of the two constituents are the same as in the corresponding liquid phases. Removal of Acids by Evaporation. The mixtures of this kind which are most frequently dealt with in quantitative work are aqueous solutions of acetic, hydrochloric, nitric and sulfuric acids; the first three of these mixtures belong to type II. The rate at which any one of these acids is driven out of an aqueous solution thru evaporation depends mainly upon the concentration of that acid in the mixed vapor phase. Useful data can therefore be secured by evaporating aqueous solutions of these acids at their boiling points, condensing and collecting the vapor given off at definite time intervals, and determining the composition of the condensed liquid and of the solutions from which they were dis- tilled. The results of a series of determinations * of this kind are given in the curves of Fig. 15. The ordinates represent the per- centages of the various acids in the distillates and the abscissas those of the acids in the corresponding solutions. These curves at once show the comparative volatilities of the different acids and the concentrations which must be attained before they can be driven out with even reasonable rapidity by * From experimental data obtained by the writer. 72 QUANTITATIVE CHEMICAL ANALYSIS evaporation. It will be noted that in evaporating solutions of acetic acid the concentration of the liquid increases at a uniform rate until the residual solution contains about 80 per cent. Solu- 1UU H 2SC^4 90 85 80 75 70 |65 1 60 Q c 55 |50 -045 25 20 15 10 5 H ^ 3 H( : 2 H 3 2 \ P /> / / / / / X r // f X / / / ^ ' / \ Cl & X / / / j> /f / /0 ^ / ^ ? X f- -"-^ > it- * } ' t=2 . ^ _J J 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Percentage of Acid in Solution Fig. 15. Curves Showing the Changes in Concentration which Result when Dilute Acids are Distilled tions of hydrochloric acid concentrate very rapidly at first, then more slowly until a mixture which has a constant maximum boil- ing point of 110, and contains 20.2 per cent of acid, is obtained. The behavior of nitric acid resembles that of hydrochloric, but the constant-boiling mixture contains 68 per cent of acid, and boils at 120. Sulfuric acid on the other hand is not appreciably vola- tilized until the solution has attained a concentration of about 98 REMOVAL OF UNDESIRABLE CONSTITUENTS 73 per cent, which requires a temperature of more than 250. Com- plete removal of any of these acids cannot be effected unless the solution is evaporated to dryness; the total amount left in any solution which has been concentrated to a constant boiling point mixture can be calculated from the volume left and the composition of this mixture. The theory, of the removal of acids from solutions containing two or more acids is not so easily followed, for, altho the addition of a second acid reduces the volatility of the first, interaction between the two acids may take place. Thus when both hydro- chloric and nitric acids are present a reaction represented by the equation given below becomes possible : HN0 3 + 3 HC1 -> NOC1 + 2 H 2 + C1 2 . The reaction constant has a relatively small value, and unless the concentrations of the two acids are large but little chlorine is liberated. At high concentrations and especially at moderately high temperatures the NOC1 formed breaks down into NO and Cl2, and complete decomposition and expulsion of the acid which is not present in excess is rapidly effected. Hence it is possible to expel either acid by adding an excess of the other acid, and evaporating the solution sufficiently. CHAPTER IX THE CALCULATION OF RESULTS Calculation of Chemical Factors. The general formula for the calculation of the results of any direct gravimetric process is Weight of substance separated ., . . irvr . , . , . . . = - X / X 100 = desired percentage. Weight of sample used In this formula / represents the factor by which the weight of the separated substance must be multiplied to give the equivalent weight of the substance whose percentage is to be reported. Since the substance weighed and the substance reported may have the same chemical formula, / may have the value 1 ; usually it has a different value, which may be either greater or less than 1, and can be calculated from the atomic and molecular weights of the substances concerned. If a precipitate of Mg 2 P 2 O7 has been separated, and it is desired to report the percentage of P present, it would be reasoned that every molecule of Mg 2 P20 7 separated represents two atoms of P in the sample, and hence the desired factor is obtained by dividing two times the atomic weight of phosphorus by the molecular weight of magnesium pyrophosphate. If a precipitate of Fe 2 03 has been separated, and it is desired to report the FeaC^ present, the reasoning would be that for every three molecules of Fe 2 03 found, two of Fe 3 04 must have been present and the proper factor to employ is 2 FesC^ -s- 3 Fe 2 03. It should be especially noted that the number and character of the reactions concerned in the production of the substance which is separated from the sample are of no significance. When a substance which contains FesC^ is analyzed by separating Fe 2 Oa 74 THE CALCULATION OF RESULTS 75 from it, it can be assumed that since the process is a quantitative one all of the iron present as Fe 3 4 is transformed into FegOs, and, further, that no additional iron in any form is introduced. Determination of Chemical Factors Experimentally. The value of / can also be determined experimentally by submitting a sample containing a known percentage of the substance which is to be reported upon to the process concerned, and calculating the ratio of the weight of the substance known to be present in the sample used to the weight of product separated. An empirically determined factor of this kind is subject to errors of the same kind and magnitude as those concerned in the actual determination. If the process is a complex one, in which subsidiary reactions are possible, and large errors of any kind are to be expected, the empirically determined factor is the logical one to use, for by using it the errors involved in the actual determination are partly or wholly counterbalanced. If the process is based upon a few simple and definite reactions and is not subject to any large errors the calculated factor should be used, since it is based upon experi- mental work of much greater accuracy than that employed in the determination of the empirical factor. The System of Atomic Weights Used. The atomic weights of th various elements are calculated with respect to the atomic weight of hydrogen with a value of 1, or with respect to that of oxygen with a value of 16. The actual ratio of the atomic weights of these elements is 1.008 : 16 and, hence, the systems based upon the two standards differ slightly. In calculating the factors used in analytical chemistry either system may be used with equal accuracy, provided all the weights made use of are referred to the same system, and with about equal facility. The atomic weights which will be used in this book are those adopted by the International Committee on Atomic Weights in 1916. Form in Which Results Are Reported. The form in which the results of an analysis is reported admits of some degree of choice, which depends largely upon the object for which the analysis is 76 QUANTITATIVE CHEMICAL ANALYSIS Element Sym- bol Atomic weight Element Sym- bol Atomic weight Al urn i num Al 27 10 Mercury Hg 200 6 Antimony Sb 120.20 Molybdenum Mo 96.00 Ars6nic As 74 96 Nickel No 58 68 Barium Ba 137 37 Nitrogen N 14 01 Bismuth Bi 208 00 Oxygen o 16.00 Boron B 11 00 Phosphorus P 31.04 Bromine Br 79 92 Platinum Pt 195.20 Cadmium Cd 112 40 Potassium K 39.10 Calcium Ca 40.07 Selenium Se 79.20 Carbon c 12 00 Silicon Si 28 30 Chlorine Cl 35 46 Silver Ag 107 88 Chromium Cr 52 00 Sodium Na 23 00 Cobalt Co 58 97 Strontium Sr 87.63 Copper Cu 63 57 Sulfur S 32.06 Fluorine F 19 00 Tellurium Te 127.50 Gold Au 197 20 Thallium Tl 204.00 Hydrogen H 1.008 Tin Sn 118.70 Iodine I 126.92 Titanium Ti 48.10 Iron Fe 55 84 Tungsten W 184 00 Lead Pb 207 20 Uranium u 238 20 Lithium Li 6 94 Vanadium . V 51 00 Magnesium . . . Mg 24 32 Zinc Zn 65.37 Manganese Mn 54.93 Zirconium Zr 90.60 made. In general, it is advisable to report all results in such a form as will indicate most nearly the actual composition of the sample. Thus, if nitrogen is determined and reported as such, there is no means of knowing which one of the various forms in which that element may be combined is represented, whereas if the report is in terms of NH 3 , NzO^ or N 2 03, the presence of cor- responding percentages of ammonia, of nitrates or of nitrites is clearly shown. Since oxygen, unless it is in the free condition, is but rarely determined it is customary to combine it with the metals or metalloids actually present in the report made. This makes it readily possible to show the degree of oxidation of these elements and to account for everything present, that is, to make the analysis sum up to 100 per cent. Thus in the analysis of THE CALCULATION OF RESULTS 77 crystallized ferrous sulfate it is desirable to report the percentages of FeO, S0 3 and H 2 O rather than Fe, S, and H. It should be noted that if salts, such as chlorides or sulfides, which do not contain oxygen, are present, and all of the bases present are reported as oxides, more oxygen will be included in the summation than is actually present. The proper correction is then made by subtracting the oxygen equivalent of the chlorine and sulfur from the summation; this then appears in the summary as "less oxygen due to chlorine and sulfur." When a solution is submitted to analysis it is now customary to report the ions present. Formerly an attempt was made to cal- culate and report the probable salts present, that is, to combine the acidic and basic radicals according to certain arbitrary rules. This method is misleading if the validity of the electrolytic dis- sociation theory is granted. Abbreviation of Calculations. Altho the calculations of ana- lytical chemistry involve simple multiplications and divisions only it will be found advantageous to make use of logarithms or of a slide rule. Where a large number of determinations are made by the same process and the same chemical factor is used, time can be saved by preparing a table showing the values of those multiples of this factor which may be needed most frequently. Still another method of arriving at the same result is to plot a curve, in this case a straight line, showing the relation between this factor and certain multiples of it. Many handbooks containing tables of this kind and other information frequently needed by the analyt- ical chemist have been prepared.* Another device which is sometimes used is to employ "factor weights" in making the analysis. If the quantity of sample employed is made equal to / of the general formula the desired percentage is exactly 100 times the weight of the separated sub- * Van Nostrand's Chemical Annual by J. C. Olsen; Chemists' Pocket Manual by R. Meade; Laboratory Calculations and Specific Gravity Tables by Adriance; Conversion Tables for Iron Analysis, by Allen. 78 QUANTITATIVE CHEMICAL ANALYSIS stance. If the factor weight is larger or smaller than it is desirable to use, a simple fraction or multiple of it can be used with nearly equal advantage. Calculation of Indirect Determinations. It is sometimes ad- vantageous to analyze certain kinds of mixtures by so-called "indirect methods." Thus it is possible to calculate the per- centages of sodium and potassium chlorides in mixtures of these salts from the total percentage of chlorine in the mixture, which can be easily determined with great accuracy. If the percentage of sodium chloride in such a mixture be represented by x, then 100 x must represent the percentage of potassium chloride, and if the percentage of chlorine in it be represented by a, the following relation is true: from which the percentages of sodium and potassium chlorides are easily calculated, Another method of attaining the same result consists in ascer- taining the factor representing the relation between a known weight of the mixture and the weight obtained when the chlorides present are completely changed into sulfates, which change is easily effected by evaporating with an excess of sulfuric acid. If this factor be represented by b, the following relation is true : Na 2 S0 4 ^ 24 - 1006 c) " )b > from which the desired percentages can be calculated. The former process is based upon the difference between the ratio Cl -r- NaCl and the ratio Cl -f- KC1. This amounts to only 0.131 and an error in the determination of chlorine in the unknown mixture is multiplied by 1 -f- 0.131 or 7.64 in the per- centages reported. This suggests the chief objection to such processes, that is, relatively small errors in the determination of chlorine in the mixture arid the presence of small amounts of THE CALCULATION OF RESULTS 79 additional substances make large errors in the final results. The second process depends upon the difference between the ratio K 2 S0 4 -5- 2 KC1 and Na 2 S0 4 *- 2 NaCl, which has the value 0.0465 and considered from this standpoint is less desirable than the first process. Calculation of Chemical Formulae. The analytical chemist is sometimes required to calculate the probable formula of an unknown substance from the results of his analysis. If each of the percentages obtained are divided by the respective atomic or molecular weights, a series of figures are obtained which repre- sent the relative number of atoms or molecules present in the molecule whose formula is sought. The numbers actually ob- tained will not usually be entire integers and some of them may be less than unity. Since no chemical formula which involves the use of fractions is permissible it becomes necessary to multiply or divide the entire series by a factor which will most nearly reduce them all to whole numbers. The simplest method of procedure is to first note which of the series has the smallest value, and to divide the entire series by this value. The results represent the simplest formula which can be assigned to the substance; the cor- rect formula cannot be calculated unless the molecular weight is also known. For .example the analysis of an unknown mineral gave the series of figures which appear in the first column given below : K 2 = 15.41 -^ 94.3 = 0.1634 1.00 MgO = 6.58 -5- 40.36 = 0.1630 1.00 CaO = 18.80 -5- 56.10 = 0.3351 -f- 0.163 = 2.05 SO 3 = 52.91 * 80.07 = 0.6597 4.05 H 2 O = 5.84 -f- 18.02 = 0.3241 1.99 Dividing by the proper molecular weights gives the figures which appear in the third column, and dividing these by 0.163 those of the last column. The simplest probable formula of the mineral is therefore K 2 MgCa2(S0 4 ) 4 2 H 2 0, which represents the mineral polyhalite. 80 QUANTITATIVE CHEMICAL ANALYSIS Calculation of Volumes of Gases. The analytical chemist frequently finds it necessary to calculate the volumes occupied by specified weights of solids or liquids after they have been changed into the gaseous state. Such calculations are easily carried out by making use of the fact that one mole of any gaseous substance when measured at zero degrees and 760 mm. pressure, occupies a volume of 22.4 liters. Another form of this relation is expressed by the statement that the weight of one liter of oxygen under these conditions is 1.428 gm. and that of any gas equals 1.428 times the ratio between the molecular weight of that gas and the molecular weight of oxygen. Changes in volume resulting from changes in pressure are easily calculated by use of the Law of Boyle, the variations from which are small if the gas concerned is well above its critical temperature, and the pressure does not exceed an atmosphere. According to this law, if v represents the volume of a gas at pres- sure p, its volume v' at the pressure p' is found by the relation Changes in volume resulting from changes in temperature are usually calculated with sufficient accuracy from the Law of Gay- Lussac. According to this law if v represents the volume of a gas at the temperature t its volume v' at the temperature t' is calculated from the relation 273 + t' 273 + T SECTION II GAS-EVOLUTION PROCESSES CHAPTER X GENERAL FEATURES OF GAS-EVOLUTION PROCESSES The Decomposition of Carbonates. The simplest examples of this class of determinations are those in which the formation of a gaseous product is effected by a change in temperature. The determination of carbon dioxide in certain carbonates furnishes a good illustration. The decomposition of calcium carbonate is expressed by the reaction CaC0 3 -> CaO + C0 2 . The" system here represented consists of two solid phases, each of which is a pure substance and therefore has a constant concentra- tion, and a gas phase, the composition of which can vary. Since the concentrations of CaCOs and CaO in the solid phases are con- stant the concentrations of these substances in the gas phase must remain constant so long as appreciable amounts of the two solids are present and can be represented by k and k' respectively. The expression for the equilibrium in the gas phase then becomes K _U (CO,) ~k~ which can be reduced to K p = (CO 2 ), or K' = (C0 2 ). That is, a constant which is a simple multiple of the true equilib- rium constant and which, unlike the latter, can be determined 81 82 QUANTITATIVE CHEMICAL ANALYSIS experimentally, may be used in place of the true equilibrium constant in discussing chemical equilibria in this and all similar reactions. Since equal volumes of all gases, when measured at the same temperature and pressure, contain the same number of molecules (Avogadro's hypothesis), the pressures exerted by all gases are proportional to their concentra- Pin mm of Mercury 100 CaC 3 Li 2 C0 3 BaCOa 10 8 as a meas- ure of the latter. The total pressure exercised by the gas phase in contact with a mixture of CaO and CaC0 3 must equal that of the atmosphere, unless contained in a closed vessel, and since the pressures exerted by each of these gases are in- dependent of each other (Dai- ton's Law) each kind of gas can be thought of as exercising a " partial pressure," and if so the sum of the partial pressures of Fig. 16. The Dissociation Pressures a ii the gases represented must of Carbonates * * ,, ,. , , , equal that of the atmosphere. Hence the value of K' in the preceding expression can be ex- pressed in terms of the number of mm. of mercury to which the partial pressure of the carbon dioxide in equilibrium with CaO and CaCOs is equal. If such a mixture is in contact with a gas phase in which the partial pressure of the carbon dioxide is less than K' more carbonate will decompose, and the partial pressure of the carbon dioxide will increase; if the partial pressure is greater than K' carbonate will be formed and the partial pres- sure of the carbon dioxide will decrease. The effect of varying temperature upon the dissociation pres- sures of the carbonates of calcium, lithium and barium is shown GENERAL FEATURES OF GAS-EVOLUTION PROCESSES 83 in Fig. 16; in all cases the value of K increases very rapidly with increasing temperature. As the concentration of C02 in air of normal composition corresponds to a pressure represented by a very small fraction of a millimeter of mercury, it should be possible to effect complete decomposition of all the carbonates named, by heating them to easily attainable temperatures, pro- vided the carbon dioxide produced is not permitted to accumulate in the gas surrounding the sample. If the samples are heated in covered vessels the decomposition would be incomplete unless the temperature was raised above the point at which the pressure of the liberated carbon dioxide exceeded that of the atmosphere, that is, of 760 mm. This would require a temperature in excess of 825 for CaC0 3 , of 1155 for SrC0 3 and of 1450 for BaC0 3 . It might also be noted that by careful control of the tempera- ture and carbon dioxide pressure it should be possible to analyze certain mixtures of such carbonates. If a mixture of calcium and barium carbonates is heated to constant weight in a stream of pure carbon dioxide to a temperature slightly in excess of 825 the loss hi weight is an accurate measure of the amount of cal- cium carbonate present; if next heated above 1450 the loss in weight is an accurate measure of the barium carbonate present. The Dehydration of Salts. A second illustration of this class of processes is found in the method universally used for the determination of the water present in hydrated salts. Such de- terminations are based upon reversible reactions, which can be represented by Hydrated salt > anhydrous salt + water vapor. As the hydrated and anhydrous salts are present as pure solid phases their concentrations are constant, and the very slight concentrations in the vapor phase to which they give rise are also constant. Hence the expression representing the condition neces- sary for equilibrium in the vapor phase, which determined the equilibrium of the entire system, becomes 84 QUANTITATIVE CHEMICAL ANALYSIS in which P represents the partial pressure of the water vapor present in the vapor phase which is in equilibrium with the two solids. If the condition of equilibrium has not been reached the direction in which the reaction will progress depends upon the relative values of K and the partial pressure of the water vapor in contact with the salt. Many salts are able to form a series of hydrates each of which contains a definite number of molecules of water, and are not stable unless the concentration of the water vapor by which they are surrounded lies between certain limits, which vary with the temperature. The complete dehydration of such salts is repre- sented by a series of reactions. The Dehydration of Crystallized Copper Sulfate. This salt, which contains five molecules of water, is stable under ordinary atmospheric conditions, because the partial pressure of the water vapor normally present in the atmosphere exceeds the dissociation pressure of this hydrate at 20. By increasing the temperature or reducing the concentration of the water vapor surrounding the salt a series of reactions resulting in the formation of CuS0 4 - 3 H 2 0, CuS0 4 H 2 and CuS04 can be made to take place. The conditions necessary to effect these different trans- formations are indicated by the series of curves shown in Fig. 17, in which the ordinates rep- resent water-vapor pressures Fig. 17. Vapor Tensions of Hydrates and the abscissas temperatures. of Copper Sulfate indicates the series of temperatures and pressures at which the penta- and trihydrate are in equilibrium; DO those at which the tri- and GENERAL FEATURES OF GAS-EVOLUTION PROCESSES 85 inonohydrates are in equilibrium; and EO those at which the monohydrate and the anhydrous salt are in equilibrium. The space between CO and DO represents the only series of conditions at which the trihydrate is stable, that betweer DO and EO the only conditions under which the monohydrate is stable, and that below EO the only conditions under which the anhydrous salt is stable. Complete dehydration can be effected within the range of conditions represented by the field EOY. The Evolution Method. The weight of the gas liberated by such reactions as those under discussion can often be estimated by determining the total loss in weight of the apparatus in which the reaction takes place, that is, by determining the weight of liberated gas by the " evolution method." In general, there are two extremes represented in the method of procedure adopted. In one the temperature is kept very high, and no attempt made to reduce the partial pressure of the liberated gas below that normally present; in the other the temperature is kept low, and the partial pressure of the liberated gas is artificially reduced. Where, owing to volatilization of the residual product or to other changes which affect its weight, the maximum temperature which' can be used is too low to cause complete and rapid decomposition of the sample, it is desirable or even necessary to reduce the partial pressure of the liberated gas by passing a current of air, or some other gas, over the sample. This necessitates the use of a some- what elaborate apparatus similar to that used for the direct method described in the next paragraph. The Absorption Method. Since the residual compound is often hygroscopic, and, therefore, difficult to weigh, and since it is sometimes impossible to entirely avoid reactions involving changes in weight in addition to the one desired, it is sometimes necessary to pass the liberated gas into an apparatus which absorbs it completely, and determine its weight by the direct or " absorption method." The decomposition must then be made in a closed vessel and all of the liberated gas washed thru the absorb- 86 QUANTITATIVE CHEMICAL ANALYSIS ing apparatus by means of a current of air, or some other gas which contains no substances which are also taken up by the absorbing apparatus. Fig. 18. Muffle Furnace for Heating Tubes When the liberated gas is to be determined by the absorption method, or when a gas is to be passed over the substance to be analyzed and determined by the evolution method, an apparatus similar to the one represented in Fig. 18 becomes necessary. This consists of a cylindrical muffle of sheet nickel or monel metal supported hori- zontally on four legs and enclosing a glass tube, the diameter of which is sufficiently large to con- tain a porcelain "boat," which holds the sub- stance to be analyzed. The temperature of the air space within the muffle, which is somewhat higher than that of the substance within the boat, can be measured with a thermometer. It is possible to heat the substance in such an apparatus by means of a single Bunsen burner up to as high as 350 and where the danger of exceeding the maximum permissible temperature is but small, an opening can be made in the bottom of the muffle and Fig. 19. Glass- stoppered U-tube GENERAL FEATURES OF GAS-EVOLUTION PROCESSES 87 the tube heated directly, even up to the point at which the glass begins to soften. Where still higher temperatures are necessary, a tube of porcelain should be used. The absorption of the liberated gas can be effected in several types of apparatus, which should be as light and compact as possible. For solid absorbents a U tube, as represented in Fig. 19, is most convenient; for liquid absorbents a U-tube containing pieces of pumice stone saturated with the liquid, or certain special forms of absorption bulbs such as that of Geissler, Fig. 20, can be used. General Theory When the Reagent Is a Gas. Reactions re- sulting in the liberation of a gas, which are brought about by the addition of a reagent, form the basis of many useful quantitative processes. The reagent itself may be a gas, in which case the system concerned is one involving equilibrium between one or more solid phases and a mixed gas phase. The method of "combustion" invariably used for the determination of carbon and hydrogen in organic com- pounds is representative of this class. They involve reactions similar to Ci 2 H220ii + 12 2 - 12 C0 2 +11 H 2 0. Fig. 20. Geissler Bulb Altho this reaction is not appreciably reversible the tend- ency for formation of intermediate oxidation products, such as carbon monoxide, is reduced to a minimum and the speed of the reaction is increased by keeping the concentration of the oxygen large and that of the carbon dioxide and water vapor small. In general, in all jorocesses dependent upon reactions of this type it is desirable to- keep the concentrations of the gases formed low and that of the gaseous reagent used high. This is easily effected by use of the apparatus already described, that is, 88 QUANTITATIVE CHEMICAL ANALYSIS by placing the substance to be analyzed in a narrow tube, and passing the gas used as a reagent over it. General Theory When the Reagent Is a Liquid. When the re- agent used is a liquid, the system concerned involves equilibrium between a liquid, a gas and a solid, as, for example, in the reaction: CaC0 3 + 2 H+ + 2 Cl- - Ca++ + 2 Cl~ + H 2 + C0 2 . If we disregard the concentration of water, which in the solutions usually used remains practically constant, the expression for equilibrium reduces itself to (C0 2 ) Evidently such reactions can be made complete if the concen- tration of the reagent used can be made sufficiently large, and the solubility of the liberated gas can be made sufficiently small. The weight of the liberated gas can be determined by the evolution method, the absorption method, or by direct measure- ment of its volume, and calculation of the corresponding weight. For the evolution method a large number of special forms of apparatus, which are known as alkalimeters, can be employed. One of these is represented in Fig. 23, in which A represents the receptacle which contains the substance to be analyzed, and in which the reaction takes place, B the receptacle for the reagent used, and C the receptacle for the reagent used to dry and purify the liberated gas. The weight of the entire apparatus as first charged with sample and reagents, and again after the reaction has been completed, is accurately determined; the difference gives the desired weight of the liberated gas. For the absorption method an apparatus similar to the one represented in Fig. 24 is used. The essential features are again a container for the reagent, a container for the substance to be analyzed, which also serves as the vessel in which the reaction takes place, one or more absorbing tubes by which the liberated GENERAL FEATURES OF GAS-EVOLUTION PROCESSES 89 gas is dried and purified, and an absorption apparatus containing the proper reagents for the retention of the gas which is to be weighed. General Theory When the Reagent Is a Solid. The salts of certain acids, especially H 2 C0 3 , HC1, HN0 3 and HC1O 3 , are completely decomposed with the liberation of a gas by heating them with certain oxides such as Si02 or B 2 03, or with certain acid salts such as Na2B 4 07. A typical illustration is furnished by the reaction between sodium paratungstate and potassium nitrate, which is represented by NaioWi 2 4 i + 14 KN0 3 - 5 Na 2 W0 4 + 7 K 2 W0 4 + 7 N 2 6 . Since both of the substances which are concerned in such reactions are solid at ordinary temperatures, it is necessary to raise the temperature of the mixture to the point at which one or both of them is partly or wholly fused in order co insure complete inter- action; hence the factors which determine the reversibility of such reactions are the same as those which determine the reversibility of the reactions considered in the preceding paragraph. As most of the processes of this class can be carried out by heating a known weight of the sample with a known weight of the reagent in an open crucible they are extremely simple and in many cases extremely accurate. CHAPTER XI DETERMINATION OF WATER IN GYPSUM I. FACTS UPON WHICH THE DETERMINATION Is BASED Composition of Gypsum. The composition of this mineral is represented by the formula CaSO 4 2 H 2 0. It is frequently found in the form of colorless, transparent and beautifully crystalline masses, which are practically free from other minerals and mechani- cally occluded impurities of all kinds, and which contain the theoretical percentage of water. Conditions Necessary for Complete Dehydration. When a small amount of gypsum is placed in a loosely-covered vessel and the latter is slowly heated very little water is driven off until a temperature of 102 is reached, and even if kept at this tem- perature for a week only three-fourths of the water present in the sample is lost by it. These facts indicate that under these conditions the reaction 2 CaS0 4 2 H 2 -* (CaSO 4 ) 2 H 2 O + 3 H 2 O has been completed and also that the partial pressure of the water vapor, which is in equilibrium with both the di-hydrate and the hemi-hydrate of calcium sulfate, slightly exceeds atmos- pheric pressure at 102. If the temperature of the vessel is still further increased the remainder of the water present in the sample is slowly driven off when a temperature of 160 is reached, indi- cating that under these conditions the reaction (CaS0 4 ) 2 H 2 -> 2 CaS0 4 + H 2 has been completed. 90 DETERMINATION OF WATER IN GYPSUM 91 The rate at which both of these transformations take place under the conditions specified is very low and it is necessary to use a temperature of at least 180 if it is desired to completely expel the water from gypsum by heating in a loosely-covered vessel. Since the only other decompositions involving a change of weight which can result from a change in temperature pro- duce either calcium oxide or a basic sulfate of calcium, and sulfur trioxide and since neither of these changes begins to take place until a temperature of at least 600 has been reached, there is no objection to using a temperature much higher than 180. Properties of Anhydrous Calcium Sulfate. Two forms of cal- cium sulfate are known; one of these, the so-called " soluble anhydrite," is formed when gypsum is heated to moderate tem- peratures only, and is both more soluble and much more hygro- scopic than the " insoluble anhydrite." When gypsum is dehy- drated below 500 it is difficult to weigh the residual salt accurately, owing to the speed with which it takes up water vapor from the atmosphere. The difficulty can be avoided by heating in a vessel, which can be closed by means of a tightly-fitting stopper, and since ordinary glass does not begin to soften until a tem- perature of 400 is reached, a glass weighing bottle can be used for the determination, altho it must be heated and allowed to cool slowly to prevent it from cracking. Satisfactory results can also be obtained by heating in a covered porcelain or platinum crucible, but some experience is necessary to weigh the residual salt with sufficient speed to prevent slight errors due to the slow absorption of water. The difficulties can also be avoided by using the absorption method, that is, by collecting and weighing the liberated water, but this requires a more elaborate apparatus and takes more time. Possible Sources of Error. If gypsum is heated rapidly it sometimes shows a tendency to "boil," that is, the sudden con- version of the chemically combined water into steam rends the larger masses into extremely fine particles, and this may lead to 92 QUANTITATIVE CHEMICAL ANALYSIS an appreciable mechanical loss. The difficulty can be avoided entirely by heating slowly until most of the water is expelled, preferably in a deep vessel and by reducing the size of the particles of which the sample is composed. Care must be taken, however, to avoid long-continued grinding, as it has been shown that this may result in the loss of appreciable amounts of water, probably owing to the heat developed by friction. II. DETAILS OF METHOD OF PKOCEDURE Preparing and Weighing Out Sample. Crush several grams of the air-dry sample in a clean mortar until the resulting grains are about the size of a pin head, and transfer to a clean, dry " sample tube"; that is, a test tube about 1 cm. in diameter and 8 cm. long, which is provided with a good cork stopper. Procure a weighing bottle of not more than 20 cc. capacity, clean carefully and wipe both inner and outer surfaces with a dry cloth, then allow to stand, preferably in the balance room, for twenty minutes or until it has taken up the normal amount of moisture from the air. Weigh the bottle and cover accurately to within 0.5 mg. Remove the cover, and add about 2 gm. of the prepared sample, and again cover and weigh accurately to within 0.2 mg. Dehydration. Procure a nickel crucible of some 50 cc. capacity, cut a circular Fig. 21. Apparatus for piece of wire gauze slightly larger than Ermination of Water ^ bottom Qf ^ ^^ j gnite it oyer a flame, and place in the crucible as shown in Fig. 21. Cut a piece of asbestos cloth of slightly smaller size and place on top of the gauze. Support the crucible on a piece of wire gauze which is placed some two inches above the top of a Bunsen burner, then remove the cover from the weighing bottle and place the bottle DETERMINATION OF WATER IN GYPSUM 93 inside the crucible. Heat the gauze with a low flame for ten minutes, then gradually increase the gas supplied until the wire gauze under the muffle is heated to dull redness, and keep at this temperature for a half hour, but do not let the gas take fire and burn above the gauze. The temperature attained inside the muffle should be about 250; it can be measured by means of a mercury thermometer suspended as shown in the figure. Weighing the Residual Salt. Shut off the gas, place the cover in position and allow the muffle to cool for about three minutes, then transfer the bottle to a piece of paper, wood or some poor conductor of heat; and after a few minutes, place in the balance room and allow to remain for twenty minutes. If the hot bottle is brought into contact with a piece of cold metal or any other good conductor of heat it is certain to crack. Weigh the bottle to within 0.2 mg. ; if it shows any tendency to increase in weight while on the balance pan allow it to stand for another ten minutes and again weigh. Finally place the bottle in the muffle, heat as before for ten minutes, and again cool and weigh. If the difference between the two weighings does not exceed 0.3 mg. the dehydration of the sample can be assumed to be complete. Calculate the percentage of water present. III. FURTHER DETAILS REGARDING THE ANALYSIS Meaning of Percentage Error. In discussing the accuracy of quantitative processes care should be taken to distinguish between " percentage error" and what will be designated in this book as "departure." Percentage error always means the error for every one hundred parts of the substance determined; departure, the difference between the correct percentage and the percentage reported. Thus, if a substance contains exactly 70 per cent of a certain constituent and 69.8 is found by analysis, the departure is 70 - 69.8 = 0.2, but the percentage error is 100 (70 - 69.8) -5- 70 = 0.285. The difference between departure and percentage error becomes zero when the substance analyzed contains 100 per 94 QUANTITATIVE CHEMICAL ANALYSIS cent of the constituent reported. In general the percentage error of a quantitative process should be expected to increase somewhat as the percentage reported on decreases, but in neither case is the one change proportional to the other. Accuracy of Method. The determination outlined above rep- resents an ideal quantitative process, as regards both simplicity and accuracy. The entire estimation can be made within two hours, and the results should not differ from the theoretical figure by more than one-tenth of a per cent if the work is carefully executed. The accuracy of the method can be still further in- creased by increasing the amount of sample used, altho the time needed for complete dehydration is thereby increased. IV. QUESTIONS AND PROBLEMS. SERIES 2 1. If the result obtained in this determination is 20.80 instead of 20.93, what is the percentage error? If the same percentage error was made in determin- ing the water in a salt containing 60 per cent of water, what result would you obtain? 2. If 2 gm. of the sample were used in making the determination as directed and the only errors involved were a plus error of 1 mg. in weighing the empty bottle and a plus error of 0.2 mg. in weighing the bottle and residue after igni- tion, what departure would be obtained? If the only errors involved were a plus error of 0.2 mg. in weighing the empty bottle, and a plus error of 1 mg. in weighing the bottle and residue, what departure would be obtained? 3. What weight of water is present in 1 liter of air saturated at 50 and 760 mm., assuming that the partial pressure of water vapor at this temper- ature is 92 mm., that a liter of water vapor at and 760 mm. weighs 0.803 gm. and that water vapor obeys the laws of Boyle and Gay Lussac? 4. What are the partial pressures of water vapor, oxygen, and nitrogen in a mixture if the total pressure is 760 mm., and one liter of the mixture con- tains 0.022 gm. of H 2 O, 0.8796 of N 2 and 0.2665 of O 2 ? 6. If 2 gm. of gypsum are heated to 70 in an open flask, which has a volume of 500 cc., how much gypsum would be left and how much of the hemi-hydrate formed, assuming that the dissociation pressure of gypsum at this temperature is 161 mm., that no water is expelled from the flask, that the water vapor is uniformly distributed in it after equilibrium has been DETERMINATION OF WATER IN GYPSUM 95 established, and that one liter of water vapor at 70 and atmospheric pres- sure weighs 0.641 gm.? Ans. 1.5676 gm. left. 6. What difficulties would you anticipate if the method used for the deter- mination of water in gypsum was used for the compounds CaCla 6 H 2 O, Mg(N0 3 ) 2 6 H 2 O, FeSO 4 7 H 2 O, ZnSO 4 (NH 4 ) 2 SO 4 6 H 2 O? 7. If 1 gm. of a mixture which contained CaCO 3 and SrCO 3 lost 0.15 gm. when heated to 900, and .1292 gm. when heated from 900 to 1200, what percentages of the two carbonates were present? (For data see page 83.) 8. What methods might be used to determine the water in a mixture of a hydrated salt, which was known to give a dissociation pressure of 200 mm. when heated to 300, and a carbonate, which was known to give a dissociation pressure of 400 mm. when heated to the same temperature? 9. Show why you are justified in neglecting the error from buoyancy in the determination of water in gypsum, assuming that only brass weights are used, that the specific gravity of brass is 8.33, that of gypsum is 2.32, and that of anhydrous calcium sulfate is 2.964. CHAPTER XII DETERMINATION OF WATER IN CRYSTALLIZED COPPER SULFATE I. FACTS UPON WHICH THE DETERMINATION Is BASED Purification of the Salt. When copper sulfate is purified by recrystallization the pentahydrate alone separates since the vapor pressure of the solution is greater than that of this hydrate even if the temperature of the saturated solution used reaches a value of 50. The separated crystals should be dried by pressing them between folds of filter paper, and preserved in stoppered bottles at a temperature not in excess of 25. The salt sold by reliable dealers as chemically pure usually contains very nearly the theo- retical percentage of water. Conditions Necessary for Dehydration. Although the vapor pressure exerted by even the monohydrate of copper sulfate at 100 exceeds the partial pressure of water vapor normally present in the atmosphere, experience shows that the last traces of water are driven off from this salt very slowly at this temperature. As the salt does not begin to decompose further until a temperature of 341 is attained, there is no objection to dehydrating at 200, at which temperature all of the water is rapidly and completely expelled. The anhydrous salt is extremely hygroscopic, and altho the method used for the determination of water in gypsum can be employed in this case also the more widely applicable absorption method will be described here. The Efficiency of Different Dehydrating Agents. The accu- racy of the absorption process for the determination of water depends upon the efficiency of the reagent used to absorb the liberated water vapor. The activity of all such reagents depends 96 WATER IN CRYSTALLIZED COPPER SULFATE 97 upon their capacity to combine with water, and is large in pro- portion as the dissociation pressure of the compound formed by the addition of water is small. Phosphorus pentoxide is the most powerful dehydrating agent known, which is due to the fact that the water- vapor pressure of the phosphoric acid formed is practically zero. As it is obtained in the form of a fine white powder, whose surface rapidly becomes coated with an impervious layer of phosphoric acid, and as it is an expensive reagent, its use is avoided except when an unusual degree of dehydration is necessary. Concentrated sulfuric acid owes its power to the formation of a series of liquid hydrates, which are miscible with water in all proportions. The vapor pressure of the concentrated acid is but little less than that of phosphoric acid ; that of the diluted acid in- creases rapidly with the dilution. It has been measured for a wide range of concentrations at a number of temperatures and the data obtained is extremely useful for the preparation of dehydrating reagents of specified power. The gas to be dehydrated can be passed thru tubes, which are designed to hold the acid in liquid form, or thru U-tubes containing pieces of pumice stone saturated with it; the acid in such tubes must be renewed frequently. Calcium chloride forms a series of hydrates, all of which are extremely soluble. It is to be had from dealers in two forms. The " fused" salt is almost anhydrous, and is dense and heavy; the " granular" reagent, if fresh, contains from 15 to 20 per cent of water, and is light and porous. Its dehydrating power decreases as its water content increases. Samples containing from 14 to 24 per cent of water (CaCl2 1 to 2 H 2 0) yield a vapor pressure of 0.54 mm. ; those containing from 24 to 40 per cent (CaCl2 2 to 4 H 2 0) yield a pressure of 1.47 mm.; those containing from 40 to 50 per cent (CaCl 2 4 to 6 H 2 0) yield a pressure of 2.47 mm. The vapor pressure of the fused salt should be less still, but its action is much slower than that of the lower hydrates, and its efficiency may not be greater unless the gas to be dehydrated is passed over 98 QUANTITATIVE CHEMICAL ANALYSIS it very slowly. Altho the granular reagent is a less efficient dehydrating agent than concentrated sulfuric acid the fact that it can be obtained in the form of a light porous solid makes it more convenient to use. The Use of Granular Calcium Chloride. If the partial pres- sure of the water vapor hi the air passed thru the apparatus during the determination is not equal to or less than the vapor pressure of the dehydrating agent used to retain the water sep- arated from the sample being analyzed, the result may be increased by water taken up from the air. If the air passed thru the appa- ratus is dehydrated by the same reagent that is used to absorb the water liberated from the sample no such error should result. Under these conditions also no error should result from the use of a dehydrating agent, which fails to remove the last traces of water from the air passed thru the absorbing tubes since both tubes should reduce the concentration of the water vapor to the same value, and the amount of water taken up by the second absorbing tube represents the increase in the concentration of water vapor produced by the decomposition of the sample under analysis. Conditions Necessary for Complete Absorption. If the liber- ated water vapor is drawn thru the absorbing tube too rapidly some of it may not be retained. If the air current used is not made to pass continuously in the proper direction some of the liberated water vapor may find its way into the absorption tube thru which the air enters. A steady and continuous stream of air can be drawn thru the apparatus at any desired rate by the use of an " aspirator bottle" (E of Fig. 22). If air enters the apparatus at any point except thru the tube designed to purify it, the moisture which it contains may be absorbed and weighed with the separated water. Hence the joints of the apparatus must be tight, but since the pressure inside and outside of the apparatus need not differ much, no difficulty should be experienced in making them so. The time needed for the determination depends largely upon WATER IN CRYSTALLIZED COPPER SULFATE 99 the amount of air which must be passed thru the apparatus to free it from water vapor before the sample is heated, and also to wash the separated water vapor into the absorption tube after the sample has been decomposed; it increases, therefore, with the capacity of the apparatus, which should be made as small as possible. II. CONSTRUCTION OF THE APPARATUS Procure and fit together the parts of an apparatus similar to that shown in Fig. 22 as follows: For A procure a simple U-tube about 18 cm. in length. Clean and dry it carefully and fill with lumps of dry granular calcium Fig. 22. Plan of Apparatus for Determination of Water chloride of about the size of a pea. Place small wads of cotton on top of the reagent in both limbs and insert in the two ends well- fitting cork stoppers provided with an inlet and outlet tube respectively. Prepare also two " plugs" by inserting short pieces of glass rods into pieces of rubber tubing of slightly smaller internal diameter, and use to cover the inlet and outlet tubes, and thus protect the reagents from deterioration when the tube is not in use. For B procure a piece of either hard or soft glass tubing about thirty centimeters long, the diameter of which is sufficient to permit the insertion and removal of the porcelain boat C without 100 QUANTITATIVE CHEMICAL ANALYSIS difficulty. The sharp edges at the end of the tube should be rounded off by heating in a flame until they begin to soften. Pro- cure two rubber stoppers which fit the ends of the tube snugly and are bored with holes for the admission of the tubes connecting with A and D. For D procure a smaller U-tube, preferably of the Marchand form, in which one limb of the tube is sealed directly to an inlet tube of smaller diameter, the latter being bent at right angles and provided with a bulb-like enlargement near the middle of the horizontal portion. This bulb serves to condense and retain a large part of the water vapor passing thru the tube, which can be poured out, or removed by a shred of filter paper after the tube has been used; it increases the number of determinations that can be made with it without renewing the absorbing reagent. Clean and dry the tube, heating it in an air bath if necessary to expel the last traces of water. Insert a small wad of cotton just below the inlet tube, and fill with pieces of granular calcium chloride; then introduce a good cork stopper, which is provided with a narrow outlet tube, into the open limb. Place a few small pieces of sealing wax upon the top of the cork, and melt these by means of a piece of hot metal till the cork and the joint between it and the glass are covered uniformly and smoothly. Prepare well-fitting plugs, by which the inlet and outlet tubes can be cov- ered, and a support of nickel or aluminum wire by which the tube can be suspended. For E procure an aspirator bottle of about two liters capacity provided with an exit tube which can be easily opened or closed by means of a screw pinchcock. For F procure a thermometer capable of indicating temperatures of 300. III. DETAILS OF METHOD OF PROCEDURE Preliminary Operations. Prepare the sample by crushing several grams of the dry crystalline salt to a fine powder in a clean agate mortar and placing in a clean, dry sample tube.. WATER IN CRYSTALLIZED COPPER SULFAT& 101 Ignite the porcelain boat by holding it in the flame of a burner, slightly above the apex of the inner blue cone, for a few minuted, then place in a desiccator until perfectly cool, which should re- quire about twenty minutes, and weigh accurately to 0.2 mg. Next add to the boat about 1 gin. of the sample and again weigh accurately. Wipe the Marchand tube with a clean dry cloth, place it in the balance room for twenty minutes, then weigh with the two plugs in position accurately to within 0.2 mg. If the tube ap- pears to gain in weight while on the balance pan it must be allowed to stand longer, that is, until the weight is constant. Assembling the Apparatus. Connect the larger U-tube with the combustion tube by means of a rubber stopper. Fill the aspirator bottle with water, attach it directly to the other end of the combustion tube and allow about 200 cc. of water to flow out rather rapidly, that is, within a period of about ten minutes. Disconnect the aspirator and place the porcelain boat and con- tents in the combustion tube at the point indicated in the figure. Connect the Marchand tube with the combustion tube by means of the rubber stopper, taking pains to press it firmly into place. Connect the aspirator with the free end of the Marchand tube and adjust the pinchcock until the water flows from it at a rate of about five drops per second, and maintain this rate of flow during all the subsequent operations. Decomposing the Hydrate. Light the burner under the muffle, and allow the temperature as shown by the thermometer to slowly rise to about 100, and maintain it as near this figure as possible for twenty minutes. This should expel four-fifths of the water somewhat rapidly; decrepitation may take place but does no harm as the residue is not to be weighed. Some of the water may condense in the colder portions of the tube just outside of the muffle and it may be necessary later to heat that part of the tube slightly, by changing the position of the muffle, but this must be 102' QUANTITATIVE CHEMICAL ANALYSIS watched carefully, or small amounts of water vapor or sulfur may be expelled from the rubber stopper. Next increase the height of the flame and allow the temperature to gradually rise to 200 and maintain between 200 and 250 for twenty minutes longer. At the expiration of this period the residue in the boat should be of a dead white or slightly gray color; if it shows a tinge of blue the heating should be continued longer. Weighing the Liberated Water. Disconnect the aspirator, remove the Marchand tube and cover the inlet and outlet with the proper plugs, place in the balance room and weigh as before. Remove the porcelain boat by means of a small wire hook and dis- connect and cover the ends of the larger U-tube. Calculate the percentage of water present. IV. QUESTIONS AND PROBLEMS. SERIES 3 1. Would you expect the sulfates of sodium, zinc, aluminum and iron, respectively, to decompose into the corresponding oxides at higher or lower temperatures than the sulfate of copper? 2. Ten liters of moist air measured at 20 are passed thru a tube filled with calcium chloride containing 45 per cent of water, then thru a tube filled with calcium chloride containing 18 per cent of water, what weight of water might be taken up by the latter tube? Ans. 0.019 gm. 3. A saturated solution of Na^HPC^ is placed in a desiccator, which also contains a large vessel filled with 65 per cent sulfuric acid and is kept at 30. If the vapor pressure of the acid is 7 mm., the dissociation pressure of Na2HPO 4 -12H 2 O is 26 mm., that of Na2HPO 4 -7H 2 O is 18 mm., that of Na2HPO4 2 H 2 O is 2 mm., what changes would take place in both solutions? What difference might it make if the volume of the NasHPO* solution was large and that of the H 2 S04 solution small? 4. How could you prove that copper sulfate formed a hydrate having the formula CuSO 4 3 H 2 0? 6. Calculate the probable formula of a hydrate of magnesium sulfate which was found to contain 64.2 per cent of water 6. Show how the data given by Fig. 17 enables you to determine whether heat is absorbed or liberated during this determination. CHAPTER XIII DETERMINATION OF CARBON DIOXIDE IN LIMESTONE BY THE EVOLUTION METHOD I. FACTS UPON WHICH THE DETERMINATION Is BASED Choice of Method. The value of a sample of limestone for many purposes is determined by the percentage of carbon dioxide which it contains. This de- termination can be made by ascertaining the loss which takes place when a known weight is ignited in a crucible, but this method is inaccurate if the sample also contains chemically combined water or organic matter. When these substances are present the determination can be rapidly made by the evolution method with an alkalimeter ; the use of the Bunsen alkalimeter (see Fig. 23) will be described here. The results obtained by this method should not differ from the correct figure by more than .2 per cent. Fig - 23. Bunsen's Alkalimeter Possible Sources of Error. The errors involved in weighing a Bunsen apparatus are necessarily somewhat large owing to variations hi the amount of hygroscopic water which condenses 103 104 QUANTITATIVE CHEMICAL ANALYSIS on its surface, they should be made as small as possible by using a counterpoise as suggested on page 21. The use of a large amount of sample reduces the effect of this error; as much as 2 gm. can be used to advantage. The carbon dioxide liberated in the Bunsen apparatus is satu- rated with water vapor which must be absorbed before the gas is permitted to escape. Calcium chloride can be depended upon to remove all but a trace of water from the escaping gas, provided the escaping gas is not passed thru the absorbing tube too rapidly. Some samples of calcium chloride contain small amounts of cal- cium oxide and therefore absorb carbon dioxide; hence the calcium chloride in the tube C should be saturated with carbon dioxide before it is used. Altho the reactions between the carbonates found in limestone and either dilute hydrochloric or sulfuric acids are practically complete, the solution which remains after the decomposition is saturated with carbon dioxide, and to this extent the separation of the latter is incomplete. If a moderate excess of dilute hydrochlo- ric acid is used and the residual solution heated slowly to about 50 practically all of the dissolved carbon dioxide is expelled, and there is little danger of expelling either acid or water vapor. The specific gravity of carbon dioxide is greater than that of air and the gas retained and weighed with the apparatus after use will weigh slightly more than that present in it before use, unless a sufficient amount of air is drawn through it, after the decom- position has been completed. This air should be dehydrated by passing it thru the drying tube E, otherwise the moisture which it contains may be taken up by the" drying tube C. II. PREPARATION OF THE APPARATUS Carefully clean the three parts A, B and C of a Bunsen apparatus (see Fig. 23), by rinsing with acid if necessary, then with water, allowing them to drain and then wiping the outer surfaces dry with CARBON DIOXIDE IN LIMESTONE 105 a clean cloth. Dry the inner surface of the tube C by heating either in an air bath or very cautiously over a wire gauze. Charge the drying tube by placing a small wad of cotton in its enlarged end, filling to within 1 cm. of the other end with lumps of dry, granular calcium chloride of about the size of a pea, covering with a second wad of cotton, and closing with a cork of the proper size, which is provided with an inlet tube of small diameter. Press the cork into the tube till flush with its end and cover with a little sealing wax. Pass carbon dioxide from a generator thru the tube for about twenty minutes and displace the excess by means of a current of air. III. DETAILS OP THE METHOD OF PROCEDURE Charging and Assembling the Apparatus. Prepare a long narrow sample tube, which is small enough to pass into the flask A , by sealing up one end of a piece of thin-walled glass tubing with a flame and closing the other with a cork, and charge with about 2 gm. of the sample. Weigh the tube accurately and deliver its contents without loss into the bottom of the flask A, then withdraw the sample tube and again weigh accurately. Pour about 15 cc. of dilute hydrochloric acid into a small beaker, insert the shorter of the two tubes attached to the reservoir tube B into the acid and suck up about 10 cc. of the acid, then remove the tube B and invert, so that the shorter tube again stands above the acid. Carefully remove the acid which adheres to the shorter tube by means of narrow shreds of filter paper. Next unite A, B and C as shown in the figure, place the plugs D and D f over the two open ends, let the apparatus stand for a half hour in the balance room and weigh accurately, using a 200 cc. flask, which has also stood in the balance room during the previous half hour, as a counterpoise. Decomposing the Sample. Remove the plugs D and D' and set aside where they can not be mixed with the" plugs belonging to E and F. Now cause the acid to siphon over, drop by drop, 106 QUANTITATIVE CHEMICAL ANALYSIS from B into A, controlling the flow by holding the finger against the end of B and preventing any of the liberated gas from escap- ing through the reservoir tube. When all of the acid has been drawn into A and when the decomposition seems to be complete, which should take about 15 minutes if the sample has been finely ground, heat the bulb A slowly over a wire gauze until the solu- tion attains a temperature of about 50. Next connect the free ends of the apparatus with the tubes E and F t attach the latter to an aspirator, and draw 1500 cc. of ah* thru the apparatus, which should require about 20 minutes. Disconnect the tubes E and F and replace with the plugs D and D', let the apparatus stand for a half hour in the balance room and weigh as before. Report the percentage of C0 2 . IV. QUESTIONS AND PROBLEMS. SERIES 4 1. Assuming that the capacity of the Bunsen apparatus is 50 cc., that the weight of a liter of air under the prevailing conditions is 1.2 gm., while that of carbon dioxide is 1.84 gm., how large a departure would be made in a determination of carbon dioxide in 2 gm. of pure sodium carbonate if only half the carbon dioxide was displaced by air before the final weighing was made? 2. What other determinations might be made with a Bunsen apparatus? 3. Assuming that the available air space of the Bunsen apparatus was 50 cc. and that of the absorption tube was 10 cc., calculate the volumes of air which should be passed thru the apparatus to reduce the carbon dioxide left after the decomposition to 1 mg., assuming first, that all the air used is uniformly mixed with the carbon dioxide present and second, that none of it is so mixed. Ans. 59.46 and 6570 cc. 4. If it was found that 1 gm. of a sample consisting of a mixture of sodium carbonate and sodium bicarbonate yielded a loss of 0.46 gm. in a Bunsen ap- paratus, what percentage of Na^COa and NaHCO 3 must have been present? (For the method of solving see page 78.) Ans. 58.69 and 41.31 per cent. 5. If an error of 0.2 mg. was made in making the determination indicated in the last problem, how large an error would appear in the results of the calculation? CHAPTER XIV DETERMINATION OF CARBON DIOXIDE IN BAKING POWDER BY THE ABSORPTION METHOD I. FACTS UPON WHICH THE DETERMINATION Is BASED Composition of the Sample. The essential constituents of these mixtures are starch, bicarbonate of sodium, and some reagent which has weakly acidic properties, such as potassium bitartrate, alum or the acid phosphate of calcium. The addition of water to such mixtures brings the active reagents into contact with each other and results in the liberation of carbon dioxide, and since their efficiency as leavening agents depends upon the volume of gas which they liberate under the conditions of actual usage, the available rather than the total carbon dioxide is usually deter- mined. The weight of gas liberated when the sample is treated with water and heated can be determined with an alkalimeter, but the equally accurate absorption method, which has been more generally used, will be described here. The starch, which is added to preserve the mixture, does not affect the method except by pro- ducing a pasty mass when heated with water. Properties of Soda Lime. The substance known as " soda lime" is prepared by adding calcium oxide to a strong hot solution of sodium hydroxide; on cooling, this mixture forms a solid friable mass, which can be broken into pieces and packed into U-tubes. This reagent has the property of rapidly absorbing water vapor, carbon dioxide and other gases which possess acidic properties, with the liberation of appreciable amounts of heat. Absorption of carbon dioxide takes place most rapidly and completely if the reagent is not absolutely dry. As the lumps of reagent used 107 108 QUANTITATIVE CHEMICAL ANALYSIS rapidly acquire an impervious coating of calcium carbonate, which prevents further absorption from taking place, it is advisable to pass the gas thru two tubes filled with the reagent and to deter- mine the resulting increase in the weight of both. Tubes whose volume does not exceed 25 cc. are more efficient, and more accu- rately weighed than those of greater capacity. A tube of this size when properly charged should weigh about 25 gm., and will absorb at least 1 gm. of carbon dioxide. a 1 -L. ^ u - .E .D \ - S ^ ~J Fig. 24. Plan of Apparatus for Determination of Carbon Dioxide II. CONSTRUCTION OP THE APPARATUS Prepare and set up the apparatus represented in Fig. 24. A is the decomposition flask of about 125 cc. capacity; B is the acid reservoir, which consists of a separatory funnel of about 40 cc. capacity; C is a condenser of the Hopkins form; D a glass- stoppered drying tube filled with calcium chloride; E and F CARBON DIOXIDE IN BAKING POWDER 109 glass-stoppered U -tubes of about 25 cc. capacity filled with soda lime; G a small wash bottle, which indicates the rate at which air is drawn thru the apparatus; H an aspirator and / a soda-lime tube which removes the carbon dioxide from the air drawn thru the apparatus. The stopper of the flask A should be of rubber, and the absorption tubes should be provided with wire loops by which they can be suspended from a horizontal support when in use, and from the balance beam when being weighed. III. OUTLINE OF METHOD OF PROCEDURE Preliminary Operations. Clean the parts, A, B and C, by rinsing with acid if necessary, then with water and allowing them to drain. Clean the tubes D } E, F and I and dry by wiping them as dry as possible and then drying in an oven. Fill the tube D with lumps of calcium chloride not exceeding a pea in size, then pass dry carbon dioxide from a generator thru it for about ten minutes and displace the latter by air. In like manner fill the tubes E, F and / with soda lime. Assemble the various parts of the apparatus and test for leaks by first closing the free end of the tube I with a plug, and opening the pinchcock on the delivery tube of the aspirator; if water con- tinues to flow from the aspirator indefinitely, test each joint suc- cessively until the leak is found and stopped. Charging the Apparatus. Disconnect the aspirator, the wash bottle and the soda-lime tubes E and F and close the latter by turning the stoppers. Wipe the two tubes with a dry cloth, let them stand in the balance room for a half hour and weigh them both separately, using a glass counterpoise. Remove the flask A from the apparatus, wipe it dry and add to it from a sample tube about 2 gm. of the sample, being careful to prevent any of it from coming into contact with the side of the flask, then again weigh the sample tube. Close the stopcock of the separatory funnel and charge the latter with about 30 cc. of water. Connect the reaction 110 QUANTITATIVE CHEMICAL ANALYSIS A, the soda-lime tubes E and F and the wash bottle with the rest of apparatus. Making the Decomposition. Allow the water to run into the flask A by cautiously opening the stopcock for very short time intervals, endeavoring to produce a slow and uniform libera- tion of the gas. After all of the water has been introduced, attach the aspirator, remove the plug from 7 and by carefully regulating the aspirator draw a slow current of air through the apparatus. Next start the water running thru the condenser and heat the solution very slowly to the boiling point, then allow the flask to cool very slowly, keeping a steady stream of air passing thru the apparatus. After 4 liters of air have been passed thru the apparatus, which should take about forty minutes, disconnect the two soda-lime tubes and weigh as before. Calculate the percentage of C02 from the increase in the weight of these tubes. IV. QUESTIONS AND PROBLEMS. SERIES 5 1. Calculate the volume of CO2 measured at 25 and 760 mm. liberated by 1 gm. of a sample which contains 12 per cent of available carbon dioxide. 2. Assuming that air contains 0.04 per cent by volume of C0 2 and that 2 liters of air are passed thru the apparatus, what result would be obtained in this determination if the soda-lime tube I was not used, assuming that the correct per cent of CO 2 is 12? 3. A sample of baking powder which is known to contain only starch, NaHCO 3 and C 4 H 5 KO6 (potassium bitartrate) in equivalent proportions yields 12 per cent of CO 2 . What is its composition? 4. One gram of a mixture consisting of CaCO 3 and PbCO 8 is found to con- tain 0.25 gm. of CO 2 . What percentages of CaO and PbO must be present? 5. A sample which contains potassium nitrate is analyzed by weighing out 1 gm., adding 3 gm. of sodium paratungstate (NaioWi 2 04i) and heating to con- stant weight in a crucible. If the crucible shows a loss of 0.3 gm., what per- centage of potassium nitrate was present? Ans. 56.16 per cent. CHAPTER XV DETERMINATION OF MERCURY IN AN ORE I. FACTS UPON WHICH THE DETERMINATION Is BASED Decomposition of Mercuric Sulfide. The ores of mercury which are of commercial importance contain the element as the sulfide, that is, the minerals cinnabar or metacinnabarate, or as metallic mercury; they rarely contain more than a small per- centage. If mixed with finely divided iron filings and heated the sulfide is decomposed according to a reaction represented by: At a temperature of 100 metallic mercury gives a vapor pressure of 0.27 mm., at 300 the pressure is 246 mm.; hence it is not sur- prising to find that this reaction can be made complete by heat- ing the mixture to a temperature of 300 in an apparatus one part of which is kept at a temperature which does not exceed 100, that is, by condensing the vapor as it is formed. Condensation of Mercury Vapor. The most satisfactory de- vice which can be employed for the retention of the mercury con- densed in such an apparatus takes advantage of the tenacity with which mercury attaches itself to plates of gold, silver or copper, which is in part due to the ease with which it forms amalgams with these metals. When mercury vapor condenses on such plates it forms a thin film or series of fine drops, and altho they can be dislodged by brushing or vigorous shaking no difficulty is ex- perienced in accurately determining the weights of mercury ad- hering to such plates. After weighing, the mercury can be expelled ill 112 QUANTITATIVE CHEMICAL ANALYSIS by heating to a temperature of about 400; if plates of gold or silver are used their weights remain practically constant; if a plate of copper is used its weight increases slightly, owing to oxidation. Form of Apparatus Used. Although several forms of appara- tus which are based upon the facts cited have been suggested, one devised by Whitton,* which is repre- sented in Fig. 25, is the best. It consists of an iron retort A of 24 cc. capacity, a sheet of silver foil C about 0.2 mm. thick, a brass dish B which is kept full of water, an iron shield which protects the foil from the flame used to heat the retort, and a clamp D by which the retort, foil and dish are held together. The silver plate used is about 5 cm. SQuare, and weigns about ^.o gm.j it can be used for twenty or more de- Fig. 25. Whitton' s Apparatus for Determination of Mercury terminations, but after repeated use seems to become porous, so that some of the mercury may pass thru it. Sources of Error. As the total volume of air expelled from the retort during the heating should not exceed that due to the expansion of the air originally present, and the maximum con- centration of this air with respect to mercury vapor should not exceed that of air saturated at 100, the total loss from this source should not be large. As mercuric sulfide is itself appreciably volatile, a relatively large volume of iron filings should be used to insure complete de- composition. The ore and filings must also be carefully dried and the latter washed with gasolene or ether to remove any grease with which they may be contaminated. The maximum amount * Mineral Industry, 17, 751 (1908). Apparatus can be procured of Braun- Knecht-Heinmann of San Francisco. DETERMINATION OF MERCURY IN AN ORE 113 of mercury which can be safely retained by a plate of the size given is 0.07 gm., and the amount of ore used for the determination must be chosen with this statement in mind. It is obvious that great care should be used in weighing the foil. The temperature to which the retort is heated, and the length of time it is heated in order to insure complete decomposition, must be ascertained by experimenting with pure mercuric sulfide or ores of known composition. When the flame of an ordinary Bunsen burner is used, and the retort is so placed that the flame covers the bottom and reaches a point one-half inch above the bottom, heating for 20 minutes is found to give good results. An entire determination can be made within an hour and the method is peculiarly adapted to the analysis of low-grade ores, since a large amount of sample can be used. II. OUTLINE OF METHOD OF PROCEDURE Prepare a plate of silver foil by polishing with a piece of fine emery or crocus cloth, wiping with a clean cloth, drying for a few minutes over a flame and weighing with the greatest attainable accuracy. Weigh out about 5 gm. of iron filings, which are dry and free from grease, and place in the retort. Weigh out on a watch glass a sufficient amount of the dry ore to contain from 20 to 70 mg., and transfer to the retort. Mix the ore and filings very thoroughly with a glass rod, and cover the mixture with another gram of filings. Place the foil between the retort and water cooler, clamp all three together and support on an iron ring stand above a burner so that the top of the burner is about one and one-half inches below the bottom of the retort. Fill the cooler with water, light the burner, and adjust the gas supply until the flame runs up the sides of the retort for not more than one-half an inch, which should heat the water to boiling in 7 minutes. Renew the water in the dish as it evaporates and after 20 minutes remove the flame and allow to cool for 20 minutes, then disconnect the apparatus, 114 QUANTITATIVE CHEMICAL ANALYSIS remove the plate and weigh accurately. Report the per cent of mercury. Expel the mercury from the silver plate by holding it with the mercury-coated side uppermost, several inches above the flame of a burner, until fumes are no longer given off, and the plate shows a faint red glow, but avoid using a temperature which would melt it. III. QUESTIONS AND PROBLEMS. SERIES 6 1. What weight of mercury is present in one liter of air, which has a tem- perature of 100 and is saturated with mercury vapor, if the partial pressure of mercury vapor is 0.27 mm.? Ans. 0.0023 gm. 2. If a retort which contains 24 cc. of air at 20 is heated to 300 and the expelled air is cooled to 100 before escaping, what volume is expelled? 3. If the retort referred to is charged with 0.1 gm. of pure HgS and the proper amount of iron filings and heated to 300, and if the air and mercury vapor are cooled to 100 before escaping, what weight of mercury is driven off? What is the percentage error of the determination resulting from this cause? Ans. 0.04 per cent. 4. Derive the simplified expression representing the application of the Law of Mass Action to the reaction used in this determination. 6. What objections are there to determining mercury by the evolution method, that is ascertaining the loss in weight of the vessel in which the reaction between mercuric sulfide and iron is made to take place? 6. Would you expect this method to be affected by the presence of CaCO 3 , FeSz, AssSs, ZnO or CaSO 4 -2H 2 O, and if so how? 7. Derive the simplified expression representing the application of the Law of Mass Action to the reaction which takes place when mercuric oxide is heated, assuming first, that none of the mercury formed is condensed to a liquid and second, that some of it is condensed to a liquid. SECTION III GRAVIMETRIC PRECIPITATION PROCESSES CHAPTER XVI GENERAL THEORY OF PRECIPITATION PROCESSES Equilibrium and Solubility. All precipitation processes in- volve the formation of a new solid phase from a liquid phase, and, therefore, heterogeneous equilibrium. The new solid phase may result from the addition of a reagent which changes the physical properties of the solvent and reduces the solubility of the con- stituent which separates, or from a chemical reaction brought about by the addition of a reagent, or from the action of a galvanic current. Since the concentration of the substance precipitated, in the solution from which it separates, cannot exceed that of a satu- rated solution of this precipitate, the completeness of those reactions which result in the formation of precipitates is determined by the solubility of the precipitate. The solubility at ordinary temper- atures, expressed in milligrams per liter of solution, of some of the precipitates frequently used in quantitative analysis is given in the following table.* AgCl 2 Ca(COO) 2 5 6 AgBr 13 CaSO 4 . 2004 Agl.. 0025 Cul . . . . 43 AgCNS 0.02 PbSO 4 . 44 Ag 2 CrO 4 25.0 PbCrO 4 ... . 2 Ag 2 O 25.0 SrSO 4 100 BaCO 3 . . 18.6 Sr(COO) 2 46.0 BaS0 4 2.3 * Most of the figures given here have been calculated from the data sum- marized in the Landolt-Bornstein, Physikalische-Chemische Tabellen. 115 116 QUANTITATIVE CHEMICAL ANALYSIS The Solubility of Electrolytes. Let us represent the total solubility of a binary electrolyte, such as silver chloride, expressed in moles per liter by m and its degree of dissociation in this solution by x. Then mx represents the concentration of the dissociated electrolyte and also that of the anion and cation; also m (1 x) represents the concentration of the undissociated electrolyte. If the dissociation of the electrolyte obeys the mass law the relation between the concentrations is expressed by the equation (mx) 2 = k-m(l-x). In the solution under consideration both m(l x) and (mx) 2 are constant and since both bear a simple relation to the total solu- bility either could be used as a measure of the total solubility. Since the electrolyte here concerned is a slightly soluble salt, its dissociation can be considered to be practically complete, and hence the value of mx corresponds to that of its total solubility, expressed in moles per liter, and the value of (mx) 2 is therefore easily determined This value has been designated by Ostwald by the term " solubility product"; it is one of the constants fre- quently used in discussing quantitative processes. When a precipitate results from a chemical reaction, an excess of the reagent used is invariably added, and the concentration of either anion or cation which enters into the formation of the precipitate must exceed the concentration of the anion or cation in a solution of the precipitate which contains no other substances. In discussing the effect of other substances upon the solubility of such electrolytes it was assumed by Nernst that "In any saturated solution of a slightly soluble electrolyte the concentration of the undissociated electrolyte, and also the product of the concentra- tions of the ions into which it dissociates, are constant." These theorems merely assert that the values which represent the con- centrations of the undissociated electrolyte and the solubility product in solutions obtained by saturating water with the pure electrolyte are true for all solutions of that electrolyte, that is, GENERAL THEORY OF PRECIPITATION PROCESSES 117 are not affected by the presence of other substances. If they are true the addition of an excess of the precipitating agent must decrease the solubility of the precipitate. Theory of the Precipitation of Silver Chloride. Let us assume that we precipitate the chlorine in 200 cc. of a 0.2 molar solution of sodium chloride by the addition of silver nitrate in solid form, in order to avoid changing the dilution. If we first add an exactly equivalent amount, that is, 0.04 mole of the silver salt, the ratio of the silver salt added to salt present is 1, and the mixture must contain equal concentrations of Ag and Cl ions. One liter of water saturated with AgCl contains 0.002 gm., and the concentration of the solution in moles is 0.002 -^ 143 = 1.39 X 10" 5 . This also Log of Solubility of AgCl -5 8 1.01 1.02 1.03 Ratio of Silver Added to Chlorine Present 1.04 Fig. 26. Changes in the Solubility of Silver Chloride represents (Ag+) and (Cl~) and its square, that is, 1.9 X 10~ 10 , the solubility product. Let us now add 0.0002 mole of AgNOs, which will increase (Ag + ) to slightly more than 0.001 and will change the ratio of silver added to salt present to 1.005. If we assume that both sodium chloride and silver nitrate are completely dissociated this addition must change (C1-) to 1.9 X 1Q- 10 -r- 0.001, or 1.9 X 10~ 7 , that is, a very slight increase in the amount of reagent used reduces the solubility of the precipitate enormously. The relation between solubility and amount of reagent used is shown in the curve represented hi Fig. 26, in which the abscissas represent the ratios of silver salt to 118 QUANTITATIVE CHEMICAL ANALYSIS sodium chloride, and the ordinates the logarithm of the solubility. It is important to note that the rate at which the solubility is reduced decreases very rapidly as the value of the ratio increases from 1. It is also evident that if sodium chloride is used for the precipitation of silver from a silver salt, exactly the same reduction in solubility must be effected by the addition of an amount of sodium chloride which makes the ratio of sodium chloride to silver salt the same as the ratio of silver salt to sodium chloride at the points represented on the curve. The precipitate has a maximum solubility when this ratio has the value 1. Factors Which Affect the Theory. Ideal conditions have been assumed in the preceding paragraph. The dissociation of both precipitate and added salt has been assumed to be complete, and the formation of complex ions has been entirely disregarded. In attempting to test the theory by comparing calculated with observed changes in solubility it is scarcely possible to maintain such conditions. The solubility of most of the precipitates tabu- lated on page 111 is so small that the experimental error involved in determining the change in solubility resulting from the addition of a slight amount of the added salt is large. Hence in most of the investigations made, either relatively soluble precipitates have been used, or the concentration of the added salt has been made large. In the former case the dissociation of the precipitate, and in the latter case the dissociation of the added salt cannot be considered complete, and it becomes necessary to ascertain and make use of the degree of dissociation of the electrolytes in cal- culating the change in solubility concerned. These values cannot be determined by a direct measurement in solutions which contain more than one electrolyte, and all attempts to calculate them from the experimental data involve assumptions whose validity can be questioned. In spite of these difficulties many results have been obtained which agree fairly well with the predictions of the theory, others show wide variations from them. In some cases also the formation of complex ions may render GENERAL THEORY OF PRECIPITATION PROCESSES 119 the results of such calculations valueless. It seems necessary to assume that all ions, especially those which possess a slight degree of affinity for their charges, show a variable tendency to increase this affinity by taking up undissociated molecules from the solu- tion. The large number of double salts which can be prepared, and which can be assumed to result from the combination of such ions with others of opposite sign, support this statement. This tendency for the formation of complex ions increases with the concentration of the electrolyte taken up; it is responsible for two effects which are of importance in quantitative analysis. In some cases it leads to the formation of precipitates of abnormal com- position, as shown in the chapter on occlusion; in others it increases the solubility of a precipitate thru the formation of complex ions, which makes it possible for the solution to attain a higher concen- tration of the constituent which is being separated than would be possible if the simpler ions only were present. For example, it was found that the solubility of silver choride* in a solution containing 0.933 mole, of sodium chloride per liter was 8.6 X 10~ 5 , that is, more than six times as great as its solubility in pure water, which was explained by assuming that such solu- tions contain ions of the formula AgCl 3 and AgCl 4 . Altho some chemists entirely reject one or both of the fun- damental assumptions of Nernst, it is now generally believed that the results of all the calculations based upon them are limiting values toward which the actual values converge in proportion as the ideal conditions which they assume are realized; that is, where the concentrations are so small that the dissociation of the electrolytes concerned is complete and the nature of the ions is such that no complexes are formed. This view has been adopted thruout this book. The use of these principles in calculating the changes in the solubility of precipitates, such as PbC^, which dissociate with * Forbes, Journ. of Amer. Chem. Soc., 33, 1186 (1911). 120 QUANTITATIVE CHEMICAL ANALYSIS the formation of one or more bivalent ions, presents no theoretical difficulties. Since, however, such salts dissociate in stages, solu- tions of them may contain appreciable concentrations of inter- + mediate ions, such as PbCl, and it is less probable that the ideal conditions referred to can be realized than when salts of a simpler type are concerned. Theory of Separation of Two Closely Related Ions. The pos- sibility of separating two ions by the addition of a reagent which is capable of forming slightly soluble compounds with both can be discussed with advantage from the standpoint of the theory already elaborated. Let it be assumed that silver nitrate is slowly added to a solution containing equivalent concentrations of potassium iodide and potassium chloride. Silver iodide must begin to separate as soon as the product (Ag + ) X (I~) exceeds S, where S represents the solubility product of silver iodide, and silver chloride must begin to separate as soon as the product (Ag + ) X (Cl~) exceeds S' 9 where S' represents the solubility product of silver chloride. As more silver nitrate is added, more silver iodide separates, and (I~) is progressively reduced. Since, further, the solution remains saturated with respect to silver iodide, and S is constant, the concentration of the silver ions must progressively increase. Both of these changes will continue until (Ag + ) has become so large that the solution is also saturated with respect to silver chloride. At this point (Ag+) X (I-) = S, and (Ag+) X (C1-) = S'. Since both these expressions relate to the same solution (Ag + ) has the same value in both, and hence (i-) s_ (C1-) S'' This expression tells us that the condition for saturation with respect to both compounds is that (I~) shall bear the same relation to (Cl~) that S bears to S'. If still more silver nitrate is added GENERAL THEORY OF PRECIPITATION PROCESSES 121 further quantities of both silver iodide and silver chloride must separate, but the relation of (I~) to (Cl~) must remain constant. The solubility product of silver iodide can be calculated from the data given on page 115 to be 1 X 10~ 16 , and that of silver chloride to be 1.9 X 10~ 10 . Therefore the condition for saturation with both salts is (I-) 1 X IP" 16 = 5.3 X IP" 7 (C1-) 1.9 X 10- 10 1 That is, the concentration of the iodide ions must be reduced to 5.3 X 1(H X (Cl) before precipitation of the chlorine ions can begin to take place. If, further, it is assumed that one equivalent of silver is added for every equivalent of iodine present, the concentration of both iodine and silver would be Vl X 10~ 16 , or IX 10~ 8 , and hence the maximum concentration of chlorine ions which could be present without causing some silver chloride to separate would be (1 X 10~ 8 ) 4- (5.3 X 10~ 7 ), or 0.019; that is, if the concentration of Cl reached the value 0.019 and if one equivalent of silver was added for every equivalent of iodine present, the solution would be just saturated with both precipitates. It is clear that an accurate separation of the iodine from solution which contains both iodine and chlorine ions would not be possible except within certain narrow limits. Obviously one equivalent of silver would have to be added for every equivalent of iodine present if the precipitation is to be even approximately complete, but even if no excess were used some silver chloride would separate if the concentration of the chlorine ion exceeded 0.019. The separation of two ions which yield precipitates with the same reagent is scarcely possible unless the solubilities of these precipitates differ by large amounts, and even then the amount of reagent used must be properly adjusted to the concentrations of the two ions present. CHAPTER XVII FILTERING, WASHING AND IGNITING PRECIPITATES Media Used for Filtration. The separation of precipitates from liquids is essentially a process of straining, in which solid particles are separated from liquid particles by the use of a, porous diaphragm. A variety of media which differ greatly as to their efficiency and adaptability to different purposes are employed for such separations. Cellulose made into the form of paper of a loose, open texture has many advantages; it should represent the purest possible form of this substance, and is, therefore, digested with both hydrochloric and hydrofluoric acids and washed very carefully before use, for the purpose of reducing the percentage of inorganic salts present to a minimum. It is not appreciably dissolved or otherwise affected by solutions of salts or by acids and bases of moderate concentration, but is attacked by strong solutions of acids and bases, and cannot be used for the filtration of such solutions. The papers made from it for quantitative separations differ greatly as to thickness and texture; those of an open and porous character permit very rapid filtration, but are unable to retain very fine precipitates; the more compact varieties are more efficient but slower. Asbestos or mineral wool, unlike cellulose, is non-combustible; it should not be appreciably hygroscopic. Different grades of the mineral vary greatly as to their freedom from associated minerals, length of fiber, and the ease with which they can be reduced to a satisfactory pulp. The best is the pure white long-fibered variety, which can be easily reduced to a pulpy mass by triturating with 122 FILTERING, WASHING AND IGNITING PRECIPITATES 123 water in an agate mortar. It is customary to digest with strong hydrochloric acid before use in order to remove any impurities present which might be dissolved during its use as a filter and thereby change its weight, or contaminate the resulting filtrate. It is not readily made into a fabric which can be used like paper, but must be supported on a plate or disk of platinum or porcelain, which is provided with a number of fine holes (Witt filter plates), or on a crucible the bottom of which is similarly provided. Glass wool is used in the same manner as asbestos. As the fibers of which it is composed are more elastic and pack together less compactly than asbestos it is not so readily made into a filter of equal efficiency. Platinum sponge, which is easily made by reducing the salts of that element to the metallic state, is also used like asbestos but is too expensive for any but certain special purposes. Alundum, or fused aluminum oxide, which has been crushed to a fine powder, can also be made into an efficient filter. It is usually mixed with a small amount of cementing material and molded into the form of crucibles or cylinders. It is not appreciably affected by treatment with even strong acids or strong alkalies. Devices for Filtering When the Precipitate Is Not To Be Weighed. In discussing the devices used in filtration we can dis- tinguish between those cases in which the precipitate is to be weighed at once, and those in which the separation is only one of the preliminary operations which precede the final separation of the desired substance. In the latter case the precipitate may be discarded entirely, or it may be again brought into solution by treatment with other reagents, and the desired substance can be separated from the resulting solution by further operations. Two classes of devices are usually employed in such cases. The first and simplest consists of a paper filter supported on a glass funnel. The rate at which a liquid passes thru such a device depends, aside from the character of the filter paper, upon the nature of the precipitate and the viscosity of the liquid filtered. It 124 QUANTITATIVE CHEMICAL ANALYSIS can be greatly increased by lengthening the funnel stem, that is, by attaching to the latter a piece of glass tubing, which is bent to form a complete turn near its upper end and is slightly constricted at its lower end as represented in Fig. 27. If the paper is accurately fitted to the funnel and the outlet of the stem is small enough to prevent air from entering, the tube gradually fills with liquid and V ~~7 the pressure exerted by the \ ' liquid assists in drawing fur- ther quantities of it thru the filter. If the tube is made too long the pressure may be great enough to break the paper at the apex of the fun- nel as it is unsupported at that point; hence it -is often necessary to introduce a sup- port in the form of a cone made of very thin platinum foil and provided with a num- ber of fine openings or of a small piece of linen cloth folded to fit the apex of the funnel. Whenever a paper filter is used some of the precipitate, especially if the latter is finely divided, is carried into the interior of the paper, and when it is desired to bring this precipitate into solution or to treat it with other reagents a large volume of reagent must be poured thru it, or the entire filter must be opened out and digested in a separate vessel. This often consumes much time, requires the use of an undesirably large volume of reagent and increases the total volume of the solution to an undesirable amount; also the cellulose of the filter may be attacked by the reagent which it is desired to use. Fig. 27. Fun- nel for Rapid Filtration Fig. 28. Filtering Tube and Suction Flask FILTERING, WASHING AND IGNITING PRECIPITATES 125 These difficulties are all avoided by the use of an asbestos filter such as is shown in Fig. 28, in which a Witt filter plate is used in the bottom of a " filtering tube." In this and all devices in which asbestos pulp is used, suction greater than that easily obtained by increasing the length of the stem of the funnel is necessary. In the device shown in the figure the filter tube is attached to a closed filter flask by means of a rubber stopper, and the flask is attached thru its side neck to a Bunsen pump or some other suction device. It permits of extremely rapid filtration and by varying the thick- ness and fineness of the asbestos layer, precipitates of any desired fineness can be retained. After the filtration has been completed the filter and adhering precipitate can be readily and completely transferred to another vessel, and treated with any desired reagent, even with strong bases or acids, after which the residual asbestos can be removed by a second filtration. Devices for Filtration When the Precipitate Is To Be Weighed. If the precipitate is to be weighed it must be freed from water and other adhering substances, and often must be strongly ignited before it can be accurately weighed. It is extremely desirable, therefore, that the medium used for the filtration shall have such properties, that it can be treated exactly as the precipitate is treated without danger of affecting changes in its weight, and that the filter used shall be of such a form that it can be easily ignited and accurately weighed both before use and after the precipitate has been separated on it. Cellulose is decidedly hygroscopic and furthermore slowly loses water and carbonizes even at a temperature of 100, and altho it is sometimes considered necessary to weigh a precipitate on a paper filter it should be avoided wherever possible. When this medium is used for filtration it is customary to destroy the entire filter by burning in a good supply of air and to weigh the residual precipitate mixed with the ash of the paper in a crucible. As the ash content of the filter should not exceed .1 mg. it can usually be disregarded. Asbestos, glass wool and platinum sponge can be ignited strongly 126 QUANTITATIVE CHEMICAL ANALYSIS without suffering appreciable changes in weight, and are, therefore, to be preferred to paper in such cases. The most convenient form for a filtering device hi which such media are to be used and the precipitate is to be ignited, is that of a crucible of tall form but of moderate size and weight such as is represented hi Fig. 29. This is the device first used by Gooch and is usually known as a Gooch crucible. Its bottom is pierced by a number of fine holes and furnishes a support for the media named. It is connected with a filtering tube by means of a rubber band and this tube is at- tached to a filter flask as shown in the figure. A crucible of alundum is equally satisfactory, but since the entire"Cru- Fig. 29. Gooch c ibl e is made of porous material Fi S- 30. Glass more time and care must be ex- Filtering Tube pended in washing the filter free from soluble salts than where the bottom layer only constitutes the filtering medium. When it is not necessary to heat the precipitate after filtration to more than 350 a glass filter tube, similar to the one represented in Fig. 30, which is used in conjunction with a Witt plate or platinum cone can be used to advantage. The Different Classes of Precipitates. All substances which have ^been separated as precipitates possess certain physical peculiarities, altho these peculiarities may be modified to some extent by varying the conditions of precipitation. They may be roughly classified as follows: Crystalline precipitates, such as calcium sulfate, calcium oxalate and magnesium ammonium phosphate. They frequently contain water of crystallization and possess a definite crystalline form, which can be recognized by a magnification of about three hundred FILTERING, WASHING AND IGNITING PRECIPITATES 127 diameters. In this type the tendency for the formation of super- saturated solutions, from which the normal amount of precipitate separates but slowly, is most pronounced, and often makes it de- sirable to make use of mechanical shaking devices when it is nec- essary to reduce the time needed for the complete separation of the precipitate to a minimum. The solubility of these precipitates is comparatively large, and the addition of special reagents for the reduction of the error from solubility often becomes necessary. They are, however, extremely easy to filter and wash. Pulverulent precipitates, such as the sulfates of lead and barium, and the phosphomolybdate of ammonium, are composed of spherical or indefinitely bounded particles, which are too small to be recognized as individuals except by very high magnification. The particles are sometimes so fine that it is difficult to retain them on paper filters, unless these are very hard and dense. It is often possible to avoid the formation of such particles by using condi- tions which make the precipitate separate very slowly, that is, by diluting both the original solution and the added reagent, and by adding the latter slowly and with constant stirring. Long-con- tinued digestion also will frequently increase the size of the smaller grains as explained on page 34. Some precipitates of this class are more satisfactory if separated from a hot, others from a cold solution, and the best conditions of treatment for every precipitate must be learned thru experiment. Another peculiarity of such precipitates is their tendency to " creep, " that is, small amounts of the very fine particles are carried thru capillary action over the sides of the filter and above the liquid which it contains, and where a paper filter is used appreciable amounts may be carried entirely out of the filter and on to the^sides of the funnel. The method of treatment adopted, and the pres- ence of certain reagents seems to have some effect on this pecu- liarity. Curdy precipitates are very similar to those classed as pulveru- lent but are peculiar in that the very fine particles of which they 128 QUANTITATIVE CHEMICAL ANALYSIS are composed readily coalesce to form curdy masses. This is often spoken of as " coagulation " and can be assisted -by heating, violent stirring, and by the presence of certain reagents. This class of precipitates is one of the most desirable, as they are easily and rapidly filtered and washed. The chloride, iodide and cyanide of silver and cuprous sulfocyanate are good examples. Flocculent precipitates are entirely amorphous and very bulky. They are made up of large aggregates of fine particles, which are normally of a loose flocculent nature, but may become hard and compact if allowed to dry, or if sucked against the bottom of the filter by pressure. Under some conditions, they become slimy or gelatinous, and are then extremely difficult to filter. They are usually separated in the best conditions for filtration if the solution is hot, but long-continued boiling sometimes makes them slimy. They retain soluble salts readily and are hard to wash completely. Ferric hydroxide furnishes a typical illustration. Gelatinous precipitates, such as the hydroxide of aluminum, are also composed of extremely fine particles which tend to aggregate into jelly-like masses. They are extremely bulky and as they rapidly clog up the pores of the filter are very hard to filter and wash. In general, they are best kept off the filter' until nearly all of the liquid present has been passed thru it. Colloidal precipitates, good examples of which are silicic acid, the sulfide of arsenic and the hydroxide of chromium, are distinguished by their tendency to form " pseudosolutions " or " hydrosols." When treated with water these solids undergo a transformation which results in the formation of a mixture that seems to be a homogeneous solution and readily passes thru a filter, even tho the latter is capable of retaining extremely fine particles. Such mixtures are not homogeneous, for it can be shown by the use of the ultramicroscope that they actually contain solid particles of too small a size to be recognized by the usual methods of mag- nification. The formation of such pseudosolutions can be entirely prevented by keeping a small concentration of some electrolyte FILTERING, WASHING AND IGNITING PRECIPITATES 129 in the liquid with which they are in contact. As most precipitates are formed in the presence of one or more electrolytes no difficulty is usually experienced in filtering them, but when they are washed with pure water pseudosolutions may form as soon as the con- centration of the electrolyte has been sufficiently reduced; the solid which passes thru ,the filter in this form is usually reprecipi- tated on coming into contact with the main filtrate. It becomes necessary, therefore, to wash such precipitates with a solution of some electrolyte. Electrolytes differ greatly in their ability to prevent the formation of pseudosolutions and altho the salts of di- or tri-valent metals are much more efficient than the salts of ammonium the latter are very generally used for this purpose, as they can be entirely volatilized by igniting the pre- cipitate. The Theory of Washing Precipitates. The precipitate finally separated on the filter is contaminated with various soluble substances present in the solution associated with it. If these substances are easily volatilized during the subsequent ignition, and if they do not react with the precipitate in such a manner as to give rise to volatile compounds with the precipitate during the ignition, their removal is not necessary. In the great majority of cases both of these conditions are not complied with and the precipitate must be washed with an appropriate liquid, the amount of which should be made as small as possible, owing to the solvent action of the liquid on the precipitate. The efficiency of the method used in washing precipitates is readily calculated if ideal conditions only are considered. If A represents the weight in grams of the impurity to be removed and V the volume in cubic centimeters of the wash solution added, and if it is assumed that the filter is in all cases allowed to drain until only 1 cc. of liquid remains in contact with it, and that there is an equal distribution of the soluble salt thruout the volume of y liquid used, each washing would remove ,y , ^A gin. of the 130 QUANTITATIVE CHEMICAL ANALYSIS impurity and leave (V . A gm. behind. The general expres- sion for the amount of impurity left on the filter after n treatments (1 \ n v J A. If, for example, the amount of impurity to be removed was 0.2 gm. and the precipitate. was washed four times with 9 cc. of solution under the conditions named above, only 0.00002 gm. would remain, an amount which can be safely neg- lected. The formula shows further that the efficiency of the process decreases greatly as the volume of the liquid left in contact with the precipitate increases, and that the use of several portions of wash solutions of small volume is decidedly more effective than the use of a smaller number of large portions. If the 36 cc. of wash solution used in four equal portions in the above example had been used as a single portion the weight of impurity still left in the filter would amount to 0.0054 gm. Discrepancy Between the Theory and Practice. Experience does not agree with the predictions of the theory outlined above and the assumption that the impurities are equally distributed thruout the wash solution used is not valid. When the latter is merely poured thru the filter it may not remain in contact with the precipitate long enough to bring about a uniform distribution of the soluble salts, and it is often difficult to prevent the formation of channels in the mass of precipitate, especially where the latter is of a gelatinous character, which prevents the solution from coming into intimate contact with the soluble impurities. The only reliable method of procedure is to wash the precipitate until an actual test of the washing shows that soluble substances are no longer being removed in appreciable amounts. It is often con- venient to ascertain this by evaporating a reasonably large volume of the last washings (at least 20 cc.), to complete dryness and noting the amount of residue left. In other cases it is more convenient to test the washings for the compound which is being FILTERING, WASHING AND IGNITING PRECIPITATES 131 removed by an appropriate and sufficiently delicate qualitative test. It is usually safe to assume, however, that precipitates which have been brought down under identical conditions from solutions of the same composition require the same amount of washing, and in repeating quantitative processes much unnecessary labor can be avoided by ascertaining the amount of washing necessary in the first determination. Washing by Decantation. It is desirable to wash precipitates which rapidly clog up the pores of the filter in the original vessel, that is, to avoid bringing them on the filter as far as possible until the impurities have been removed. This can be effected by allowing the precipitate to settle to the bottom of the vessel, " decanting" off the clear supernatant liquid thru the filter, add- ing wash water, stirring and repeating the same cycle of operations as long as may be necessary. The separation of precipi- tates of low density is often an extremely slow process, and where they are also bulky, comparatively large amounts of solution must be left in contact with the precipi- tate after each decantation; on the other hand the wash solution remains in contact with the entire precipitate long enough Fi S- 31 - ~ Support for to insure an equal distribution of the soluble impurity thruout its volume. On the whole the process of washing by decantation is slow but with certain types of precip- itate it is the best method to employ. Ignition of Precipitates. The precipitate finally separated is necessarily wet, and must be dried before it can be weighed; frequently it is retained on a paper filter, which must be burned up; and it often consists of a mixture, that must be converted into a compound which has a definite composition. All of these 132 QUANTITATIVE CHEMICAL ANALYSIS changes represent gas-evolution processes, and hence precipitation processes involve the use of the principles discussed hi Chapter X. The chief difficulty encountered in igniting precipitates which have been separated on a paper filter is the partial reduction which they may undergo thru the action of the carbon monoxide and volatile hydrocarbons formed during the decomposition of the paper. The difficulty is largely eliminated by adopting the following procedure: First, the filter is dried at a temperature of 100 or less in order to make it possible to separate the greater part of the precipi- tate from the filter before it is destroyed. This is conveniently effected by placing the funnel containing it in a support similar to that shown in Fig. 31 and heating on a hot plate or sand bath. Second, the filter is removed from the funnel, inverted over a clean dry watch glass which rests on a piece of glazed paper, the precipitate detached and transferred to the watch glass without loss by crumpling slightly between the fingers. Third, the filter is made into a compact roll and dropped into the crucible in which the ignition is to be made, and heated cautiously until all volatile matter has been "smoked off"; the temperature is then raised to redness and the heating continued until the resid- ual carbon is entirely consumed. Obviously these operations should be carried out in a good supply of air and hence the crucible should be supported on the triangle in an inclined position and the flame allowed to play against its bottom only. Fourth, the precipitate temporarily set aside is transferred without loss to the crucible by means of a camel's hair brush, which requires careful manipulation. Finally, the crucible is heated under whatever conditions are necessary to convert it into a pure substance of known com- position. This may require heating in a current of some par- ticular gas* CHAPTER XVIII THE PHENOMENA OF OCCLUSION Theories Advanced to Explain the Phenomenon. Many pre- cipitates are found to possess the property of retaining certain soluble constituents of the solution from which they have separated in such a form that they cannot be removed, even by long-con- tinued washing. The phenomenon is a complex one; three theories have been advanced to explain it. Schneider suggested that the soluble salt was taken up by the precipitate as the latter separated, and remained distributed thruout the interior of the solid particles; that is, the phenomenon is the result of the formation of a solid solution in which the precipitate is the solvent and the soluble salt the solute. If this is true we should expect to find definite saturation limits for every precipitate with respect to the occluded substance, but such limits have not been found in most of the cases which have been investigated. Ostwald designates the phenomenon by the term "adsorption." This term was first used by E. du Bois Reymonds to represent the retention of soluble substances by porous or finely divided solids when placed in solutions containing them. A typical illustration of it is the well-known property of bone-charcoal of removing coloring matter from solutions. According to the theory elabo- rated by Ostwald an attractive or restraining force is exerted by the solid, which tends to hold the molecules of dissolved substance in the immediate neighborhood of its bounding surfaces, and either delays or entirely prevents the removal of these substances by washing. The action of bone-charcoal seems to be remarkable as the great majority of solids possess this property to a much 133 134 QUANTITATIVE CHEMICAL ANALYSIS smaller degree. Very few precipitates absorb coloring matters, and their ability to retain soluble salts is of a decidedly selective character. Richards believes that the phenomenon is due to chemical rather than physical forces, and designates it by the term "occlu- sion." According to this theory complex basic salts or molecular compounds, which are but slightly soluble, are formed to a greater or less extent along with the desired precipitate. Thus the oc- clusion of ferric salts by barium sulfate is explained by assuming that the latter precipitate is contaminated with small amounts of a double sulfate of the formula BaS0 4 Fe 2 (S0 4 ) 3 H 2 0. When this compound is ignited the ferric sulfate is decomposed, and three molecules of 80s and one of water are expelled, and one molecule of BaSCU and one of Fe 2 0s are obtained. This explains why the results are too low, when this salt separates with the precipitate, in spite of the fact that it is contaminated with Fe203. Altho it is probable that solid solution and adsorption are in many in- stances concerned with the phenomenon in question, it will be designated in this book by the term occlusion. Occlusion Varies with the Concentration of the Soluble Salt. One of the most important and well-established facts relating to the phenomenon is that the amount of occlusion increases as the concentration of the salt in the solution from which the precipitate separates increases, but is not proportional to that concentration. Some experiments on the occlusion of nitrates by barium sulfate illustrate this statement. In these experiments 25 cc. of a solution of sulfuric acid containing exactly 0.425 gm. of H 2 S04, which should, therefore, yield exactly 1.0118 gm. of BaS04, were used. Variable amounts of potassium nitrate were added in the different experiments, but the solution was in every case diluted to exactly 200 cc., heated to boiling, and the BaS04 precipitated by the addition of 50 cc. of a solution containing 1.3 gm. of BaCl 2 ; after standing for sixteen hours the precipitate was filtered off, washed thoroughly, ignited and weighed. The results were as follows: THE PHENOMENA OF OCCLUSION 135 Series No. 1 2 3 4 Wt. of KN0 3 present 0.0000 0.2000 1.0000 5.0000 Wt. of ppt. found (A) 1.0131 1.0199 1.0308 1.0476 Wt. of ppt found (B) 1 0134 1 0160 1 0291 1 0468 Average of A. and B 1 0133 1 0180 1 0300 1 0472 Excess of wt. found . 0015 0062 0182 0354 A qualitative examination showed that the precipitates obtained in the first series contained very slight amounts of chlorides, those obtained in the other series gave a slight alkaline reaction. It is probable that the 1.5 mg. in excess of the theoretical weight obtained in the first series represents occluded barium chloride, the much larger excesses obtained in the other series represents barium oxide, which resulted from the decomposition of barium nitrate occluded by the precipitate. The last three series of experiments show clearly that the amount of occlusion increases with the concentration of potassium nitrate, but is not proportional to it. Occlusion Takes Place While the Precipitates Separate. A second well-established fact is that occlusion takes place especially during the time the precipitate is separating from the solution. This was shown by a fifth series of experiments, which were car- ried on exactly as those of the third series except that the 1 gm. of potassium nitrate was added after the precipitant had been added and the mixture had been allowed to stand for ten minutes. The weights obtained were 1.0140 and 1.0144 gm. respectively. These figures show that the occlusion of the nitrate was very small if added after the precipitate had separated from the solution. Some experiments are on record which show that barium sulfate and other precipitates do occlude soluble salts even after they have separated from the solution, but to a very slight extent only. Occlusion Varies with the Method of Precipitation. A third factor which has a pronounced effect upon the amount of occlusion 136 QUANTITATIVE CHEMICAL ANALYSIS is the concentration of the precipitant used, and the manner in which it is added. If a solution of barium chloride is added to a solution of sulfuric acid the latter will hi general be hi excess in the resulting mixture up to the time at which an equivalent amount of barium chloride has been added; if a solution of sulfuric acid is added to a solution of barium chloride the latter will in general be in excess up to the time at which an equivalent amount of sulfuric acid has been added. The former set of conditions will favor the occlusion of sulfuric acid, the latter of barium chloride. As barium chloride is occluded more readily than sulfuric acid, and further is not appreciably volatilized on ignition whereas sulfuric acid is completely volatilized, the method of procedure first named might be expected to yield lower results than the one named last. This was shown in a sixth series of experiments in which the conditions of the first series were maintained except that the sulfuric acid, diluted to 200 cc. was added to the barium chloride, diluted to 50 cc. The results obtained were 1.0249 and 1.0212. In series 1, owing to the dilution of the solution to which the precipitating agent was added, occlusion of sulfuric acid was small and was more than counterbalanced, that is, to the extent of 1.5 mg., by the occlusion of barium chloride, In the sixth series, on the contrary, the occlusion of sulfuric acid was reduced to a minimum, while the occlusion of barium chloride was at a maximum and hence the average result was nearly 12 mg. too high. It should be noted that it is impossible to insure an absolutely uniform distribution of the precipitating agent thruout the mixture during the time it is being added. There is a pronounced tendency for the concentration of both reagents to exceed temporarily the average concentration of the entire mixture at certain portions of the solution. For this reason, some of the precipitate may separate in the presence of a much greater concentration of one reagent or the other than corresponds to its average composition, and the effect of mixing the two reagents in the predetermined order may be greatly diminished. These difficulties may be THE PHENOMENA OF OCCLUSION 137 largely avoided by using dilute solutions, by adding the precipitant very slowly, and by stirring vigorously while it is being added. Complete separation of the precipitate also requires an appreciable time interval, and if the rate at which it separates is less than that at which the reagent is added, much of the precipitate may separate in the presence of an unduly large concentration of the reagent. In the experiments described above the barium chloride was added during an interval of ten seconds, and altho the mix- ture was stirred vigorously while the reagent was being added, even in experiment 1 an excess of 1.5 mg. was obtained. The actual amount of chloride occluded by the precipitate included not only the excess of 1.5 mg. but also the normal deficiency due to the solubility of the precipitate, which probably represented 1 or 2 mg. more. It could have been greatly reduced by adding the precipitant more slowly and by reducing the excess added. This was actually shown to be the case in a seventh series of experi- ments in which the precipitations were made under the same con- ditions as the first series, excepting that the precipitant was added drop by drop during an interval of twenty minutes. The weights obtained were 1.0102 and 1.0095. Owing to the extreme difficulty of obtaining absolutely identical conditions with respect to these factors decided differences in the amount of occlusion may result, even where the attempt is made to carry out the determinations under parallel conditions. This is largely responsible for the variations which appear in some of the series of experiments here described; these variations are especially large where the total amount of occlusion is also large. What Salts Are Occluded. Certain ions are largely occluded, others to a slight extent only. This is shown in the following series of experiments, which were made under the same conditions as the first series, excepting that amounts of chlorides on the one hand and of nitrates on the other sufficient to yield equal concen- trations of Cl and NOa ions, respectively, were introduced into the solution before precipitation. 138 QUANTITATIVE CHEMICAL ANALYSIS Series No.. 10 Salt added.... Wt. of ppt. A . Wt. of ppt. B. Avg. A and B . Error.., 0.0000 1.0131 1.0134 1.0133 +0.0015 0.37HC1 1.0135 1.0143 1.0139 +0.0021 0.59NaCl 1.0088 1.0103 1.0096 -0.0022 0.75KC1 1.0054 1.0064 1.0059 -0.0059 Series No.. . 12 14 Salt added.... Wt. of ppt. A . Wt. of ppt. B. Avg. A and B . Error... 0.54(NH 4 )C1 1.0080 1.0091 1.0086 -0.0032 0.56CaCl 2 0.9954 0.9961 0.9958 -0.0160 0.48MgCl 2 1.0140 1.0155 1.0148 +0.003 0.0000 1.0136 1.0137 1.0137 +0.0019 Series No.. 16 18 Salt added.... Wt. of ppt. A . Wt. of ppt. B. Avg. A and B. Error... 0.63HNO 3 1.0376 1.0400 1.0388 +0.0270 0.85NaNO 3 1.0368 1.0413 1.0391 +0.0273 1.0 KNO, 1.0308 1.0291 1.0300 +0.0182 Series No.. 20 Salt added.... Wt. of ppt. A . Wt. of ppt. B. Avg. A and B. Error... 0.8(NH 4 )NO 3 1.0244 1.0238 1.0241 +0.0123 0.82Ca(NO 3 ) 2 1.0144 1 .0174 1.0159 +0.0041 0.73Mg(NO 3 ) 2 1.0339 1.0330 1.0335 +0.0217 By comparing the entire series of results in which chlorides were present with the series in which equivalent concentrations of nitrates were present it is apparent that the substitution of N0 3 for Cl ions increased the total weight of precipitate found by an approximately equal amount. The very high results obtained when even moderate amounts of most of the nitrates used were present are evidently due to the fact that the precipitates contained nitrates in addition to BaS(>4, probably as the result of the forma- THE PHENOMENA OF OCCLUSION 139 tion of complex compounds. It is not improbable that the 864 ions possess an appreciable tendency to unite with electrically neutral Ba(NOs)2 molecules and that the complex ion formed unites with Ba ions to form a salt of the formula BaSO4 Ba(N03) 2 , or that the solution contained small concentrations of ions having the + formula BaNOa which combined with 864 to form (BaNOa^SCU.* The probability of such reactions as these would be determined for the most part by the solubility of the hypothetical com- pound, as compared with that of BaSC>4. The occlusion of chlorides may be due to an analogous series of reactions, but the tendency for these reactions to take place is decidedly less. A further study of these results indicates that there are decided differences in the extent to which the metallic ions represented are occluded. The introduction of sodium, potassium, ammo- nium and calcium ions reduces the positive errors resulting from the presence of equivalent concentrations of chlorine anc} nitrate ions necessarily added at the same time, and when chlorine is the anion added these negative errors exceed the positive ones and the net results are low. The probable explanation is in all cases the presence of compounds similar to BaSO 4 Na 2 S0 4 , that is, the formation of double salts in which a metal having a smaller atomic weight than that of barium is substituted for that element. The results obtained in the experiments in which hydrogen and magnesium ions were added are not so conclusive. In general there is a very slight increase in the weights of precipitates obtained, but these increases are not far from those that might properly be attributed to the chlorine and nitrate ions also added at the same time. Some work done by other experimenters has shown that the presence of moderate concentrations of hydrogen ions gives slightly low results, probably owing to the formation of an acid sulfate of barium. Methods of Avoiding the Error from Occlusion. It is impos- sible to predict to what extent a given substance will be occluded * Hulett and Duschak, Zeit. fur anorganische Chemie, 40, 196 (1904). 140 QUANTITATIVE CHEMICAL ANALYSIS by a given precipitate and even where the error from this source is known to be large it is difficult to avoid or overcome it. If the ion in question is occluded but slightly and the solubility of the precipitate is very small the error can often be reduced to negligible proportions by making the precipitation from a suffi- ciently diluted solution. In some cases it is preferable to remove the ion which is occluded by an evaporation process, or to replace it by another ion which is occluded to a smaller extent by the use of a reagent which renders it insoluble, or converts it into a gas. In other cases it is possible to reduce the concentration of the ion that is occluded by adding reagents which reduce its degree of ionization. In many cases it becomes necessary to purify the precipitate containing the occluded compound by dissolving and reprecipitat- ing under more favorable conditions, that is, by the process of " double precipitation." The difficulty with this method is to find a solvent which dissolves the precipitate readily without introducing large concentrations of other ions, which are also largely occluded. CHAPTER XIX GENERAL THEORY OF ELECTROLYTIC SEPARATIONS Chemical Changes Effected by the Electric Current. The transmission of an electric current, of a sufficiently high intensity, thru a solution of an electrolyte is associated with physical and chemical changes, some of which can be used to advantage in quantitative analysis. The chemical effect at the cathode is always some form of reduction. The hydrogen ion here loses its positive charge, and either forms gaseous hydrogen or acts directly as a reducing agent. Certain metallic ions, such as ferric and stannic ions, either first lose a part of their charges and form ferrous and stannous ions, or separate as metals. Certain other metallic ions, such as those of the alkali group, are first reduced to the metallic state, but the resulting metals react with water to form hydrogen and an alkaline hydroxide. The chemical effect at the anode is always some form of oxida- tion. The anions of the halogen group are liberated as such and act directly as oxidizing agents. The SC>4 ion decomposes into sulfur trioxide and oxygen, but the former reacts with water and forms sulfuric acid; the NOa ion decomposes into nitrogen pen- toxide and oxygen, but the former reacts with water and forms nitric acid. The oxygen thus liberated may separate as a gas or may act as an oxidizing agent. Altho in general the simple metallic ions separate as such at the cathode, lead, manganese and thallium ions separate at the anode in the form of insoluble per- oxides, especially if the concentration of the hydrogen ions is large. Metals Which Can Be Determined. Under certain conditions the metals precipitated at the cathode, and the peroxides precip- 141 142 QUANTITATIVE CHEMICAL ANALYSIS itated at the anode adhere to the electrode firmly, and the weight of the metal or oxide precipitated can then be determined readily, if the weight of the electrode is known. The necessity of filtration, which forms a troublesome feature of many quantitative processes is thereby avoided. A large number of factors affect the rapidity and completeness with which the different metals are precipitated, as well as the physical properties and purity of the resulting precipitate. Thus far electrolytic methods have been most suc- cessfully applied* to the determination of copper, mercury, silver, antimony, tin, iron, nickel, cobalt, cadmium and zinc as metals, and of lead and manganese as oxides. The Voltage Needed. If the difference of potential between two electrodes immersed in a solution of an electrolyte is small a barely perceptible current passes thru the solution: if the po- tential difference is gradually increased a point is finally reached at which the amount of current carried by the solution shows a marked increase, which corresponds to the point at which the ions present first begin to lose their charges. This voltage represents the so-called " decomposition voltage" of the electrolyte con- cerned. Its value is mainly dependent upon the algebraic sum of the numbers representing the voltages necessary to separate the element or radical composing the anion and cation from their respective charges. It depends further upon the concentration of the solution, the temperature, and to a slight extent upon the size and distance between the two electrodes and the metal of which they are composed. Decreasing the concentration by the factor ten increases the value of the decomposition voltage by - volts, hi which n represents the valence of the ion concerned. It is difficult to determine these values accurately, owing to the large number of variables concerned, and the fact that disturbing * The literature of electrochemical processes is extensive. Summaries of the more important methods will be found in Edgar F. Smith's Electrochemical Analysis and Alexander Classen's Quantitative Analysis by Electrolysis. GENERAL THEORY OF ELECTROLYTIC SEPARATIONS 143 secondary actions often take place. The approximate values of the voltages necessary to deprive some of the more important ions, in solutions of normal concentration, at ordinary temperatures, of their charges are as follows: Al Zn Cd Fe Ni Pb H Cu Sb Hg Ag SO 4 +1 +0.49 +0.14 +0.06 -0.05 -0.13 -0.28 -0.61 -0.75 -1.03 -1.05 +2.18 From this table it is easy to calculate that it would be necessary to maintain a difference of potential greater than 1.57 volts in order to cause metallic copper to separate from a solution contain- ing normal concentrations of Cu and S0 4 ions, but as the copper is deposited the concentration of the copper ions continually decreases, and this necessitates a continuous tho slight increase in the voltage used, if the separation is to be even approximately complete. This fact is not of especial importance unless the solution also contains other metallic ions, which have a slightly greater decomposition voltage. In this case it may be impossible to completely separate one metal without using a voltage which causes the second metal to begin to separate also. In general, only those metals whose decomposition voltages differ by several tenths of a volt can be separated from each other by maintaining a constant voltage during the electrolysis. The addition of certain reagents, such as potassium cyanide, to solutions containing two metals sometimes reduces the concentration of one metallic ion to a greater extent than the other, and makes it possible to carry out the separation by the " constant voltage" method which would otherwise be impossible. The voltage used also affects the current strength, for according to Ohm's law the strength (expressed in amperes) must equal the tension (expressed in volts) divided by the resistance (expressed in ohms). In a circuit in which electrolysis is being effected the voltage actually available is diminished by the decomposition voltage of the electrolyte decomposed; hence the current strength actually available is represented by the voltage available minus 144 QUANTITATIVE CHEMICAL ANALYSIS the decomposition voltage of the electrolyte divided by the resist- ance of the circuit. Forms of Electrodes Used. Electrodes of platinum are to be preferred to those of any of the more common metals, since they can be ignited directly in the flame, are not attacked by solutions of acids or alkalies during electrolysis, and can be treated for the removal of the precipitated metal after electrolysis with strong acids. Owing to the cost of the metal the cathode should be as light as possible for the surface exposed; it should also have such a form as to favor circulation of the solution as much as possible; and should be capable of being easily removed from the solution, washed and weighed. Some of the types of electrodes in general use are described below. The Classen dish represented in Fig. 32 serves to contain the solution being electrolyzed, and is itself made the cathode; the anode used with it is a disk of foil or a horizontally coiled spiral of wire. The size in general use has a capacity of 220 cc. and weighs about 37 gm. This arrangement is not favorable to circulation of the solution; further, the removal of the solution and washing of the precipitated metal is not conveniently carried Fig. 32. Classen ou t. Its chief advantage is that many deposits Dish and Anode w ^ c ^ even un( jer favorable circumstances, are but poorly adherent are more easily retained by it without loss than by other forms. The Mansfeld electrode shown in Fig. 33 consists of a cylinder of thin foil usually about 5 cm. in length and 2| cm. in diam- eter, soldered with gold to a supporting wire. The anode used with it consists of a cylindrically coiled spiral of wire placed in the center of the cylinder, or a horizontally coiled spiral placed at the bottom of the containing vessel. If the former anode is used, that portion of the solution which is surrounded by the cathode is effectively stirred by the currents produced by the gas GENERAL THEORY OF ELECTROLYTIC SEPARATIONS 145 liberated at the anode; these currents affect the annular space out- side the cathode to a slight extent only, and a much larger per- centage of the deposit separates on the inside than on the outside of the cylinder. The un- equal distribution of the action of the current over the surface is often shown by the appear- ance of a spongy deposit on the lower edges of the cylinder, whereas the other portions of the deposit are smooth and adherent. Its efficiency may be greatly increased by drilling a large number of holes in the cathode. If the horizontal form of anode is used the circulation of the solution is more equally distributed but is still very poor. The Winkler electrode shown in Fig. 34 con- Fi g- 33. Mans- sists of a cylinder of fine gauze supported by a feld Electrodes wire of small diameter. The form represented is 3 cm. in diameter and 6 cm. in length; the gauze is composed of wires 0.06 mm. in diameter with 41 meshes per linear centimeter. Unlike the Mansfeld form it offers practically no barrier to the circulation of the solution and hence the deposition is much more rapid, and there is comparatively little danger of obtaining spongy deposits. The use of a small amount of mercury, which is placed in the bottom of the beaker or flask containing the solution, and connected with the battery by means of a platinum wire, as a cathode, has been suggested and used to some extent.* It ||P has advantages over the other form of cathodes in Fig. 34. Winkler ^ ne precipitation of metals which give poor deposits Cathode or are acted upon by the solution. Its com- paratively large weight and the need of great care in washing and * Jour. Amer. Chem. Soc., 25, 883 (1903) and 29, 1445 (1907). 146 QUANTITATIVE CHEMICAL ANALYSIS drying before weighing make it less convenient than the other forms. The comparative efficiencies of the first three electrodes de- scribed above are shown in the following table,* which gives their approximate weights, available surfaces and the length of time needed for the precipitation of 0.1975 gm. of copper under identical conditions. Cathode used Surface exposed Weight of cathode Time required Classen dish Sq. cm. 100 Gm. 37 Minutes 400 Mansfeld cathode 79 11 450 Mansfeld cathode with holes 78 11 390 W inkier cathode 93 4 2 50 Effect of Varying Current Strength. The amount of metal separated from the solution during a given time interval depends upon the rate at which the charges on the electrodes are renewed; that is, upon the quantity of electricity which flows thru the solu- tion during a given time interval. Hence the rate at which the metal is deposited depends upon the current strength, as measured in amperes. The law of Faraday states that the amounts of different metals separated by the same current during the same time interval is directly proportional to their atomic weights and inversely proportional to their valencies. A current of one ampere passing thru a solution of a silver salt for one hour deposits 4.026 gm. of silver and equivalent amounts of other metals. This law might be used to calculate the time needed for complete deposition of all of the metal present if all of the current which passes thru the solution was carried by the electrolyte whose cation is being deposited. Since, however, the concentration of the solution with * The data quoted in this and the following paragraphs are given in detail hi Jour. Amer. Chem. Soc., 32, 1264 (1910). GENERAL THEORY OF ELECTROLYTIC SEPARATIONS 147 Milligrams of Copper respect to the metal which is being determined gradually decreases and must finally become nearly zero, the resistance of the solution and the decomposition voltage must gradually rise and finally reach a point at which other ions begin to lose their charges and take part in the transport of the current. The law of Faraday is valid only when the concentration of the ion which is being deposited is so great that a sufficient num- ber of these ions are within the sphere of attraction of the elec- trode to neutralize the charges on the electrode. Since circula- tion of the solution brings these ions into the sphere of attraction of the electrode it favors the de- position of the ions which have smaller decomposition voltages. The effect of increasing the current strength upon the rate of deposition is illustrated by the curves shown in Fig. 35. The solutions used contained in every case 0.1975 gm. of copper as sulfate, 2 gm. of ammonium nitrate and 4 cc. of concentrated nitric acid, and were diluted to 140 cc. Winkler gauze electrodes 10 20 30 40 50 60 70 80 90100 Mmutes Fig. 35. Curves Showing Rate at which Copper is Precipitated were used and current strengths of 0.19, 0.34, 0.5, 0.78 and 5.5 amperes, respectively, were maintained continuously thruout the different experiments. Increasing the current strength also increases the probability of obtaining spongy deposits, which are difficult to weigh accu- rately. In some cases this seems to be due to the inability of the metal to form a continuous layer if deposited too rapidly, in others to the fact that hydrogen is deposited to a greater or less extent 148 QUANTITATIVE CHEMICAL ANALYSIS with the metal. The maximum current strength which can be safely employed increases in direct proportion to the surface of the cathode available. In expressing the proper conditions for the separation of a given metal it is customary to express the permissible current strength with reference to the so-called " normal density," which represents the ratio between the current used in amperes, and the cathode sur- face exposed in units of 100 sq. cm. A current of one ampere used with a cathode exposing 100 sq. cm. would represent a normal density of one; doub- ling both amperage and cath- ode surface would not affect the normal density; doubling the amperage would double it; doubling the cathode surface would halve it. Effect of Varying Concen- tration. The effect of varying concentration on the rate of precipitation is shown by the curves of Fig. 36. The solu- tions used in these experi- ments contained 0.1975 gm. of copper as sulfate and were diluted to 70, 140, 210 and 280 cc., respectively. They also contained 1 cc. of concentrated nitric and 2 cc. of concentrated sulfuric acid for each 140 cc. of solution present. A Winkler gauze electrode and a current of 0.34 ampere were used in all experiments. These curves show that the rate of precipitation decreases rapidly as the concentration decreases, which is partly due to the fact that with the greater concentrations a greater percentage 10 20 30 40 50 60 70 80 90100 Minutes Fig. 36. Curves Showing Rate at which Copper is Precipitated GENERAL THEORY OF ELECTROLYTIC SEPARATIONS 149 of the current used was carried by the copper ions than by the hydrogen ions. Since rapid circulation of the solution reduces to some extent the effect of decreasing concentration, and since the circulation of the solution depends upon the convection cur- rents produced by the gases liberated at the electrodes, part of the effect here shown is due to the fact that the larger volumes are less efficiently stirred. It is desirable, therefore, to keep the volume of the solution as small as possible, that is, just sufficient to cover the electrodes. The Composition of the Solution Used. Since the rate of precipitation depends upon the concentration of the metallic ion which is to be precipitated, the addition of any other salts that are capable of forming complex ions containing that metal should be avoided. The simple nitrates and sulfates are usually to be preferred as electrolytes, owing to their comparatively large dis- sociation constants. The use of nitrates as electrolytes, and in general the presence of NOa ions, has the further advantage of reducing the danger of obtaining spongy deposits, since the hydro- gen liberated at the cathode is at once oxidized by the solution and does not contaminate the deposited metal. The presence of halogen salts in addition to an acid has usually been avoided, unless the concentration of the former is extremely small, since the free halogen which is liberated at the anode may attack the platinum, and the resulting platinum ions, which have a low decomposition voltage, may be precipitated with the desired metal. Further, the presence of halogen ions sometimes results in the formation of spongy deposits. These difficulties can be avoided by the addition of a sufficiently strong reducing agent. It is often necessary, however, to deposit metals from solutions of their complex salts. Silver gives very poor, crystalline deposits when separated from solutions of its simple salts, but good ones when in the form of double cyanides or oxalates. Iron and zinc are not easily precipitated completely in the presence of even a small amount of an acid, but form double oxalates from which 150 QUANTITATIVE CHEMICAL ANALYSIS they are readily precipitated. In all these cases the small amounts of simple metallic ions present are removed by the action of the current, the decrease in the concentration of the simple ions causes the complex ions to break down into simpler ones and ultimately the precipitation is complete. The addition of an acid to a solution frequently makes it possible to separate one of the metals present in a solution which contains several metals in a pure condition. If the hydrogen ion con- centration of such a solution is made sufficiently large and the amperage is kept constant none of the metallic ions having a decomposition voltage greater than that of hydrogen can sepa- rate. This is the principle upon which the so-called " const ant current" method of separating metals by the electric current is based. Apparatus for Carrying on a Single Determination at a Time. A special form of stand is needed to support the anode and cathode in the solution, and provide an easy method of connecting the former with the positive and the latter with the negative pole of the battery. Short-circuiting of the current thru the stand is usually avoided by making the central rod supporting the two arms to which the electrodes are clamped out of glass. The voltage available should be sufficiently high to overcome the counter electromotive force of the electrolyte and the external resistance of the circuit, and yield a current of sufficient strength to deposit the metal within a reasonable length of time. It is further desirable that the voltage available be much greater than that actually needed, for, by introducing a variable resistance or " rheostat" in the circuit, currents of a wider range of strengths are available. These conditions are easily satisfied by the use of a storage battery or a series of galvanic cells which can be depended on to yield an approximately constant voltage for a long period of time. Two storage cells of the usual lead 1 1 lead peroxide type which give about 4.4 volts or -four Daniell cells suffice for the usual range of determinations made- GENERAL THEORY OF ELECTROLYTIC SEPARATIONS 151 In order to determine whether the necessary conditions are being complied with, an "ammeter" showing the current strength should be introduced into the main circuit, and a "voltmeter" showing the difference of potential between electrodes should be connected in a shunt circuit. The proper arrangement of the various parts of the apparatus is shown in Fig. 37. Apparatus for Carrying on Several Determinations at the Same Time. Altho several solutions may be electrolyzed in the same circuit if a sufficiently large voltage is used, the same Fig. 37. Apparatus for a Single Electrolytic Determination current necessarily passes thru all, and if several different metals are being precipitated it may be impossible to satisfy the proper conditions for each. Furthermore, after precipitation in any of the solutions has been completed, the current must be interrupted while the electrodes are being removed, possibly permitting much of the precipitate in some of the other solutions to redissolve. For these reasons it is necessary to split up the main circuit into as many shunt circuits as there are determinations to be made. If all these solutions offer the same counter electromotive force and resistance, the current passing thru each shunt circuit would be the same and could be easily regulated by varying the number of battery cells used, or by introducing resistance in the main 152 QUANTITATIVE CHEMICAL ANALYSIS circuit. If the different solutions offer varying counter electro- motive forces and resistances the current flowing thru each shunt circuit must be regulated by a separate resistance. By using the proper switches and making the necessary connections the same set of measuring instruments may be used for the entire series of shunt circuits. Such an arrangement is presented in Fig. 38 Fig. 38. Plan of Wiring of Bench for Electrolytic Determinations showing two out of any desired number of the shunt circuits, each of which is provided with a separate rheostat, and the connections by which either of two ammeters or a voltmeter may be thrown in or out of the circuit. One of these ammeters is used for the measurement of currents exceeding an entire ampere, the other GENERAL THEORY OF ELECTROLYTIC SEPARATIONS 153 for fractions. The wires used for the connections are of copper and so large that their resistance may be disregarded. The Use of Mechanical Stirring Devices.* It has already been shown that the efficiency of the current used is increased by improving the circulation of the solution. It is also easy to show that improving the circulation permits of the use of currents of much higher normal densities than would otherwise give satis- factory deposits under normal conditions. It becomes possible, therefore, to make precipitations with extreme rapidity by stirring the solution with a mechanical stirrer and using very strong currents, that is, from six to ten amperes. The stirrer used may be a small paddle wheel of glass rotated by a small electric motor or the anode or cathode may be made of such a form that they can be rotated by the same means. * An excellent summary of the methods and results obtained with such devices will be found in A. Fisher's Electroanalytische Schnellmethoden. CHAPTER XX DETERMINATION OF CHLORINE IN SODIUM CHLORIDE I. FACTS UPON WHICH THE DETERMINATION Is BASED Purity of Sodium Chloride. Sodium chloride which contains the theoretical percentage of chlorine can be obtained from dealers. Impure samples can be easily purified by preparing a nearly sat- urated solution, and passing a stream of hydrochloric acid gas into it until a sufficient amount of the salt precipitates, which is then separated on a Witt filter-plate and dried. It is not sufficiently hygroscopic to make accurate weighing difficult, but samples, which have stood in a moist atmosphere for some time may contain as much as one per cent of water. Properties of Silver Chloride. When first precipitated silver chloride is very finely divided and is then retained on a filter with some difficulty; if, however, the solution is slightly acid, and if kept hot and stirred vigorously, or if allowed to stand for several hours the fine particles gradually coalesce, and, owing to their high specific gravity, rapidly settle to the bottom of the containing vessel. A solution of silver nitrate containing 24 gm. of the crystallized salt per liter forms a convenient reagent for the precipitation of chlorine; 1 cc. of such a solution should precipitate 0.005 gm. of chlorine. The solubility of silver chloride is extremely small; it is increased by the presence of large concentrations of nitric and hydrochloric acid and the chlorides and nitrates of ammonium and the alkali metals. When digested with pure water it slowly changes into a colloidal form, but this change is prevented by the presence of a small amount of nitric acid or any other soluble electrolyte. 154 DETERMINATION OF CHLORINE IN SODIUM CHLORIDE 155 When freshly precipitated silver chloride is exposed to strong sunlight it darkens; this change is associated with the formation of a subchloride and the liberation of chlorine. Since the precipi- tate is not transparent the action is superficial only, and the percentage acted upon is small unless the mass of precipitate is continually broken up by stirring. Pure silver chloride fuses at 460 without change of composition and produces a yellow viscous liquid, which forms a tough, horny mass when allowed to solidify. It begins to volatilize at about the same temperature, and appreciable amounts may be driven off if the heating is continued for some minutes. Like most of the compounds of silver this precipitate is easily reduced to the metal by even weak reducing agents. The efficiency of organic matter as a reducing agent makes it necessary to use extreme care in igniting the precipitate when separated on a paper filter, and renders the use of an asbestos filter preferable. II. PREPARATION OF A WASH BOTTLE This determination requires the use of an efficient and convenient "wash bottle," similar lg> g ZJ to the one represented in Fig. 39. It should be provided with a flexible joint at A and two or more easily detachable nozzles, which can be used to produce streams of varying size. The delivery tube should be bent at B in order to permit of a more complete expulsion of the water when the flask is held in an inclined position. III. OUTLINE OF METHOD OF PROCEDURE Weighing Out the Sample. Place about 3 gm. of the salt in a porcelain or platinum crucible, cover and heat gradually with 156 QUANTITATIVE CHEMICAL ANALYSIS a burner until the salt no longer decrepitates. Allow the crucible to cool somewhat, but while still warm pour the salt into a clean, well-stoppered sample tube; when the tube has assumed the tem- perature of the balance-room weigh accurately to a tenth of a milligram. Hold the tube over a clean 300 cc. beaker, remove the stopper and carefully pour into the beaker from 0.2 to 0.4 gm. (not more) of the sample, then replace the stopper and again weigh accurately. Preparation of Solution and Precipitation. Dissolve the sample in 100 cc. of pure water, add 1 cc. of dilute nitric acid and then slowly and with constant stirring a slight excess of silver nitrate solution; 5 cc. of the reagent referred to above hi excess of the amount theoretically required is sufficient. Next heat the solution gradually to the boiling point, and keep somewhat below this temperature, stirring continuously, until the precipitate coagulates and the supernatant liquid is clear; or allow the beaker to stand for several hours after heating to the boiling point. The beaker should be kept away from direct sunlight as much as possible. Filtration and Ignition of Precipitate. Connect a clean Gooch crucible with a suction flask as shown in Fig. 29. Attach the flask to the suction pump and add to the crucible sufficient asbestos pulp to leave a compact layer about 2 mm. thick when drawn against the bottom of the crucible by means of the pump and place a thin Witt filter plate on top of the asbestos. Pass 100 cc. or more of water thru the filter till all loosely adhering fibers are rinsed from the outside of the crucible. Remove the crucible from the filter tube, place in a muffle and heat for about twenty minutes at a temperature of 200. Cool in a desiccator and then weigh accurately. Clean and rinse out the suction flask, connect the crucible with it as before, start the suction pump and decant the solution from the silver precipitate thru the crucible. Add to the precipitate in the beaker about 25 cc. of water, stir the mixture for a few DETERMINATION OF CHLORINE IN SODIUM CHLORIDE 157 minutes, then allow it to settle and again decant thru the filter. Wash with three more 25 cc. portions of water, to each of which about one half cc. of dilute nitric acid has been added. Transfer the precipitate from the beaker to the filter by means of a stream of water from the wash bottle directed back of the precipitate. Finally loosen all particles of precipitate which adhere to the surface of the beaker by means of a rubber-tipped rod and rinse these also into the filter. Empty the filter flask and rinse with distilled water, again connect with the filter and pass 25 cc. of water acidified with nitric acid thru it and test the washings by adding a drop of dilute hydrochloric acid. If this test shows an appreciable turbidity continue washing with water containing a little nitric acid until another test shows that the silver salts have been removed. Finally wash with 10 cc. of pure water. Place the crucible in a muffle, heat slowly to 200 and keep at that temperature for twenty minutes, then allow it to cool in a desiccator and weigh accurately. Again heat for ten minutes and reweigh and if necessary continue heating and weighing until two consecutive weighings do not differ by more than 0.3 mg. Cal- culate and report the percentage of chlorine found. Further Details. This is an ideal precipitation process. The very slight solubility of the precipitate and the accuracy with which as much as two or even three grams of it can be transferred to a filter, dried and weighed, make it readily possible to reduce the error of the determination to a very small figure. The de- parture from the theoretical value need not exceed one-tenth of a per cent, and the entire determination can be made in a two-hour period after some experience has been acquired, if economy in the use of time is observed. The facts made use of in this deter- mination can obviously be applied to the determination with equal accuracy of the silver in solutions of silver salts. IV. QUESTIONS AND PROBLEMS. SERIES 7 1. Calculate the concentrations, as denned on page 39, of the Ag and NO 3 ions in a solution containing 25 gm. of AgNO 3 per liter, assuming the salt at 158 QUANTITATIVE CHEMICAL ANALYSIS this concentration is 70 per cent dissociated; also the concentrations of Pb and Cl ions in a solution containing .74 gm. of PbCl 2 in 135 cc., assuming the salt is 80 per cent dissociated. 2. Calculate the solubility products of AgCl, AgBr, and AgCNS from the data given on page 115, assuming that dissociation is complete. 3. Calculate the solubility in gm. per liter of AgCl in the solution obtained by dissolving .25 gm. of NaCl in 100 cc. of water and then adding 35.4 cc. of reagent AgNO 3 solution, assuming that all salts are completely disso- ciated. Am. 4.1 X 10- 6 . 4. If a dilute solution of AgNO 3 is slowly added to a solution which con- tains .2 gm. of NaC] and 0.005 gm. of KCNS, will AgCl or AgCNS separate firstr 6. How would this determination be affected (a) by acidifying with dilute H 2 S0 4 or H(C 2 H 3 O 2 ) instead of HNO 3 , (b) by dissolving in 150 instead of 100 cc. of water, (c) by using tap instead of distilled water, (d) if KCN or K 2 S or Na 2 S 2 O 3 were present in the solution before the nitric acid was added? 6. If so much of the precipitate was reduced that one-fourth of the pre- cipitate actually weighed consisted of Ag 2 Cl, how large a departure from the correct result would appear in the report? Ans. 2.06 per cent. 7. If you were required to determine the percentage of iodine in sodium iodide by precipitating as silver iodide, would it be desirable to either increase or decrease the amount of sample used, as compared with the amount used in this determination? Ans. No. 8. How would you utilize the silver precipitates obtained in these deter- minations for the preparation of silver nitrate reagent? CHAPTER XXI DETERMINATION OF MAGNESIUM IN CRYSTALLIZED MAGNESIUM SULFATE (MgSO 4 -7H 2 O) I. FACTS UPON WHICH THE DETERMINATION Is BASED Outline of Method. The magnesium ion is precipitated by neutral or alkaline solutions of soluble phosphates, but the resulting precipitates may consist of mixtures of di- and tribasic phosphates, or of a number of double phosphates. Under certain conditions a pure precipitate of Mg(NH 4 )PO 4 -6 H 2 can be obtained, and since this precipitate is converted into Mg 2 P20 7 by ignition, mag- nesium is usually determined in this form. Solubility of the Precipitate. The solubility of this precipi- tate is greater than that of most precipitates used; it cannot be accurately determined owing to a partial decomposition in pure water, which is represented by the expression Mg(NH 4 )P0 4 6 H 2 -> MgHP0 4 + (NH 4 )HO + 5 H 2 0. This reaction is reversed by the presence of moderate concen- trations of ammonium hydroxide, and an excess of this reagent must be used in making the precipitation and in washing the precipitate, but a large excess should be avoided. Conditions Necessary for Precipitation. A solution of Na2HP0 4 12 H 2 containing 74.50 gm. per liter, which is equiva- lent to 0.005 gm. of Mg per cc., is a convenient reagent to use for this precipitation. Experience shows that unless one and one-half times the theoretically required amount of reagent is present in the solution while the precipitate is separating, the results obtained are slightly low. It has also been shown that if the solution contains very large concentrations of NH 4 ions, high 159 160 QUANTITATIVE CHEMICAL ANALYSIS results are obtained. This has been attributed to the formation of small amounts of (NH 4 ) 4 Mg(P0 4 )2 which yields Mg(P0 3 ) 2 on ignition. The concentration of the NH 4 ions depends for the most part upon the concentration of the ammonium salts present, but in part upon the concentration of ammonium hydroxide. Several chemists- have formulated the exact conditions neces- sary to effect complete separation of magnesium in the desired form; the method devised by Gooch and Austin* will be used here. In this method the proper excess of sodium phosphate is first added to the neutral or slightly alkaline solution, which produces a precipitate assumed to contain small amounts of Mg 3 (PO 4 ) 2 . This precipitate is redissolved by adding a few drops of dilute hydrochloric acid and the magnesium reprecipitated by the very gradual addition of dilute ammonium hydroxide. Suffi- cient soluble phosphate is present during the second precipitation to insure complete precipitation and an undesirably large concen- tration of (NH 4 ) ions is avoided by this procedure. The precipitate obtained should be coarsely crystalline; it shows some tendency for the formation of supersaturated solutions, but under ideal conditions complete separation should take place within a half hour. The separation is retarded by the presence of large concentrations of ammonium salts, and it is sometimes necessary to allow the mixture to stand for twelve hours or to stir vigorously for an hour. Conditions Necessary for Ignition. A very high temperature must be used to convert Mg(NH 4 )P0 4 into Mg 2 P20 7 , hence the precipitate should be ignited in a small crucible with a Meker or Chaddock burner, or over a blast lamp. At the temperature finally attained a slight sintering of the precipitate takes place, and if particles of unconsumed filter paper are still present they may be so surrounded as to prevent complete oxidation. Hence the temperature should be kept rather low until the combustible matter has been consumed. This difficulty can usually be avoided * Zeit. fur anorganische Chemie, 20, 121 (1899). MAGNESIUM IN MAGNESIUM SULFATE 161 by moistening the precipitate and filter with a few drops of a strong solution of ammonium nitrate before ignition. Some chemists prefer to separate this precipitate on a Gooch crucible, but the large size of these crucibles increases the difficulty of bringing the precipitate to the proper temperature. Altho the precipitate is not readily reduced, it is not wise to ignite it in a platinum crucible as the latter becomes brittle and soon cracks if used repeatedly for this purpose; this is probably due to the forma- tion of a small amount of a phosphide of platinum. II. OUTLINE OP THE METHOD OF PROCEDURE Weighing Out and Precipitating the Sample. Place 3 to 4 gm. of the pure dry salt in a clean sample tube and weigh out about 1 gm. into a 200 cc. beaker. Dissolve the sample in about 50 cc. of water, add one and one-half times the theoretically required volume of sodium phosphate solution, and then add dilute hydro- chloric acid drop by drop until the precipitate which usually separates redissolves. Dilute in a separate vessel 10 cc. of dilute ammonium hydroxide to 50 cc., and add this solution drop by drop with constant stirring until the solution when tested with a narrow piece of red litmus paper shows a slight alkaline reaction. Next add slowly 20 cc. of dilute ammonium hydroxide and allow the mixture to stand, stirring it occasionally, for one-half hour. Filtration. Fold an 11 cm. ashless filter paper to accurately fit a funnel of slightly larger size and moisten with water. Decant the clear portion of the solution thru the filter, then transfer the precipitate to it by means of a stream from a wash bottle which contains a mixture of one volume of dilute ammonium hydroxide to four of water. Continue washing with this mixture until 20 cc. of the washings give no recognizable test for chlorine. Finally moisten the precipitate and filter with a few drops of a five per cent solution of ammonium nitrate. Igniting and Weighing the Precipitate. Dry the filter and while waiting for it to dry ignite and weigh a small porcelain 162 QUANTITATIVE CHEMICAL ANALYSIS crucible. Separate the precipitate as far as possible from the filter and complete the ignition as directed on page 132. The final ignition should be made with a cover on the crucible using the full heat of a Meker or Chaddock burner for at least twenty minutes, and repeating until consecutive weighings, which do not differ by more than 0.3 mg., are obtained. Difficulty is sometimes expe- rienced in obtaining a perfectly white precipitate owing to incom- plete combustion of small amounts of carbon. This is sometimes due to imperfect removal of soluble phosphates. It can often be corrected by adding a few drops of ammonium nitrate solution to the crucible and repeating the ignition. Calculate and report the percentage of magnesium present. III. QUESTIONS AND PROBLEMS. SERIES 8 1. Why would you expect that the compound Mg(NH 4 )PO 4 - 6H 2 O might react with water? What reagents should reverse this reaction? Which of these could be used in washing the precipitate? 2. What reagents ought to reduce the solubility of Mg(NH 4 )P0 4 - 6H 2 O? Which ones could be used for this purpose in the quantitative determination (a) of magnesium, (b). of phosphoric acid? 3. What factors would determine whether Mg(NH 4 )PO 4 6H 2 O or Mg(NH4) 4 (PO 4 )2 would separate in this determination? 4. What factors determine the completeness of the reaction which takes place when Mg(NH4)PO 4 6 H 2 O is ignited? What would you expect to happen when (a) MgNaPO 4 , (b) Mg(NH4) 4 (PO 4 ) 2 or (c) NaH 2 PO 4 are heated? heated? 5. Calculate the chemical factors (see page 74) for converting Mg 2 P 2 O 7 into (a) MgO, (b) P 2 O 5 , (c) MgSO 4 -7H 2 O, (d) MgSO 4 - NaoS0 4 4 H 2 0. 6. What is the probable formula of a salt which is found to contain 5.97 per cent of Mg, 19.40 of K, 47.76 of SO 4 and 26.80 of water? 7. What other metallic ions "may be present when this method is used for the determination of magnesium? CHAPTER XXII DETERMINATION OF IRON IN FERROUS AMMONIUM SULFATE BY THE USE OF THE ELECTRIC CURRENT I. FACTS UPON WHICH THE DETERMINATION Is BASED Composition of Ferrous Ammonium Sulfate. This salt has the formula FeS0 4 (NH 4 )2S0 4 6 H 2 and is readily obtained in a high degree of purity. As it slowly oxidizes and loses some of its water, even at 25, it should be preserved in a stoppered bottle in a cool place. If these changes have taken place the crystals show a reddish color and lack their usual transparency. Conditions Necessary for the Separation. The decomposi- tion voltage of the ferrous ion is 0.34 volt higher than that of the hydrogen ion and the metal cannot be separated from solutions by an electric current unless the concentration of the hydrogen ion is small. It is not possible to separate the metal in a satisfactory form from solutions of simple ferrous salts, but good results are obtained if the solution also contains a large concentration of ammonium or potassium oxalate. The solubility of ferrous oxalate is only 0.077 gm. per liter, and since double oxalates of ammonium and potassium are easily pre- pared, it is probable that most of the iron in such solutions is in the form of a complex ion. The composition of this ion is not definitely known, but its formation can be represented by x FeC 2 4 + y CA + 2 ?/(NH 4 ) - (FeC 2 4 "),(C 2 4 ) y + 2 2/(NH 4 ). It has been shown that for every atom of iron present in such solutions four molecules of potassium oxalate must be present to prevent the separation of a precipitate containing iron. Such precipitates are not easily dissolved by the addition of further 163 164 QUANTITATIVE CHEMICAL ANALYSIS amounts of soluble oxalates, and in preparing the solution care must be taken to add the iron solution to a concentrated solution of the soluble oxalate. The voltage necessary for the separation of iron from such solutions is somewhat higher than that necessary to separate it from solutions of simpler composition. Secondary Effects of the Electrolysis. The C 2 4 ions present are slowly oxidized to COs ions at the anode and since the tem- perature of the solution may rise to 60, owing to the large am- perages usually employed, much carbon dioxide is expelled. As NHs is not expelled to the same extent, the solution may acquire a sufficient degree of alkalinity to precipitate some of the iron; it then becomes necessary to add sufficient oxalic acid to dissolve the precipitate. Properties of the Precipitate. The separated metal forms smooth coherent deposits even when deposited on foil electrodes, by the use of a current measuring as much as three amperes (normal density). It is not acted upon appreciably by the solution as usually prepared, but is rapidly dissolved by even small concen- trations of mineral acids. It is easily oxidized, especially when moist, and must be rinsed with at least two changes of alcohol to displace the adhering water, dried at a temperature not in excess of 60, and weighed without delay, if oxidation is to be avoided. Effect of Additional Substances. Solutions containing ferric sulfate or chloride also form double oxalates, but since reduction to the ferrous condition precedes precipitation of the metal the time needed is greater. The presence of the NOs ion must be avoided, owing to its oxidizing power. The presence of all metals which stand below, or only slightly above iron in the electro- potential series must be avoided. II. OUTLINE OF METHOD OF PROCEDURE Splitting a Watch Glass. The large amount of gas liberated during this electrolysis makes it necessary to cover the containing vessel; a watch glass which has been split into halves can be used IRON IN FERROUS AMMONIUM SULFATE 165 with advantage. To split the glass make a scratch on its convex surface with a steel or diamond glass-cutter, using a piece of card- board for a straight edge, and then bring the glass along the scratched line into contact with a piece of fine nichrome wire which is heated to dull redness by means of an electric current. If the glass does not fall apart at once place a drop of cold water on the line heated by the wire. Preparation of the Solution. Place about 5 gm. of the salt in a dry sample tube and weigh out about 1 gm. into a 100 cc. beaker. Add 25 cc. of water and stir until the salt dissolves. Weigh out approximately 6 gm. of crystallized ammonium oxalate into a 200 cc. beaker of narrow form, add 50 cc. of water, warm and stir till the salt dissolves. Add the iron solution to the oxalate solu- tion, and rinse out the beaker with three 10 cc. portions of water. The resulting mixture should be perfectly clear and of a deep yellow color. Electrolysis of the Solution. Ignite a clean platinum cathode of the Mansfeld or Winkler type in the flame of a burner, allow to cool without placing in a desiccator, and weigh accurately. Place the cathode in the iron solutions and an anode in the center of the cathode cylinder. Carry the beaker to the bench contain- ing an installation similar to that represented in Fig. 38. Throw the ammeter and voltmeter switches opposite one of the vacant electrolytic stands to the point marked zero, and turn the arm of the adjustable rheostat well over to the left of the center as shown in the figure. Connect the cathode with the lower arm of the electrolytic stand and the anode with the upper arm, carefully adjusting both electrodes so that both extend to within a few mm. of the bottom of the beaker, but do not come into contact with one another. Next note whether the needle of the ammeter (the one reading up to fifteen amperes) stands at zero, which means that the instrument is not being used on any of the other circuits, and if not at zero wait until out of use. As soon as the pointer of the instrument 166 QUANTITATIVE CHEMICAL ANALYSIS stands at zero throw the ammeter switch to the point marked two and slowly turn the arm of the rheostat till the instrument shows that a current of one and one-half amperes is flowing thru the circuit ; then throw the ammeter switch back to the point marked one. Next turn the voltmeter switch to the point nearest the circuit in use and after recording the reading of the needle return the switch to the central point. Allow the current to run for 80 minutes if the Winkler cathode is used, or two hours if a Mansfeld cathode is used. At the end of this time the solution should be perfectly colorless and should show no traces of precipitate. Washing and Weighing the Cathode. Fill a 200 cc. beaker with distilled water and place on the desk near the solution; raise the electrolytic stand without breaking the circuit or disconnecting the attached wires and plunge the electrodes without loss of time into the beaker of water. Add to the beaker containing the residual solution a few cc. of potassium ferrocyanide; if it gives a perceptible reaction for iron the determination should be repeated. If no iron is found in the solution, disconnect the cathode and rinse in the water of the beaker, then remove and bring into contact with a large piece of filter paper until most of the adhering water has been absorbed. Rinse the cathode in alcohol, using first the cylinder marked "for first washing, " then the cylinder marked "for second washing," which should contain 98 per cent alcohol, and drain on a piece of filter paper. Dry in an air bath at a temperature of about 60. Do not allow the alcohol on the cathode to catch fire; if it does so the precipitated iron will also burn, and the heat liberated will cause some of it to alloy with the platinum and spoil the electrode. Weigh the electrode accurately and calculate the per cent of iron present. Place the cathode in a beaker containing dilute sulfuric acid and allow it to remain until absolutely all the deposited iron has been dissolved off; this can be determined by noting whether hydrogen is liberated. IRON IN FERROUS AMMONIUM SULFATE 167 III. QUESTIONS AND PROBLEMS. SERIES 9 1. Explain why a large amount of gas is liberated at the cathode during the later stages of the deposition but not during the earlier. 2. On the basis of Faraday's law how long a time would be required to deposit all the iron present in 1 gm. of ferrous ammonium sulfate if a current of 0.5 ampere is used? Why is the calculation of no practical value? 3. Exactly why is the formation of a precipitate prevented by adding the iron solution to the oxalate solution? 4. If the ferrocyanide test used showed that iron was still present why not replace the electrodes in the solution and continue the electrolysis instead of discarding the determination? 6. If the decomposition voltage of a normal solution of the ferrous ion is +0.34 volt, what voltage would it be necessary to use to reduce the concen- tration of the ferrous ions to 0.00056 gm. in a volume of 100 cc.? Ans. +0.456. 6. Why is the voltage necessary for the deposition of iron from a neutral solution of ferrous sulfate increased by the addition of ammonium oxalate? 7. Outline an electrolytic method for the determination of iron in a sample of iron wire and give all the reactions concerned. 8. How many storage battery cells, each of which is capable of furnishing 2.2 volts, would be necessary to give the voltage required for ten simul- taneous determinations, assuming that the fall of potential per solution is 0.5 volt, that the resistance of each solution and connections is 0.5 ohm and that a current of at least one ampere is maintained (a) when the solutions are in series, (b) when they are in parallel? Would it be advisable to decide upon the number of cells from the voltage calculated? 9. Show by means of a simple diagram the course of the current during electrolysis when the ammeter switch (a) is at the point 2, (b) is at the point 4 of Fig. 38, (c) when the voltmeter switch is at such a position that the voltage is registered. CHAPTER XXIII DETERMINATION OF SULFUR IN IRON PYRITES I. FACTS UPON WHICH THE DETERMINATION Is BASED Composition of Pyrites. This mineral is represented by the formula FeS2, but it is frequently associated with the sulfides of other metals, especially copper, zinc, arsenic and lead, with the sulfates of calcium and barium, and almost invariably with silica and various insoluble silicates. It is assumed that the sample used for this determination contains at least 35 per cent of sulfur, only small amounts of copper, zinc and arsenic, and neither barium nor lead. It is assumed further that the sample has been crushed and passed thru a sixty-mesh sieve, carefully mixed and dried. Methods of Oxidizing Sulfides. Two methods are in general use for the oxidation of naturally-occurring sulfides; in one the mineral is treated with a strong mineral acid and a strong oxidizing agent, such as potassium chlorate, nitric acid or bromine; in the other it is fused with a mixture of sodium carbonate and either sodium peroxide or potassium nitrate. The presence of NOs ions in the solution from which barium sulfate is to be precipitated must be avoided, owing, as shown on page 135, to the extent to which nitrates are occluded. Since, however, the NOa, ClOs and Br ions can be easily expelled by evaporating the solution with a large excess of hydrochloric acid, and since no sulfuric acid is expelled if this evaporation is made on a steam bath, there is no objection to the method of oxidation first named. The presence of the large amounts of sodium and potassium salts necessarily introduced in oxidizing by the fusion process also results in errors from occlusion, and since these salts cannot be removed from the 168 DETERMINATION OF SULFUR IN IRON PYRITES 169 solution by any satisfactory process this method of oxidation is to be avoided. Most samples of pyrites can be completely and rapidly oxidized by means of a mixture of three volumes of concentrated nitric and one of concentrated hydrochloric acid. In some instances, especially where the temperature of the mixture is allowed to rise too high, and the decomposition of the sample takes place too rapidly, small amounts of free sulfur may separate; this can usually be oxidized by the addition of a few drops of liquid bromine, whose oxidizing properties are stronger than those of nitric acid. Treatment of the sample with this mixture and the subsequent evaporation with hydrochloric acid insures complete oxidation of the iron and arsenic, and renders all constituents soluble except silica and the insoluble silicates. Separation of the Iron Before Precipitation of Barium Sulfate. The filtrate from the insoluble matter will contain large amounts of ferric chloride, also the chlorides of the other metals present. If barium sulfate is precipitated from such a solution it will contain occluded ferric sulfate and, as shown on page 134, this will lead to very low results. If the iron is precipitated by the addition of ammonium hy- droxide, appreciable amounts of ammonium salts are added to the solution, and as ammonium sulfate is both occluded by the precip- itate and expelled during ignition, a rather large error may result unless the amount of acid present in the solution before precipita- tion is reduced to a minimum. The precipitate obtained by the addition of ammonium hy- droxide to a solution containing ferric sulfate may contain appreci- able amounts of basic sulfates, unless a relatively large excess of precipitant is used and the mixture heated for some time. Even when no basic sulfates have been formed, it is difficult to wash out the last traces of soluble sulfates from the precipitate, and it is not safe to. discard the latter until it has been proved to be free from these compounds. The washed precipitate can be dissolved 170 QUANTITATIVE CHEMICAL ANALYSIS in a very small amount of warm dilute hydrochloric acid, the iron again separated and the sulfur precipitated in the resulting nitrate. Under the proper conditions the weight of barium sulf ate obtained from the second filtrate should not exceed 10 mg., and is often inappreciable. Where extreme accuracy is not essential the method may be abbreviated somewhat by precipitating the small amount of barium sulfate in the hydrochloric acid solution of the precipitate, without removing the iron. Properties of Barium Sulfate. The solubility of barium sul- fate amounts to 2.2 mg. per liter; it is increased by small concen- trations of nitric or hydrochloric acid; it is decreased by small concentrations of sulfuric acid or salts which yield SC>4 ions, but the salt is decidedly soluble in concentrated sulfuric acid. It has a density of 4.49 gm., and when precipitated under the proper conditions settles rapidly. As much as 2 gm. of the precipitate can be easily and rapidly filtered and washed on an 11 cm. filter. The barium sulfate precipitate is usually classed as pulverulent, but its properties are affected to a large extent by the conditions of precipitation. That produced by the addition of a salt of barium to a cold concentrated solution of a soluble sulfate is often so finely divided that it cannot be retained on the filters usually employed. Altho long-continued digestion increases the size of the particles of which such a precipitate is composed, it is preferable to avoid the formation of such precipitates by causing it to separate from a hot solution whose concentration does not exceed 3 gm. of S0 4 per liter. The presence of a small amount of acid makes the precipitate more compact, causes it to settle more rapidly, and reduces its tendency to creep. The conditions which result in the formation of a precipitate of the most desirable physical properties also result in a slight tendency for supersaturation. Under the conditions which are recommended later the precipitate should be allowed to stand for at least one hour before filtration; increasing the amount of acid increases the time necessary for complete separation. DETERMINATION OF SULFUR IN IRON PYRITES 171 The precipitate produced by the addition of a salt of barium to a slightly alkaline, or even to a neutral solution of a soluble sulfate may contain, in addition to barium sulfate, small amounts of basic sulfates, and, also, as the result of the absorption of carbon dioxide from air, of barium carbonate. The presence of a slight concen- tration of hydrogen ions prevents the formation of either of these compounds. If, however, the concentration of the hydrogen ions is not kept very small, low results are obtained, owing to the fact that under these conditions appreciable amounts of an acid sulfate of barium is occluded. The maximum concentration of hydrogen ions should not exceed 0.02 gm. per liter. Conditions Necessary for Ignition. Pure barium sulfate is not decomposed appreciably by heating in dry air up to a tempera- ture of 1400. If heated in the presence of carbon, carbon mon- oxide, or other reducing agents it is partly reduced to the sulfide even at a temperature of 600; the presence of moisture also seems to favor this reduction. If the precipitate is ignited with the filter paper without previous drying appreciable amounts of barium sulfide may form, unless the temperature is kept very low until all of the water and volatile organic matter has been driven off. If some of the precipitate has been reduced it can be changed back into the sulfate by moistening with dilute sulfuric acid, evaporating to dryness and igniting. II. OUTLINE OF METHOD OF PROCEDURE Oxidation of the Sulfur. Weigh out 0.5 gm. of the sample into a 150 cc. beaker, cover with a watch glass, add 10 cc. of a mixture of three volumes of concentrated nitric and one of con- centrated hydrochloric acid and allow to stand for ten minutes. If brown fumes are not evolved at the expiration of this time warm the beaker gently until the mixture begins to react; if the action becomes too violent, restrain it by placing the beaker in a dish of cold water. When brown fumes are no longer given off and when the residue contains no particles of a brassy-yellow color it may be 172 QUANTITATIVE CHEMICAL ANALYSIS assumed that the decomposition of the sample is complete. If decomposed too rapidly, yellow or greenish-yellow particles, which consist for the most part of free sulfur, will float in or on the solu- tion; the oxidation should then be completed by adding one or two drops of liquid bromine (not bromine water) and allowing to stand on the steam bath for a few minutes. Displacement of Nitric Acid. Remove the cover from the beaker, rinse off the former with a little water and evaporate the solution to dryness on the steam bath, then add 10 cc. of dilute hydrochloric acid and evaporate to dryness as before. Moisten the residue with 1 or 2 cc. of dilute hydrochloric acid, add 50 cc. of water and digest until all soluble salts have been brought into solution, noting especially that the ferric sulfate present in the residue often dissolves very slowly. Separation of Gangue and Iron. Filter through a 7 cm. filter into a 300 cc. beaker and wash with at least 50 cc. of cold Water. Dilute the filtrate to 150 cc., heat nearly to boiling and add ammonium hydroxide until the resulting mixture smells of ammonia and all of the iron seems to be precipitated. Keep the mixture near the boiling point for about five minutes, then allow the solution to stand till most of the precipitate has settled. Decant off the clear portion of the solution thru an 11 cm. filter, receiving the filtrate into a 500 cc. beaker, then transfer the precipitate to the filter and wash with hot water "churning up" the precipitate frequently with a stream from the wash bottle, and using about 200 cc. of wash water in all; this forms filtrate No. 1. Set aside the beaker containing the filtrate and place the beaker in which the iron was precipitated under the funnel. Transfer as much of the precipitate as can be readily picked up by means of a stirring rod to the bottom of the empty beaker, taking care to avoid rupturing the filter; at least three-fourths of the precipitate can be easily transferred by this means in a few minutes. Add suffi- cient warm dilute hydrochloric acid, drop by drop, to the precipitate DETERMINATION OF SULFUR IN IRON PYRITES 173 still remaining on the filter, to completely dissolve it, using not more than 1(X cc. of the reagent, preferably less. Wash the filter with cold water long enough to remove the ferric chloride and make it colorless, finally warm the mixture in the beaker until a perfectly clear yellow solution is obtained. Dilute the solution to 150 cc., reprecipitate the iron as before and again filter and wash, receiving the filtrate (filtrate No. 2) in a 500 cc. beaker. Precipitation of Barium Sulfate. Add to both filtrates (No. 1 and 2) a drop of methyl orange indicator, then dilute hydrochloric acid until the solutions are slightly red and then three drops of acid in excess. Heat filtrate No. 1 to boiling and add with constant stirring 30 cc. of barium chloride solution, 1 cc. of which is equiva- lent to 0.01 gm. of sulfur, also heated nearly to boiling. Heat filtrate No. 2 .in like manner and add 10 cc. of barium chloride solution. Allow both precipitates to stand for at least one hour, then filter on separate filters and wash thoroughly with hot water and dry. Igniting and Weighing Precipitate. Burn the filter contain- ing the precipitate from filtrate No. 2 in a porcelain or platinum crucible; separate the precipitate obtained from filtrate No. 1 from its filter and burn the latter, in the same crucible. Finally add the main precipitate to the crucible and ignite for at least ten minutes over a good flame, allow to cool and weigh accurately. Calculate the percentage of sulfur present in the original sample. III. ADDITIONAL NOTES ON THE DETERMINATION This determination is of much industrial importance and has been made the subject of many investigations.* Duplicate deter- minations by the method here outlined need not differ by more than 0.2 per cent, and give very nearly the true percentage of * See Hinze and Webber, Zeit. fur analytische Chemie, 45, 31 (1906); Allen and Johnston, Jour, of Industrial and Eng. Chem., 2, 196 (1910); Allen and Bishop, Eighth Int. Congress of Applied Chemistry, Vol. I, page 33 (1913). 174 QUANTITATIVE CHEMICAL ANALYSIS sulfur present. An entire determination can be completed within three hours in addition to the time the precipitate is allowed to stand before filtering. IV. QUESTIONS AND PROBLEMS. SERIES 10 1. A lump of ore weighs 500 gm. and consists of 20 per cent quartz (sp. gr. 2.8) and 80 per cent pyrite (sp. gr. 5). If the sample is crushed, mixed and quartered twice, and again crushed and mixed, what is the maximum permis- sible size of particle for the three crushings in order that the portions removed at the two successive quarterings and the 0.5 gm. portion used for the analy- sis shall represent the correct composition of the sample with an error not exceeding 0.1 per cent? (For method of calculation see page 27.) Arcs. 4.7, 2.96 and .75 mm. 2. What advantages are there in keeping the nitrate from the two iron precipitates separate rather than uniting them? 3. How would you proceed in order to determine the amount of barium chloride occluded by the precipitate of barium sulf ate found? 4. What is the percentage error of a determination of sulfur in which the 0.874 gm. of precipitate found and assumed to be pure BaSC>4 actually contains 0.02 gm. of Na if the Na is occluded as suggested on page 139? 6. If the ash of the filter paper used weighed 0.0002 gm., how large a de- parture from the correct percentage would result from failure to correct for it, assuming that 0.5 gm. of sample is used and that it contained 40 per cent of sulfur? 6. Write the reactions which probably take place when pure pyrite is treated with aqua regia. What is the action of (a) pure bromine, (b) of bromine water? CHAPTER XXIV SEPARATION OF CALCIUM FROM MAGNESIUM AND PARTIAL ANALYSIS OF LIMESTONE I. FACTS UPON WHICH THE ANALYSIS Is BASED Composition of Limestone. This rock invariably contains, in addition to calcium and magnesium carbonates, small amounts of the carbonates and oxides of iron, manganese and alumina, and more or less quartz, clay and other silicates. The minerals pyrite, graphite, apatite and gypsum are frequently associated with limestone. Proximate Method of Analysis. This analysis forms one of the problems frequently presented to the analyst since limestone is an essential raw material in many branches of chemical tech- nology. The complete analysis takes much time and labor, and for many technical uses is unnecessary; hence in many factories it is customary to make a more rapid " proximate analysis," in which certain groups of constituents, which are present in small amounts only, are separated and reported as a whole, rather than being resolved into their ultimate elements. If the sample is treated with nitric or hydrochloric acid the quartz, graphite and most of the silicates remain undissolved. If the amount of insoluble matter left is very small it is frequently ignited, which effects combustion of the graphite, weighed, and reported as "gangue" or "insoluble matter." If the amount present is larger it is usually considered necessary to treat the sample as an insoluble silicate (see Chapter XXVII), or to treat the gangue matter which has been separated as an insoluble silicate. 175 176 QUANTITATIVE CHEMICAL ANALYSIS The iron, aluminum and phosphoric acid are almost invariably separated from the other bases present by the use of ammonium hydroxide. The resulting precipitate can be resolved into its ulti- mate constituents by methods discussed in other chapters of this book; they are more frequently weighed together and reported as mixed oxides. The small amount of manganese which is some- times present can be separated with approximate accuracy from the nitrate by the addition of bromine, which causes this element to separate as the hydrated dioxide. The loss which results from ignition represents still a third group of constituents of which carbon dioxide is by far the most important; this determination is sometimes substituted for the more accurate estimation of this constituent. After eliminating all of the elements named only calcium and magnesium remain. As the percentages of these elements often have an important practical significance they are usually deter- mined with considerable care and accuracy. Sources of Error in the Determination of Gangue. This de- termination furnishes an illustration of a solution process depend- ent upon the chemical action of a reagent (see Chapter XXVIII). Since certain silicates such as clay are but slowly acted upon by the acids used the results obtained depend to some extent upon the fineness of the sample, the length of time it is treated and the composition of the acid used; there is no generally accepted standard method of procedure. Sufficient nitric acid should be present to dissolve any pyrite, and to effect complete oxidation of the iron. After decomposition has been effected the solution should be evaporated to complete dryness to dehydrate and render in- soluble the silicic acid formed (see Chapter XXVII). Sources of Error in the Determination of Iron and Alumina. Ferric hydroxide and aluminum hydroxide form bulky precipitates, which are extremely difficult to filter and wash. When separated by the addition of ammonium hydroxide, from a solution which also contains calcium and magnesium, the resulting precipitate SEPARATION OF CALCIUM FROM MAGNESIUM 177 invariably contains these elements also, even tho a large amount of ammonium chloride was present. This is due in part to the difficulty of washing the precipitate and to occlusion; it may also have resulted from the absorption of carbon dioxide by the reagent before use or by the mixture after precipitation and formation of insoluble calcium carbonate. Ammonium hydroxide acts upon glass, especially the ordinary soft glass, appreciably, and solutions which have stood hi bottles for some time invariably contain a scale-like precipitate which is largely composed of silica-; it can be removed by filtration, but the filtered solution may still contain small amounts of soluble silica, some of which may separate when the reagent is used. Hence when results of the greatest accuracy are demanded this precipita- tion must be made, in vessels of resistant glass or still better of platinum, and the ammonium hydroxide used must be freshly distilled. In commercial work the only precaution usually taken is to filter the reagent, and to reduce its concentration and the time it is in contact with the containing vessel to a minimum. The hydroxides of iron and aluminum are converted into the corresponding oxides at a temperature of about 600 and much higher temperatures can be used without danger of further changes. Ferric oxide is easily reduced to lower oxides by organic matter at this temperature. Properties of Calcium and Magnesium Oxalates. Crystalline calcium oxalate (CaC 2 4 2 H 2 0) dissolves in water to the extent of 5.6 mg. per liter. If precipitated from an alkaline solution it is finely divided and bulky, but if precipitated from an acid solution it is coarsely crystalline. It occludes magnesium, and to a less extent sodium, potassium and ammonium salts, probably as the result of its tendency to form double salts of these metals. The amount of occlusion is reduced by precipitating from a solution containing a slight excess of free acid; under such conditions, however, the precipitation is incomplete and altho about 80 per cent can be separated from a solution which is distinctly acid, the 178 QUANTITATIVE CHEMICAL ANALYSIS remainder must be separated from a solution which is distinctly alkaline. For these reasons it is decidedly preferable to separate most of the precipitate by the addition of a solution of oxalic acid to the neutral or barely acid calcium-containing solution, and the balance by neutralizing the resulting mixture. A reagent which contains 45 gm. of crystallized oxalic acid (C 2 H 2 4 2 H 2 0) per liter (1 cc. of which is equivalent to 0.02 gm. of CaO) is a convenient one to employ. Magnesium oxalate (MgC 2 04 2 H 2 0) is soluble in water to the extent of 300 mg. per liter, but shows a remarkable tendency to form supersaturated solutions, so that the apparent solubility may rise to three hundred times the normal value. Supersaturated solutions of this kind deposit a large part of the excess of dissolved salt rapidly but much of it is retained in solution even after long standing. Calcium is not completely precipitated from solutions containing large amounts of magnesium salts unless an excess of C 2 04 ions are present. If sufficient C 2 04 ions are present to combine with both the calcium and magnesium present the precipitation is complete; excessive concentrations of C 2 4 ions must be avoided to prevent the solution from becoming supersaturated with respect to magnesium oxalate. The properties of these oxalates which are enumerated above make it necessary to adopt and adhere to certain definite conditions in separating calcium from magnesium. The weight of oxalic acid used, as compared with the weights of calcium and magnesium present, and the total volume from which the precipitate is made to separate are of especial importance. The directions which are given below are especially designed for the analysis of limestone;* they also apply to samples in which the proportion of magnesium to calcium is much greater than that found in limestone provided the amount used is sufficient to furnish a total weight of 0.4 gm. of the two oxides. * Jour, of Amer. Chem. Soc., 31, 918 (1909). SEPARATION OF CALCIUM FROM MAGNESIUM 179 Theory of the Method Used. The occlusion of magnesium by calcium oxalate has been made the subject of many investigations, but it was first shown by Richards * that the error from this source could be greatly reduced by the presence of large concentrations of NH 4 ions or of small concentrations of hydrogen ions. This seems to be due to the fact that a large concentration of NH 4 ions must increase that of the complex magnesium-ammonium ion and reduce that of the simple magnesium ion, and, therefore, that of the undissociated magnesium oxalate. Similarly, since the hydrogen ion represses the ionization of oxalic acid, it reduces the concentration of the C^Q* ion, and, therefore, that of the undisso- ciated magnesium oxalate. As the amount of occlusion depends upon the concentration of the undissociated magnesium oxalate either reagent should reduce the error from this source. Weighing the Calcium Precipitate. Altho crystallized cal- cium oxalate loses most of its water at 200 it is difficult to expel all of it without causing some of the precipitate to decompose into calcium carbonate and carbon monoxide. It can be completely changed into the carbonate by heating for a long time at 400 or into the oxide by heating to 850. As the oxide rapidly absorbs both water and carbon dioxide it must be weighed in a covered crucible as rapidly as possible. The Separation of Magnesium. The filtrate from the calcium has a large volume and contains a large amount of ammonium chloride and some ammonium oxalate. These conditions make it necessary to modify somewhat the method used in Chapter XXI. The large concentration of the NH 4 ion greatly retards the sepa- ration of the precipitate and gives it an abnormal composition. Hence it becomes necessary to concentrate the solution, to make a preliminary precipitation in which the precipitate is allowed to stand for ten hours, to separate and redissolve this precipitate and to make a final precipitation as in the analysis of magnesium sulfate. * Proc. Am. Acad. of Arts and Sciences, 36, 375 (1901). 180 QUANTITATIVE CHEMICAL ANALYSIS II. OUTLINE OF METHOD OF PROCEDURE Separation of the Gangue. Weigh out about .7 gm. of the finely-ground sample into a 200 cc. beaker, cover with a watch glass and gradually introduce 20 cc. of dilute hydrochloric and 5 of dilute nitric acid. When violent action ceases, heat the beaker on a steam bath long enough to insure complete decomposition, that is, until no more gases are liberated. Then remove the watch glass, rinsing off the under surface with a stream from a wash bottle, and evaporate to complete dryness. To the residue add 10 cc. of dilute hydrochloric acid and digest five minutes, or until the basic salts or oxides which may have formed have been entirely dissolved. Add 20 cc. of water, filter thru a 7 cc. filter, wash four times with 10 cc. portions of water and drain. Place the still moist filter in a weighed crucible and heat cautiously over a wire gauze until the water has been expelled and the paper con- sumed; finally ignite over a direct flame for about ten minutes, then cool and weigh accurately. Calculate and report the per cent of gangue present. Separation of Iron and Aluminum. Warm the filtrate from the gangue and add to it slowly and with constant stirring recently filtered ammonium hydroxide until the solution smells distinctly of the reagent. Place the beaker on the sand bath and keep at a temperature slightly below the boiling point for about ten minutes, or until the odor while still easily recognizable is not unpleasantly strong. This should cause the separation of a small amount of a precipitate whose color may vary from red-brown to white; if it is dark brown or black it indicates that manganese is present in it, probably because the concentration of ammonium chloride in the solution was too small. Filter on a 7 or 9 cm. filter and wash with water containing about 20 gm. of ammonium chloride per liter, which prevents the aluminum hydroxide from forming a hydrosol. Redissolve the precipitate in a small amount of warm dilute hydrochloric acid and dilute to 50 cc.; reprecipitate, SEPARATION OF CALCIUM FROM MAGNESIUM 181 filter and wash as before, receiving the filtrate in the beaker con- taining the first filtrate, and acidify with hydrochloric acid. Treat the precipitate finally separated like the gangue matter, calculate and report the total percentage present. Determination of Manganese. Concentrate the solution to 75 cc. or less, neutralize with ammonium hydroxide and add 5 cc. of the reagent in excess, then add a few drops of liquid bro- mine or 30 cc. of bromine water and heat slowly to the boiling point. If a precipitate forms filter at once on a 7 cm. filter, wash with hot water and ignite at a good red heat, without separating from the filter, till the weight is constant. Calculate and report the per cent of MnO from the weight of Mn 3 4 found. Determination of Calcium. Acidify the filtrate from the manganese and boil till the liberated bromine is expelled and the solution colorless, then dilute to 300 cc., add a drop of methyl orange indicator and sufficient ammonium hydroxide to change the color from pink to salmon yellow. Heat to boiling and add slowly and with constant stirring 22 cc. of oxalic acid solution, set aside for ten minutes, then add very slowly, that is, over an interval of at least five minutes, 3 cc. of ammonium hydroxide, which has been diluted to 30 cc. with water. If this does not make the solution distinctly alkaline add a further quantity of the reagent in the same manner. After the precipitate has stood for an hour, filter thru a 9 cm. filter and wash with water until free from chlorine. Place the filter in a porcelain or platinum crucible, which has been weighed with its cover, and destroy the filter as in the determination* of gangue; finally heat the crucible over a Meker or Chaddock burner for at least twenty minutes. Cool in a desiccator for thirty minutes, and weigh as rapidly as possible. Continue igniting and weighing until two consecutive weighings do not differ by more than 0.3 mg. Calculate and report the percentage of calcium oxide thus obtained. Determination of Magnesium. Acidify the filtrate from the calcium with dilute hydrochloric acid, evaporate to a volume of 182 QUANTITATIVE CHEMICAL ANALYSIS 200 cc. and cool. Add 25 cc. of the sodium phosphate reagent, then slowly introduce 25 cc. of dilute ammonium hydroxide, which should impart a strong odor of ammonia to the solution, and finally set aside for at least ten hours. Decant off the solution thru a 9 cm. filter and discard the filtrate; place the beaker con- taining the main part of the precipitate under the filter and pour thru it the smallest possible amount of hydrochloric acid needed to dissolve the precipitate on the filter and in the beaker (some 5 cc. of the reagent diluted to 25 cc. should suffice) ; then wash the filter free of soluble compounds. Next add to the solution in the beaker, which should have a volume of about 50 cc., 5 cc. of sodium phosphate solution and then sufficient ammonium hydroxide to make it distinctly alkaline and give an excess of 3 cc. Stir the mixture occasionally during an interval of twenty minutes, then filter on a 9 cm. filter and wash with dilute ammonium hydroxide as in the analysis of magnesium sulfate. Separate the precipitate and weigh as in the analysis of mag- nesium sulfate. Calculate the percentage of magnesium oxide present. Determination of Hygroscopic Water. Weigh out 0.8 gm. of the sample in a 10 cc. platinum or porcelain crucible, which is provided with a cover. Place in a drying oven and heat to a temperature of 105 for an hour, and weigh accurately. Calculate the per cent of hygroscopic water from the loss in weight thus found. Determination of Loss on Ignition. Place the crucible con- taining the residue from the previous determination on a wire triangle and heat over a Meker or Chaddock burner until the weight is constant, using all of the precautions used in the ignition of the calcium oxalate precipitate. Calculate the percentage loss and report as loss on ignition. Finally recalculate all the percentages thus far obtained to show the composition of the water-free sample. SEPARATION OF CALCIUM FROM MAGNESIUM 183 III. QUESTIONS AND PROBLEMS. SERIES 11. 1. Are there any objections to precipitating iron (a) with KOH instead of (NH 4 )OH, (b) in the ferrous instead of the ferric condition, (c) from a solution of the sulfate or nitrate rather than the chloride? 2. What experiments might be made for the purpose of showing that A1(HO) 3 forms a hydrosol? What reagents might be used to prevent the formation of a hydrosol in the quantitative determination of aluminum? 3. Express all of the important reactions which take place when MnClz, (NH 4 )C1, (NH 4 )HO and Br are added to water in the order named. What takes place when the mixture is made acid with HC1? 4. What reaction takes place when MnO 2 is ignited? What is the simplest form of the equilibrium expression representing this reaction? 5. If the sample of limestone used for this analysis contained small amounts of strontium or barium carbonates, in what manner would it have affected the determinations here outlined? 6. Under what conditions would it be possible to dehydrate calcium oxalate without changing some of it into the carbonate? 7. How can you determine from the curves of Fig. 16 whether heat is absorbed or liberated, when you determine the loss or ignition? 8. Indicate the equilibria which are of importance when the occlusion of magnesium by calcium is reduced by the presence of HC1. 9. Suppose a sample of limestone contained, in addition to 5 per cent of insoluble silicates, only CaCO 3 and MgCO 3 , and suppose further that the loss on ignition amounted to 45 per cent, what percentages of calcium and mag- nesium are present? CHAPTER XXV ANALYSIS OF ALLOYS CONTAINING TIN AND LEAD I. FACTS UPON WHICH THE METHOD Is BASED Composition of Samples. These alloys contain from 20 to 70 per cent of tin and are used as solders; their market value depends mainly upon the percentage of tin present which is the more expensive metal. Traces of other metals, especially copper, zinc, iron and antimony are sometimes present. As the alloy is usually cast and sold in the form of long, thin bars, which are fairly homogeneous, an average sample is easily obtained by cutting thin shavings from the length of the bar. Decomposition of the Alloy. Alloys which contain large per- centages of lead are but slowly attacked by either sulfuric or hydro- chloric acids, largely owing to the slight solubility of the sulfate and chloride of lead; dilute nitric acid acts more energetically, and forms lead nitrate and metastannic acid; concentrated nitric acid acts more slowly, owing to the slight solubility of lead nitrate in strong nitric acid. If dissolved in concentrated nitric acid, or if dissolved hi dilute nitric and evaporated to dryness the tin present is completely changed into metastannic acid.- This treatment also favors the separation of metastannic acid in a form which permits of easy and rapid nitration. Properties of Metastannic Acid. The solubility of this com- pound in water and dilute nitric acid is known to have a very small value only; its solubility in dilute hydrochloric is greater, and in dilute sulfuric it is quite large. It possesses a remarkable tendency to occlude metals, especially iron, lead, copper, zinc and man- ganese, probably owing to the formation of insoluble salts of 184 ANALYSIS OF ALLOYS CONTAINING TIN AND LEAD 185 metastannic acid. The amount of lead occluded when tin-lead alloys are decomposed is less when the nitric acid used is very strong, but even under the most favorable circumstances the error from this source is too large to neglect when the precipitate amounts to more than a few milligrams. Freshly precipitated metastannic acid is readily dissolved by moderately strong solutions of ammonium sulfide with the forma- tion of ammonium sulfostannate; if precipitates which contain any of the occluded metals named above are treated with this reagent these metals separate as insoluble sulfides. If nitric acid is added to a solution of ammonium sulfostannate, a mixture of sulfur and stannic sulfide separates, but when the concentration of the acid is large, or if the mixture is heated, the stannic sulfide slowly forms metastannic acid. The resulting mixture is difficult to filter, owing to the fineness of the particles. If a solution of ammonium sulfostannate is evaporated to complete dryness and the residue treated, first with dilute and then with concentrated nitric acid, the sulfur which separates can be fused into a single globule, which can be readily removed; the metastannic acid can then be separated by filtration and ignited without being recon- verted into stannic sulfide. Metastannic acid is slowly but completely converted into stannic oxide by heating to 500. It is easily reduced by organic matter even at lower temperatures; the oxide is not appreciably hygro- scopic. Properties of Lead Sulfate. This is a pulverulent precipi- tate; it has a specific gravity of 6.23, settles rapidly and as much as 1 gm. of it can be readily filtered and washed. Its solubility in pure water is about 44 mg. per liter. This is reduced by the addition of sulfuric acid up to the point at which the mixture contains about 10 per cent by volume of the concentrated acid; beyond this concentration the solubility begins to increase. It is also increased by the presence of even small concentrations of hydrochloric and nitric acids, and in the quantitative separation 186 QUANTITATIVE CHEMICAL ANALYSIS of lead sulfate these acids must be expelled by evaporating with an excess of sulfuric acid. Its solubility is greatly decreased by the presence of even small concentrations of alcohol. Pure lead sulfate can be heated without danger of decomposition up to 400. As it is very easily reduced by heating in the presence of organic matter, and as the metal is decidedly volatile, extreme care must be taken hi igniting the precipitate. II. OUTLINE OF THE METHOD OF ANALYSIS Preparation and Decomposition of the Sample. Prepare the sample by cutting about 2 gm. of thin shavings from a bar of the alloy by means of a dull knife, and place in a clean, dry sample tube. Weigh out 0.5 gm. of the sample into a 200 cc. beaker, cover with a watch glass, add 10 cc. of concentrated nitric acid and then from 5 to 10 cc. of water, using the larger amount if the sample is but slowly attacked. Heat the beaker on the steam bath long enough to disintegrate the sample, that is, until all hard lumps have disap- peared and a fine white powder only remains; then remove the cover and evaporate to a volume of 3 cc. Separation and Purification of Metastannic Acid. Add to the beaker 5 cc. of concentrated nitric acid and 30 cc. of water, heat nearly to boiling and digest for ten minutes; while waiting prepare a glass filter tube with a thin layer of finely shredded asbestos and connect with a clean filter flask. Pass the liquid in the beaker thru the filter, refiltering if necessary, to obtain a perfectly clear filtrate, and wash three times with 10 cc. portions of water. Transfer the filtrate to a clean 250 cc. beaker, wash out the flask with at least four portions of water and place on a steam or sand bath to evaporate. Invert the filter tube over the bottom of a clean 200 cc. beaker, push the filter plate and asbestos into the beaker by means of a glass rod or wire passed thru the stem of the tube, and rinse any adhering fibers of asbestos into the beaker by a few cubic centi- meters of water. Next remove the filter plate and rinse this also, ANALYSIS OF ALLOYS CONTAINING TIN AND LEAD 187 then add 10 cc. of a strong solution of ammonium sulfide made by saturating concentrated ammonium hydroxide with hydrogen sul- fide. Disintegrate the asbestos by means of a glass rod, warm the mixture slightly until all white particles have been dissolved and only a fine black residue of lead sulfide remains. Prepare a second asbestos filter, moisten with a few drops of ammonium sulfide solution, filter the solution of sulfostannate of tin thru it, wash four times with water containing a few drops of ammonium sulfide and twice with pure water. Transfer the solution in the filter flask to a clean 400 cc. beaker, wash four times with water, place on a steam or sand bath and evaporate to complete dryness. Warm about 5 cc. of dilute hydrochloric acid in a small beaker and pour over the filter containing the lead precipitate, which should cause the filter to become pure white, then wash with hot water and transfer the solution to the beaker containing the main part of the lead. Determination of Lead. Add to the beaker containing the lead solution 5 cc. of concentrated sulfuric acid, which should be introduced cautiously if the solution is warm; evaporate on the sand bath till white fumes of sulfur trioxide are given off, watching the mixture very carefully during the later stages of the process as it may bump and sputter. When cool, add 45 cc. of water and set aside for at least one-half hour. While waiting for the completion of these operations, prepare a Gooch crucible with a good layer of asbestos; ignite and weigh accurately. Fil- ter the lead sulfate precipitate thru the crucible thus prepared, wash four times with 10 cc. portions of 20 per cent alcohol, dry at about 300 and weigh. Calculate the percentage of lead present. Determination of Tin. Add to the beaker containing the dry residue resulting from the evaporation of the sulfostannate solution 10 cc. of dilute nitric acid, cover at once with a watch glass and warm gently till further action ceases; next add 10 cc. of concentrated nitric acid and again warm for a few minutes. Rinse off the sides of the beaker and the watch-glass cover and set the latter aside, then evaporate the mixture to nearly complete 188 QUANTITATIVE CHEMICAL ANALYSIS dryness. The large amount of sulfur which separates in a free condition should finally fuse to form a clear yellow liquid, all of which should be collected into a single large globule before it solidifies. Add to the residue 5 cc. of dilute nitric acid and 50 cc. of water, digest for ten minutes, then filter on a 9 cm. filter and wash free from acid for if much acid is left in contact with the pre- cipitate the filter will become brittle and will crumble on drying. Separate the filter as completely as possible from the precipitate and set the latter aside on a watch glass. Remove the globule of sulfur from the precipitate, which may contain very small amounts of tin, and burn in the crucible. Next, burn the filter in the crucible and finally add the main precipitate and ignite over a wire triangle with a Meker burner or blast lamp, for twenty minutes. If the resulting precipitate is decidedly gray moisten with a few drops of concentrated nitric acid, evaporate off the acid, and again ignite. Calculate the percentage of tin from the weight of stannic oxide found. III. QUESTIONS AND PROBLEMS. SERIES 12 1. Show how the action of nitric acid on metallic tin might give rise to either stannous nitrate, stannic nitrate or metastannic acid. 2. Indicate the reaction of ammonium sulfide on the tin-lead precipitate. 3. What determines the volume of sulfuric acid which should be added to the solution which contains the lead before evaporating to dryness? 4. What factors make it easy to completely displace the nitric acid from this solution? 5. What effect would you expect the presence of large amounts of Cu, Fe, Zn or Sb to have on the analysis? 6. What weight of PbSCX should be dissolved by 100 cc. of a solution made by diluting 2 cc. of concentrated sulfuric acid to 100 cc., assuming that the normal solubility is reduced according to the solubility product principle? Why does the method of calculation used involve large errors in this case? CHAPTER XXVI ANALYSIS OF BRASS I. FACTS UPON WHICH THE METHOD Is BASED Composition of Sample. The essential constituents of this alloy are copper and zinc; it sometimes contains small percentages of tin and lead and traces of iron, antimony and other metals, which represent impurities in the metals of which the alloy was made. A homogeneous sample can usually be obtained by drilling holes in the ingot or bar, or by placing in a turning lathe and cutting thin shavings from it. If the sample has been already made into drillings or shavings it should be carefully examined for particles of wood or iron with which it is sometimes contaminated. Conditions for Separation of Tin and Lead. The alloy is readily dissolved in either strong or dilute nitric acid and essentially the same conditions as were used for the determination of tin and lead in solder can be used here. The amount of tin present is usually so small that it is not ordinarily necessary to purify it for occluded metals. Conditions for Separation of Copper from Zinc. The decom- position voltage of copper is 0.33 volt lower and that of zinc 0.71 volt higher than that of hydrogen, hence the two metals are easily separated in the presence of sufficient free acid by the constant current method. But little difficulty is experienced in obtaining good deposits of copper in the presence of NOs ions, and currents of 0.5 ampere normal density can be used if a gauze electrode is employed. If a foil electrode is used it is scarcely safe to use currents greater than 0.05 ampere normal density. The precipitated metal is rapidly dissolved by even dilute nitric acid and is slowly oxidized even at a temperature of 100. 189 190 QUANTITATIVE CHEMICAL ANALYSIS Conditions for Determination of Zinc as Phosphate. When a soluble phosphate is added to a neutral solution of a zinc salt which also contains a large concentration of ammonium salts, a flocculent precipitate separates; if this precipitate is digested for a short time it is slowly converted into a crystalline precipitate having the formula Zn(NH 4 )PC>4 H 2 0. This precipitate is appreciably soluble in solutions containing even small concentrations of either hydrogen or hydroxyl ions; hence the solution must be made as nearly neutral as possible. It is also essential that the solution should contain a large concentration of NH 4 ions and a large ex- cess of P(>4 ions. The solubility of the precipitate in either hot or cold water is but slight, and it is easily washed free from soluble salts. The crystalline zinc ammonium phosphate readily loses all of its water if dried at 105; it can also be converted into the pyrophosphate on direct ignition, but, as with the correspond- ing transformation of the magnesium compound, it undergoes partial reduction and fusion at a bright red heat; hence it is preferable to separate on a Gooch crucible rather than on a paper filter. II. OUTLINE OF THE METHOD OF PROCEDURE Determination of Tin. Weigh out 3 gm. of the sample into a 100 cc. beaker, add 25 cc. of dilute nitric acid and cover with a watch glass. Action should begin to take place almost at once and complete solution should be effected within a few minutes; if not, warm the beaker slightly by placing on the steam bath. If the action at any time becomes too violent it should be restrained by placing the beaker in a vessel of cold water. When the alloy is completely dissolved remove and rinse off the watch-glass cover, again place on the steam bath, and allow to evaporate to complete dryness. Add to the residue 5 cc. of dilute nitric acid and 25 cc. of water and allow to digest till the basic salts of copper, which usually ANALYSIS OF BRASS 191 separate as a voluminous blue-white precipitate, are brought into solution. If a fine white residue of metastannic acid still remains, filter on a small filter, wash till free from acid, dry, ignite and weigh. Calculate the percentage of tin from the stannic oxide thus found. Determination of Lead. Add to the filtrate from the tin 7 cc. of concentrated sulfuric acid and evaporate until the nitric acid has been expelled and dense white fumes of sulfur trioxide are given off. This will not occur until the total volume is less than 7 cc. and the temperature of the solution has risen to about 250. During the evaporation of the solution the sulfates of lead, copper and zinc separate, and unless the precipitate is kept in constant motion, and unless the temperature is kept below 100, violent bumping and spiriting is certain to take place. For this reason it is best to evaporate on the steam bath until most of the water is driven off, and to complete the evaporation on a sand bath or sheet of asbestos while stirring the mixture vigorously and con- tinuously. When the dish is cold add 50 cc. of water, stir until the soluble sulfates have been dissolved and only sulfate of lead remains, then set aside for half an hour. While waiting for these operations, prepare and weigh accurately a Gooch crucible, con- nect the crucible with a clean filter flask, filter off the precipi- tate on it, wash four times with a mixture of equal parts of water and dilute sulfuric acid, and twice with 20 per cent alcohol. Heat the crucible slowly to a temperature of about 250, cool and weigh accurately. Calculate the percentage of lead present from the weight of lead sulfate thus found. Division of the Solution. Transfer the solution containing the copper and zinc to a 250 cc. graduated flask, dilute till the lowest part of the meniscus corresponds to the line on the neck of the flask, stopper with a tightly fitting cork and mix thoroughly by alternately inverting and rotating the flask. Measure out three 50 cc. portions of the solution as follows: pour out about 20 cc. of the brass solution in a small beaker and use this to rinse 192 QUANTITATIVE CHEMICAL ANALYSIS out a clean but not necessarily dry 50 cc. pipet, discarding the solution after using it. Next, suck up a further quantity of the liquid into the pipet until it rises above the mark on the stem of the pipet and allow to drain back into the flask until the lowest point on the curve of the meniscus corresponds to the mark on the stem of the pipet; remove the pipet from the flask and allow the solution to flow into a clean 150 cc. beaker and to drain for two minutes, but do not wash out with water. Determination of Copper by Electrolysis. To one of the so- lutions which has been separated, add sufficient ammonium hy- droxide to make it slightly alkaline, then 2 cc. of concentrated nitric acid. Ignite and weigh accurately a clean platinum cath- ode, place in the solution and add water enough to cover the electrode. Introduce a spiral anode and connect both with the terminals of a storage battery. Change the resistance in the circuit by means of a rheostat until a current of 0.5 ampere if a gauze electrode is used, or of 0.05 ampere if a foil electrode is used, passes thru the" solution. Allow the electrolysis to pro- ceed for fifteen minutes after the solution has become colorless, if a gauze electrode has been used, or for three hours after the solution has become colorless, if a foil electrode has been used. The entire time necessary should be about ninety minutes and twelve hours, respectively. Place a small beaker containing sufficient water to cover the cathode on the bench near the solution being electrolyzed, raise the stand supporting the electrodes and, without disconnecting the attached wires, plunge the electrodes into the beaker of pure water. Allow the current to pass for a few minutes, rinse the electrodes by rotating the beaker, then disconnect the cathode, remove from the water, allow to drain and absorb as much of the water as possible by bringing into contact with a piece of filter paper. Rinse the cathode in at least two changes of 95 per cent alcohol, absorb the excess of alcohol by means of filter paper and dry for a few minutes at a temperature of about 50, which can ANALYSIS OF BRASS 193 be done by holding over a sand bath for a few minutes; then weigh accurately, and calculate the percentage of copper present. Determination of Zinc. Evaporate the aqueous washings from the cathode to a small bulk and transfer both the washings and the residual solution to a 300 cc. beaker; add ammonium hydroxide until the solution is neutral to litmus paper, heat to boiling, add 80 cc. of sodium phosphate solution and again neutralize the solution very carefully with either dilute ammonium hydroxide or hydro- chloric acid, as may be found necessary. Heat the solution almost to the boiling point and keep at that temperature for fifteen minutes, that is, until the flocculent precipitate which separates at first becomes crystalline. Set the mixture aside for half an hour and while waiting, prepare and weigh a Gooch crucible. Filter off the precipitate, wash free from soluble salts with pure water, dry, ignite gently at first and then at a bright redness, cool and weigh accurately. Calculate the percentage of zinc present from the weight of zinc pyro- phosphate found. % III. QUESTIONS AND PROBLEMS. SERIES 13 1. Would it be desirable to vary the volume of sulfuric acid added before evaporation if the amount of sample used was varied, or if the relative amounts of copper and zinc in the sample varied? 2. Calculate by means of Faraday's law the time theoretically required to precipitate 0.3 gm. of copper with a current of 0.5 ampere, and show why the calculation has but little significance in this determination. 3. Explain how the addition of sodium hydrogen phosphate to the neutral solution containing zinc and ammonium salts may increase the concentration of the hydrogen ions present. 4. Explain the advantage of starting with 3 gm. of sample and using a fractional part of the solution for the determination of copper and zinc. 5. What other metals would separate with the copper under the conditions used in this determination? 6. If small amounts of copper were left unprecipitated, would it be recog- nized later? CHAPTER XXVII DETERMINATION OF SILICA IN A HORNBLENDE I. FACTS UPON WHICH THE DETERMINATION Is BASED Methods of Decomposition. Silicates of the insoluble class, such as the hornblendes and the great majority of the naturally- occurring silicates, must be decomposed by means of hydrofluoric acid, or changed into silicates of the soluble class by fusion with certain fluxes. If the hydrofluoric acid method is employed the decomposition must be carried out in vessels of platinum, and since the silicon present forms volatile silicon fluoride, it cannot be deter- mined unless the apparatus has a form which makes it possible to absorb all of the liberated gas in an appropriate reagent. Such an apparatus would be too expensive for general use. The transformation into silicates of the soluble class can be effected by fusion with any strongly basic reagent, such as the hydroxides, oxides or carbonates of metals of the sodium and calcium group. Such fusions must necessarily be carried out in vessels free from silicon; a platinum crucible is to be preferred, but one of silver or nickel is sometimes used. A mixture of four parts sodium and five parts potassium carbonates, which melts at 685 is most frequently used; it does not attack platinum appreciably. As these reagents usually contain appreciable per- centages of silica it becomes necessary to determine the percentage present and apply a correction to the final result. When a finely- powdered sample of hornblende is heated to a temperature of about 600 with this mixture, silicates and aluminates of sodium and potassium are produced and the corresponding amount of carbon dioxide liberated. 194 DETERMINATION OF SILICA IN A HORNBLENDE 195 The Dehydration of Silicic Acid. When a soluble silicate is treated with an excess of hydrochloric acid, free silicic acid and the chlorides of all the metals present are formed. If the acid used is dilute and the temperature is kept low the silicic acid may remain in solution, but if these conditions are not complied with most of it separates as a gelatinous colloid, which is extremely difficult to filter. When the mixture is evaporated to dryness the silicic acid gradually loses water and assumes a fine, powdery form. Experience shows that complete conversion of the silicic acid into an insoluble form is not easily effected. Some chemists dry the residue from evaporation at a temperature of 120 for a half hour or more, but this results in the formation of compounds of iron and alumina which are very difficult to dissolve; others dry at 105 or evaporate to complete dryness on the water bath several times. Two evaporations with an intermediate filtration of the dehydrated silicic acid are more effective than two successive evaporations, but even when this method is adopted small amounts of silica may be left in the solution. In dissolving the soluble salts from the residue left after evaporation either cold water or hot dilute acid should be used; if hot water alone is employed the iron and aluminum present may form insoluble basic salts. Even when the mixture is evaporated on the water bath only, the silica obtained may contain small amounts of iron and aluminum, but the error resulting from this is largely counterbalanced by the error from incomplete dehydration. Where the highest degree of accuracy is demanded it becomes necessary to volatilize the silica in the precipitate by treating it with hydrofluoric and sul- furic acids hi a platinum crucible, and determining the impurities, representing iron and aluminum oxides, remaining; also, to separate the silica, which has remained in the solution, but is subsequently precipitated with the iron and alumina. These refinements are not usually considered necessary hi commercial work. The ignition of a silica precipitate requires extreme care owing 196 QUANTITATIVE CHEMICAL ANALYSIS to its fine, powdery nature. If the paper filter used is heated too rapidly, and especially if it catches fire and burns at the mouth of the crucible, appreciable amounts of the precipitate may be carried off by the air currents formed. There is no danger of reducing or otherwise changing the composition of the precipitate, but long-continued ignition at the highest temperature readily attainable with a burner is necessary to completely convert the precipitate into the dioxide. II. OUTLINE OF METHOD OF PROCEDURE Selection and Preparation of the Sample. Carefully select from the roughly crushed sample about 3 gm. of the pure mineral. Place half gram portions at a time in a clean agate mortar and grind each portion until the resulting powder tends to form a compact thin layer on the side of the mortar and no longer feels gritty when rubbed between the fingers. Place a perfectly clean 100- mesh sieve over a piece of glazed paper, brush the powdered mineral into the sieve and tap it until all of the fine powder has passed thru it. Return the powder left on the sieve to the mortar and continue grinding and sifting until all of it has passed thru the sieve. Finally transfer the powdered mineral into a clean, dry, well-stoppered weighing tube. Fusion. Weigh out in a platinum crucible of at least 10 cc. capacity about 4 gm. of fusion mixture. Weigh the tube contain- ing the silicate and pour from it into the crucible about 0.7 gm. of the sample and again weigh accurately. Thoroughly mix the silicate with the fusion mixture by the use of a platinum spatula or a stirring rod, which has a carefully rounded end, then brush from the latter any of the adhering mixture and tap the crucible till the mixture is well settled. Place the crucible on a triangle and heat it with a low flame for about five minutes, then gradually increase the temperature until the mass begins to fuse and keep at this point until carbon dioxide is no longer evolved. The crucible should be kept covered DETERMINATION OF SILICA IN A HORNBLENDE 197 to avoid loss from spattering and the temperature must be care- fully controlled or the mixture may boil over. The entire fusion should require from twenty minutes to half an hour and should finally yield a quiescent mass of perfectly sintered but only par- tially fused material. Decomposition. Remove the crucible from the triangle by means of a pair of forceps while still hot, and by carefully tipping and rotating the latter cause the contents to solidify as a layer around its inner surface. When cold place the crucible on its side in the bottom of a five-inch casserole, add 50 cc. of water, warm and stir until the fused mass is disintegrated and falls out of the crucible, then remove the crucible from the dish with the aid of a glass rod and wash both inner and outer surfaces thoroughly. Cover the dish with a watch glass and gradually introduce 20 cc. of hydrochloric acid. The dish should now contain only gelatinous silicic acid and a clear yellow solution. If sandy or gritty particles are present the decomposition is probably incomplete and a second sample must be fused. Sometimes the precipitated silica has a reddish color owing to the presence of difficultly soluble iron compounds, which usually dissolve on digestion. Separation of Silica. Place the dish on the steam bath and evaporate to complete dryness, that is, till powdery dry. The evaporation may be made more rapidly by heating on a sand bath, or over a gauze placed some distance above the flame of the burner if the precipitate is kept in constant motion with a stirring rod. Moisten the residue with about 10 cc. of concen- trated hydrochloric acid and then add 1 cc. of nitric acid and 50 cc. of water, and digest on the steam bath until all basic salts have been decomposed and white silicic acid only remains. Filter thru an 11 cm. filter and transfer the precipitate to the filter, then wash twice with 10 cc. portions of cold water. Next transfer the filtrate and washings which may still contain small amounts of silicic acid to the casserole previously used, evaporate the mixture to complete dryness on the steam bath and keep the 198 QUANTITATIVE CHEMICAL ANALYSIS dry residue on the bath one half hour longer. While the solution in the dish is evaporating continue to wash the silica precipitate until the washings are shown to be free from chlorine, receiving the washings in a clean 300 cc. beaker. Treat the residue from the second evaporation with 20 cc. of dilute hydrochloric acid and digest until all basic salts have been decomposed, add 50 cc. of water an4 then filter thru a fresh 9 cm. filter, receiving the filtrate hi the beaker containing the washings from the first silica precipitate. Next rub the entire inner surface of the dish with a rubber-tipped rod until the adhering precipitate has been loosened, and rinse into the filter; finally wash the latter until free from soluble salts. If this treatment has failed to re- move all of the precipitate from the dish, moisten with a little dilute ammonium hydroxide and again rub with a rubber-tipped rod. Place the two still moist filters hi a weighed crucible and heat cautiously over a wire gauze until combustible gases are no longer given off; if these gases are permitted to take fire a sufficiently strong draft may be created to cause a mechanical loss of some of the precipitate, which is very light. Place the crucible over a wire triangle and gradually increase the temperature until the paper is entirely consumed; finally ignite over a blast lamp, or Meker burner for at least twenty minutes and weigh. Repeat the ignition till the weighings are practically constant. Determination of Silica in Reagents. Weigh out 10 gm. of the fusion mixture used into a casserole, cover with a watch glass and cautiously introduce sufficient dilute hydrochloric acid to decompose it. Evaporate to complete dryness and separate the silica as hi the analysis. Calculate the weight of silica in the weight of fusion mixture used in the analysis and subtract from the weight of precipitate found. Report the corrected per cent of silica present. SECTION IV SOLUTION AND EXTRACTION PROCESSES CHAPTER XXVIII GENERAL FEATURES OF SOLUTION AND EXTRACTION PROCESSES Solution Processes Which Depend Upon the Physical Action of the Solvent. These processes depend upon the differential action of liquids on mixtures composed of two or more solids. The simplest possible example is one in which the mixture consists of two distinct solid phases, each phase representing a single component, one of which is much more soluble in some particular liquid than the other. If the difference in solubility is sufficiently large, and if the mixture is so finely divided that every particle of the more soluble constituent is exposed to the action of the solvent, treatment of the mixture with a sufficient amount of the solvent at once yields a liquid phase which contains all of the more soluble component, and a residual solid phase composed of the less soluble component. The action concerned is the converse of that of precipitation processes, but the rate at which equilibrium is attained when a liquid acts upon a solid is slower than when a precipitate is formed in a liquid, and altho the theory of the two classes of methods is essentially the same the methods by which they are carried out are decidedly different. The ideal method of making such a separation would be to use only sufficient solvent to bring into solution all of the more soluble component, but such a method of procedure would not be practi- cable owing to the slowness with which solution of the last particles of the more soluble constituent is effected, and the adherence of 193 200 QUANTITATIVE CHEMICAL ANALYSIS some of the liquid to the solid phase, which makes it necessary to wash the residue with further quantities of the solvent. The general theory of the method actually used in carrying out such processes is similar to that elaborated in Chapter XVII for the washing of precipitates. The comparative rates at which the two components pass into solution, the effect of one component upon the solubility of the other, the size of the particles of which the mixture is composed, and the relative amounts of the two com- ponents, all affect the accuracy and efficiency of such processes. An ideally perfected method for making a separation of this kind would prescribe the weight of the mixture to be used, the compo- sition and amount of the solvent to be used for each treatment, the number of treatments, and the length of time allowed for each treatment. These details are best determined empirically, that is, by quantitative experiments with mixtures of known com- position; in many of the processes largely used these details have only been determined very roughly. In discussing the theory of this class of methods it is assumed that the two components of the mixture exist as distinct and separate solid phases. Some doubt should always be entertained as to whether the method can be successfully applied to the separation of a mixture of isomorphous substances which has separated from a solution, or has resulted from the solidification of a molten magma; that is, wherever the presence of solid solutions is possible. A solvent which readily dissolves one of the two components of a solid solution will often, especially where the less soluble component is present in relatively small amounts, readily disintegrate and decompose such a mixture, but not in all cases. This class of methods is of especial use in the separation of those elements all of whose compounds are largely soluble in aqueous solvents, and which, therefore, cannot be separated by the use of precipitation methods. In using them it is often necessary to convert the substance to be separated into those particular FEATURES OF SOLUTION AND EXTRACTION PROCESSES 201 compounds which possess the necessary differences in solubility in some particular solvent. Solution Processes which Depend Upon the Chemical Action of the Solvent. Processes in which the action of the solvent is chemical as well as physical are also extensively used. In all such cases two sets of equilibria must be considered. The equilibrium resulting from the contact of solvent and one of the solids must result in the formation of a single liquid phase, that is, must involve a change from heterogeneous to homogeneous equilibrium; that resulting from contact of the solvent with the other solid must involve maintenance of the original condition. As in the case of processes in which the action of the solvent is purely physical the formation of solid solutions often makes it impossible to effect separations which could otherwise be easily made. The chemical as well as the physical properties of solid solutions are specific properties of the mixture, and vary with the comparative amounts of the two components actually present. Thus, altho metallic silver is readily changed into a solution of silver nitrate by treatment with a dilute solution of nitric acid, it is not possible to separate silver from gold in an alloy which contains more than 30 per cent of gold because the two metals form a continuous series of solid solutions. Extraction Processes. Further difficulties are encountered in applying this class of methods to the analysis of certain classes of materials such as plant and animal tissues. In such substances the soluble constituent may be diffused thru or surrounded by cell walls, which act as semi-permeable membranes and prevent diffusion of the solvent. The difficulty can be overcome to some extent by mechanical disintegration and crushing of the sample, but even where the sample is reduced to a very fine powder it is often necessary to treat it with the solvent for many hours. To successfully carry out such a separation by supporting the mixture on a filter and washing with the solvent is impracticable, as it necessitates the use of very large amounts of the solvent, which is 202 QUANTITATIVE CHEMICAL ANALYSIS often an expensive reagent, and demands a large amount of time and care from the analyst. It is then necessary to " extract" the substance in an apparatus of especial construction, which is known as an "extraction apparatus." Extraction methods are of especial importance in the analysis of mixtures containing organic compounds, for, owing to the low temperatures employed in carrying on the process, and the slight activity of the solvents which are most frequently used, the probability of decomposing these compounds is reduced to a minunum. They are universally used in the analysis of substances of animal or vegetable origin, of all classes of ex- plosives, and of asphalt paving materials. Apparatus for Continuous Extraction. The conditions necessary for the rapid and complete extraction of any solid substance are most readily and effectively maintained by boiling the solvent in a small flask attached to an inverted condenser so arranged that the condensed solvent is made to fall into, and drip thru, a filter containing the substance to be extracted. An apparatus of this kind is represented in* Fig. 40. It consists of a wide-mouthed flask A of about 125 cc. capacity, which contains the boiling solvent; an extraction tube B, which supports the " extraction shell" C containing the sample; and the condenser D. The vapor of the boiling solvent passes thru Fig. 40. Contin- the side tube E into the condenser, and after con- densation f alls into the extraction shell, where it comes into contact with the sample, passes thru the shell, and falls back into the flask. Fresh portions of the pure warm solvent are thus continuously brought into con- tact with and made to pass thru the shell and its contents, and B FEATURES OF SOLUTION AND EXTRACTION PROCESSES 203 gradually wash out those constituents which are soluble. As these are usually much less volatile than the solvents used they accumu- late in the flask in the form of a solution, whose concentration increases as the process of extraction progresses. A more compact, and in some respects more de- sirable, apparatus is the one devised by Wiley, which is represented in Fig. 41. The substance to be extracted is here placed in a Gooch crucible C, which is suspended from the very efficient metallic condenser E\ both crucible and condenser are con- tained in the tube A, which holds the boiling sol- vent. Both figures represent forms of extraction apparatus in which the distilled and condensed solvent is made to leach the sample continu- ously and are therefore designated as "continuous." Apparatus for Intermittent Extrac- Fig. 41. Wiley tion. Another type of apparatus, of Extraction which there are also many forms, acts A PP aratus intermittently. It is represented by the Soxhlet apparatus shown in Fig. 42 and differs from the apparatus already described in the form of the extraction tube. This is closed at the point A, but is provided with a side tube B thru which the vaporized solvent passes into the condenser, and a siphon tube C thru which the solution, which accumu- lates in the extraction tube, runs back into the flask Fig.42. Soxh- as goon as ft rea ches the level D. The action of this tion Tube* " tyP e f apparatus i s distinguished by the fact that a large volume of the solvent remains in contact with the sample for a relatively long time; since, however, there is little circulation, that portion of the solvent hi immediate contact with the sample soon attains a fairly large degree of concentra- 204 QUANTITATIVE CHEMICAL ANALYSIS tion with respect to the soluble compound, which delays further solution. By using the method of reasoning already employed in discussing the theory of washing precipitates it is easy to show that the continuous type of apparatus should be more efficient than the intermittent, and a comparison of the efficiency of the two types under similar conditions confirms the accuracy of this conclusion; furthermore, the amount of solvent required to operate the continuous type of apparatus is much less than that required for the intermittent. Construction of Joints to Apparatus. The sol- vents which are most extensively used are alcohol, ethyl ether, petroleum spirit, chloroform, carbon disulphide and carbon tetrachloride. All of these are extremely volatile, and all except chloroform are extremely inflammable. It is essential, there- fore, that all joints of the apparatus should be tight, and that the condensation of the vaporized solvent should be as perfect as possible. Rubber dissolves in all of the solvents named except alcohol to some extent, and such media as wax or paraffin, which are sometimes used to remedy the deficiencies of cork stoppers, are also dissolved by these sol- vents appreciably. It is desirable, therefore, to use an apparatus, like the Wiley apparatus already described, which has no joints, or one which is made entirely of glass; if the latter alternative is Fig. 43. Knorr adopted the ground-glass joints which become neces- Extraction garv mus ^ b e ver y carefully made, and they are Apparatus . . ., , , both expensive and easily broken. Still another alternative involves the use of an apparatus, such as the Knorr apparatus represented in Fig. 43 or the Ames appa- ratus represented in Fig. 44, in which the only joint which is exposed to the action of the solvent is provided with a "mercury FEATURES OF SOLUTION AND EXTRACTION PROCESSES 205 B seal." In both forms the flask in which the solvent is made to boil is provided with a groove into which the tube B fits loosely, the intervening space being filled with sufficient mercury to pre- vent the escape of any of the vaporized solvent. Where these more elaborate and therefore more expensive types of apparatus are not available, recourse must be had to simpler forms, in which the joints are made by means of cork stoppers. These can usually be made to give tight joints if corks of good quality and large size are chosen, boiled in water for an hour, and while still hot and plastic forced into the opening to be closed, and then allowed to dry in this position; they should be bored to fit the necessary connections when dry and cold. Methods of Heating the Apparatus During Extraction. Since the rate at which the soluble constituent is leached out depends upon the rate at which the solvent circulates thru the extraction shell, it is desirable to heat the solvent by means of a device which causes it to boil vigorously and steadily, that is, with- out danger of boiling over. Direct heating of the flask with a flame is always to be avoided, since it is hard to regulate the rate of boil- Fig. 44. Ames Ex- ing, and if the flask cracks or if the joints of Action Apparatus the apparatus are not tight the flame may set fire to the escaping solvent. The use of a water bath is more satisfactory but has some disadvantages. An electric hot plate or an air bath heated by a current passing thru resistance wires or incandescent lamps is to be preferred to all other devices, since the danger from fire is reduced to a minimum and any desired temperature can be main- tained by the use of proper resistances in the circuit. 206 QUANTITATIVE CHEMICAL ANALYSIS Determination of the Separated Constituent. The weight of the constituent dissolved from the sample can be determined from the difference between the weight of the sample and that of the solid residue left, or if the substance extracted is not appreciably volatile, the solvent can be distilled off from the solution and the desired weight determined directly. Where the former method is used difficulties may arise from the hygroscopic character of the residue or of the extraction shell used. The alternative method of procedure is always to be preferred unless the dissolved con- stituent is so volatile that appreciable amounts of it are carried over with the solvent during the distillation. Multiple Extraction Apparatus. Altho the actual labor involved in making a determination by an extraction method is small, it is often necessary to extract a sample for several hours, and where a large number of such determinations have to be made it becomes almost imperative to operate a number of such appara- tus simultaneously. Many forms of multiple extraction apparatus in which a series of extraction units are supported on a common frame, and supplied with a common source of heat and condenser water, are in use. An apparatus* consisting of five such units is represented in Fig. 45; this apparatus is also provided with a common device for the distillation and condensation of the solvent after the extraction has been completed. The heating device here used consists of five electrically-heated iron plates supported on a wooden base, but separated from it by a sheet of asbestos. The edge of each plate is surrounded by a strip of mica, which prevents the plate from short-circuiting the resistance wire by which it is heated, but does not prevent the transfer of heat to it. A nichrome wire 0.01 mm. in diameter passes thru a series of cleats fastened to the bed and makes three complete turns around, and in close contact with, the edge of each of the five plates; this wire is connected directly with the ter- * Further details concerning the construction of this apparatus will be found in the Jour, of Ind, m& Eng. Chem., 4, 302 (1912). FEATURES OF SOLUTION AND EXTRACTION PROCESSES 207 Fig. 45. Plan of a Multiple Extraction Apparatus 208 QUANTITATIVE CHEMICAL ANALYSIS minals of a 110-volt alternating current by means of a switch. The wire offers a resistance of 75 ohms and consumes 1.5 amperes. The condenser used during distillation consists of a worm of block tin tubing supported in and surrounded by a cylindrical copper vessel thru which the waste water from the other series of condensers can be made to flow. One end of the worm passes thru the bottom of the copper vessel, the other is prolonged and supported in a position slightly inclined to the horizontal on a strip of wood fastened to the back of the frame of the apparatus. The prolonged end is provided with five vertical branches placed at points opposite to the centers of the five heating plates. Con- nection can be easily established between any of the flasks resting on one of the plates and the lateral opposite it by means of a glass tube. CHAPTER XXIX DETERMINATION OF POTASSIUM IN COMMERCIAL POTASSIUM SULFATE I. FACTS UPON WHICH THE METHOD Is BASED Composition of Samples. This salt is largely used as a ferti- lizer and its commercial value is proportional to the percentage of potassium, usually reported as K 2 0, which it contains. In addi- tion to sulfate of potassium it contains sulfates and chlorides of sodium and magnesium. Choice of Method. With the exception of a complex nitrite, which has the formula KNa 2 Co(N0 2 ) 6 , the compounds of potassium are too soluble in water to make it possible to determine this element by a precipitation process. The two methods, which have been most largely used up to the present tune, involve conversion of the element into the perchlorate (KC10 4 ) or chloro- platinate (K 2 PtCl 6 ) in a solid form, and elimination of all of the other salts present in the mixture thus obtained, by treating it with certain solvents, that is, by methods which are essentially solution processes. Of the three methods suggested the chloro- platinate method is to be preferred, especially where the amount of potassium present is small, on account of the large molecular weight of the compound finally separated and weighed, and also because the details of the method have been carefully worked out. Altho the reagent used is very expensive the platinum can be easily recovered after use and reconverted into a further quantity of reagent. Formation of Potassium Chloroplatinate. Solutions contain- ing mixtures of potassium and sodium chlorides are completely converted into K 2 PtCl 6 and Na 2 PtCl 6 -6H 2 O respectively, by evaporating almost to dryness with the theoretically required 209 210 QUANTITATIVE CHEMICAL ANALYSIS amount of chloroplatinic acid. The potassium salt separates in well-formed octahedra belonging to the regular system; the sodium salt in plates belonging to the triclinic system. The two compounds do not form double compounds nor solid solutions with each other, nor with the chlorides of sodium, potassium, platinum or magnesium. The sulfate of potassium is readily changed into the chloroplatinate by the same treatment, but the sulfate of sodium is not so readily changed into the corresponding sodium compound. The reagent used for this purpose should be of known strength and of high concentration if economy in its use and in the time needed for the evaporation is to be attained. A solution which contains H 2 PtCl 6 equivalent to 0.1 gm. of Pt per cc. is a suitable one to employ. Properties of Potassium Chloroplatinate. At a temperature of 20 one part of this compound requires about 98 parts of water, or 26,400 of 80 per cent alcohol, or 42,600 of absolute alcohol for complete solution. Ammonium chloroplatinate, which may be formed by the absorption of ammonium hydroxide from the atmosphere of the laboratory, is also extremely insoluble in these reagents. Both the hydrated and anhydrous sodium chloro- platinate and chloroplatinic acid are readily soluble in 80 per cent alcohol, but the chlorides and sulfates of sodium, potassium and magnesium are but slightly soluble in this reagent. When made to separate by the evaporation of moderately dilute solutions, potassium chloroplatinate is coarsely crystalline and does not contain either combined or occluded water. It can be dried at a temperature of 135 without danger of decomposition or volatilization; at higher temperatures it is slowly decomposed into potassium chloride, chlorine and metallic platinum; it is not appreciably hygroscopic. Development of the Lindo-Gladding Method. In 1881 Lindo* showed that potassium could be determined in solutions * Chemical News, 44, 77, 86, 97, 129 (1881), Bull. 7, Division of Chem. U. S. Dept. of Agriculture. POTASSIUM IN COMMERCIAL POTASSIUM SULFATE 211 containing chlorides of sodium and potassium by evaporating to dryness with sufficient chloroplatinic acid to convert both elements into chloroplatinates, leaching out the sodium salt with strong alcohol and weighing the residual potassium salt. The method could not be used when S0 4 ions were present owing to the in- solubility of sodium sulfate in alcohol and altho this ion could be removed by the use of barium chloride, and the excess of barium added could be removed by the use of ammonium carbonate this procedure greatly increased the length and difficulties of the method. In order to avoid these difficulties Gladding modified the method by washing the mixture first obtained with sufficient alcohol to remove all of the sodium chloroplatinate and chloro- platinic acid, and then with sufficient ammonium chloride solution to remove the sodium sulfate. This modification made it possible to apply the method to substances containing organic matter and ammonium salts, for, by evaporating with a slight excess of sulfuric acid and igniting gently, both classes of substances could be expelled without loss of potassium. It also made it possible to apply the method to substances containing magnesium salts as they are readily dissolved by solutions of ammonium chloride. The slight solubility of potassium chloroplatinate in the solution of ammonium chloride used was reduced to zero by saturating it with potassium chloroplatinate before use. The method has been investigated by the Official Association of Agricultural Chemists and the exact details of the best method of procedure as applied to different classes of substances formulated. The outline given below is the official method* as applied to commercial potassium sulfate. II. OUTLINE OF METHOD OF PROCEDURE Preparation of Solution. Weigh out 10 gm. of the sample into a 500 cc. beaker, add 300 cc. of water, boil for a few minutes, then transfer to a 500 cc. graduated flask. Allow to cool, dilute to * Bull. 107, Bureau of Chemistry, U. S. Dept. of Agriculture. 212 QUANTITATIVE CHEMICAL ANALYSIS exactly 500 cc., mix thoroughly, filter about 300 cc. through a dry filter and preserve in a stoppered flask. Separation of Potassium. Measure out 25 cc. of the solution by means of a pipet, add an equal volume of water, acidify with a few drops of hydrochloric acid, add 10 cc. of chloroplatinic acid (1 cc. =0.1 gm. Pt) and evaporate on the water bath almost to dryness. Remove from the bath and add 25 cc. of 80 per cent alcohol, stir the mixture with a rod and break up any large masses, and after about five minutes decant off the clear liquid thru a weighed Gooch or alundum filtering crucible. Treat the residue with three 10 cc. portions of 80 per cent alcohol, stirring the mixture for several minutes after each addition and decanting as before. The last addition should remain colorless; if it acquires even a faint yellow color continue the washing. Finally transfer the residue to the filter by means of a stream of 80 per cent alcohol from a wash bottle. Wash the residue on the filter five times with 10 cc. portions of ammonium chloride wash solution,* then with three 10 cc. portions of 80 per cent alcohol. Dry the crucible for a half hour at 100 and weigh accurately. Calculate and report the percentage of potassium as K 2 present. Save both the precipitate in the crucible and the filtrate and washings for the recovery of the platinum present. III. QUESTIONS AND PROBLEMS. SERIES 13 1. How much larger percentage error is involved in determining potassium when separated as KC1O 4 than when separated as K 2 PtCl6, assuming that the sample contained 2 per cent of K, that one-half gram was used and that an error of 0.1 mg. was made in weighing both compounds? 2. What is the maximum error from solubility in the determination of K 2 O in a substance which contains 20 per cent, assuming that all of the details outlined above are followed? * Prepared by dissolving 100 gm. of ammonium chloride in 500 cc. of water, adding from 5 to 10 gm. of pulverized potassium chloreplatinate and shaking at intervals for from six to eight hours. Allow this mixture to settle over night, then filter. The residue may be used for the preparation of more solution. POTASSIUM IN COMMERCIAL POTASSIUM SULFATE 213 3. Why is it desirable to evaporate on a water bath after adding the E^PtCU? Why is it necessary to wash out all Na^PtCle and H 2 PtCl before washing with ammonium chloride? What might happen if the mixture was heated after alcohol was added? Why is it desirable to avoid changes in temperature while washing with the (NH 4 )C1 solution? 4. What modification of the method outlined would be necessary if the sodium and potassium were present as nitrates or phosphates respectively? 6. Outline a method for reconverting the platinum saved from the deter- mination into H 2 PtCle. 6. The potassium and sodium in a 0.5 gm. sample of K 2 S0 4 are converted into a mixture of KC1 and NaCl, which is found to weigh 0.35 gm.; the potassium is then separated as K 2 PtCl 6 , which is found to weigh 0.65 gm.; what percentages of K 2 O and Na^O are present? 7. Outline all the transformations necessary to carry out the determinations represented in the last problem. CHAPTER XXX DETERMINATION OF CRUDE FAT IN PEANUTS I. FACTS UPON WHICH THE DETEKMINATION Is BASED Chemical Nature of Fats and Oils. In the analysis of foods the different constituents are classified and determined with reference to the function they perform hi the nutrition of the animal body. One of the most important of these groups consists of fats and oils; it includes a very large number of organic com- pounds, which are analogous to inorganic salts, in that they rep- resent combinations of certain organic acids and glycerine, which acts as a trivalent base. The most important are olein, palmatin and stearine, which represent normal salts of oleic (Ci 7 H 33 COOH), palmitic (Ci 5 H 3 iCOOH) and stearic (Ci 7 H 35 COOH) acids, respec- tively. These compounds are not appreciably hygroscopic and do not absorb oxygen from the air, but the "drying oils," which are obtained when flax and certain other seeds are extracted, con- tain linoleic acid (C 17 H 3 iCOOH), and since this compound rapidly absorbs oxygen from the air such oils are difficult to weigh accu- rately. Meaning of " Crude Fat." All of the compounds referred to above are distinguished by their extreme insolubility in water, and very slight solubility in alcohol; also by the readiness with which they are dissolved by ethyl ether, petroleum spirit, carbon disulfide and carbon tetrachloride. The remaining constituents of most food materials are not appreciably soluble hi the four solvents last named. Many classes of food materials contain small amounts of other substances such as wax, resin, chlorophyll and various coloring matters, which are also more or less soluble 214 DETERMINATION OF CRUDE FAT IN PEANUTS 215 in these solvents, especially in ethyl ether. Long-established custom has led to the use of dry ethyl ether for the determina- tion of this group of food constituents. Since the results obtained by extracting a material with ether may include small amounts of substances other than fat the result should always be designated as " crude fat" or " ether extract." Purification of Ether. Unless especially purified ether con- tains both alcohol and water, and is then capable of dissolving appreciable amounts of certain sugars and other compounds which are not true fats. The alcohol can be removed by shaking the solvent with water and allowing the mixture to stand until it separates into two layers. The upper ethereal layer is then re- moved and the large amount of water which it contains separated by adding solid calcium chloride, and allowing the resulting aqueous solution of calcium chloride to separate out; the residual ether is then made anhydrous by adding metallic sodium and distilling. The purified solvent should boil at 35. From 35 to 50 cc. are needed for each extraction where the continuous type of apparatus is used, but nearly 25 cc., which can be again used without further treatment, should be recovered when it is distilled from the fat. Composition of Peanuts. The seeds of the peanut contain from 40 to 50 per cent of substances soluble in ether, nearly all of which are true fats. At least 80 per cent of the ether-soluble substances is tri-olein and the remainder is made up of the glycerides of stearic, arachidic (CigHsgCOOH) and lignoceric (C 23 H 4 7COOH) acids. None of these substances absorb oxygen from the air at an appreciable rate and hence no difficulty is experienced in weighing the crude fat separated directly. On the other hand, the cellulose-containing residue, which remains after extraction, is appreciably hygroscopic. Conditions Necessary for Complete Extraction. Ether pene- trates cellular tissue even when dry but slowly, and still more slowly when the tissue is moist. If the sample contains much 216 QUANTITATIVE CHEMICAL ANALYSIS moisture it is slowly taken up by the dry ether used, and gradually accumulates in the ethereal solution. Since the water cannot be easily distilled off from the crude fat without using an undesirably high temperature an appreciable error may result if the sample is not dried before it is extracted. The large amount and liquid character of the fat present makes it impossible to grind these seeds in a mill, or to pass the ground pulp through a sieve. They can be crushed to a sticky mass in an agate mortar but this will still contain small lumps unless great care is taken. The pulp can be completely dehyolrated by drying for an hour at 105 and the residue can usually be com- pletely extracted in three hours if the apparatus used is efficient, and if not more than 3 gm. of sample is used. Time can be saved and greater accuracy assured if the extraction is continued for an hour, the almost completely extracted residue ground very fine and the extraction continued for an hour longer. II. OUTLINE OF THE METHOD OF PROCEDURE Preparation of the Sample. Select eight or ten nuts of aver- age size and maturity and remove the husks and the brown skin which envelops the seeds by means of a thin-bladed knife. Place the seeds on a porcelain plate or watch glass and cut into thin slices with a knife, then place in an agate mortar and crush to a pulpy mass till free from lumps. Weigh out 3 gm. of the sample into a closed, dry weighing bottle, place in a drying oven and keep at a temperature of 105 for an hour. Determine the loss in weight which results and calculate the percentage of water present. The Extraction. Transfer the dried sample to a paper or alundum extraction shell and cover with a half-inch layer of cotton wool, which has been previously extracted with ether to remove the small amount of fat which it usually contains. Place the shell in an extraction tube similar to B of Fig. 40 or to Fig. 42. Weigh accurately a clean, dry fat-flask of 125 cc. capacity, add 35 cc. of pure dry ethyl ether and connect with the extraction tube by means DETERMINATION OF CRUDE FAT IN PEANUTS 217 of an accurately-fitting cork stopper. Connect the extraction tube with the vertical condenser as shown in Fig. 45 and adjust the cork stoppers so that the flask rests directly on one of the iron heating plates, then start the water running thru the condenser. Close the switch which operates the heating device and after the ether begins to boil reduce the rate at which it boils, if this seems to be necessary, by interposing a thin sheet of asbestos over the heating plate. Adjust the end of the condenser so that all of the condensed ether falls inside the extraction shell and allow the process of extraction to continue for three hours. Weighing the Crude Fat. Disconnect the extraction tube and flask from the condenser, remove to some distance from any source of heat and allow to drain for about five minutes. Dis- connect the flask from the extraction tube and then connect the flask with one of the branches of the block-tin condenser tube. Place a receiving flask under the other end of the tin condenser tube and allow the ether to distil over until only about 2 cc. of yellow or brown oil remains. Then remove the flask and place in a water-jacketed oven, heat the water to boiling and keep at this temperature for an hour. Draw a current of dry air thru the flask by means of an aspirator until the residue gives no odor of ether. Allow the flask to cool and weigh accurately. Calculate the percentage of crude fat in the dried sample and in the original selected nuts. CHAPTER XXXI ANALYSIS OF BLACK POWDER I. FACTS UPON WHICH THE ANALYSIS Is BASED Composition. " Black powder " designates a mixture of char- coal, sulfur and either sodium or potassium nitrate which is largely used as an explosive, especially for blasting. Such mixtures are easily resolved into their essential constituents by first leaching out the soluble salts with water, then extracting the sulfur by means of carbon disulfide and assuming that the residual solid is charcoal. Altho the different ingredients are ground very fine, and intimately incorporated in the mixture, the solvents named readily act upon it since the charcoal makes the mixture porous, and there are no cell membranes thru which the solvents must pass to bring the soluble constituents into solution. II. OUTLINE OF THE METHOD OF ANALYSIS* Determination of Moisture. Weigh out 2 gm. of the sample on a 3-inch watch glass, spread out as a thin layer and dehydrate, either by allowing to remain in a desiccator which contains con- centrated sulfuric acid, for a period of three days, or by heating in an oven at 70 for several hours or until the weight remains constant. The temperature must be kept low to avoid any possibility of volatilizing some of the sulfur. Calculate the per- centage of water lost. Determination of Nitrates. Weigh out 10 gm. of the crushed sample into a Gooch crucible, which is designed to be used in a * Bull. 51 of the U. S. Bureau of Mines by Walter O. Snelling and C. G. Storm. 218 ANALYSIS OF BLACK POWDER 219 Wiley extraction apparatus (see Fig. 41), weigh accurately and connect with a suction flask in the usual manner. Wash with at least 200 cc. of warm water added in quantities of about 10 cc. at a time, and test the last washings for nitrates by removing a few drops and adding at least an equal volume of strong sulfuric acid in which a few crystals of diphenylamine have been dissolved. This test will yield a deep blue color if even traces of nitrates are present. When all the nitrates have been leached out, remove the crucible, dry at 70 until the weight is constant and calculate the percentage of nitrates present from the difference between the total loss in weight and that due to the moisture originally present in the sample. Determination of Sulfur. Place the crucible containing the residue from the last determination in a Wiley extraction appara- tus and extract with about 35 cc. of recently distilled carbon disul- fide for about one hour. Remove the crucible, allow most of the carbon disulfide to evaporate spontaneously, dry to constant weight at 70 and calculate the percentage loss as sulfur. Determination of Charcoal and Ash. Calculate the percent- age of charcoal from the weight of residue left in the crucible. Burn off the organic matter in the crucible, weigh the residual ash and calculate the percentage present. SECTION V PARTITION PROCESSES CHAPTER XXXII GENERAL FEATURES OF PARTITION PROCESSES Consulate Liquids. When two liquids, which do not react with each other chemically, are mixed, one or more liquid phases, depending on the specific properties of the two liquids, may result. With certain pairs of liquids an infinite number of homo- geneous solutions representing every possible ratio of the two constituents can be prepared; this is true of the liquids, alcohol and water. With other pairs of liquids the possibilities are limited; either liquid may become saturated with respect to the other, and if a greater amount of one liquid than is required to saturate the other is added, a new liquid phase separates. One of the resulting liquid phases usually contains a relatively large amount of the first liquid but is saturated with the second; the other usually contains a relatively large percentage of the second liquid but is saturated with the first. If small amounts of water are successively added to ether, and the mixture is shaken after each addition, a single phase containing a relatively large amount of ether is first obtained, but when the amount of water added exceeds 3 per cent by volume of the ether used, a second phase containing about 90 per cent of water separates. The addition of further quantities of water does not change the composition of either phase, but increases the amount of the water-rich phase at the expense of the ether-rich phase, and if a sufficient amount is added 220 GENERAL FEATURES OF PARTITION PROCESSES 221 will cause the entire disappearance of the latter. The addition of still further quantities of water merely increases the percentage of water hi the water-rich phase. Many pairs of liquids, such as kerosene and water, are so slightly soluble in each other that the addition of a very small amount of one liquid to the other at once produces two distinct phases, whose composition is practically the same as that of the pure solvents. Any pair of liquids which exist as independent phases after being shaken together and allowed to stand until equilibrium has been attained are spoken of as "consolute" liquids. The mutual solubility of two consolute liquids is affected very greatly by tem- perature changes. Increasing the temperature usually increases their mutual solubility and may cause them to become soluble in any proportions whatever, that is, may result hi the disappearance of one of the two phases. The Distribution Coefficient. When a small amount of a third substance is added to a system consisting of two consolute liquids, the whole shaken for some time, and allowed to stand until per- fect equilibrium has resulted, the added substance, or a certain part of it, distributes itself between the two phases. The ratio of the concentration of the dissolved substance in one phase to the concentration in the other is a definite quantity, which is inde- pendent of the magnitude of the concentrations concerned, pro- vided the dissolved substance does not dissociate and does not form molecular aggregates. This ratio can be easily determined experimentally and is known as the " distribution coefficient." Its value is affected to some extent by temperature changes. If the two liquids are but slightly soluble in each other, and if the added substance is much more soluble in one than in the other the value of the distribution coefficient will be either very large or very small, depending upon which of the two solutions concerned is taken as the standard of comparison. If, however, the two liquids possess a more nearly equivalent solvent power. for the added substance, or if the two liquids dissolve one another to a large 222 QUANTITATIVE CHEMICAL ANALYSIS extent, so that the composition of the two resulting liquid phases does not greatly differ, the value of the distribution coefficient becomes more nearly equal to unity. The Separation of Consolute Liquids. The two liquid phases which make up a consolute mixture can be mechanically separated by a variety of de- vices. The simplest method is to insert a pipet or a tube, similar to the one shown in Fig. 46, into the mixture till its end is slightly above the plane separating the two layers, to draw the upper layer into the tube by suction, and transfer the liquid to another vessel. The separation thus effected is Fig 46 a l wavs imperfect as it is impossible to remove all of Separatory the upper layer without also removing some of the Pipet lower layer, but this error is comparatively small if the area of the containing vessel at the point of contact of the two layers is small. A much more satisfactory device is a "separatory funnel," one of the many forms of which is represented in Fig. 47. This is provided with a glass stopper and a side tube, which can be closed with the finger or a good cork, so that the two consolute liquids can be shaken together vigorously. The lower of the two resulting layers can then be allowed to drain into another vessel by opening the glass stopcock at the bottom of the funnel. The inaccuracy of the separations made with such a device is due almost wholly to the small volume of the heavier liquid which adheres to the inner surface of the tube below the stopcock; for this reason this tube should be made as short as possible and of such a Fig. 47. diameter that capillarity does not prevent it from Separatory discharging readily after the stopcock has been closed. Difficulties arise in the separation of two consolute liquids when one or both liquids show a tendency to " emulsify," that is, to 100 75 50 GENERAL FEATURES OF PARTITION PROCESSES 223 form an intimate mixture composed of small bubbles of the two liquids, which do not segregate except after very long standing. Instances occasionally arise in which this difficulty is sufficient to make the process concerned an impracticable one. The pres- ence of any finely divided solid matter always retards and may prevent an entirely satisfactory segregation of the two liquids. General Theory of Partition Processes. Iodine is much more soluble in the liquid carbon tetrachloride than in water and these two liquids are but slightly soluble in each other. As a consequence of these facts the distribution coefficient of iodine between the consolute liquids which result when carbon tetrachloride is added to an aqueous solution of iodine has at ordinary temperatures the value 85. This means that every unit volume of the carbon tetra- chloride-rich phase will contain eighty-five times as much iodine as each unit volume of the water-rich phase. The total amount of iodine separated from an aqueous solution by this treatment would also depend on the volume of the aqueous, as compared with that of the carbon tetrachloride phase. Suppose, for example, it is assumed that the aqueous solution has a volume of 100 cc. and contained 0.2 gm. of iodine, that 50 cc. of carbon tetrachloride is added, and that the changes in volume which result after equilib- rium has been established are insignificant. If x represents the weight of iodine in the resulting aqueous phase 0.2 Ic must represent the weight of iodine in the carbon tetrachloride phase. The distribution coefficient would require that x .0.2-a; Too' ~^o~ When this expression is solved for x the latter is found to have the value 0.0046, that is, the weight of iodine in the aqueous solution is reduced to 4.6 mg. by this treatment. If now the carbon tetrachloride solution is separated from the mixture, and the residual aqueous solution is again treated with 50 cc. of carbon tetrachloride a further quantity of iodine will be 224 QUANTITATIVE CHEMICAL ANALYSIS taken up by the latter. If y represents the weight of iodine left in the aqueous solution after this second treatment, the distribu- tion coefficient would require that y .0.0046-j/ TOO* ~50~~ The value of y calculated from the expression is found to be 0.0001016. The calculation shows then that practically all of the iodine can be separated from the aqueous solution by two treatments with 50 cc. portions of carbon tetrachloride. It can be readily shown that the use of only 75 cc. of this liquid in three 25 cc. portions would have left only 0.018 mg. of iodine in the aqueous solution and in general, several treatments with small amounts of carbon tetrachloride is more efficient and economical than fewer treat- ments with larger amounts. It is also obvious that the smaller the volume of the solution from which the substance is to be determined is separated, the greater the efficiency of the process. In general, the theory of partition processes shows a close analogy to that already developed in discussing the washing of precipitates, but unlike the latter it does not involve the use of assumptions which are never actually realized. Further emphasis should be laid, however, on the qualification already noted, namely, that the value of the distribution coefficient may change with varying concentration. This may result from the effect of varying concentration upon the degree of ionization or of hydration, or upon the nature of the substances actually present in the solution concerned. CHAPTER XXXIII DETERMINATION OF NICKEL IN NICKEL STEEL I. FACTS UPON WHICH THE DETERMINATION Is BASED Composition of the Sample. Alloys of nickel and iron, which contain from 1 to 14 per cent of nickel, are frequently used for structural purposes where extreme hardness and toughness are demanded, and where the importance of these factors warrants the extra cost of such an alloy. They usually contain small amounts, up to 1 per cent, of combined carbon, very small amounts of silicon, sulfur and phosphorus and sometimes appreciable amounts of manganese and copper. Altho nickel hydroxide is readily soluble in an excess of am- monium hydroxide this reagent cannot be used to effect a quantita- tive separation of nickel from iron, unless the process is repeated several tunes, or unless the percentage of iron present is very small, owing to the occlusion of nickel by ferric hydroxide. The partition process devised by J. W. Rothe is an extremely con- venient and rapid method for making this separation. Theory of the Separation. Anhydrous ferric chloride, unlike the chlorides of aluminum, nickel, cobalt, chromium, manganese, zinc and copper, is readily soluble in ethyl ether. If, however, ether is added to an aqueous solution of ferric chloride very little iron is taken up by the resulting ethereal solution unless a large concentration of hydrochloric acid or some soluble chloride is also present. It is probable that only unionized ferric chloride is appreciably soluble in ether, and that the element cannot be separated by the use of ether unless the ionization of the ferric chloride is repressed by the addition of hydrochloric acid. The 225 226 QUANTITATIVE CHEMICAL ANALYSIS best results are obtained when the iron solution treated contains from 20 to 25 per cent of this acid. The value of the distribution coefficient which is concerned here is not constant but varies with the temperature and the concentration of both acid and ferric chloride in the aqueous solution; under favorable conditions it may attain a value of 100. The values for the distribution coefficients of the chlorides of the metals named above, except possibly copper, are represented by extremely small fractions. Conditions Necessary for the Separation. The rate at which iron was removed from an aqueous solution, which had a volume of 20 cc. and contained in addition to 20 per cent of hydrochloric acid 0.2054 gm. of iron as ferric sulfate, by successive treatments with 25 cc. portions of ether, is shown in the following results. Iron removed by first treatment 0. 1964 gm. Iron removed by second treatment . 0075 gm. Iron removed by third treatment 0.0016 gm. Iron removed by fourth treatment 0.0007 gm. Iron removed by fifth treatment . 0002 gm. Since ferrous salts are not appreciably soluble in ether all of the iron must be kept in the ferric condition during the separation. As ether reduces ferric salts appreciably at a temperature slightly above the normal the mixture must be kept cold. It is further necessary to keep the concentration of all aiiions except chlorine low; if such anions are present they may keep some of the iron in such a form that it is not easily taken up by the ether. Determination of the Separated Iron. Most of the ether present in the ethereal solution can be recovered for subsequent separations by distilling in a suitable apparatus; were it not so the cost of the method would often be prohibitive. The last traces can be driven off by evaporating in an open vessel; the iron which has been reduced during the distillation and evaporation must be oxidized before it is precipitated. DETERMINATION OF NICKEL IN NICKEL STEEL 227 Determination of the Separated Nickel. The decomposition voltage of the nickel ion is about 0.22 volt higher than that of the hydrogen ion. It can be rapidly and completely separated in a dense form from a neutral solution of the double oxalate, or from solutions of the sulfate to which a large excess of ammonium hydroxide has been added. In the presence of the NOs ion a small amount of nickel oxide, which is not easily redissolved, may sepa- rate at the anode. The precipitated metal is not dissolved appre- ciably by the ammoniacal solution and it is not easily oxidized. II. OUTLINE OF METHOD OF PROCEDURE Preparation of the Solution. Weigh out 2 gm. of the sample, which should be in the form of drillings or shavings, into a 300 cc. beaker, add 20 cc. of dilute hydrochloric acid, 5 of dilute nitric acid, cover with a watch glass and warm the mixture until the alloy is dissolved. Remove the watch-glass cover and evaporate the solution cautiously to avoid loss from spattering until a thick syrupy liquid or solid residue remains. Add 10 cc. of concentrated hydro- chloric acid to the residue and evaporate as before; finally dissolve the residue in 10 cc. of dilute hydrochloric acid, dilute to 20 cc., filter off the small residue of silica and carbon on a 7 cm. filter and wash free from soluble salts, using the smallest necessary amount of cold wash water. Separation of the Iron. Concentrate the filtrate to a volume of 10 cc., allow to cool and then transfer the solution to a 100 cc. separatory funnel with the aid of 10 cc. of dilute hydrochloric acid and 50 cc. of ether. Place both glass and cork stoppers in the funnel, cool the latter under a stream of water from the tap, shake cautiously once and release the excess of pressure created in the funnel by cautiously opening the cork stopper. Replace the cork stopper, again cool the funnel and shake vigorously for about three minutes. Support the funnel in a vertical position by means of a clamp and allow it to stand until the plane separating the two consolute liquids is clearly defined. Remove the cork stopper 228 QUANTITATIVE CHEMICAL ANALYSIS and cause the aqueous phase to drain into the beaker previously used, allowing sufficient time to permit the aqueous phase to flow down the inner surface of the funnel and several drops of the ethereal phase to flow through the stopcock; then rinse off the lower end of the funnel with 2 or 3 cc. of water. These precau- tions become necessary for the purpose of rinsing every drop of the aqueous phase out of the funnel before attempting to remove the ethereal phase. Allow the ethereal phase to flow into a 200 cc. Erlenmeyer flask, rinse off the inner and outer surfaces of the tube below the stopcock with 3 to 5 cc. of water, then close the stop- cock and set the flask aside. Transfer the aqueous solution in the beaker to the funnel with the aid of 25 cc. of ether and again mix and separate the ethereal layer. Connect the Erlenmeyer flask containing the combined ether extracts with a condenser and carefully distil off the ether, which can be used for subsequent determinations. Separation of Last Traces of Iron. Add cautiously 5 cc. of concentrated sulphuric acid to the aqueous solution and warm gently until the ether present is expelled, then heat nearly to the boiling point and evaporate the solution until fumes of sulphur trioxide appear; next add 50 cc. of water, and digest until soluble salts are dissolved, then add 5 cc. of hydrogen peroxide to oxidize any iron which may have been reduced by the ether, heat to the boiling point and add an excess of ammonium hydroxide, that is, sufficient to impart a strong odor to the solution. Keep the solution at or near the boiling point for a few minutes, then filter off the precipitated iron and manganese on a 7 cm. filter and wash with the smallest necessary amount of hot water. Determination of Nickel. Ignite and weigh accurately a clean platinum electrode, preferably of gauze. Place the electrode and a platinum spiral in the nickel solution, add 20 cc. of dilute am- monium hydroxide and make the proper connections with the terminals of a storage battery. If a gauze electrode has been prepared use a current of one ampere and allow the action to con- DETERMINATION OF NICKEL IN NICKEL STEEL 229 tinue for at least fifteen minutes after the solution has become colorless. If a foil electrode has been prepared, it will be prefera- ble to use a current of one half ampere only. Remove the cathode, wash in alcohol, dry at 100 and weigh. Calculate the percentage of nickel present. Remove the nickel from the cathode by allow- ing it to stand in a cylinder of strong nitric acid for twenty minutes and rinse off the acid with water. III. QUESTIONS AND PROBLEMS. SERIES 15 1. Calculate the values of the distribution coefficient for iron in the ethereal as compared with the aqueous phase at different concentrations from the data given on page 226. 2. Discuss the factors to which the changes in the values of this distribu- tion coefficient are due. 3. A solution, which has a volume of 100 cc. and contains 0.4 gm. of HgBr 2 , is treated successively with 20 cc. portions of benzene; if the distribution coefficient, that is (HgBr 2 ) in H 2 O -T- (HgBr 2 ) in C 6 H 6 , has the value 0.88, how many treatments are needed to reduce the amount of HgBr 2 to 0.1 mg.? 4. Write out a probable reaction for the reduction of ferric chloride by ether. 6. Suggest a probable effect of the presence of alcohol in the ether used for this separation. 6. What objections are there to precipitating the iron by means of ammo- nium hydroxide without previous oxidation? 7. Explain how nickel might separate at the anode during electrolysis and how NO 3 ions could favor the separation. 8. Would you expect the electrolytic determination of nickel to be affected by the presence of Co, Cu, Zn, Pb or Ag? CHAPTER XXXIV DETERMINATION OF CAFFEINE IN TEA I. FACTS UPON WHICH THE DETERMINATION Is BASED Properties of Caffeine. The stimulating properties of tea and coffee are due for the most part to caffeine. This compound is rep- resented by the formula CgHioN^, but it crystallizes with one molecule of water, which it begins to lose when heated to 110. It belongs to that class of organic compounds which, owing to their weakly basic properties, are known as alkaloids. It begins to be appreciably volatile at 100, melts at 225, and can be sublimed without decomposition. It is soluble in about seventy-four parts of water, eight of chloroform and 2270 of ether. The salts which it forms with acids are more soluble in water than the free base. Properties of Chloroform. One volume of chloroform requires nearly 183 volumes of water to dissolve it and the composition and properties of the consolute liquids formed when chloroform and water are mixed are essentially those of the pure compo- nents. Pure chloroform has a specific gravity of 1.526, it boils at 61 and its vapor is not inflammable; although it is an expen- sive reagent it is easily recovered and purified after use. When caffeine is in equilibrium with chloroform and water the concentration in the chloroform layer is about thirteen times as great as in the aqueous layer. Altho this ratio is not very large it is so much larger than the ratio representing the distribu- tion of inorganic salts between chloroform and water that caffeine can be easily separated from these salts by a partition process. Composition of Tea Leaves. Tea contains in addition to from 1 to 5 per cent of caffeine, soluble inorganic salts, tannic acid, 230 DETERMINATION OF CAFFEINE IN TEA 231 coloring matter and small amounts of essential oils and organic acids. If the leaves are extracted with a sufficient amount of hot water all of the caffeine and most of the tannin, inorganic salts and organic acids are brought into solution. If the aqueous solu- tion is treated with a sufficient amount of a solution of basic lead acetate the tannin and organic acids form insoluble lead salts, but the caffeine remains unprecipitated. The excess of lead acetate necessarily added can be separated by passing hydrogen sulfide through the solution, and the excess of hydrogen sulfide used can be boiled off. Sources of Error. The small amount of caffeine present in tea makes it desirable to use several grams of the sample for the determination. The residue which remains after the extraction occupies a large volume and is difficult to filter and wash thor- oughly. The precipitate of lead salts is also very bulky and forms a dense, impervious coating on the filter, which is difficult to wash. These errors are made as small as possible by weighing out about 5 gm. of the sample and, after digesting with water and separating the impurities, diluting to 500 cc., allowing the insoluble residue to settle and removing an aliquot part of the clear solution. This procedure involves a positive error since it is assumed in the sub- sequent calculations that the total volume of the solution was 500 cc. Altho a rough estimate of the volume occupied by the solid matter could be made and a correction introduced the proc- ess involves other negative errors, and a better result is obtained if the error is disregarded. Even where the greatest care is ex- ercised the percentage error of the method is comparatively large. II. OUTLINE OF METHOD OF PROCEDURE Preparation of Aqueous Solution. Prepare the sample by crushing the leaves in an agate mortar till fine enough to pass thru a forty-mesh sieve. Weigh out 5 gm. of the sample, transfer to a 500 cc. graduated flask, add 400 cc. of water, heat slowly to the boiling point, taking care to prevent the mixture from boiling 232 QUANTITATIVE CHEMICAL ANALYSIS over, and keep slightly below this temperature for a half hour. Cool the mixture to the temperature of the room and add slowly and with constant agitation 4 cc. of a solution of basic acetate of lead; * this should be sufficient to precipitate all of the tannin and coloring matters present. Dilute the mixture to exactly 500 cc., mix thoroughly and allow to stand until the solid matter present settles. Remove by means of a pipet 20 cc. of the clear solution and allow it to pass thru an 11 cm. filter into a clean 200 cc. graduated flask but discard the filtrate thus obtained since the paper may have absorbed an appreciable amount of caffeine. Remove and filter further quantities of the solution until the flask is filled to the 200 cc. mark. Transfer the 200 cc. of filtrate to a 400 cc. beaker and pass hydrogen sulfide thru the solution until the precipitated lead sulfide becomes granular. Filter into another 400 cc. beaker, wash with a small amount of cold water, evaporate the solution to 100 cc. and allow to cool. Separation of Caffeine. While waiting for the solution to evaporate, clean a 100 cc. Erlenmeyer flask dry in an air bath, allow it to cool in the balance room for at least half an hour and weigh accurately, using a glass counterpoise of about the same surface area. Transfer the aqueous solution to a 200 cc. separatory funnel, add 20 cc. of chloroform, place both stoppers in the funnel and shake vigorously for three minutes. Support the funnel in a vertical position by means of a clamp, remove the cork stopper, place the previously weighed flask under the funnel and by care- fully manipulating the stopcock allow the chloroform solution to drain into it until the plane dividing the two liquids barely reaches the stopcock. Rinse off the lower end of the funnel with a few drops of pure chloroform added from a pipet and receive the * Prepared by boiling 430 gm. normal lead acetate, 130 gm. litharge and 1000 cc. water for an hour, allowing to cool and settle, and diluting until the specific gravity is 1.25. DETERMINATION OF CAFFEINE IN TEA 233 rinsings in the flask. Repeat the treatment with two more 20 cc. portions of chloroform. Weigh accurately 1 or 2 inches of fine platinum wire and add to the flask. Connect the flask with a condenser by means of a glass tube and cork stoppers, start the water running through the condenser and cautiously distil off the chloroform until only a few drops of solution remain but avoid heating the flask much above the boiling point. The platinum wire should reduce the tendency of the solution to boil over materially. Return the distillate obtained to the stock bottle for future determinations. Again extract the aqueous solution with three 20 cc. portions of chloroform, receiving the chloroform solution in the Erlenmeyer flask previously used and again distil off the chloroform. Disconnect the flask from the condenser while still warm, introduce a glass tube, which is attached to an aspirator or water pump, to within a half inch of the bottom of the flask and draw air thru it for several minutes. Place the flask in an air bath heated to 75 for a half hour, again draw air thru it, allow to cool and weigh. The separated caffeine should consist of fine needle- like crystals of a nearly white color. Calculate the percentage present. III. QUESTIONS AND PROBLEMS. SERIES 16 1. Calculate the weight of caffeine which should be removed by each suc- cessive treatment of the pure aqueous solution, assuming that the weights and volumes used correspond exactly to those called for in the method outlined and that the sample contains 3 per cent of caffeine. 2. Calculate, as in the previous problem, the weights of caffeine which should be removed, assuming however that 1 cc. of the chloroform solution is left with the mixture after each treatment. 3. What compounds would you expect to find in the aqueous solution finally left from the determination of caffeine in tea? 4. What methods could you use to test the purity of the caffeine finally separated from the tea? 5. Is it at all probable that any of the caffeine would remain in the aqueous solution as a salt of hydrogen sulfide? SECTION VI GENERAL FEATURES OF VOLUMETRIC PROCESSES CHAPTER XXXV THEORY OF VOLUMETRIC PROCESSES Fundamental Definitions. Volumetric analysis is that branch of quantitative analysis in which the amount of an element or compound, which is present in the substance submitted to analysis, is calculated from the volume of some reagent of known strength that is found to be necessary to complete a reaction with the element or compound being determined. A reagent especially prepared for making such a determination is known as a " standard solution." The value of this solution may be expressed either in terms of the number of grams of reagent actually present in a unit-volume, or in terms of Ihe number of grams of any substance with which the reagent in one unit-volume reacts. The process of determining the volume of standard solution necessary to com- plete a reaction with a solution of the substance which is being analyzed, and in general the process of comparing the relative strengths of two solutions which react with each other chemically, is designated as " titrating." The essential difference between gravimetric and volumetric processes consists in the substitution of a measurement of a stand- ard solution for a determination of the weight of a precipitate, or of some product, which is separated from the substance being analyzed. Since volumetric processes necessarily involve calcu- lating the magnitude of a weight, which corresponds to the weight 234 THEORY OF VOLUMETRIC PROCESSES 235 of precipitate or other product separated in a gravimetric process, they are virtually indirect methods of carrying out gravimetric processes. Reactions Suitable for Volumetric Processes. Volumetric processes are usually based upon definite chemical reactions but only a limited number of reactions can be employed in making volumetric determinations. In general only those reactions which take place completely and instantaneously when equivalent amounts of the reacting substances are present are suitable for volumetric processes. For this reason reactions which result in the formation of new phases, or which give rise to products which are but slightly ionized, are largely used. A number of reactions which are sufficiently complete but not instantaneous become so upon the addition of a slight excess of the reagent used for the preparation of the standard solution. Such reactions are some- times used as the basis of volumetric processes by the method of "back titration." In employing this device a slight excess of the standard solution is added, and the excess added is then titrated with a second standard solution, which reacts completely and instantaneously with the standard solution first employed. If the volumetric relation between the two standard solutions has been previously determined, the proper correction for the excess of standard solution first added is easily made. Determination of the End-point. A second requirement, which reduces still further the number of reactions which can be used for volumetric determinations, is that some method can be devised to determine the point at which the amount of standard solution added is equivalent to the substance being titrated. As this point is approached certain of the physical and chemical properties of the solution change very rapidly in some cases there is a marked change in the color or electrical conductivity of the mixture, in others a precipitate may begin to form or may just cease to form, in still others the addition of another reagent, that is, an "indicator," causes a decided color change to take place. 236 QUANTITATIVE CHEMICAL ANALYSIS The point at which a sufficient amount of the standard solution has been added to make these changes recognizable is known as the "end-point" of the titration. The difference between this point and the point at which an equivalent amount of the standard solution has been added, that is, the true end-point, must be small if the process is to be sufficiently accurate. Theory of Indicators: First Case. Whenever an indicator is used, the physical change which is recognized is the result of a chemical reaction, in which the indicator itself is one of the active reagents. The indicator may react either with the substance being determined or with the standard solution employed in making the determination. In the latter case the reactions concerned may be represented by the following equations, in which X represents the substance being determined, R the reagent in the standard solution being used, and 7 the indicator employed: (1) X + I + R^RX + I, (2) I + R-+IR, (3) IR + X-+RX + I. The appearance of the end-point is here dependent upon the con- centration of IR which should remain equal to zero as long as an appreciable concentration of X is present, but should increase in direct proportion to the amount of R added as soon as the con- centration of X has been reduced to zero. In other words, re- action (1) must be completed before reaction (2) begins to take place, but reaction (2) must take place promptly, even when the concentrations of I and R are very small. It is further necessary that in case a small amount of the com- pound IR has been formed during the earlier part of the titration, which may readily result from imperfect stirring and consequent accumulation of R in the upper layers of the solution, it should react with X according to equation (3), thus preventing the appearance of false end-points, Reaction (3) is also a direct THEORY OF VOLUMETRIC PROCESSES 237 measure of the preponderance of reaction (1) over reaction (2) in the presence of X, that is, it insures the completion of (1) before (2) begins to take place. It is evident, therefore, that the closeness of the agreement between the end-point actually recognized and the true end-point depends upon the values of the equilibrium constants of the three reactions concerned. A second factor which is of some importance is the amount of indicator used. In those cases in which the end-points obtained depend upon a change from one specific color to another the two colors often tend to mask one another and give rise to a series of indeterminate transition tints. It is then desirable that the entire amount of indicator present should be completely transformed into the compound possessing the different color by the slightest possible excess of the titrating solution; in such cases only a small amount of indicator may be used. If, however, the solution of the indicator is colorless, and the addition of an excess of the standard solution produces a specific color, a relatively large amount of indicator may sometimes be used to advantage. Increasing the concentration of the indicator favors the completion of reaction (2) but inhibits reaction (3). If, therefore, the equilibrium constant for (2) is somewhat small and that of (3) is sufficiently large, an increase in the amount of indicator used should increase the accuracy of the process. On the other hand if the reaction constant for (3) is too small and that of (2) is sufficiently large, a decrease in the amount of indicator used should increase the accuracy of the process. Theory of Indicators : Second Case. If the indicator used re- acts with the substance being determined the series of reactions concerned may be represented as follows: (5) (6) 238 QUANTITATIVE CHEMICAL ANALYSIS The appearance of the end-point is here dependent upon the concentration of /, which should remain equal to zero as long as an appreciable concentration of the excess of -X" is present. The accuracy of the process is determined largely by the magnitude of the three equilibrium constants concerned. The Advantages of Volumetric Processes. Volumetric proc- esses can usually be carried out much more rapidly and often demand less experience and skill than the corresponding gravi- metric processes. The time needed to make the actual titration is usually a few minutes only but the necessity of removing inter- fering substances and of transforming the substance to be deter- mined into the most suitable form often increases the time required for the entire analysis to several hours. Many are more accurate than the corresponding gravimetric processes but in other cases the reverse is true. They avoid the errors which are involved in making an actual separation, that is, the errors resulting from solubility, from occlusion or from other difficulties which yield an impure product, and from actual mechanical losses. On the other hand they necessarily involve certain errors in the preparation and measurement of the standard solution used and in the deter- mination of the end-point of the reaction upon which the process depends. Principle of Compensating Errors. A principle which can be used to great advantage in volumetric processes is that of counter- acting the errors involved in the actual determination by equal errors in the standardization of the solution used. Assuming that there is always a discrepancy between the true and the observed end-point, it will generally be true that this discrepancy will be constant so long as the conditions remain constant. If the solu- tion is standardized under exactly the same conditions as those which must obtain in the actual determination, practically all errors are eliminated as the standard solution used becomes merely an instrument by means of which the strengths of two solutions of the same substance, one representing a known amount of a pure THEORY OF VOLUMETRIC PROCESSES 239 compound and the other the solution of unknown concentration, are compared. Considered from this point of view it is preferable to standardize the solution by comparing with a known weight of the substance being determined, and wherever it is possible to use the same solution for the determination of a number of sub- stances, strict accuracy would demand that the solution be re- standardized for every one of the substances for which it is to be used. Determination of Standard Solution Used by Weight. When results oi extreme accuracy are required, or when the volume of standard solution used is so small that the percentage error in- volved in measuring it is large it may be found advantageous to determine the amount of standard solution used by weight. When this procedure is adopted the solution should be standardized in a similar manner, that is, its value should be ascertained in terms of the weight to which one gm., rather than one cc., is equal. A special form of apparatus, which can be conveniently attached to the beam of the balance and weighed before and after the titra- tion, is used to contain the standard solution. There is no gain in using standard solutions in this manner unless the accuracy with which the end-points of the process used can be determined ap- proaches that with which the weights of the solutions used are determined. CHAPTER XXXVI MEASUREMENT OF THE SOLUTIONS USED IN VOLUMETRIC DETERMINATIONS I. SOURCES AND METHODS OF AVOIDING ERRORS Volumetric Apparatus. The accuracy of volumetric deter- minations depends in part upon the accuracy attained in the measurements made and necessitates the use of certain special forms of apparatus. Burets are calibrated glass tubes of uniform, small diameter, designed to measure variable amounts of liquids delivered by them, when supported in a vertical position. The delivery of the liquid which is being measured is controlled in the form first used by Geissler (see Fig. 49), by a glass stop- cock, and in the form first used by Mohr (see Fig. 48), by a rubber joint which connects the end of the tube with a glass nozzle, and is provided with a pinchcock or a screw clamp. The former has the disadvantage of re- quiring the use of some lubricant, such as a mixture of beeswax and vaseline. . Fig. 48. Mohr . Fig.49. Geiss- Buret to Prevent leakage, and of being more ler Buret expensive and more easily broken. The latter has the disadvantage that the rubber connection is acted upon to some extent by solutions of strong alkalies and by 240 MEASUREMENT IN VOLUMETRIC DETERMINATIONS 241 certain oxidizing agents, which may reduce the concentrations of the solutions measured in them appreciably. The total capacity of the burets usually employed is either 100, 50, 25 or 10 cc.; the 50 cc. buret should be graduated to read tenths of a cubic centimeter and its diameter should be small enough to permit of estimating fiftieths of a cubic centimeter with reasonable accuracy. Burets of smaller capacity should be made of tubes having a still smaller diameter in order to make measurements with a corresponding degree of accuracy. Since two readings are involved in each measurement the maximum possible error in the use of a 50 cc. buret should not Exceed one twenty- fifth of a cubic centimeter which corresponds to one-eighth of one per cent when the amount measured is as much as 50 cc. Pipets are tubes of much smaller bore than burets, designed to measure definite amounts of liquid only. They are usually provided with an enlarge- ment at their center, as in Fig. 50, which greatly increases their capacity, and a single mark near the upper end, which indicates the point to which they must be filled to deliver the volume for which they are calibrated. Sometimes they are calibrated by means of two marks, one above and , Fig. 50. Pipet ,, ,, , t , Fig. 51. Pipet the other below the enlargement, and in this case the value of the pipet is determined by the volume of liquid delivered during the passage of the meniscus from the upper to the lower mark. The so-called measuring pipets (Fig. 51) lack the enlargement at the center, and are calibrated like burets; they are rarely used for amounts greater than 10 cc. The form of 242 QUANTITATIVE CHEMICAL ANALYSIS the pipet should be such as to permit of a free flow of the liquid over its entire inner surface when held vertically, and the orifice should be small. The time required for the delivery of the liquid from a 50 cc. pipet should not be less than 20 seconds; from a 10 cc. pipet it should not be less than 10 seconds. Where properly used the error involved in the measurement with a 25 cc. pipet should not exceed one one-hundredth of a cubic centimeter. They are to be preferred to burets wherever it is possible to use them, on account of the greater ease and accuracy with which they can be manipulated. Graduated flasks (Fig. 52) are flat-bottomed, and have a long narrow neck. They are usually calibrated to contain a definite volume, but may be calibrated to deliver that volume. The diameter of the neck should be small as compared with its capacity; that of a 1000 cc. flask should not exceed 20 mm.; that of a 100 cc. flask should not exceed 10 mm. The uncertainty involved in the use of a 1000 cc. flask should not exceed a tenth of a cubic centi- meter; for a 100 cc. flask it should not exceed Fig. 52. Gradu- , , , ,,, ,. ated Flask one ~ nun( iredths of a cubic centimeter. Graduated cylinders are cylindrical glass tubes provided with an enlarged base or foot and with a lip for pour- ing. They are calibrated to indicate the varying amounts of liquid which they can contain and are employed for rough measurements only. Error from Parallax. Errors may result from inaccuracies in reading the level of the liquid in the apparatus used. Unless the liquid being measured is intensely colored the lowest point on the curve of the meniscus forms the most satisfactory point of refer- ence, with which to compare the graduations on the apparatus. Since this point lies at the center of the tube the error from paral- lax, especially where the tube is of large diameter, must be avoided. MEASUREMENT IN VOLUMETRIC DETERMINATIONS 243 The simplest method of doing this is to hold the tube so that its main axis is perfectly vertical, and make all measurements with the eye held at such a level that the line of sight makes an angle of 90 with the axis that is, the measurement is made from the point at which the plane tangent to the meniscus at its lowest point and perpendicular to the axis of the tube cuts the wall of the apparatus. A number of devices may be employed to assist in maintaining the eye at the proper position. A piece of looking glass may be held in contact with the back of the tube and the level of the eye shifted till the lowest point of the meniscus, the graduation nearest to it, and the reflection of that graduation in the mirror are all on .the same line, as j ^ represented in Fig. 53. A piece of stiff ^ paper with a perfectly straight edge may be folded around the tube hi such a manner that the two edges of the paper, the one being at the front, the other Fig. 53. Use of a Mirror at the back of the tube, in Reading Buret and the lowegt point o f tne meniscus are all in line with one another. A more convenient device is found in the Schellback burets (see Fig. 54) and pipets in which a strip of dark blue or black glass, and two adjoin- ing strips of white enamel glass are introduced at the back of the tube directly opposite the graduations. If the level of a liquid in a tube of this kind be observed the dark strip seems to contract to a point just opposite the meniscus, as shown in the sketch. If the eye is held at the proper level this becomes an exceedingly sharp point of reference from which to compare the graduations on the tube. Fig. 54 Schell- back Buret 244 QUANTITATIVE CHEMICAL ANALYSIS Still another device employed with burets only is a cylindrical glass float (Fig. 55) provided with an encircling line etched on its outer surface. By comparing the projection of the plane of this circle with the graduations on the tube an exceedingly accurate reading can be made. Unless the float is properly adapted in form and size to the bore of the buret, capillary action retards its movement as the level of the liquid changes, and gives rise to large errors. If the liquid being measured is intensely colored the circle formed by the uppermost points on the curve of the meniscus forms the most satisfactory plane of reference with which to compare the gradua- tions on the tube. Error from Drainage. When a liquid is permitted Fig. 55. Float ^ o p ass ou t o f a buret somewhat rapidly small amounts adhere to its inner surface, and some of it gradually flows down and unites with the liquid still remaining in the buret. The rapidity with which the level of the liquid in the buret attains its ultimate position depends upon the viscosity of the solution, the area and form of the surface drained, and the rapidity with which the solution has been permitted to flow from the tube. The viscosity depends in turn upon the chemical nature, concentration and temperature of the solution. In order to avoid errors from this source a sufficient interval must elapse between the time at which the flow from the apparatus is stopped, and the time at which the reading is made. The minimum value of this time interval is easily ascertained by a series of simple experiments. In the use of pipets both the drainage from the inner surface, and the capillary action at the nozzle have to be considered, and a definite method of procedure must be adopted, both in calibrating the pipet and in its subsequent use. The conditions which yield the most uniform results are obtained when the nozzle of the pipet MEASUREMENT IN VOLUMETRIC DETERMINATIONS 245 is permitted to touch the wall of the receiving vessel while the liquid is flowing from it, and to remain in contact with it for 20 seconds after the main part of the liquid has been delivered; the attempt to blow out the few drops, which are retained by the nozzle as the result of capillary action, is not to be recommended. Error from Water in the Apparatus. It is usually necessary to rinse measuring apparatus with water before using and the amount of water retained by the apparatus may effect an appreci- able change in the concentration of the solution measured. The error can be avoided by drying the apparatus before use, but a more convenient method is to rinse it out with some of the solution which is to be measured and discard the rinsings. The amount of liquid used for this purpose should be at least 10 per cent of the total capacity of the measuring vessel, and should be made to flow over the entire inner surface by repeatedly shaking or by inverting the apparatus. Error from Changes in Temperature. A change in tempera- ture affects both the size of the vessels used and the density of the liquid measured. The first effect is practically constant for tem- peratures ranging from zero to 100. For glass vessels of the usual form this so-called "coefficient of cubical expansion " has the value 0.000025, which represents the increase in the capacity of the vessel for an increase of one centigrade degree. The second effect is not constant even over small ranges of temperature and varies greatly with the liquid concerned; it is much greater than the effect on the containing vessel. All or- ganic liquids show a large expansion as compared with water. The expansion of dilute aqueous solutions, such as are used in most volumetric determinations, does not differ greatly from the expansion of pure water. The actual error which results from the use of a piece of gradu- ated apparatus at a temperature which differs from that at which it has been calibrated is due to the difference between the effect on the liquid and the effect on the containing vessel. It is a 246 QUANTITATIVE CHEMICAL ANALYSIS simple task to calculate, from the coefficient of cubical expansion of glass and from a table showing the expansion of water for dif- ferent temperatures, a series of factors which represent the num- ber by which the observed volume should be multiplied to correct for departures in temperature from that for which the apparatus was calibrated. Error from Variations in the Unit of Volume Employed. The choice of a unit of volume is determined solely by convenience, but it is essential that the same unit be employed in all the opera- tions involved in any one determination. The standard liter, that is, the volume occupied by a kilogram of water, when weighed in a vacuum and measured at a temperature of 4 is manifestly inconvenient. The so-called "Mohr unit" which is the volume of a kilogram of water when weighed in the air with brass weights at a temperature of 17.5 is more convenient, since these condi- tions do not differ greatly from those normally prevailing in the laboratory. Other units involving measurements at tempera- tures of 15, 16 or 20 have been used by other chemists. The exact value of any of these units, in terms of absolute metric units, can be determined by calculating the changes in volume which take place when a flask containing sufficient water to counter- balance a kilogram brass weight at 4 in a vacuum is heated to a temperature corresponding to the unit of volume concerned, and when an amount of water sufficient to counterbalance the buoyant effect of the air, which results from allowing air at atmospheric pressure to replace the vacuum, is added. Much of the calibrated apparatus sold by manufacturers bears no mark by means of which the unit volume represented can be determined, and even when this is clearly designated the percentage error represented may be large. It is not advisable, therefore, to use any piece of calibrated apparatus, when the work in hand demands great accuracy, until its actual value has been ascertained by the analyst. In this book the volume occupied by that amount of water which MEASUREMENT IN VOLUMETRIC DETERMINATIONS 247 counterpoises a kilogram of brass when measured either at 15 or (preferably) at 20 are the units adopted. The factors by which the volumes found at temperatures ranging from 10 to 25 must be multiplied in order to obtain the true volume when measured in these units are given in the following table: Temperature of actual measure- ment Factor for appa- ratus calibrated at 15 Factor for appa- ratus calibrated at 20 10 1.00047 1.00124 11 1.00040 1.00117 12 1.00032 1.00109 13 1.00023 1.00100 14 1.00012 1.00089 15 1.0 1.00077 16 0.99987 1.00064 17 0.99972 1.00049 18 0.99956 1.00034 19 0.99940 1.00018 20 0.99923 1.0 21 0.99904 0.99981 22 0.99884 0.99961 23 0.99861 0.99941 24 0.99841 0.99919 25 0.99820 0.99897 II. DETAILED DESCRIPTION OF METHOD FOB THE CALI- BRATION OF VOLUMETRIC APPARATUS Cleaning Graduated Apparatus. Carefully clean a 50 cc. buret and two pipets, preferably of 10 and 25 cc. capacity. If their inner surfaces are contaminated with a film of organic matter, water will adhere to them in streaks and drops. These impurities should be removed by rinsing either with a strong solution of sodium hydroxide or with a cleaning mixture made by saturating sulfuric acid of 1.6 specific gravity with sodium dichromate; in extreme cases it may be necessary to allow the apparatus to stand over night in a cylinder filled with this solution. If the buret is of the Mohr type the rubber connection should be removed since 248 QUANTITATIVE CHEMICAL ANALYSIS it is injured by contact with this solution. This connection should be pliable and not too long and the glass tip should have a fine, round opening. The pinchcock should be strong enough to pre- vent leakage even when the buret is full of water. Reading the Buret. Practice reading the buret partly filled with water until you can read its level accurately to a fiftieth of a cubic centimeter by the use of one of the devices described on page 243. Determine the minimum length of time which must be allowed for drainage by filling with water to the zero point and allowing the water to flow rapidly from the delivery tube until its level reaches one of the lowest graduations, and noting the changes in level at intervals of one minute from the time of closing the pinchcock. Calibration of the Buret. Weigh accurately to 0.01 gm. a dry 35 cc. weighing bottle or a small beaker with a watch-glass cover. Fill the buret with distilled water whose temperature does not differ by more than 1 from eitheT 15 or 20, depending upon whether the normal temperature of the laboratory corresponds more nearly to 15 or 20. Raise the delivery tube of the buret until nearly horizontal and while still holding in this position open the pinchcock until the air-bubble, which is sometimes present, has been driven out then lower the delivery tube and again open the pinchcock until the lowest point of the meniscus corresponds exactly with the zero point of the buret. Place the delivery tube of the buret inside the weighing bottle, open the pinchcock, and allow 5 cc. of water to pass thru it. Close the bottle and weigh as before, then read and record the exact position of the water in the buret. Continue to remove and weigh 5 cc. portions of the water until 25 cc. have been removed. Empty the water from the bottle, dry and again weigh, and then calibrate the remaining 25 cc. portion of the buret. Prepare a table, of which one column represents the weights of water delivered between the zero point and the ten other points at which readings were made; a second column, the corresponding MEASUREMENT IN VOLUMETRIC DETERMINATIONS 249 readings; and a third column, the figures in column one diminished by those in column two. The figures in the third column repre- sent the corrections to be added or subtracted from the apparent readings. If any of these errors amounts to as much as 0.05 cc. calibrate the buret in the neighborhood of the point giving this error at intervals of 1 cc. Calibration of Pipets. Weigh to 0.01 gm. a clean and dry weighing bottle of about 30 cc. capacity. Suck up pure water whose temperature is either 15 or 20 into the 25 cc. pipet until the level of the liquid is above the mark on the stem. Close the upper end of the pipet with your finger, which should be perfectly dry, and then by gently releasing the pressure allow water to flow out until the lowest point on the curve of the meniscus corre- sponds to the mark on the pipet. Place the nozzle of the pipet in contact with the inner surface of the weighing bottle and allow the water to flow into it and to drain for 20 seconds. Close the weighing bottle and weigh to 0.01 gm. Calibrate the 10 cc. pipet in the same manner. Calibration of Flasks. Clean a 100 cc. and a 250 cc. flask and rinse with distilled water. Insert a long piece of glass tubing which is attached to a foot bellows, or other device for producing a blast of air, into the 250 cc. flask, hold the latter in an inclined position with the neck down and slowly heat the body of the flask by means of a smoky flame rotating the flask about its axis until drops of moisture can no longer be recognized in the interior of the flask. Allow it to cool, clean the outside surface, and weigh accurately. Fill the flask with water at the standard temperature until the lowest point on the meniscus corresponds to the mark on the neck of the flask. Place on a balance designed to carry a load of at least 500 gm. and weigh to 0.01 gm. Subtract the weight of the flask from the weight last obtained to find the capacity of the flask. % Calibrate the 100 cc. flask in a similar manner. 250 QUANTITATIVE CHEMICAL ANALYSIS III. QUESTIONS AND PROBLEMS. SERIES 17 1. How many absolute metric units are there in the (20) unit of volume used in the calibrations made, assuming that the specific gravity of water at 20 is 0.99823, the specific gravity of brass is 8.3 and that one liter of air weighs 1.2 gm.? Ans. 1.0028. 2. What weight of water would you use if you desired to calibrate a liter flask to represent an absolute metric unit, but found it necessary to do the work at a temperature of 20 and under ordinary atmospheric conditions? 3. A solution which has been standardized at a temperature of 15 by the use of a buret which was also calibrated for this temperature was found to contain 0.02 gm. of hydrochloric acid per cc.; if some of this solution is meas- ured out of the same buret at a temperature of 10, what weight of hydrochloric acid is present in each cc. as measured out? 4. In preparing a one-tenth normal solution of silver nitrate (which should contain 0.010788 gm. of Agper cc.) 5.7 gm. of silver was weighed out, dissolved and diluted to 500 cc. in a graduated flask. The solution in this flask 'was emptied into a bottle, which had not been dried and which contained 0.5 cc. of water adhering to its sides, and further 0.4 cc. of the silver solution was left adhering to the flask. If 28.36 cc. of water was added to the bottle and the mixture shaken, what relation would the resulting mixture bear to one- tenth normal strength? Ans. 0.99916. 5. The volume of water which remains adhering to a 500 cc. flask is 0.4 cc., how large a volume of a solution which is to be measured in it should be added to the flask for the purpose f rinsing it out so that the concentration of the original solution shall not be changed by more than one-hundredth of one per cent? Ans. 2.8 cc. CHAPTER XXXVII SYSTEMS USED IN THE PREPARATION OF STANDARD SOLUTIONS The Unitary System. The general expression by means of which the result of a volumetric determination is calculated is : Vol. of standard solution . . - .^ irvrk , . , ^r- 7 : = X / X 100 = percentage desired, Wt. of sample used in which / is the weight of substance being determined, which re- acts with one cubic centimeter of the standard solution used. It is clearly advantageous to use a standard solution of such a concen- tration that / is an integer. If, for example, a solution of sodium chloride is being employed for the determination of silver, it is desirable to make / = 0.01, and if so each cubic centimeter of sodium chloride solution must contain Mol.Wt.ofNaCl At.Wt.ofAg ' r O- 00542 ^' Even when the process concerned is a complicated one, that is, involves the use of a series of reactions, the standard solution used for the final titration can be made to conform to this system, which can be conveniently designated as the " unitary system." If, further, the weight of sample used for the analysis is exactly one hundred times as great as the value of 1 cc., every cubic centi- meter used for the determination represents 1 per cent of the substance being determined, and the percentage present corre- sponds to the number of cubic centimeters used in making the determination. If, for instance, 1 gm. of alloy is weighed out for the determination of silver and the latter is determined by titrat- ing with a sodium chloride solution containing 0.00542 gm. per 251 252 QUANTITATIVE CHEMICAL ANALYSIS cubic centimeter the percentage of silver in the alloy corresponds to the number of cubic centimeters used. So long as standard solutions are to be used for the determina- tion of only one substance the unitary system is the most con- venient one to employ, but it is often desirable to use such solution for the determination of a variety of substances, and in such in- stances the necessary calculations possess the desired simplicity for only one of the substances concerned. If, for example, the solution used for the determination of silver is also used for the determination of mercury by means of the reaction Hg 2 (N0 3 )2 + 2 NaCl -* Hg 2 Cl 2 + 2 NaN0 3 the value of / becomes It becomes necessary therefore, when this system is used, to pre- pare a separate solution for every substance determined; if a very large number of determinations of these substances are to be made this may be a desirable thing to do, but frequently the extra labor involved in preparing and using the several different solutions more than offsets the gain in making the calculations. General Features of the Normal System. When the standard solution is to be employed only occasionally, and for the determi- nation of a variety of substances, it is preferable to make use of the so-called " normal system." The essential idea upon which this system is based is to use such concentrations that equal vol- umes contain equivalent amounts, of the different reagents and therefore that a mixture composed of equal volumes of any two such solutions which react with each other will not contain an excess of either reagent. In order to prepare such a series of so- lutions it is necessary that the standard volume, usually the liter, should contain amounts of the active reagents which bear a simple relation to the molecular weights of the compound concerned. The exact value of this relation may be conveniently estimated by comparing the chemical activity of the molecule with that of THE PREPARATION OF STANDARD SOLUTIONS 253 the hydrogen atom as a unit or standard. A normal solution is then denned as one which contains in a liter an amount of the active reagent chemically equivalent to 1.008 gm. of hydrogen. Thus a normal solution of any acid, which contains a single replace- able hydrogen atom, and which is used in a reaction involving simple neutralization, must contain as many grams of that acid as there are units in its molecular weight. A normal solution of any base must be equivalent to a normal solution of any acid; and hence, if the base contains a single hydroxyl group, the liter should contain an amount corresponding to its molecular weight expressed in grams; if it contains two hydroxyl groups it should contain one- half as many grams as there are units in its molecular weight. Where the reagent is used in a reaction involving oxidation, or reduction, or precipitation, exactly the same principle is used. In every case the oxidizing, or reducing, or replacing power of the molecule concerned, as compared with the oxidizing or reducing or replacing power of the hydrogen atom, determines the number by which the molecular weight must be divided to give the normal value. This number will be designated in this book as the " equivalency." Further details as to the method of comput- ing the normal values of different reagents will be discussed as the different processes are described. Normal Values Dependent Upon the Reaction Concerned. It should be especially noted that the normal value of a substance may vary according to the type of reaction in which it is used. Thus the normal value of a solution of oxalic acid is determined by dividing its molecular weight by two, no matter whether used as a neutralizing, a reducing, or a precipitating agent; whereas the normal value of nitrous acid is the entire molecular weight, when used as a neutralizing agent, but is one-half its molecular weight when used as a reducing reagent. Further than this the same reagent may be used in two reactions which belong to the same type and have a different normal value for each. Thus phosphoric acid may be used in reactions in which it acts as a 254 QUANTITATIVE CHEMICAL ANALYSIS monovalent or a divalent acid; in the former case its normal value is the entire molecular weight, in the latter case it is one-half its molecular weight. Advantage of the Normal System. Since a normal solution of any reagent must, according to definition, be chemically equiv- alent to a normal solution of any substance with which it reacts, every cubic centimeter of such a solution must be equivalent to as many grams of that substance as are present in a cubic centi- meter of a normal solution of that substance. In other words the value of 1 cc. of a standard solution, in terms of any substance with which it reacts, is determined by dividing the molecular weight of the substance by one thousand times its equivalency. The general expression for the calculation of the results of a volumetric determination, where a normal solution is used then becomes : Vol. of solution used . . M - , m. f j X -, ,. xx ^ X 100 = per cent of substance, Wt. of sample 1000 X E where M is the molecular weight and E is the equivalency of the compound determined. The advantage of the system is most striking where the process concerned is an indirect one, that is, where the method involves the use of a series of reactions. In such cases the usual stoichio- metric method requires a separate calculation, involving one multiplication and division, for every reaction concerned. By the use of the normal system it is possible from a mere inspection of the reactions concerned, to calculate the value of the solution being used in terms of the substance being determined, by a single division. For example, potassium bitartrate may be determined by dissolving in water, neutralizing and precipitating as calcium tartrate, filtering off the precipitate and converting into calcium carbonate by igniting in an open crucible and titrating the result- ing carbonate with standard hydrochloric acid. The reactions involved are: THE PREPARATION OF STANDARD SOLUTIONS 255 (1) C 4 H 5 K0 6 + KOH -> C 4 H 4 K20 6 + H 2 0, (2) C 4 H 4 K20 6 + CaCl 2 + 4 H 2 - C 4 H 4 Ca0 6 4 H 2 + 2 KC1, (3) 2 C 4 H 4 Ca0 6 4 H 2 + 5 2 - 2 CaC0 3 + 6 C0 2 + 12 H 2 0, (4) CaC0 3 + 2 HC1 - CaCl 2 + H 2 + C0 2 . An inspection of these reactions shows that each molecule of bitartrate yields one of neutral tartrate, one molecule of neutral tartrate yields one of calcium tartrate, one of calcium tartrate yields one of calcium carbonate and one of calcium carbonate is equiv- alent to two of hydrochloric acid. Since the hydrochloric acid contains one replaceable hydrogen atom its equivalency is one, hence the equivalency of the calcium carbonate is two and also the equivalency of potassium bitartrate, when determined by this process, is two. The formula for the calculation of the result of the determination is: Vol. of sol. MoLWt of C 4 H 5 KOe xlOQ=per cent rf Wt. of sample 2 X 1000 Use of Solutions Which Bear a Simple Relation to Normal Strength. Normal solutions are too concentrated to give the best results, and it is customary to prepare solutions which bear a simple relation to normal strength, that is, are either one-half, one-fifth or one-tenth normal. The results obtained by the use of such solutions are correctly calculated by introducing the factors one-half, one-fifth or one-tenth in the formula given above. Even where the solution has not been prepared to bear a simple relation to normal strength this method of calculation may still be employed to advantage. The relation of any solution to normal strength can be calculated by dividing the number of grams of active reagent in 1 cc. by the number of grams present in 1 cc. of normal solution of that reagent; or, it may be determined by dividing the number of grams of any substance with which 1 cc. reacts by the number of grams in 1 cc. of a normal solution of that substance. The resulting factor representing the exact relation of the solution to normal strength is then used in the above formula just as the simpler factors one-half, etc. SECTION VII VOLUMETRIC PROCESSES INVOLVING PRECIPI- TATION CHAPTER XXXVIII DETERMINATIONS WHICH DEPEND UPON THE USE OF A STANDARD SOLUTION OF SILVER NITRATE I. THEORY UPON WHICH THE METHODS DEPEND Reactions Between Silver and Halogen Ions. The addition of a solution of silver nitrate to one containing a soluble salt of hydrochloric, or hydrobromic or hydriodic acid yields silver halides, whose solubilities are so small that their dissociation can be considered to be practically complete; further, when these reactions are used in volumetric analysis the concentrations of the soluble silver salt and of the soluble halide are so small, at least in the neighborhood of the true end-point, that their dissociation can be considered to be complete; hence the con- centration of the halogen left unprecipitated in these reactions depends upon the solubility product of the silver halide formed. As all three of these halides are very slightly soluble the reactions concerned in forming them are sufficiently complete to justify using them as the basis of volumetric processes. There is further, in dilute solutions at least, no tendency for the formation of complex ions or the separation of salts of abnormal composition. Determination of End-Points Without an Indicator. When silver chloride first separates as a precipitate it is finely divided and a very minute quantity of it can be recognized; if the solution 256 USE OF A STANDARD SOLUTION OF SILVER NITRATE 257 containing it is shaken vigorously the precipitate coagulates, leav- ing a supernatant liquid which is perfectly bright and clear. Hence if a soluble chloride is titrated with silver nitrate and the mixture well shaken in a stoppered bottle after every addition of silver solution, the point at which the addition of a further quantity of solution fails to produce a further quantity of precipitate can be recognized. Under certain conditions this method of determining the end-point admits of a very high degree of accuracy and is widely used in determining the fineness of silver bullion. As it is a somewhat tedious method and demands skill and experience a less accurate but more convenient method, which depends upon the use of an indicator, is usually employed when the less valuable halogen is determined by the use of this reaction. Determination of End-Points With a Chromate Indicator. The neutral chromate of silver has an intense red color, and altho its solubility is small, it is decidedly greater than that of the silver halides. These facts suggest the possibility of using a solution of a neutral chromate as an indicator in the titration of the halo- gens with a silver salt. The series of reactions concerned is represented by (1) Na + Ci + Ag + N0 3 -> AgCl + Na + N~O 3 , (2) 2Na + Cr6 4 + 2Ag + 2 N0 3 -> Ag 2 Cr0 4 + 2Na + 2NO 3 , (3) Ag 2 O0 4 + 2 N + a + 2 Cl -> 2 AgCl + 2 Na + CrO 4 . The process evidently corresponds to the first of the two general cases discussed in Chapter XXV. The changes which take place during the progress of the titration can be readily followed by means of some simple calculations. When a very dilute solution of silver nitrate is slowly added to a solution containing both sodium chloride and a soluble chromate a very slight amount of silver solution is sufficient to produce a precipitate of silver chloride, that is, as soon as the concentration of the silver ion exceeds the quotient obtained by dividing the 258 QUANTITATIVE CHEMICAL ANALYSIS solubility product of silver chloride, which has the value 1.96 X 10~ 10 (see page 116), by the concentration of the chloride ion present. As further quantities of silver nitrate solution are added silver chloride continues to separate, the value of (Cl) must therefore continue to decrease and since (Ag) X (Cl) must always equal 1.96 X 10~ 10 the value of (Ag) must continue to increase. When the silver added is just equivalent to the chlorine present (Ag) and (Cl) must both have the value 1.40 X 10~ 5 , but the addition of still further quantities of silver nitrate solution continuously reduces (Cl) below and increases (Ag) above this value. A point will finally be reached at which (Ag) 2 X (Cr0 4 ) exceeds the solubility product of silver chromate, which will be indicated by the red color which the silver chromate imparts to the mix- ture. The solubility of silver chromate is 0.025 gm. per liter and the concentration of the CrO 4 ion in water saturated with Ag 2 Cr0 4 is therefore 0.025 -f- 332 or 7.5 X 10~ 5 , but since one molecule of silver chromate yields two silver ions the concentration of the Ag ion in such a solution is 2 X 7.5 X 10~ 5 . Hence the solubility product of silver chromate is (7.5 X 10~ 5 ) X (15 X 10~ 5 ) 2 or 1.7 X 10~ 12 , and the concentration of Ag ion at which silver chromate will begin to separate must equal the square root of the quotient obtained by dividing 1.7 X 10~ 12 by (CrOO- Evidently the concentration of Ag ion at which silver chro- mate will begin to separate is determined by the ratio of (Cr0 4 ) to (Cl) 2 in a solution which is saturated with both silver chloride and silver chromate. This ratio can be calculated as follows: + - + H 40 v (Ag)(Cl) = (1.40 X 10- 5 ) 2 , or (Ag) 2 = - U (Ag) 2 (Cr0 4 ) = 1.70 X 10- 12 , or (Ag) 2 (Cl) 2 1.70 X IP" 12 (CrOO USE OF A STANDARD SOLUTION OF SILVER NITRATE 259 + Since both equations concern the same solution (Ag) has the same value for both equations and hence (i.4o x io- 5 ) 4 + (ci) 2 = i.7o x io- 12 ^ (Cr"6 4 ), or (Cr6 4 ) : (Cl) 2 : : 1.70 X 10~ 12 : 3.84 X 10~ 20 , and (Cr6 4 ) : (Cl) 2 : : 4.4 X IO 7 : 1. In titrating a soluble chloride with silver nitrate the true end- point is that at which exactly one equivalent of silver has been added. At this point both (Cl) and (Ag) must have the value 1.40 X 10~ 5 . The value of (Cr0 4 ), which must be present in order to cause Ag 2 Cr04 to separate as soon as sufficient silver has been added to reduce (Cl) to 1.40 X 10~ 5 , is evidently 4.4 X IO 7 X (1.40 X IO- 5 ) 2 , or 0.86 X 10~ 2 . The amount of soluble chromate which must be added to give (Cr0 4 ) this value is large; if K 2 Cr04 + is used and it is assumed that all of the salt is dissociated into (K) and (Cr0 4 ), each 100 cc. of solution would have to contain 0.17 gm. This concentration is sufficient to impart a deep yellow color to the solution and increases to some extent the difficulty of recognizing small amounts of Ag 2 Cr0 4 . Reducing (Cr0 4 ), however, produces a much smaller reduction in the corresponding value of (Cl) . If, for example, (CrO 4 ) is given the value 0.86 X 10~ 3 Cl becomes 0.45 X 10~ 5 , that is, reducing (Cr6 4 ) one-tenth reduces (Cl) only one-third. Furthermore, the total volume of standard solution needed to change (Cl) from 1.4 X 10~ 5 to 0.45 X 10~ 5 is very small; it can be calculated to be about one drop of a one-tenth normal solution when the total volume of the solution is 100 cc. It should also be noted that a certain minimum amount of Ag 2 Cr0 4 must be formed before it can be recognized with cer- tainty. This minimum depends upon the total volume of the 260 QUANTITATIVE CHEMICAL ANALYSIS mixture, the amount of AgCl and the extent to which it is co- agulated, and the ability of the analyst to recognize slight color changes. This discussion indicates that altho a relatively large amount of indicator should be used in the titration, moderately large variations in this amount produce a comparatively slight effect upon the final result. It is also evident that a personal factor is involved in the titration and it is desirable to eliminate this as far as possible by standardizing the silver solution with a known weight of a pure chloride and making all determinations under exactly the same conditions as were adopted in the standardization. Effect of Acids Upon the Titration. Altho moderate concen- trations of even largely dissociated acids do not affect reaction (1) appreciably very slight concentrations affect reaction (2) to such an extent as to make it impossible to determine the true end- point with even approximate accuracy. This can be explained by considering the reactions which take place when silver chro- mate is treated with nitric acid, namely, (4) Ag 2 Cr0 4 + H + N0 3 -> HCrO 4 + 2 Ag + NO 3 , (5) 2 HCr0 4 - Cr 2 O 7 + H 2 0. Both of these reactions have been studied quantitatively.* The equilibrium constant for (4), that is, (HCr0 4 ) -f- (H) (Cr0 4 ) has the value 1.2 X 10 6 and the equilibrium constant for (5), that is, (Cr 2 7 ) + (HCr0 4 ) 2 has the value 74. The combined effect of these reactions is to decrease (CrO 4 ) by an amount which nearly equals the total amount of hydrogen ion present. As the solu- bility product of Ag 2 Cr 2 7 has the value 2 X 10~ 7 there is but little probability that this salt will separate unless both (H) and + (Ag) in addition to (Cr0 4 ) are large. Still another effect results from the fact that Cr 2 7 ions impart a red instead of a yellow color * Sherrill, Jour, of Am. Chem. Soc., 29, 1641 (1907). * USE OF A STANDARD SOLUTION OF SILVER NITRATE 261 to the solution and materially increase the difficulty of recog- nizing small amounts of Ag 2 Cr04. The presence of small concentrations of hydroxyl ions is not objectionable provided the solubility product of silver hydroxide is not exceeded. If the solution is made neutral toward such an indicator as litmus or rosolic acid no difficulty from either H or HO ions will be experienced. Reactions Between a Silver Salt and a Cyanide. When a silver salt is first added to a solution of a soluble cyanide a com- plex ion is formed; the process is represented by (6) A + g + N0 3 + 2K + 2CN-2K + Ag(CN) 2 + N0 3 . The value of the equilibrium constant for this reaction, that is, Ag(CN) 2 -f- (Ag) (CN) 2 is 1 X 10 21 , hence the amount of silver left in the form of a simple ion is extraordinarily small. As the solubility product of KAg(CN) 2 is large no precipitate forms nor is there any other indication of the progress of the re- action. The solubility product of the salt AgAg(CN) 2 has the value 2.25 X 10~ 12 and as soon as sufficient silver has been added to complete reaction (6) a slight further addition brings about the reaction (7) K + Ag(CN) 2 + A + g + N~0 3 -* AgAg(CN) 2 + NO 3 + K. Determination of End-Point in Titration of Cyanides. When a soluble cyanide is titrated with a silver salt the point at which reaction (6) has been completed and (7) begins to take place is shown by the appearance of a white precipitate, that is, AgAg(CN) 2 . Altho the solubility product of this salt is small it has the property of coagulating almost at once and small amounts of it are not readily recognized. Silver iodide is less soluble and more difficult to coagulate than silver cyanide and when freshly precipitated an extremely small amount of it can be easily recognized. If a solution of silver nitrate is added to a solution containing both cyanides and iodides 262 QUANTITATIVE CHEMICAL ANALYSIS silver iodide will not separate as long as (CN) has an appreciable value, since the equilibrium constant for reaction (6) is 1 X 10 21 whereas the solubility product of silver iodide has the value 1 X 10~ 16 ; that is, unless the concentration of the iodide ion is very large. When the titration has been carried to the point at which (CN) is extremely small (Ag) begins to increase very rapidly and soon attains a value sufficient to cause either Agl or AgAg(CN) 2 to separate. As the solubility product of Agl is 1 X 10~ 16 and that of AgAg(CN) 2 is 2.25 X 10~ 12 the latter precipitate should not separate as long as a reasonably large concentration of soluble iodide is present. Experience shows that there is a very slight tendency for the separation of some silver cyanide with the iodide, but this tendency is entirely suppressed by the addition of a small amount of ammonium hydroxide. This is one of the most easily recognized and accurately denned end-points known. Method of Preparing a Standard Silver Solution. Silver which is 999.5 fine can be obtained from dealers and an accurately stand- ardized solution of silver nitrate can be prepared by weighing out the proper amount of metal, dissolving in nitric acid without loss and diluting accurately to the calculated volume. If the solution is to be used with the chromate indicator the excess of nitric acid used must be completely expelled or accurately neutralized. Com- plete expulsion cannot be assured unless the solution is evaporated to dryness and the residual salt heated to about 198, that is, to the fusion point of the salt. As silver nitrate begins to decom- pose slightly above this temperature it must be heated with great care. II. PREPARATION AND STANDARDIZATION OF A ONE-TENTH NORMAL SOLUTION OF SILVER NITRATE Preparation of Solution. Weigh out accurately from 5.4 to 5.8 gm. of pure metallic silver, place in a casserole or porcelain dish, cover with a watch glass, and add 20 cc. of dilute nitric acid. If action does not begin to take place after a few minutes, or if it USE OF A STANDARD SOLUTION OF SILVER NITRATE 263 becomes too slow, warm gently or add a small amount of strong acid. When the metal is dissolved rinse off the under side of the watch glass and set it aside, then place on the steam or sand bath and evaporate the solution to complete dryness. If the sand bath is used the mixture must be stirred during the later stages of the evaporation to avoid losses from spattering. Finally raise the temperature to the point at which the nitrate just fuses, noting that since the solubility curve terminates in the fusion curve and the molten nitrate forms a nearly colorless liquid this transition may escape recognition. The complete absence of white fumes when air is blown over the hot dish is sufficient evidence of the complete removal of nitric acid. Allow the dish to cool, dissolve the salt in a little water and transfer the solution to a 500 cc. graduated flask, using the rinsings of the dish to dilute to exactly 500 cc. Place a cork in the flask and invert several times or until the mixture is homogeneous, then transfer to a clean glass-stoppered bottle, which has been allowed to drain for about five minutes. Calculate the volume to which the silver weighed out should be diluted to make the residual solution exactly one-tenth normal, that is, to make 1 cc. contain 0.010788 gm. of silver, and add to the bottle from a buret the necessary amount of water, then shake thoroughly. Test the solution with a piece of blue litmus paper for acidity; if it gives a perceptible reaction it must be neutralized by cautiously adding very dilute sodium hydroxide and the small amount of insoluble precipitate formed filtered off. Standardization. Weigh out from 0.23 to 0.28 gm. of pure recently dried sodium chloride into a 200 cc. Erlenmeyer flask, add 35 cc. of water and one of a 5 per cent solution of pure potas- sium chromate. Rinse out a clean 50 cc. buret with 10 cc. of the silver solution and discard the rinsings, then fill to the zero mark. Add the silver solution to the salt solution somewhat rapidly until the red precipitate which forms temporarily disappears 264 QUANTITATIVE CHEMICAL ANALYSIS slowly, then add it more slowly until the mixture acquires a faint but permanent reddish tinge. If shaken vigorously the red chromate of silver may separate with the silver chloride instead of remaining suspended. Calculate the weight of sodium chloride found to be equivalent to 1 cc. of the silver solution and divide by the weight of sodium chloride in 1 cc. of a normal solution of sodium chloride to obtain the normality factor. III. DETERMINATION OP CHLORINE IN KAINITE Preliminary Statements. The mineral kainite is found in the Stassfurt salt deposits, and is one of the important sources of potassium salts. It is sometimes rep esented by the formula KC1 MgS04 6 H 2 0, but it rarely corresponds exactly with this, and furthermore is usually associated with sodium chloride and other salts. Large amounts of it are ground and used directly as a fertilizer. The Analysis. Weigh out from 0.5 to 0.8 gm. of the sample into a 200 cc. Erlenmeyer flask, add 50 cc. of water and titrate with the silver solution exactly as in the standardization. Calcu- late and report the percentage of chlorine present by making the proper substitutions in the general formula. IV. DETERMINATION OF CHLORINE IN TAP WATER Preliminary Statements. The percentage of chlorine in well or river water varies greatly and its determination often yields results which are of much significance in deciding whether a sample is suitable for domestic use, for irrigation or for the production of steam. Usually the amount present is relatively small and it is desirable to measure out from 200 to 500 cc. for the determina- tion. The volume of silver solution required to produce a recog- nizable amount of silver chromate is much larger than in the previous titrations; it can be ascertained by determining the volume which must be added to an equal volume of distilled water, USE OF A STANDARD SOLUTION OF SILVER NITRATE 265 to which some white precipitate such as zinc oxide or calcium carbonate has been added, to yield a mixture which after titration shows the same color change as the sample. The white precipi- tate is added to produce an effect similar to that produced by the silver chloride in the sample. The Analysis. Test the sample for alkalinity by means of a piece of red litmus paper. Measure out exactly 250 cc. of the sample into a 400 cc. Erlenmeyer flask and if necessary neutralize by careful addition of very dilute nitric acid. Next add 1 cc. of the chromate indicator and titrate with the silver solution until a recognizable amount of silver chromate is produced, and set the flask aside. Measure out 250 cc. of distilled water, add 0.2 gm. of zinc oxide or calcium carbonate, and titrate this mixture with the silver solution until it shows a color exactly equal to that of the sample in the flask set aside. Subtract the volume used in titrating the distilled water from that used in titrating the sample and calculate the weight of chlorine corresponding to this volume of silver solution. Report results in terms of grams of chlorine per liter of water. V. DETERMINATION OF POTASSIUM CYANIDE IN COM- MERCIAL "CYANIDE" Preliminary Statements. The commercial " cyanide " which is so largely used for the extraction of gold and silver from their ores consists of a mixture of sodium and potassium cyanides together with small amounts of carbonates, chlorides, ammonium salts and hygroscopic water. As sodium and potassium cyanide are about equally efficient solvents for the treatment of gold and silver ores it is customary in the evaluation of such cyanides to determine the total cyanogen and to calculate the corresponding amount of potassium cyanide. As the cyanide is extremely hygroscopic it is somewhat difficult to secure an average repre- sentative portion of a large sample, unless a large amount is taken for the analysis dissolved in water and a fractional part of the 266 QUANTITATIVE CHEMICAL ANALYSIS solution used for the analysis. Great care should be exercised in handling the sample as it is extremely poisonous. The Analysis. Crush several pounds of the original sample until the particles do not exceed grains of wheat in size, place at once in a glass-stoppered bottle and rotate and shake the latter until thoroughly mixed. Add about 5 gm. of the sample to a weighing bottle and weigh accurately. Transfer the salt to a 250 cc. graduated flask, dissolve in water, dilute to exactly 250 cc. and mix thoroughly. Remove a 25 cc. pipet full of the solution to a 200 cc. Erlenmeyer flask, being very careful to avoid getting any of the solution into the mouth, add 5 cc. of dilute ammonium hydroxide, then 2 cc. of a 5 per cent solution of potassium iodide and finally titrate with the silver solution until a very faint but permanent turbidity, due to the formation of silver iodide, appears. The accuracy of the determination can be increased by holding the flask against a black background while determining the end- point. Calculate the percentage of potassium cyanide present from the volume of silver solution required, noting that E of the general formula has the value one-half. VI. QUESTIONS AND PROBLEMS. SERIES 18 1. What volume of a one-tenth normal solution of silver nitrate would be required to saturate 100 cc. of a solution which contained 0.3 gm. of potassium chromate with silver chromate, assuming that the solubility product of silver chromate is 1.70 X 1Q- 12 ? Ans. 0.01 cc. 2. If a standard solution of silver was used to titrate a solution containing bromine ions, what concentration of potassium chromate should be present in order to cause silver chromate to separate as soon as an equivalent amount of silver nitrate had been added, assuming that the solubility product of silver bromide was 0.49 X 10~ 14 ? Ans. 3.5 X 10 2 , which is impossible. 3. If solid silver nitrate was added to 100 cc. of a solution, which con- tamed 0.2 gm. of potassium chromate and 1.64 gm. of sodium acetate, what weight of silver nitrate would have to be added before silver acetate would begin to separate, assuming that the solubility product of silver acetate was 3.48 X 10-* and that all the salts concerned were completely dissociated? USE OF A STANDARD SOLUTION OF SILVER NITRATE 267 4. The concentration of the chlorine ion in a solution which is saturated with AgCl and which has a volume of 100 cc. is 1 X 10~ 6 ; what volume of a one- tenth normal solution of silver nitrate would it be necessary to add in order to reduce the concentration to 1 X 10" 6 ? Ans. 0.19 cc. 6. Calculate the solubility product of lead iodide, assuming that its solu- bility is 0.44 gm. per liter. 6. A solution of silver nitrate contains exactly 0.015 gm. of AgNO 3 per cc., and 24 cc. of it are required to precipitate the chlorine in 0.5 gm. of a sample which contains BaCl 2 2H 2 O; calculate by the general formula the percentage of this salt present. 7. It is found that 30 cc. of the solution referred to above are needed to react with the cyanide in 0.7 gm. of a sample which contains Ca(CN) 2 ; cal- culate in a like manner the percentage of this salt present. 8. The volume of tenth normal silver solution used in titrating 0.5 gm. of a sample of kainite is 35 cc.; if one drop (0.04 cc.) of this volume is used in producing a recognizable amount of Ag 2 Cr04, what percentage error and what departure from the correct result does it cause? 9. If the results obtained for the determination of potassium cyanide in commercial "cyanide" exceeded one hundred per cent, what explanation might be suggested? CHAPTER XXXIX DETERMINATION OF ZINC BY MEANS OF A SOLUTION OF POTASSIUM FERROCYANIDE I. THEOKY UPON WHICH THE METHOD DEPENDS The Reaction Concerned. When a dilute solution of potas- sium ferrocyanide is slowly added to a solution of a zinc salt a flocculent precipitate of a bluish color separates, but a point is finally reached at which the precipitate becomes pulverulent and pure white. The precipitate finally obtained contains both potassium and zinc, the relative amounts of which may vary according to the conditions under which the precipitate separates. It is not known whether a double ferrocyanide of zinc and potas- sium is formed or whether potassium ferrocyanide is adsorbed by the zinc ferrocyanide which first separates. In devising a method for the determination of zinc based upon this reaction it is necessary to adopt certain standard conditions, and a preliminary study of the manner in which varying condi- tions affect the reaction is a necessary prerequisite to the intelli- gent use of the reaction. Under the conditions which are here adopted the reaction is represented with approximate accuracy by (1) 2 K 4 Fe(CN) 6 + 3 ZnCl 2 -> K 2 Zn3[Fe(CN) 6 ]2 + 6 KC1. Determination of the End-Point. When a soluble ferrocya- nide is added to an iron salt a deep blue, or when added to a salt of copper^ cobalt or uranyl a deep red-brown, precipitate sepa- rates. It is possible to recognize a smaller amount of a soluble ferrocyanide by means of a uranyl salt than of the other salts 268 DETERMINATION OF ZINC 269 mentioned, and these salts form the best indicators for this titra- tion. The reaction with a uranyl salt is probably represented by (2) 2 (U0 2 ) (C 2 H 3 2 )2 + K 4 Fe(CN) 6 -> (U0 2 ) 2 Fe(CN) 6 + 4K(C 2 H 3 2 ). If a solution of potassium ferrocyanide is added to one which con- tains approximately equivalent concentrations of salts of both zinc and uranyl both reactions (1) and (2) can be shown to take place, and further, if a solution containing zinc and potassium chlorides is added to a solution which contains suspended uranyl ferro- cyanide the latter is not affected. This indicates that the factor which determines the completeness of the reaction (3) 2 (U0 2 ) 2 Fe(CN) 6 + 3 ZnCl 2 + 2 KC1 - Zn-jK 2 [Fe(CN) 6 ] 2 + 4 (U0 2 )C1 2 has a comparatively small value or that the velocity is small. On the other hand, reaction (3) does not proceed in the reverse direc- tion, at least when the time allowed is short, and a solution of a uranyl salt can be used to test a solution which is being titrated, for potassium ferrocyanide, since the addition of a uranyl salt will not produce a precipitate of uranyl ferrocyanide unless an excess of potassium ferrocyanide is present. In using a uranyl salt as an indicator, however, it is necessary to remove portions of the solution from time to time during the progress of the titration and bring it into contact with a drop of the indicator solution. Since it may be necessary to make a large number of these tests before the true end-point is reached, and since that portion which is removed cannot be returned to the main solution without pro- ducing a permanent precipitate of uranyl ferrocyanide the total amount of zinc taken out may represent a rather large error. This error is small if the analyst has an approximate idea of the total amount of zinc present and can safely add sufficient ferro- cyanide to precipitate most of the zinc before beginning to test 270 QUANTITATIVE CHEMICAL ANALYSIS the solution. When the amount present is entirely unknown it becomes necessary to divide the solution into a number of frac- tional parts and use one of these for an approximate determina- tion, that is, to titrate by the addition of 1 or 2 cc. of the standard solution at a time; a second portion is then titrated to within 1 or 2 cc. of the required amount at once and completed by the addition of 0.1 cc. at a time. This method of determining an end-point which involves the use of an " outside" indicator is necessarily tedious but is the best method known for this titration. It is found that from 0.5 to 0.7 of the ferrocyanide solution usually employed must be added to 200 cc. of water before a clearly recognizable test is produced with the indicator. If all titrations are made with the same volume of solution the error from this source is constant, and if all the solutions titrated contain the same amount of zinc the error bears the same relation to the total ^amount of zinc represented. Suppose, for example, the ferro- cyanide solution is standardized, by titrating a solution which con- tains 0.150 gm. of zinc and has a volume of 200 cc., and that 30 cc. are required to react with the zinc. The total volume of solution required would be 30.5 cc. and the apparent value of each cubic centimeter 150 -- 30.5, or 0.004918. If now this solution is used to titrate a zinc solution which has a volume of 200 cc. and contains 0.05 gm. a volume of 10.5 cc. would be required and the calculated amount of zinc would be 10.5 X 0.004918, or 0.0516 gm. That is, an error of 1.6 mg. results, which would have been avoided if 0.5 cc. had been subtracted from the vol- umes of ferrocyanide solution used in the two titrations. Effect of Varying Temperature Upon the Process. In the experiments, the results of which are recorded below, a zinc solu- tion containing 0.005 gm. of zinc per cc. was titrated with a ferro- cyanide solution containing 21.6 gm. of K 4 Fe(CN) 6 3 H 2 O per liter at varying temperatures. The results show that altho the ratio between the volume of zinc solution used, and the volume of ferrocyanide solution needed DETERMINATION OF ZINC 271 ZnCl 2 sol. (NH 4 )Cl HC1 (oonc.) H,O Temp. Vol. of K 4 Fe(CN) 8 sol. cc. gm. CO. cc. Degrees cc. 30 5 5 140 20 25.5 30 5 5 140 50-45 29.85 30 5 5 140 80-75 29.85 30 5 5 140 100-95 30.02 to react with it, decreases when the temperature is increased from 20 to 100 it is constant between 45 and 80. In the practical use of this method it is very desirable to adopt among other standard conditions, a temperature at which the ratio is as nearly constant as possible, since it is not always convenient to maintain a particular temperature thruout an entire titration. It should also be noted that at 20 it is much more difficult to recognize the true end-point than at any of the higher temperatures. A tem- perature of 80 can be advantageously adopted- for one of the standard conditions. Effect of Varying Concentrations on the Process. The effect of varying the concentration of the zinc salt, while maintaining the same concentration of hydrochloric acid and ammonium chloride, is shown in the results of the experiments recorded in the following table: ZnClj (NH 4 )C1 HC1 (cone.) H 2 Temp. K 4 Fe(CN), used cc. 30 gm. 1.25 cc. 1.25 cc. 12.5 Degrees 80 cc. 29.5 30 2.50 2.50 55.0 80 29.70 30 3.75 3.75 97.5 80 29.75 30 5.0 5.0 140.0 80 29.80 30 7.50 7.50 225.0 80 30.01 The slight increase in the volume of ferrocyanide solution used with increasing dilution is undoubtedly due to the larger amount of ferrocyanide required to produce a sufficient concentration of 272 QUANTITATIVE CHEMICAL ANALYSIS the latter to yield a recognizable test with the uranyl indicator. There is no reason to believe that the ratio here concerned varies, provided the concentration of the other reagents remains constant. Convenience alone should therefore determine the best volume to use for the titration. Since in the actual application of the method the zinc must usually be separated from other metals and a large volume of solution is necessarily obtained a volume of 200 cc. is a desirable standard to adopt. Effect of the Hydrogen Ion on the Process. In titrating a solution of a zinc salt with a solution of a ferrocyanide the end- point is much more accurately determined when the solution con- tains a small amount of acid than when perfectly neutral. The presence of sufficient acid also assists in bringing about the change from a blue flocculent to a white pulverulent precipitate, which is a desirable feature. Further, when lead is present in the zinc solu- tion the presence of sufficient acid suppresses the formation of insoluble lead ferrocyanide, and makes it possible to titrate zinc in the presence of this element. The effect of varying concentrations of hydrochloric acid on the titration is shown in the following table : ZnCl 2 sol. (NH 4 )C1 HCl (cone.) H 2 Temp. K 4 Fe(CN) 6 used cc. gm. cc. cc. Degrees cc. 30 5 145 80 29.4 30 5 1 144 80 29.8 30 5 5 140 80 29.90 30 5 10 135 80 30.10 30 5 25 120 80 31.50 30 5 50 95 80 32.90 These results show a gradual increase in the volume of ferrocyanide solution required for the same amount of zinc with increasing concentration of acid altho the rate of increase is not large. Both very large and very small amounts of acid greatly increase the DETERMINATION OF ZINC 273 difficulty of obtaining accurate end-points and indicate the de- sirability of adopting for one of the standard conditions 5 cc. of the acid for each 200 cc. of solution. Preparation and Standardization of the Solution. This method is very widely used for the determination of zinc in ores and alloys, and it is found desirable to make 1 cc. of the ferro- cyanide solution used equivalent to 0.005 gm. of zinc, that is ; to prepare it according to the unitary rather than according to the normal system. Under the conditions already adopted as stand- ard, that is, where the temperature at the beginning of the titration is 80, the volume before titration is 200 cc., and where 5 gm. of ammonium chloride and 5 cc. of concentrated hydrochloric acid are present it is found that a solution of potassium ferrocyanide containing 21.6 gm. of the crystallized salt per liter will precipitate 0.005 gm. of zinc per cc. The exact value of the solution should be determined ' by titrating against a known amount of zinc. Either pure metallic zinc or pure zinc oxide, which has been recently ignited to convert any zinc carbonate which it may con- tain into zinc oxide, is used for the standardization. The ferrocyanide solution is not a very stable one and may show an appreciable change in standard even after standing for a week, which necessitates frequent restandardization. An appreciable tendency for the ferrocyanide to change into ferricyanide, which results in less clearly defined end-points, is also recognizable. II. APPLICATION OF THE METHOD TO THE ANALYSIS OF ZINC ORES Preliminary Statements. Most of the important ores of zinc contain that element as sphalerite (ZnS) or smithsonite (ZnCOs), both of which are easilydissolved by concentrated hydrochloric acid; in certain classes of ores it is present as calamine (Zn 2 Si04 H 2 0), which is but slowly or imperfectly decomposed by treatment with acids and such ores must usually be fused with some 274 QUANTITATIVE CHEMICAL ANALYSIS basic substance such as sodium carbonate to render them easily soluble. All classes of zinc ores invariably contain silica or insoluble sil- icates, iron in the form of pyrites, and very often lead, copper, cadmium and manganese, also, as sulfides. As the zinc in such mixtures is frequently intimately associated with the other sul- fides it is usually necessary to decompose these minerals, also, in order to insure complete solution of the zinc, which necessitates treatment with nitric as well as hydrochloric acid. Separation oi Zinc in Simple Ores. When the ore does not contain copper or cadmium, and where the percentage of iron is small as compared with the zinc, the latter can be separated "with a sufficient degree of accuracy for the ferrocyanide titration by the use of ammonium hydroxide and bromine. The separation of zinc from iron by the use of ammonium hydroxide is unsatis- factory, owing to the occlusion of zinc by the ferric hydroxide precipitate, but where the total amount of iron does not exceed 0.1 gm. a double precipitation usually suffices to give a satis- factory separation. Manganese if present in small amounts is usually completely precipitated with the iron as the dioxide, if a moderate excess of bromine water is also added. The excess of bromine thus added to the zinc-containing filtrate must, however, be driven off by evaporation before titration with the ferrocyanide solution, as it readily oxidizes ferrocyanide to ferricyanide. III. OUTLINE OF METHOD FOB THE PREPARATION AND STAND- ARDIZATION OF THE FERROCYANIDE SOLUTION Preparation. Weigh out 21.63 gm. of crystallized potassium ferrocyanide, dissolve in water and dilute to 1000 cc. Titration of a Known Weight of Zinc. Ignite about 2 gm. of pure zinc oxide in a platinum or porcelain crucible for 20 minutes at a good red heat and then allow to cool. Weigh out 0.25 gm. of the ignited oxide into a 400 cc. beaker, add 10 cc. of dilute hydrochloric acid and warm until dissolved. Neutralize the DETERMINATION OF ZINC 275 solution with ammonium hydroxide, add 5 cc. of concentrated hydrochloric acid and then dilute to 200 cc. Heat the solution thus obtained to 80 and add somewhat slowly 38 cc. of the ferro- cyanide solution. Complete the titration by adding the ferro- cyanide solution in quantities of not more than four drops at a time, and after vigorous stirring bringing a drop of the mixture into contact with a drop of a 5 per cent solution of uranyl acetate, which has been previously placed on a white porcelain plate or a sheet of glazed white paper. The drop of solution taken for the test should be mixed thoroughly with the drop of indicator, but the rod should be wiped or rinsed off before it is again placed in the solution which is being titrated. The true end-point represents the point at which a slight but clearly defined brownish tinge can be recognized with certainty. The intensity of the color finally adopted as the true end-point should be carefully noted, and all subsequent titrations should be carried to the same color shade. As the intensity of this color increases on standing, an effort should be made to allow the same time interval to elapse between the first admixture of the two drops and the final decision as to whether the end-point has been reached. Determination of Excess Required for the End-Point. To a second beaker add 10 cc. of dilute hydrochloric acid, sufficient ammonium hydroxide to neutralize it and then 5 cc. of concen- trated hydrochloric acid. Dilute the mixture to 240 cc., heat to 80 and titrate with the ferrocyanide solution as before, noting that the absence of the white potassium-zinc ferrocyanide precip- itate may decrease slightly the excess of ferrocyanide required to produce a color shade as intense as that adopted in the previous titration. Calculation of Value of Ferrocyanide Solution. Subtract the volume of ferrocyanide solution used in this titration from that used in titrating the zinc solution. Calculate the weight of zinc equivalent to the zinc oxide weighed out and divide by the volume (corrected) of ferrocyanide solution used. 276 QUANTITATIVE CHEMICAL ANALYSIS IV. OUTLINE OF METHOD FOR DETERMINATION OF ZINC IN AN ORE WHICH CONTAINS NEITHER COPPER NOR CADMIUM Decomposition. Weigh out 1.5 gm. of the finely ground sample into a 200 cc. beaker, add 10 cc. of concentrated hydro- chloric acid, cover with a watch glass and warm gently until violent action ceases and hydrogen sulfide is no longer given off. Add 5 cc. of dilute nitric acid and again warm to insure complete decomposition of pyrite, which might otherwise retain some zinc, and also to effect complete oxidization of all the iron present. After violent action ceases remove the watch glass and evaporate almost to complete dryness, but avoid a temperature in excess of 100. Separation of the Zinc. Add to the residue 10 cc. of concen- trated hydrochloric acid, slowly heat to the boiling point and then add 50 cc. of water. Heat the solution to the boiling point, add a moderate excess of ammonium hydroxide and then 10 cc. of bromine water and keep near the boiling point for about 5 minutes. Allow the precipitate of iron, manganese and gangue-matter to settle, then filter thru a small filter receiving the filtrate into a 250 cc. graduated flask, allow to drain and wash 4 times with 10 cc. portions of water. Replace the graduated flask by the beaker just emptied and pour over the filter sufficient warm dilute hydro- chloric acid to change all of the ferric hydroxide into ferric chloride, then wash the filter free from iron. Dilute the solution in the beaker to at least 50 cc., heat to boiling and again precipitate with ammonium hydroxide and bromine water; filter and wash as before, receiving the filtrate in the graduated flask previously used. Add sufficient hydrochloric acid to this solution to make it slightly acid. Division of Zinc Solution. Cool the solution in the flask to the temperature of the room and dilute with water until the liquid reaches the mark on the neck of the flask. Place a stopper in the neck of the flask and mix its contents thoroughly by inverting the flask and shaking vigorously several times. Rinse out a 50 cc. DETERMINATION OF ZINC 277 pipet with some of the zinc solution and discard the solution thus used; then measure out two 50 cc. portions of the solution into 400 cc. beakers. Titration of Zinc. Add to each of the 50 cc. portions of zinc solution 5 cc. of concentrated hydrochloric acid and dilute to 200 cc. Heat one of these solutions to 80 and titrate with the ferro- cyanide solution adding 10 cc. before making the first test and then 1 cc. portions successively until an end-point is reached. Heat the second zinc solution to 80 and titrate with the ferrocyanide solution, adding 1 cc. less than the total amount used in the pre- vious titration before making the first test and then T V cc. portions successively until an end-point is reached. Calculate the per- centage of zinc present. V. QUESTIONS AND PROBLEMS. SERIES 19 1. What is the replacing power and the normal value of potassium ferro- cyanide, when used to determine zinc by the reaction given on page 268? 2. In titrating a solution which has a volume of 200 cc. and contains 0.150 gm. of zinc 30 cc. of ferrocyanide solution are required to precipitate the zinc and 0.5 cc. to give an end-point with the solution; if 20.5 cc. are added before any tests are made with the indicator and then a test is made (necessitating the removal of 0.04 cc.) after each successive addition of 1 cc. portions of solu- tion, how large a volume of ferrocyanide solution would actually be used in making the titration? Ans. 30.49 cc. 3. Should the delicacy with which the end-point is recognized be affected by the size of the drop removed for the test, assuming the volume of indicator used is not changed? 4. Explain the action of (NH 4 )HO and (NH 4 )C1 in the separation of iron from zinc. Could any other reagent be substituted (a) for (NH 4 )HO, (b) for (NH 4 )C1? 5. Outline a method for the determination of zinc in an ore which also contains copper and cadmium, SECTION VIII VOLUMETRIC PROCESSES INVOLVING NEUTRAL- IZATION CHAPTER XL GENERAL THEORY OF NEUTRALIZATION PROCESSES The Reactions Concerned. A large number of processes, which depend upon the use of a standard solution of an acid or a base, are included in this group; the most important are based upon reactions which involve simple neutralization. As shown on page 58 the equilibrium constants of such reactions can be calculated by dividing the product of ka, the dissociation constant of the acid, and kb, the dissociation constant of the base, by kw, the dissociation constant of water. Since kw has a fixed value and since either ka or kb can be made as great as one by using a strong acid or base, for the standard solution employed, the equilib- rium constant of such reactions is large in proportion as the dis- sociation constant of the acid or base being titrated is large. A second series of processes of this group is based upon reactions involving the displacement of a weak acid or base from its salts by a strong acid or base. It has been shown on page 60 that the constant for such reactions can be calculated by dividing the dis- sociation constant of the strong acid or base used by the dissocia- tion constant of the weak acid or base of which the salt is formed. The End-Points of Processes Involving Neutralization. The true end-point of a titration in which a standard solution of a base is added to an acid corresponds to the point at which an equivalent 278 GENERAL THEORY OF NEUTRALIZATION PROCESSES 279 amount of the base has been added, that is, the point at which the ratio of the base added to the acid present equals 1. This ratio is less than 1 if an insufficient amount of base has been added, and exceeds 1 if an excess has been added. The con- centration of the hydrogen ion in such mixtures depends upon the value of this ratio, the value of the equilibrium constant and the concentration of the solution. It can be calculated if all of these values are known. Suppose, for example, we titrate 50 cc. of a 0.2 molar solution of an acid, whose dissociation constant is 10~ 2 , with a 0.2 molar solu- tion of a strong base such as potassium hydroxide. The constant for the reaction which takes place has the value 1 X 10~ 2 -*- 10~ 14 = 10 12 . Let us calculate (H+) after 48 cc. of base have been added. The total concentration of base added is 0.2 X If = 0.098, that of the acid added is 0.2 X M = 0.102. Let x represent the fraction of the base which remains free and (1 a;) the fraction which combines with the acid. Then (0.098) x represents the concentration of base left uncombined and 0.098 (1 x) the con- centration of base which combines with the acid; this is also the concentration of the acid which combines with the base and that of the salt formed. Then 0.102 - 0.098 (1 - a;) represents the concentration of the acid left uncombined. The law of mass action requires that (HA) (KOH) K = (KA) (H 2 0). Making the proper substitutions and remembering that the con- centration of water is practically constant, and can be disregarded, we obtain: (0.098 Z) (0.102 - 0.098 + 0.098 x) (10 12 ) = 0.098 - 0.098s, or x 2 + 4.08 X 10- 2 z = 1.02 X 10" 11 - 1.02 X l&~ n x, from which x = 3 X 10- 10 , and 0.098 x = 3 X 10~ u . 280 QUANTITATIVE CHEMICAL ANALYSIS Since the dissociation of the base at this concentration is practi- cally complete 3 X 10~ n also represents (H0~) and hence (H + ) must have the value 10~ 14 ^ 3 X lO" 11 , or 3.3 X 10~ 4 . In a similar manner the value of (H+) after 49, 49.5, 49.7, 49.9, 50, 50.1, 50.3, 50.5 and 51 cc. have been added can be calculated. The results of these calculations are represented graphically in .960 .970 .980 .990 1.00 1.01 Ratio of Base Added to Acid Present 1.02 Fig. 56. Curves Showing Changes in (H) in the Titration of Acids the second of the series of curves of Fig. 56, in which the ordinates represent the common logarithms of (H + ) and the abscissas the ratio of base to acid present in the mixtures. It shows that the change in (H + ) associated with small changes in the value of this ratio is very much greater in the neighborhood of the point at which this ratio has the value one, than at those points at which it is slightly greater or less than one. The curve also shows that when this ratio has the value 1, (H+) has the value 3.16 X 10~ 8 instead of the value 10~ 7 , which it would have if the solution were GENERAL THEORY OF NEUTRALIZATION PROCESSES 281 perfectly neutral. This is due to the fact that the dissociation constant of the acid is less than that of the base and therefore the hydrolysis of the salt formed yields a solution in which (H + ) is less than I X 10~ 7 . If next we calculate a similar series of values for titrations in which acids having dissociation constants of 1, 10~ 4 , 10" 6 , 10~ 8 and 10~ 10 are titrated with a strong base, and plot the results as before, we obtain the series of curves represented in the same figure. They show that the ratio of the change in (H + ) to the change in ratio of base to acid decreases as the dissociation constant of the acid decreases, even in the neighborhood of the point at which the ratio of base to acid is one. When the dissociation constant of the acid is 10~ 10 the curve shows no inflection at this point and the total change in (H + ) resulting from a very large change in the ratio of base to acid is extremely small. The curves also show that the value of (H + ) when this ratio is 1 differs from 10~ 7 in pro- portion as the dissociation constant of the acid is reduced. If the method just used is employed to ascertain the changes in (H0~) which take place when a series of bases are titrated with a strong acid, it will be found that the changes in (H0~) resulting from a change in the ratio of acid to base have a maximum value in the neighborhood of the point at which the acid to base ratio is one, and are large in proportion as the dissociation constant of the base is large; also that the value of (HO~) at the point of which this ratio is one differs from 10~ 7 , hi proportion as the dissociation constant of the base is reduced. The End-Points of Processes Involving Displacement. The value of (H + ) in a mixture obtained by adding a strong acid to a salt of a weak acid depends upon the ratio of the acid added to the salt present, the value of the equilibrium constant and the concentration of the solution; it can be calculated if these values are known. Let us assume that a 0.2 molar solution of hydrochloric acid is added to 50 cc. of a 0.2 molar solution of the potassium salt of an 282 QUANTITATIVE CHEMICAL ANALYSIS acid whose dissociation constant has the value 10~ 10 . Since the dissociation constant of hydrochloric acid can be represented by 1 the constant of the reaction is 1 -f- 10~ 10 , or 10 10 . Let us first calculate (H + ) after 48 cc. of strong acid have been added. The total concentration of this acid is 0.2 X If = 0.098 and that of the potassium salt is 0.2 X |, or 0.102. If x represents the fraction of hydrochloric acid left uncombined, 0.098 x must represent the concentration left uncombined, 0.098 (1 x) the concentration of weak acid formed and 0.102 0.098 (1 x) the concentration of the potassium salt left uncombined. By making the proper substitutions in the expression representing the reaction we obtain (0.098 re) (0.102 - 0.098 + 0.098 x) (10 10 ) = [0.098 (1 - z)] 2 . When this expression is solved for x it is found to have the value 2.5 X lO- 9 and 0.098 x is 2.5 X 1Q- 10 . The total value of (H+) is the sum of that due to the dissociation of the hydrochloric acid, which is 2.5 X 10~ 10 , plus that due to the weak acid liberated. The total concentration of the weak acid liberated is 0.098 (1 x), which can be calculated to yield a concentration of hydrogen ion of 3.2 X 10~ 6 ; hence the total value of (H+) is 3.2 X 10~ 6 . The value of (H+) after 49, 49.5, 49.7, 49.9, 50, 50.1, 50.3, 50.5. and 51 cc. of acid have been added can be calculated in a similar man- ner. The results of these calculations, also of similar calculations in which the dissociation constants of the liberated acids have the values 10~ 8 , 10" 6 and 10~ 4 , are represented in the series of curves of Fig. 57 in which the ordinates represent the logarithms of (H + ) and the Log(H) -2 -3 -4 -5 -6 Tc = ~Jc^ 121 - er* r*^ f 3^* >- = 10 j ^ 1 -ft* rcr 1 s .960 .970 .980 .990 1 00 1.01 1.02 Ratio of Acid Added to Salt Present + Fig. 57. Curves Showing Changes in (H) in the Titration of Salts GENERAL THEORY OF NEUTRALIZATION PROCESSES 283 abscissas the ratio of acid added to the salt present. They show that the rate at which (H + ) changes in the neighborhood of the true end-point, that is, where the ratio is 1, is large where k = 10~ 10 , is quite large where k = 10~ 8 , is very small where k = 10~ 6 , and is scarcely recognizable where k = 10~ 4 ; also, that (H + ) at the true end-point is much greater than 10~ 7 even where k = 10- 10 . Methods Used for the Recognition of End-Points. The end- points of titrations which depend upon reactions involving either neutralization or displacement can be recognized by any device which indicates with sufficient accuracy the changes in (H + ) during the titration. The value of (H + ) can be measured directly by a method which involves the determination of the electromotive force between two hydrogen electrodes, one of which is placed in the solution being titrated, and the other in a solution contain- ing known concentration of hydrogen ion.* Advantage may also be taken of the fact that the rate of change in (H + ) is associated with a change in the conductivity of the mixture, and it is often possible to determine the true end-points by measuring the conductivity of the mixture during the titration. Both methods require the employment of elaborate and costly apparatus and have not been very largely used. The method commonly employed depends upon the use of certain organic reagents, which undergo pronounced color changes when (H + ) changes thru certain definite values. Reactions of the Indicators Used. The indicators used for this class of processes are very weak acids or bases and form salts. The structural formulae assigned to the salts of some of these indicators differ from those of the corresponding free acid or base, that is, the formation of salts is associated with a change in the position of one or more atoms in the molecule, and two "tauto- meric" forms of the indicator must be assumed to exist. For example, the neutral and acidic solutions of the indicator phenol- * Jour, of Am. Chem. Soc., 35 (1913). 284 QUANTITATIVE CHEMICAL ANALYSIS phthalein, which is a very weak dibasic acid,* are colorless, but become deep red upon the addition of a small amount of base. It seems probable that the color of the solution is due to the presence of a divalent ion which contains the group = C 6 H 4 = 0. This group is known to impart to solutions of compounds containing it a red color, and is known as a "chromophore." The free acid on the other hand does not contain this or any other chromophore, and for this reason neutral or acidic solutions of the indicator are colorless. The transformation of a colorless into a colored solu- tion involves two separate processes. The first of these involves an equilibrium expressed by (C 6 H 4 HO-C8H4O 2 -C 6 H 4 HO) ki = (C 6 H 4 HO - C 8 H 5 2 = C 6 H 4 = O) The second involves the ionization of the indicator, which takes place in two stages and depends upon two sets of equilibria, namely : (C 6 H 4 HO-C 8 H50 2 =C 6 H4=0) fe = (C 6 H 4 HO-C 8 H 4 0, = C 6 H 4 = 0) (H) and (C 6 H 4 HO - C 8 H 4 O 2 = C 6 H 4 = 0) h = (C 6 H 4 O - C 8 H 4 O 2 = C 6 H 4 = O) (H) If we multiply the three equations together and simplify the resulting expression we obtain , , , K _ (H) 2 (C 6 H 4 - C 8 H 4 2 = C 6 H 4 = O) (C 6 H 4 HO - C 8 H 4 2 - C 6 H 4 HO) The value of K can be determined experimentally. If we compare the intensity of the color of a solution containing a known con- centration of the indicator and of hydrogen ion, with the intensity of the color of a solution containing the same concentration of indicator in addition to sufficient base to change all of it into the chromophore-containing ion, we can determine the fraction of * Jour, of Am. Chem. Soc., 34, 1128 (1912). GENERAL THEORY OF NEUTRALIZATION PROCESSES 285 indicator transformed into the colored form. If we represent this fraction by x the above expression becomes (H+r* = ' from which the value of K can be calculated. This expression can be used to determine the value of K for any dibasic indicator, whose color is due to the divalent ion only. The corresponding expression for any monobasic acid differs from it only in that (H + ) replaces (H + ) 2 . The value of K is a numerical expression of the most important property* of this class of indi- cators, namely, their tendency to undergo a color change in the presence of a definite concentration of hydrogen ion. It is known as the " indicator constant" and will be referred to frequently in discussing the use of this class of indicators. It has not been shown that all indicators of this class undergo a tautomeric transformation. If there are indicators of this class which do not undergo such changes the color change is due to dissociation alone, and the value of K must then equal the value of the dissociation constant of the indicator. If, however, the value of K is always ascertained by the method outlined, the theory of the cause of the color change is of no significance. The Titration of Acids Using an Acidic Indicator. The gen- eral theory of indicators outlined in Chapter XXXV can be used in discussing these titrations. The factors which determine the completeness of the reactions concerned are the value of the indi- cator constant, and the dissociation constants of the acid and base used. Let us assume that acetic acid (k = 1.8 X 10~ 5 ) is being titrated with potassium hydroxide (k = 1), and that para-nitro-phenol, which is a monobasic acid indicator whose constant has the value 10~ 7 , is used. If we disregard the tautomeric changes which this indicator may undergo the reactions concerned are expressed by * Noyes, Jour, of Am. Chem. Soc., 32, 815 (1910). 286 QUANTITATIVE CHEMICAL ANALYSIS (1) C 2 H 3 0(HO) +KOH - C 2 H 3 0(KO) + H 2 0, (2) C 6 H 4 (N0 2 ) (HO) +KOH -> C 6 H 4 (N0 2 )KO + H 2 0, (3) C 6 H 4 (N0 2 )KO+C 2 H 3 0(HO)-> C 6 H 4 (N0 2 )HO+C 2 H 3 0(KO). Since acidic solutions of the indicator are colorless while basic solu- tions are yellow the appearance of the end-point here depends upon the concentration of the C 6 H 4 N0 2 ion, and the process corres- ponds to the first of the two classes discussed in Chapter XXXV. The value of K for (1) is 1 X 1.8 X 10~ 5 ^ 10~ 14 = 1.8 X 10 9 . The value of K for (2) is 1 X 10~ 7 -J- 10~ 14 = 10 7 . The value of K for (3) is 1.8 X 1Q- 5 -f- 10~ 7 = 1.8 X 10 2 . The values of K for (1) and (2) are sufficiently large, that for (3) is too small, that is, this reaction is sufficiently reversible to make it probable that a recognizable amount of the chromophore-con- taining ion may be formed before all of the acetic acid is neutral- ized. If a more weakly acidic indicator, such as one for which k = 10~ 10 is used, K for (2) would have the value 10 4 and for (3) 1.8 X 10 5 . In this case there is greater danger of an error from the reversibility of (2) than of (3), that is, it might be necessary to use an appreciable excess of the titrating solution to produce a recognizable amount of the chromophore-containing ion. The best indicator which could be used would have a constant of 4.2 X 10- 10 since K for both (2) and (3) would then have the value 4.2 X 10 4 . This discussion makes it clear that in the titration of acids with an acidic indicator the constant of the indicator used must be large, as compared with the dissociation constant of water, but small as compared with the dissociation constant of the acid being titrated; further, if an indicator whose constant has a certain value is used, the probability of obtaining a deferred end-point on the one hand and of a premature end-point on the other is equal. The Titration of Bases with Acidic Indicators. Let us assume that ammonium hydroxide (k = 1.8 X 10~ 5 ) is titrated with hydro- GENERAL THEORY OF NEUTRALIZATION PROCESSES 287 chloric acid (k = 1) and that para-nitro-phenol is again used as the indicator. This titration corresponds to the second of the two cases discussed in Chapter XXXV. The reactions concerned are (4) (NH 4 )HO + C 6 H 4 (N0 2 )HO -> C 6 H 4 (N0 2 ) (NH 4 )0 + H 2 0, (5) (NH 4 )HO + HC1 -> (NH 4 )C1 + H 2 0, (6) C 6 H 4 (N0 2 ) (NH 4 )0 + HC1 -> C 6 H 4 (N0 2 )HO + (NH 4 )C1. The end-point here recognized is that at which the concentration of the chromophore-containing ion changes from a recognizable quantity to one which cannot be recognized with certainty. The value of K for (4) is (10~ 7 ) (1.8XlO- 5 )^-10- 14 , or 1.8 XlO 2 . The value of K for (5) is (1.8 X 10~ 5 ) (1) -^ 10~ 14 , or 1.8 X 10 9 . The value of K for (6) is 1 ^ (10~ 7 ), or 10 7 . The values of K for (5) and (6) are sufficiently large, that for (4) is too small to insure the presence of a recognizable concentration of the chromophore-containing ion up to the point at which all of the base has been neutralized. The best indicator which could be used would have a constant of 2.4 X 10~ 5 , for with such an indicator the value of K for both (4) and (6) would be 4.2 X 10 4 . It is evident that in the titration of bases with acidic indicators the indicator constant should be large in proportion as the dis- sociation constant of the base being titrated is small, but must be small as compared with the dissociation constant of the acid used for the titration; further, if an indicator whose constant has a certain value is used the probability of obtaining a deferred end- point on the one hand and a premature end-point on the other is equal. The Use of Basic Indicators. The indicator constant of a basic indicator could be defined by an expression analogous to that used for acidic indicators, that is, by (HO") (Q-) (ROH) 288 QUANTITATIVE CHEMICAL ANALYSIS in which Q~ represents the chromophore-containing ion. Since in any aqueous solution (H+) (H0~) = 10~ 14 we can substitute 10~ 14 -5- (H + ) for (H0~) and obtain an expression for K in terms of (H + ) and the fraction of indicator transformed. There is no objection to substituting (H + ) for 10~ 14 -f- (H + ) and changing the value of K to correspond with the effect of this substitution, that is to define the indicator constant of basic indicators the same as for acidic indicators. There is further no difficulty in determining the value of this constant in such a manner as to conform to this definition. It is only necessary to use a large excess of acid in- stead of base to completely transform the indicator in the solu- tion used as a standard of comparison in order to obtain x, and from it and the known value of (H+) to calculate K. It should be noted, however, that altho the constant of an acidic indi- cator varies directly with its dissociation constant, that of a basic indicator varies inversely with its dissociation constant, and hence strongly acidic and weakly basic indicators show similar properties. By the use of this general definition it becomes unnecessary to distinguish between acidic and basic indicators, and the rules elaborated in the preceding discussion ,re valid for both classes of indicators. The Sensitiveness of Indicators. In the preceding discus- sion it is shown how the value of the indicator constant K can be calculated after having determined the value of (H + ) at which the color change corresponding to the transformation of a par- ticular fraction (x) of the total amount of indicator present takes place. It might be surmised that the color change referred to is always that at which the concentrations of the two modi- fications of the indicator are the same, since such mixtures should yield what might be called the "neutral color" of the indicator in question. Incidentally it should be pointed out that if this condition is complied with, that is, if the fraction transformed is represented by 0.5, the fraction x -5- (1 x) equals one, and GENERAL THEORY OF NEUTRALIZATION PROCESSES 289 therefore K = (H+) ; that is, the value of the indicator constant must equal the concentration of the hydrogen ion at which the color change representing the transformation of one-half the total amount of indicator present, takes place. It is found, however, that the color changes which many indi- cators undergo when x = 0.5 is less clearly defined than when x has a greater or less value. This is due to the fact that the eye is less sensitive to certain colors than others and is often unable to correctly interpret the composition of mixtures. The colors of some indicators, however, change with varying (H + ) at a fairly uniform rate, and any shade of the series can be adopted as the end-point with about equal advantage. Decided differ- ences are also apparent in the total change in the value of (H + ) within which any easily recognizable color change takes place, that is, the "sensitiveness" of the different indicators varies greatly. In general, two-color indicators, that is, those which change from one distinctive color to another, are less sensitive than one-color indicators, which change from one distinctive color to a colorless form or the reverse. Before an indicator can be used intelligently certain facts regarding it should be ascertained. First, the particular color change which can be recognized most accurately should be decided upon and always used as the correct end-point. Second, the value of (H + ), at which this change takes place, should be deter- mined by noting the effect of adding it to a series of solutions containing varying concentrations of the hydrogen ion. Third, the fraction transformed at the value of (H + ) found should be determined, and finally the value of K calculated. With indi- cators which show a continuous series of color changes, several different shades may be chosen as end-points and hence different values for (H" 1 ") found. Classification of Indicators. The uses of the different indi- cators are shown most advantageously by arranging them in a series with respect to the value of (H+) between which they show 290 QUANTITATIVE CHEMICAL ANALYSIS the most pronounced color changes. At one end of the series will be found the indicator whose constant has the largest per- missible value, and which is peculiarly adapted to the determina- tion of weak bases; at the other end, the one whose constant has the smallest permissible value, and which is peculiarly adapted to the determination of weak acids. Each member of the series can be used for the determination of acids and bases whose dissociation constants vary between certain values with a fair degree of accuracy. Where greater accuracy is demanded it is necessary to make use of different concentrations and adopt different color changes for the same indicator in order to limit still further the range of concentrations of (H + ), which can be easily recognized. A series of five indicators arranged in the order of increasing sensitiveness toward (H+) is given in the following paragraphs. Methyl Orange. This indicator is the sulfonate of dimethyl- aniline-azobenzene; altho the imino group gives it weakly basic properties, its use as an indicator probably depends upon the strongly acidic sulfonic acid group. It is used in the form of a solution which contains 1 gm. per liter of its sodium salt. When the volume of solution being titrated does not exceed 100 cc. one drop of this solution imparts an easily recognizable yellow color, which is not changed by the addition of a base, to the mixture. If sufficient acid is added to make (H + ) equal to 10~ 4 the solution becomes pink. A series of intermediate transition colors begins to appear when (H + ) = 10~ 5 . The most clearly defined color change is obtained when the minimum concentration is used and at least 80 per cent of the indicator is transformed. The value of its constant is 5 X 10~ 4 . This is the most strongly acidic indi- cator in general use. It is especially useful in the titration of very weak bases; the weaker acids, such as carbonic, boric, hydrocyanic, have almost no effect upon it, altho large concen- trations delay somewhat the speed with which it responds to changes in (H + ). GENERAL THEORY OF NEUTRALIZATION PROCESSES 291 Cochineal. This indicator is usually prepared by digesting the dried cochineal insects with ten parts of 50 per cent alcohol and filtering. The resulting tincture owes its color to carminic acid the structural formula of which is not known. With pure water it yields a ruby red color which changes to violet red upon the addition of a base and to yellow upon the addition of an acid. The most decided color change takes place when (H + ) is in the neighborhood of 1 X 10~ 5 . It is therefore slightly more sensitive toward weak acids and less toward weak bases than methyl orange. Para-nitro-phenol. This indicator is used as an aqueous solu- tion containing 4 gm. per liter. One drop is sufficient for titra- tions in which the total volume does not exceed 100 cc. Its constant has the value 1 X 10~ 7 when 20 per cent of it is trans- formed. The change from colorless to greenish-yellow takes place when (H + ) changes from 10~ 5 to 10~ 6 . Rosolic Acid. This is the anhydride of trioxy-triphenyl-car- binol. It is usually employed in the form of an alcoholic solution which contains two-tenths of 1 per cent. One drop of this solu- tion imparts to 100 cc. of water a light yellow color, which is not changed by the addition of acids but becomes violet red when (H + ) is reduced to 10~ 8 . Its constant has the value 10~ 8 when the indicator is 20 per cent transformed. Phenolphthalein. This indicator is prepared by dissolving 2 gm. in a liter of 50 per cent alcohol. One drop is sufficient for 100 cc. of solution. It imparts no color to pure water, but the solution changes to deep red when (H+) is changed from 10~ 8 to 10~ 10 . Its constant has the value 1.7 X 10~ 10 when 20 per cent of it is transformed. CHAPTER XLI APPLICATIONS OF THE METHODS OF ACIDIMETRY AND ALKALIMETRY I. DETERMINATION OF ACIDS AND ACID SALTS Titration of Monobasic Acids. In determining an acid by titrating with a strong base the general principles developed on pages 286 and 287 can be used to ascertain the proper indicator to employ, or that indicator can be chosen from the series which + gives a color change at that value of (H), which the solution should have at the true end-point. This value can be inferred with sufficient accuracy from the data given on the curves of Fig. 56, at least for the concentrations there made use of, but it is some- times advantageous to estimate (H) by calculating to what extent the reaction concerned takes place in the reverse direction. At the true end-point the solution must in every case have the same composition as one obtained by adding the proper amount of the salt formed to pure water, therefore we can calculate the value + of (H) in such solutions from the hydrolysis constant (see page 59) of the salt formed, or we can ascertain this point empirically, that is, by finding which indicator of the series shows a color change when (H) is changed very slightly from the value it has in a solution made by adding the salt to pure water. In titrating hydrochloric acid, for instance, the solution at the true end-point should contain the same concentration of (H) and (HO) as one prepared by adding pure sodium chloride to water, and if the dissociation of both acid and base be considered + complete, both (H) and (HO) must have the value 1 X 10~ 7 . 292 ACIDIMETRY AND ALKALIMETRY 293 It might be inferred that in the titration of all strong acids the indicator rosolic acid, which gives a color change when (H) equals 1 X 10~ 7 , should be used, but satisfactory results can also be obtained with any indicator of the series. The reason is that in titrating any strong acid the addition of a single drop of a solu- tion of the standard alkali in the neighborhood of the true end- point changes (H) thru differences as great as those represented by the two extremes of the indicator series, that is, where the solution used is at least tenth-normal and the volume titrated is not too large. In the titration of the weaker acids greater care must be used in the choice of an indicator, but this does not neces- sarily insure a high degree of accuracy. This depends in large measure upon the sensitiveness of the indicator and still more + upon the rate at which (H) changes during the titration in the neighborhood of the true end-point. Titration of Di- and Tribasic Acids. The theory of the titra- tion of these acids is more complex since they dissociate in stages and each stage of the process is characterized by a definite dis- sociation constant. For example the dissociation of phosphoric acid is represented by (1) (H) (H 2 P0 4 ) -*- (H 3 P0 4 ) = fa = 1 X 10- 2 , (2) (H)(HP0 4 ) -^ (H 2 P0 4 ) = fa = 2 X 10- 7 , (3) (H)(POi) -* (HP0 4 ) = k> = 4 X 10- 13 . When this acid is titrated with a base three different equilibrium constants, whose values depend upon the three dissociation con- + stants, have to be considered. The value of (H) during the titra- tion is determined for the most part by ki up to the point at which one equivalent of base has been added, by fa. up to the point at which two equivalents of base have been added, and by fa up to the point at which three equivalents of base have been added. If a curve similar to those of Fig. 56 is plotted it will be found that 294 QUANTITATIVE CHEMICAL ANALYSIS those portions of it which are in the immediate neighborhood of the points at which exactly one and two equivalents of base have been added are nearly vertical, that is, at these points (H) changes very decidedly with slight changes in the value of the ratio of base + to acid. Experience shows that the value of (H) at the first of these points corresponds approximately to the value at which the color of methyl orange changes; at the second point it corresponds to the value at which the color of phenolphthalein changes. Hence this acid can be determined by using methyl orange and assuming that it is monobasic, or by using phenolphthalein and assuming that it is dibasic. In neither case are the end-points very sharply defined and the method yields approximate results only. The proper conditions for the titration of all di- and tribasic acids can be indicated if the dissociation constants of these acids are known. Dissociation Constants of Acids. The dissociation constants of some of the acids which the chemist is frequently required to determine are given in the table on page 295. Titration of Acid Salts. When an acid salt of a strong base, + such as NaH 2 PO4, is dissolved in water the value of (H) in the resulting solution is determined for the most part by one of the dissociation constants of the acid concerned, in the illustration cited by k% of phosphoric acid. If such solutions are titrated with a base it is often possible to recognize the point at which exactly one equivalent of base has been added, owing to the very great change in the value of (H) at this point. In the solution of NaH 2 P04 the point at which one equivalent of base has been added can be recognized by the use of phenolphthalein, and the process is identical with that part of the titration of phosphoric + acid in which (H) changes from the first to the second of the two points at which it changes abruptly. The method is only appli- cable to the titration of acid salts of strong bases and a limited number of di- and tribasic acids. ACIDIMETRY AND ALKALIMETRY 295 DISSOCIATION CONSTANTS OF ACIDS Name of acid Formula First stage Second stage Acetic H(C 2 H 3 O 2 ) 1 8X1CH 5 Arsenic H 3 AsO 4 5X10~ 3 Arsenious H 3 AsO 3 6X10- 10 Boric H 3 BO 3 7X10- 10 Carbonic . H 2 CO 3 3X10- 7 3X10- 11 Chlorous .... HC1O 4X10~ 8 Chloric. ... HC1O 3 <1 Chromic H 2 CrO 4 <1 6X10~ 7 Citric C 3 H 4 (HO)(COOH) 3 8X10- 4 Formic H(COOH) 2.14X10" 4 Hydrochloric HC1 <1 Hydrocyanic HCN 1 3X10- 9 Hydrobromic HBr <1 Hydriodic HI <1 Hydrosulfurous H 2 S 9X10- 8 ixio- 15 Nitrous HNO 2 5X10- 4 Nitric HNO 3 <1 Oxalic (COOH) 2 3.8X10- 2 5X10-* Perchloric HC1O 4 <1 Phosphoric H 3 PO 4 1 1X10-2 2X10~ 7 Sulfuric H 2 SO 4 <1 3X10- 2 Succinic C 2 H 4 (COOH) 2 6 6X10- 6 Tartaric . C 2 H 2 (HO) 2 (COOH) ;4 9 7XH)- 4 * Most of the data here presented is from the table compiled by Noyes, Jour, of Am. Chem. Soc., 32, 860 (1910). Some values are from Ostwald, Zeit. fur Phys. Chemie, 3, 418 (1889), or from Chandler, Jour, of Am. Chem. Soc., 30, 713 (1908). II. DETERMINATION OF BASES AND BASIC SALTS Titration of Bases. The theory of the titration of bases is analogous to that of the titration of acids, but unfortunately the dissociation constants of bases have not been determined except in a few instances. The dissociation constants of all the alkaline hydroxides are large and at moderate concentrations can be rep- resented approximately by one. The hydroxides of the alkaline earths are but slightly soluble, and readily change into oxides; they are all dibasic and probably dissociate in stages. The hy- droxides and oxides of the remaining metals are so insoluble that 296 QUANTITATIVE CHEMICAL ANALYSIS they have no appreciable effect on the color of a solution of methyl orange. Some of them, such as ZnO, can be determined by the method of back titration, that is, by adding a measured volume of standard acid more than sufficient to react with the base, and titrating the excess of acid used with a standard base. The dissociation constant of ammonium hydroxide has the value 1.8 X 10~ 5 and it can be accurately titrated if methyl orange or cochineal is used. Some of the substituted ammonias, except those of the aromatic group, are still stronger bases. A limited number of alkaloids possess basic properties strong enough to make it possible to titrate them directly with a fair degree of accuracy. Titration of Basic Salts. Many of the basic salts which have been described are mixtures and the composition of many others is not known accurately. Where the formulae of a basic salt is known it can frequently be determined by methods exactly analo- gous to those used for the determination of acid salts. III. DETERMINATION OF SALTS OF WEAK ACIDS AND BASES Titration of Salts of a Weak Acid with a Strong Acid. The data represented by the curves of Fig. 57 show that when salts of acids, whose dissociation constants are not greater than 1 X 10~ 9 , are titrated with a strong acid, both the rate at which + + (H) changes and the absolute value of (H) at the true end-point is such as to make recognition of this end-point, by the use of such an indicator as methyl orange, possible. At the true end-point the solution must have the same composition as one obtained by adding the proper amount of the new salt formed and the acid liberated to pure water. If the dissociation constant of the base equals that of the strong acid added, the salt formed + has only a slight effect upon (H); its value depends almost en- tirely upon the dissociation constant of the liberated acid and its concentration. If, for example, we titrate sodium borate ACIDIMETRY AND ALKALIMETRY 297 with hydrochloric acid, the value of (H) at the true end-point is very nearly equal to that of the boric acid liberated. When the acid of which the salt is composed is di- or tribasic an indicator can be used which will determine the point at which either one, two or three equivalents of the stronger acid have been added. In the titration of sodium carbonate for example the method might be based upon one of two reactions, namely, (1) Na2C0 3 + HCl-*NaHC08 (2) NasCOs +2 HC1 - C0 2 + H 2 + 2 NaCl. If the former method is used the value of (H) at the true end- point would equal that resulting from the dissociation of HCOa at the concentration concerned. If the latter method is used + the value of (H) at the true end-point would equal that resulting from the dissociation of H 2 C03 at the concentration concerned, but since H 2 C03 breaks down into CO 2 and H 2 this concentration is very small. Experience shows that the latter method is much more accurate than the former. Titration of Salts of a Weak Base with a Strong Base. The theory of the titration of salts which represent combinations of very weak bases and strong acids is entirely analogous to that of the processes discussed in the preceding section. They are used for the titration of salts of the aromatic amines and alkaloids. IV. INDIRECT DETERMINATIONS Titrations Which Involve a Previous Separation. A large num- ber of substances which cannot be determined directly by titrat- ing with an acid or base may be transformed into substances which can be so determined. This includes a large number of the metallic elements which form insoluble salts with weak acids. Thus, altho calcium when present as a salt cannot be titrated directly, it can be precipitated from its solutions as a carbonate, filtered and washed, and then titrated like any other salt which 298 QUANTITATIVE CHEMICAL ANALYSIS represents a combination of a weak acid and a strong base. The accuracy of the process depends upon the insolubility of the precipi- tate, upon the completeness with which the precipitating agent, in this case ammonium carbonate, can be washed out, and upon the accuracy of the final titration. Another illustration is found in a method which is largely used for the determination of phosphoric acid when in the form of its salts. It is based upon the fact that this acid is, under proper conditions, completely precipitated by ammonium molybdate as (NH 4 )3P0 4 12 MoOs which compound reacts with a solution of sodium hydroxide as shown by the expression: 2 (NH 4 ) 3 P0 4 12 Mo0 3 + 46 NaHO -> 2 (NH 4 ) 2 HP0 4 + 23 Na 2 Mo0 4 + (NH 4 ) 2 Mo0 4 + 22H 2 0. As this reaction is practically complete and instantaneous we can titrate the MoOs combined with the ammonium phosphate, and the amount of phosphorus present can be calculated from the assumption that every twelve molecules of MoOs found represent one molecule of phosphoric acid originally present. Titrations Which Involve the Use of a Special Reagent to In- crease Dissociation. In a limited number of instances the de- sired transformation can be effected by the use of a reagent which does not itself react with the titrating solution, and in such de- terminations previous separation of the product is not necessary. Thus hydrocyanic acid, whose acidic properties are too weak to admit of a direct titration, can be completely changed into mer- curic cyanide and hydrochloric acid by the addition of mercuric chloride, and the resulting hydrochloric acid can be titrated with accuracy. The process owes its accuracy to the remarkably low dissociation constant of mercuric cyanide. V. QUESTIONS AND PROBLEMS. SERIES 20 1. Calculate (H) and (HO) in solutions made by adding to 100 cc. of water (a) 1 gm. of 80 per cent (C 2 H 3 02)H, (b) 1 cc. of concentrated hydrochloric acid, assuming that both acids obey the dilution law. (See page 54.) ACIDIMETRY AND ALKALIMETRY 299 2. Indicate the probable form of the curves representing the changes in (H) during the titration of H 3 P0 4 , assuming that three equivalents of base are used. 3. Calculate (H) and (HO) at the true end-point when a normal solution of an acid is titrated with a normal solution of a base if the dissociation constant of both acid and base is 1 X 10~ 4 . 4. What indicator would you use in titrating acetic acid with ammonium hydroxide? Why is it preferable to titrate with sodium hydroxide? 6. What is the simplest method of ascertaining experimentally whether sodium benzoate can be titrated with HC1 with accuracy? 6. An indicator which imparts no color to an acid solution gives a par- ticular shade of yellow to a solution in which its concentration is 6 X 10" 6 and (H) equals 0.81 X 10" 9 ; it is found that a layer of this solution 25 cm. thick, which contains the same concentration of indicator, has the same color absorption as one 10 cm. thick, which contains the same concentration of indicator and an excess of base; what is the value of the indicator constant? Ans. 5.4 X 10- 10 . 7. If the indicator constant of cyanin has the value 2 X 10" 9 when con- sidered an acid indicator, what is the corresponding value when considered a basic indicator? Ans. 5 X 10" 6 . 8. Would you think it possible to determine the following acid salts by a direct titration with a base; NaHSO 4 , NaHCO 3 , HCOOKCOO, NaHPO 4 ? 9. Would you think it possible to determine the following salts by titrating with an acid Na(C 2 H 3 O 2 ), (NH 4 ) 2 CO 3 , K 2 SO 3 , Na 3 P0 4 , CaCrO 4 ? 10. If required to determine the percentage of H 3 P0 4 by the method out- lined on page 298, what value would you give to E of the general formula in calculating the result? CHAPTER XLII THE PREPARATION OF STANDARD SOLUTIONS OF ACIDS AND BASES I. FACTORS TO BE CONSIDERED- Choice of the Acid and Base. As noted in Chapter XL it is essential that the acids and bases used for the preparation of standard solutions have large dissociation constants. It is also desirable that they shall be stable compounds, that their action on the glass vessels used to retain them be small, and that they exercise no oxidizing or reducing action on the indicators used. These considerations limit the acids generally used to hydrochloric and sulfuric. For bases the hydroxides of sodium and potassium are most frequently employed, but the hydroxides of ammonium and barium are sometimes used. The Most Desirable Strength. Every titration should re- quire the use of a moderately large volume of the standard solu- tion; hence in titrating substances of low percentage composition either a large amount of sample must be used or the concentration of the solution used must be small. On the other hand, strong solutions give more decisive end-points than weaker solutions and their strength is changed to a less extent relatively by carbon dioxide which may be absorbed from the air. In general it is not desirable to use solutions of acids or bases stronger than one-half, or weaker than one-tenth normal, alt ho special circumstances may make it desirable to vary these limits. Methods of Preparing Solutions. Since the concentration of moderately strong sulfuric acid (preferably about 60 per cent) can be determined with very great accuracy from its specific gravity 300 SOLUTIONS OF ACIDS AND BASES 301 (see Chapter XLIX) a standard solution of this acid can be pre- pared by diluting a weighed amount to the calculated volume. Similarly a standard solution of hydrochloric acid can be pre- pared by passing pure dry hydrochloric acid gas into a flask containing a weighed amount of water, determining the increase in the weight of the flask and diluting the solution to the calcu- lated volume. An indirect method in which a solution of approximately the desired strength is first prepared, its strength accurately deter- mined by an independent process, and then diluted to the calcu- lated volume is often preferable. The exact value of the diluted solution can be determined by a gravimetric process or by titrating against a known weight of some pure substance with which the solution reacts completely. A large number of such substances have been proposed and are -used by different chemists for this purpose. Sodium carbonate can usually be obtained sufficiently pure, except for small amounts of water and bicarbonate; if heated to 300 in a platinum crucible for a few minutes it gives the pure normal carbonate which can be weighed accurately and titrated against solutions of mineral acids using methyl orange as the indicator. Calcium carbonate which has been separated by precipitation is also to be had in a very high degree of purity, and can be used like the sodium compound. Borax (Na 2 B 4 7 10 H 2 0) is readily obtained pure by recrystalli- zation at temperatures below 50 and also gives accurate results in the standardization of acids. Succinic and benzoic acids can also be prepared in a high degree of purity and simple and accurate methods for the standardization of alkaline solutions are based upon their use. 302 QUANTITATIVE CHEMICAL ANALYSIS II. OUTLINE OF METHOD FOR THE PREPARATION OF SEMI- NORMAL ACID AND ALKALI Preparation of Solutions. Weigh out on a rough balance 50 gm. of pure sodium hydroxide, place in a 2500 cc. flask, add 2 liters of distilled water and shake occasionally until the alkali is com- pletely dissolved. Next add about 5 gm. of finely powdered C. P. calcium oxide and allow the mixture to stand for an hour with occasional shaking, or still better allow it to stand over night. Place a Witt filter-plate in a filtering tube and provide with a good thickness of washed asbestos in the customary manner; connect the filter tube with a clean two-liter bottle as shown in Fig. 58 and filter the alkali solution into the bottle. Keep the- bottle stoppered as far as possible. Measure out 100 cc. of concentrated C. P. hydrochloric acid into a clean two-liter bottle, dilute to 2 liters with water which is free from carbon dioxide and mix thoroughly. To deter- mine whether the carbon dioxide is present in Fig. 58. Device objectionable amounts add one drop of phenol- f or Filtering Al- phthalein indicator to 200 cc. of the water in question, and then one drop of the approximately semi-normal alkali solution; if the mixture does not acquire a distinct pink color the amount of carbon dioxide is excessive, and the water must be heated to the boiling point to remove it. Determination of the Volumetric Ratio. Measure out a 25 cc. pipet full of the acid solution into a 200 cc. beaker or Erlenmeyer flask, dilute to 50 cc. and add a drop of methyl orange indicator. Place a piece of white paper under the vessel and then add the alkali solution from a buret until the mixture, after passing thru a series of color shades, finally changes permanently to a clear lemon yellow. The color shade finally obtained should correspond to SOLUTIONS OF ACIDS AND BASES 303 that which results from the addition of one drop of the indicator to 75 cc. of water. Repeat this determination until the results of successive determinations do not differ by more than one part in five hundred. From the average of the results finally accepted, that is, those which are believed to involve no large errors, cal- culate the volumetric ratio of the two solutions by dividing the volume of alkali solution used by the volume of acid solution used. Titration Against Pure Calcium Carbonate. Weigh out 0.8 gin. of pure and recently dried calcium carbonate into a 300 cc. beaker, cover with a watch glass and introduce 50 cc. of the acid solution measured preferably from a pipet. Agitate the contents of the beaker until the carbonate is completely dissolved, then warm gently to a temperature not exceeding 60 for the purpose of expelling the large excess of carbon dioxide. Rinse off the under side of the watch glass and the sides of the beaker with 25 cc. of water, add a drop of methyl orange indicator and titrate as in the determination of the volumetric ratio. Calculation of Strength of the Two Solutions. Calculate the volume of acid solution equivalent to the volume of alkali solu- tion used in the last titration by dividing by the volumetric ratio, and subtract the quotient from the 50 cc. of* acid solution used. Calculate the weight of hydrochloric acid theoretically required to react with the calcium carbonate weighed out, and divide by the volume of acid solution found to be equivalent to it in the previous calculation; the quotient represents the weight of hydro- chloric acid present in 1 cc. of the solution. Repeat the standard- ization with a second portion of calcium carbonate or until results are obtained which do not differ by more than one part in 500. Calculate the weight of sodium hydroxide needed to neutralize the hydrochloric acid in 1 cc. of the solution of that reagent as originally prepared and divide by the volumetric ratio; the quo- tient represents the weight of sodium hydroxide present in 1 cc. of the alkali solution. 304 QUANTITATIVE CHEMICAL ANALYSIS Reduction to Semi-normal Strength. Calculate the volume to which 1500 cc. or some other convenient volume, of the solution should be diluted to make each cubic centimeter contain exactly 0.01823 gm. and add the necessary amount of water, assuming that neither contraction nor expansion takes place. In making this dilution first rinse out a 1000 cc. and a 500 cc. flask with a little of the acid solution and discard; then fill the flasks to the mark with the solution and discard whatever remains in the bottle, but do not rinse the latter with water; next drain the contents of the two flasks into the bottle and add the calculated amount of water which should be measured accurately from a buret. Dilute in a similar manner the alkali solution to semi-normal strength, that is, so that each cubic centimeter contains exactly 0.020 gm. Checking Work. Redetermine the volumetric ratio between the two solutions; if it differs from one by more than two parts in one thousand faulty work has been done and, since the error may be in either one or both of the two solutions, the standardiza- tion with pure calcium carbonate must then be repeated. If difficulty is experienced in attaining the requisite accuracy by this method standardize the acid solution by the gravimetric method described below. If either of the solutions has been diluted to below semi-normal strength it is not necessary to prepare a new solution, but the exact factor- representing the relation of the solution to normal strength should be calculated and used in place of the factor one-half wherever this factor would have been used. Gravimetric Method of Standardization. Remove with a pipet 25 cc. of the acid solution, dilute to 200 cc. and add a slight excess, that is, about 10 per cent more silver nitrate than is theoret- ically required to react with the chlorine present. Heat the mixture to boiling and stir until the precipitate coagulates, then filter on an asbestos filter, wash dry and weigh resulting silver chloride. Calculate the relation of the acid solution to normal strength from the weight of silver chloride obtained from each SOLUTIONS OF ACIDS AND BASES 305 cubic centimeter of acid measured out. Calculate the relation of the alkali solution to normal strength from the volumetric ratio and the normal value of the acid solution. III. EXPERIMENTS WITH INDICATORS Prepare one-tenth normal solutions of acid and alkali by diluting 50 cc. portions of the semi-normal solutions already prepared to exactly 250 cc. Remove by means of a pipet 10 cc. of the one-tenth normal acid solution to a 200 cc. beaker or Erlenmeyer flask, add 80 cc. of water, a drop of methyl orange indicator and titrate with the tenth normal alkali. Note and record all of the shades of color thru which the solution passes, the color when an equiva- lent amount of alkali has been added, the amount of alkali needed to bring about the most pronounced color change and the color when an excess of alkali has been added. Next pass a stream of carbon dioxide, which has been washed free from other acids, thru the solution and note the effect, if any, on the color of the solution. Perform a similar series of experiments with the indicators, cochineal, rosolic acid, para-nitro-phenol and phenolphthalein. IV. QUESTIONS AND PROBLEMS. SERIES 20 1. If the water used in preparing the standard acid had been saturated with carbon dioxide, how and under what conditions would it have affected the results obtained with this solution? 2. If the calcium carbonate used had contained one per cent of calcium oxide, how would the results obtained with the standard acid and standard base be affected? 3. A solution of sulfuric acid is prepared by weighing out 5 gm. of pure CuS0 4 5 H 2 O, dissolving in water, and precipitating the copper by electroly- sis; if this solution is diluted to 1000 cc., what relation does it bear to normal? 4. Calculate by the simplest method the normality of solutions of sodium hydroxide one cc. of which react with (a) 0.02 gm. of benzoic acid, C 6 H 5 (COOH) ; (b) 0.04 gm. of succinic acid, (CH^MCOOH)^ 0.015 gm. of crystallized oxalic acid, C 2 H 2 O 4 2 H 2 O. CHAPTER XLIII DETERMINATIONS WITH A STANDARD ACID AND A STANDARD BASE I. DETERMINATION OF THE STRENGTH OF CONCENTRATED SULFURIC ACID Outline of the Method. Weigh accurately a clean glass- stoppered weighing bottle of about 10 cc. capacity. Prepare a clean and dry dropping-tube or pipet of about 3 cc. capacity; in- sert into the bottle containing the sample and fill about half full. Remove from the bottle and allow about 15 drops to flow into the weighing bottle, being very careful to avoid spattering, then close the bottle and weigh accurately. Fill the bottle nearly full of water, mix and pour into a 200 cc. beaker, then rinse out at least three times with 10 cc. portions of water. Add a drop of any desired indicator and titrate with the standard alkali solu- tion. Calculate the percentage of H2S04 by the use of the general formula. II. DETERMINATION OF THE ACIDITY OF VINEGAR Preliminary Statements. The acidity of vinegar, unless adul- terated with sulfuric acid, is due almost entirely to acetic acid. When titrated with a base the coloring matter present undergoes a gradual color change which is difficult to characterize; this change can be distinguished with fair accuracy from the color change of phenolphthalein if a large amount of the indicator is added and the solution diluted sufficiently. In extreme cases, that is, where the color is very intense, it may be necessary to remove it by the addition of bone black and filtering, but since this reagent absorbs small amounts of acid its use should if 306 A STANDARD ACID AND A STANDARD BASE 307 possible be avoided. It is customary to report results in terms of the total weight of acid, calculated as acetic, per cubic centi- meter of sample. Outline of Method. Measure out 10 cc. of the vinegar into a 400 cc. beaker and dilute with 200 cc. of water free from carbon dioxide. Add three drops of phenolphthalein and titrate with the alkali solution, disregarding the changes from brown to drab and endeavoring to recognize the point at which the pink of the phenolphthalein, modified to some extent by the drab color of the vinegar, becomes apparent. Calculate the weight of acetic acid in 1 cc. of sample. III. DETERMINATION OF POTASSIUM BITARTRATE IN ARGOL OR COMMERCIAL CREAM OF TARTAR Preliminary Statements. The chief source of cream of tartar and tartaric acid is the argol which separates on the sides of the casks during the manufacture of wine. It contains in addition to potassium bitartrate (C4H 5 KO 6 ) salts of a number of organic acids and large amounts of coloring matter. The dissociation constant of the first hydrogen atom of tartaric acid is 9.7 X 10~ 4 , that of the second has not been accurately determined but it is sufficiently large to justify regarding it as a dibasic acid when titrated with a base if phenolphthalein is used as the indicator and therefore potassium bitartrate is one of the acid salts which can be titrated directly. The large amount of coloring matter present in argol often makes it difficult to recognize the true end-point; the conditions ob- served in the titration of vinegar also apply here. Outline of the Method. Weigh out 2 gm. of the finely pow- dered sample, add 150 QC. of hot water and stir for a few minutes. If a large amount of insoluble matter remains, filter on a small filter and wash with hot water until the washings are free from acidity. Add three drops of phenolphthalein and titrate with the standard alkali solution. Calculate the percentage of potassium bitartrate. 308 QUANTITATIVE CHEMICAL ANALYSIS IV. DETERMINATION OF BORIC ANHYDRIDE IN NATURAL BORATES Theory of the Method. The naturally occurring borates, which include the minerals colemanite, ulexite and pandermite, are simple or double borates of calcium and sodium. They are usually associated with the carbonates and sulfates of the alkali metals and with clay and sand. As they are the source of most of the borax and boric acid of commerce the value of ores contain- ing them depends upon the percentage of boric anhydride which they contain. The dissociation constant of boric acid is so small that it is completely displaced from solutions of its salts by an equivalent amount of a strong acid; if the salts are insoluble an excess of the acid must be used. Even concentrated solutions of boric acid do not affect the color of methyl orange and hence this indicator can be used to determine the point at which all of the mineral acid but none of the boric acid in a mixture which contains both has been neutralized. Hence if a sample which contains any of the borates named is treated with an excess of hydrochloric acid and the mixture made to give a neutral reaction with methyl orange it will contain an amount of free boric acid which corresponds to the boric anhydride present. The free acid cannot be titrated directly even where phenolphthalein is used, but the addition of glycerine or mannitol increases its acidic properties to such an extent that this titration then becomes possible. If glycerine is used it must form about 30 per cent by volume of the entire mixture; if manni- tol is used 2 per cent by weight is sufficient, and the end-point is more sharply defined. The method is not affected by the presence of carbonates if the carbon dioxide which is liberated during the decomposition of the sample is expelled, but since boric acid is very slightly volatile long boiling must be avoided. The accuracy of the method depends largely upon the maintenance of the proper concentration of the reagents used. A STANDARD ACID AND A STANDARD BASE 309 Outline of the Method. Weigh out 1.5 gm. of the finely ground sample into a 200 ce. beaker, add 5 cc. of dilute hydro- chloric acid, warm gently and stir with a glass rod until the sample seems to be completely decomposed, then add 10 cc. of water and heat to 80. If a large amount of flocculent residue remains, filter on a very small filter but keep the volume of filtrate and washings to about 50 cc. Add a drop of methyl orange and then standard sodium hydroxide until the mixture has a clear lemon yellow color. Next add 3 drops of phenolphthalein and about 1 gm. of mannitol and finally titrate with the standard alkali to a permanent pink color. Add another half gram of mannitol and if the color fades continue adding alkali until it is restored. As equilibrium is attained but slowly more time should be allowed for this titration than for those previously described. Calculate the percentage of I^Os, assuming that each molecule has a neutralizing power of two. V. THE ANALYSIS OF COMMERCIAL ALKALIES Preliminary Statements. The alkalies of commerce consist mainly of the hydroxides, carbonates and bicarbonates of sodium and potassium. Their total alkalinity can be accurately deter- mined by a direct titration with a standard acid, using methyl orange as indicator; or, by using the process of back titration and heating the solution to drive off carbon dioxide, other indicators may be used. It is sometimes necessary to distinguish between the alkalinity due to hydroxides and carbonates or between that due to carbonates and bicarbonates. Methods for the Determination of Hydroxides and Carbon- ates. If a solution which contains both hydroxides and carbon- ates is titrated with a standard acid, using phenolphthalein, the color change takes place when the hydroxide has been completely neutralized and the carbonate changed into bicarbonate; hence the difference between the result obtained for total alkalinity and that obtained by this method represents the acid needed to neu- tralize the bicarbonate formed from the normal carbonate origi- 310 QUANTITATIVE CHEMICAL ANALYSIS nally present and it is possible to calculate both the hydroxide and carbonate originally present. As the end-point in the latter titration is very unsatisfactory, this method is used only for ap- proximate determinations. A more satisfactory method of making this determination de- pends upon the addition of sufficient barium chloride to precipitate all of the carbonate and titration of the hydroxide in the resulting mixture. Outline of Method for the Determination of the Hydroxide and Carbonate of Soda in Commercial Caustic Soda. Weigh accurately a glass weighing bottle of about 10 cc. capacity and transfer to it as rapidly as possible about 10 gm. of the roughly powdered and mixed sample, and again weigh accurately. Empty into a small beaker, add about 50 cc. of carbon-dioxide-free water and stir until the sample is dissolved. Pour into a 250 cc. grad- uated flask and rinse out both bottle and beaker with more water, cool to the normal temperature, dilute to exactly 250 cc. and mix thoroughly. The very small amount of insoluble residue some- times found may be allowed to settle and is disregarded. Measure out 25 cc. of the solution, add 50 cc. of water, a drop of methyl orange and titrate with the standard acid. Remove a second 25 cc. portion, add 50 cc. of water, 5 cc. of reagent barium chloride, a drop of phenolphthalein and titrate with the standard acid, adding the latter very slowly as the titration approaches completion. Calculate the percentages of sodium hydroxide and sodium carbonate present. VI. DETERMINATION OF CRUDE PROTEIN IN FLOUR Theory of the Method. The proteins represent a group of extremely complex nitrogen-containing compounds, which form one of the three classes of nutrient materials present in foods. Altho the percentage of nitrogen present varies somewhat, experi- ence has shown that protein can be determined with fair accuracy by multiplying the percentage of nitrogen present by a factor which A STANDARD ACID AND A STANDARD BASE 311 varies somewhat with the nature of the proteid concerned. For the protein in flour the factor commonly used is 5.7, for that of meat 6.38 is used. The results obtained by this method are always designated as " crude protein." When flour is heated with concentrated sulfuric acid the acid is gradually reduced to sulfur dioxide and water, " while the carbon and hydrogen of the flour are oxidized to carbon dioxide and water and the nitrogen is changed to ammonium sulfate. When the resulting solution is distilled with an excess of a strong base ammonia is formed and distills over and can then be determined by titrating with a standard acid. Under certain conditions these operations can be carried out quantitatively, and form the basis of the Kjeldahl method which, with its various modifications, is used for the determination of all classes of nitro- gen-containing compounds. The Apparatus Needed. The Kjeldahl method involves two groups of operations. The " digestion " must be made in a round- bottomed flask, which is not easily broken by the large changes in temperature to which the different parts of it are subjected; flasks made of Jena or "pyrex" glass are commonly used. Since large amounts of sulfur dioxide and sulfur trioxide are formed this operation should be carried out in a hood which has a good draft, or each flask must be connected directly with a suction apparatus. The " distillation" must be made in a still, which is provided with a special form of still-head designed to prevent any of the boiling liquid from being carried over into the receiver while the distillation is in progress. Since the time needed for both of these operations may be long most laboratories are pro- vided with special multiple-unit pieces of apparatus, in which the digestion and distillation of from three to twenty samples can be made simultaneously. In such an apparatus the con- denser consists of a narrow trough of sheet copper thru which water slowly circulates; the condenser tubes are made of block tin, as this metal is not affected by dilute ammonium hydroxide. 312 QUANTITATIVE CHEMICAL ANALYSIS Outline of Method of Procedure. Weigh out about 2 gm. of the sample into a 500 cc. Kjeldahl flask, which should be made of hard glass. Add 20 cc. of concentrated sulfuric acid, using it to rinse down any particles of the sample which adhere to the sides of the flask, and then add about 0.7 gm. of mercuric oxide for the purpose of increasing the speed of the reaction. Place the flask in an inclined position on a cold sand bath and heat gently for ten minutes or until violent frothing ceases, then raise the tem- perature to the boiling point and boil vigorously until a color- less solution is obtained. Remove from the rack, allow to cool slightly, and add a few grains of solid potassium permanganate, using sufficient to produce a slight but permanent pink or green color. Allow to cool, dilute to 200 cc. and again cool under the tap to the temperature of the room. Add to the receiver of a distilling apparatus 10 cc. of semi- normal hydrochloric acid, 50 cc. of water and one drop of methyl orange. Place the delivery tube attached to the distillation apparatus inside the receiver and adjust the level of the latter until the end of the delivery tube touches the surface of the liquid in the receiver. Add to the solution in the Kjeldahl flask 50 cc. of a 50 per cent solution of sodium hydroxide, then 10 cc. of a 5 per cent solution of potassium sulfide (to precipitate the mercury) and 2 gm. of granulated zinc (to prevent boiling over) and at once connect with the still-head by means of a good rubber stopper. Heat to boiling and continue distilling until the volume of the solution in the receiver amounts to 200 cc. Remove the receiver, rinse out the delivery tube and titrate with a one-tenth normal solution of ammonium hydroxide. Calculate and report the per- centage of crude protein present. A STANDARD ACID AND A STANDARD BASE 313 VII. QUESTIONS AND PROBLEMS. SERIES 22 1. Calculate by the general formula the percentage of citric acid, a tri- basic acid of the formula CeHsO;, if the weight of mixture used was 0.643 gm., the volume of KOH solution used for the titration was 31 cc., and 1 cc. of KOH solution = 0.015 gm. of pure oxalic acid (C 2 H 2 O 4 2 H 2 0). 2. Calculate the percentage of P 2 O 5 in a solution of H 3 P04 if the weight of solution used was 6.43 gm., volume of KOH solution used for the titra- tion (with methyl orange) was 26 cc., and 1 cc. of KOH solution contained 0.016 gm. 3. Show how B 2 3 could be determined in pure borax more easily than in calcium borate. 4. Explain why the BaC0 3 precipitated in the analysis of caustic soda has no effect on the titration. Is there any objection to using methyl orange for the titration? Is there any objection to filtering off and washing the BaCO 3 precipitate? 5. Calculate by the simplest method the volume of semi-normal acid required to neutralize the ammonium hydroxide produced by distilling 1 gm. of FeSO4(NH 4 ) 2 SO4- 6 H 2 with an excess of KOH. 6. How would you prepare a solution of HC1 so that each cubic centimeter should equal exactly 0.01 gm. of NaNO 3 , when the latter was determined by reducing to an ammonium salt, distilling with an excess of KQH and titrat- ing the distillate with the HC1 solution? SECTION IX VOLUMETRIC PROCESSES INVOLVING OXIDATION CHAPTER XLIV GENERAL FEATURES OF PROCESSES INVOLVING OXIDATION Definition of Oxidation and Reduction. The term oxidation is here used in its broadest sense and includes all changes in which any negative element or radical is added to, or any positive ele- ment or radical is removed from, the substance under consideration. Reduction represents the converse of this and the two actions are necessarily reciprocal, that is, where one element is oxidized some other must be reduced, and the total amount of oxidation effected must be equivalent to the total amount of reduction effected. If the distinction between positive and negative valence is recognized such reactions are always associated with changes in valence. According to this conception the valence of any uncombined ele- ment is always zero, that of any combined element corresponds to the number of positive or negative bonds of affinity represented by one atom of the element in the compound concerned. For example, the valence of arsenic is sometimes said to be three in both arsine and arsenic trioxide, but since hydrogen is a positive element the valence of arsenic in arsine s properly represented by 3, and since oxygen is a negative element the valence of arsenic in arsenic trioxide is properly represented by -f 3. Hence when arsine is oxidized to arsenic trioxide the valence of the arsenic changes from 3 to +3. Definition of Oxidizing Capacity. In many of the substances used as oxidizing agents the valence of only one of the atoms in 314 PROCESSES INVOLVING OXIDATION 315 the molecule changes; in such cases the amount of oxidation which can be effected by one molecule of the oxidizing agent is determined by the change in the valence of that element. In other cases two or more atoms change their valencies, and the amount of oxidation which can be effected by one molecule of the oxidizing agent is determined by the algebraic sum of the valence changes which all of the atoms in one molecule of the oxidizing agent undergo. The " oxidizing capacity" of any agent is denned as the total number of positive valencies furnished to, or of nega- tive valencies taken from, the substance oxidized by one molecule of the agent. These statements can be illustrated by means of the following reactions: (1) CuS0 4 + Zn -* Cu + ZnS0 4 , (2) Fe(N0 3 ) 3 + Ag -> Fe(N0 3 ) 2 ;+ AgN0 3 , (3) SnCl 2 + 2 HgCl 2 -> SnCl 4 + 2 HgCl, (4) HaS + I 2 ->S + 2HI, (5) 3 H 2 S + 8 HN0 3 - 3 H 2 S0 4 + 8 NO + 4 H 2 O. In (1) the valence of zinc changes from to +2, that of copper from + 2 to 0. The oxidizing capacity of copper sulfate is here (+ 2) - (0), or -f 2. The oxidizing capacity of zinc is (0) - (+ 2), or 2, which is equivalent to saying that its reducing power is 2. In (2) the valence of silver changes from to + 1, that of iron from + 3 to + 2. The oxidizing capacity of ferric nitrate is here (+ 3) - (+ 2), or + 1, that of silver is (0) - (+ 1), or - 1. In (3) the valence of tin changes from + 2 to + 4, that of mer- cury from + 2 to + 1. The oxidizing capacity of stannous chlo- ride is (+2) (+ 4), or 2, that of mercurous chloride is (+2) - (+ 1), or 1. In (4) the valence of sulfur changes from 2 to 0, that of iodine from to 1. The oxidizing capacity of hydrogen sulfide is (- 2) - (0), or - 2, that of iodine is (0) - (- 1), or 1. In (5) the valence of sulfur changes from 2 to +6, that of 316 QUANTITATIVE CHEMICAL ANALYSIS nitrogen from + 5 to +2. The oxidizing capacity of hydrogen sulfide in this reaction is (2) (+6), or 8, that of nitric acid is (+ 5) - (+ 2), or + 3. Oxidation and lonization Changes. The five reactions can also be expressed in terms of the ionization changes concerned as follows: (1) Cu + S0 4 + Zn- Cu + Zn + S0 4 , +++ ++ + (2) Fe + 3 N0 3 + Ag-> Fe + 3 N0 3 + Ag, ++ ++ ++++ + (3) Sn + 6Cl + 2Hg-* Sn + 6Cl + 2Hg, (4) 2H+ T "s + I a ->S + 2H + 2I, (5) 14H + 3~S~+ 8N0 3 -^6H + 8NO + 4H 2 O + 3SO 4 . The first four of these reactions involve changes in the number of charges with which the different ions are associated only, and so far as these reagents are concerned oxidation can be defined as any process in which the number of positive charges associated with an element is increased, or the number of negative charges so associated is decreased; reduction would be defined by the converse statement. Furthermore, the number of positive charges gained or the number of negative charges lost is a measure of the oxidizing capacity of the reagent concerned. In the fifth reaction there is also a change in the composition of one of the ions, that is, the NOs ion not only loses its negative charge but also two oxygen atoms, which become available as oxidizing agents. Hence this method of defining oxidation and reduction, which in many respects is an extremely convenient one to use, is not universally applicable, even when the process takes place in an aqueous solution. Normal Values of Oxidizing Agents. The oxidizing capacity of oxidizing and reducing reagents measures one of the forms of chemical activity which these agents exhibit. Since the unit of PROCESSES INVOLVING OXIDATION 317 oxidizing capacity which has been adopted is the change in valence, and the unit of valence is that ordinarily exhibited by the hydro- gen atom, the oxidizing capacity of a reagent is identical with E of the general formula, for volumetric determinations and the normal value of any oxidizing or reducing agent is found by dividing its molecular or atomic weight by its oxidizing capacity. Meaning of Oxidation Potential. Altho four of the five reac- tions cited have very large constants, reactions (2) and many others of this class are appreciably reversible. In discussing the reversibility of such reactions it will be found desirable to conceive of every oxidizing and reducing agent as possessing a definite " oxidation potential." which is but one form of chemical potential, and to ascribe the ability of one reagent to oxidize another to the fact that its oxidizing potential is large as com- pared with that of the reagent oxidized. Thus the negligible reversibility of reaction (1) would be ascribed to the very large oxidation potential of copper sulfate as compared with that of metallic zinc. The reversibility of (2) would be ascribed to the fact that the oxidizing potential of ferric nitrate exceeds that of silver by a small amount only. The comparative values of the oxidizing potentials of the two reagents which react in any re- action involving oxidation is shown by the equilibrium constants of these reactions. The equilibrium constants of but few reactions of this type have been determined directly; they can be calcu- lated more easily in many cases by use of the methods of electro- chemistry. Oxidation and the Theory of the Galvanic Cell. The electro- motive force produced when reactions involving oxidation are made to take place in such a manner that electrical energy instead of heat is produced is found to be directly proportional to the equilibrium constant of the reaction. If, for example, reaction (1) is made to take place in the apparatus represented in Fig. 59, in which A represents a vessel containing a bar of metallic zinc in contact with a solution of zinc sulfate, and B a vessel containing a 318 QUANTITATIVE CHEMICAL ANALYSIS bar of metallic copper in contact with a solution of copper sulfate the voltage shown by the voltmeter V measures the difference between the oxidizing potentials of copper sulfate and zinc. The voltage shown by such cells is found to increase with an increase in the concentration of the copper ion in the copper solution and to decrease with the concentration of the zinc ion in the zinc solution, and a formula, which was first suggested by Nernst, makes it possible to calculate at what concentrations all action would cease, that is, the concentrations of zinc and copper ions in a solution in which me- tallic zinc and copper sulfate would be in equilibrium. The ratio of these con- ++ ++ centrations, that is, (Zn) -f- (Cu) has been found to have the value 10 38 . In a similar manner the equilibrium con- stant of reaction (2) has been found to have the value 0.1. Determination of Electrode Poten- tials. The electromotive force of a galvanic cell is determined by the dif- ference between the electrode poten- tials at the two electrodes of which the cell is composed. The difference of potential at each electrode is determined by the oxidizing potential of the agent which undergoes a change at the electrode. Thus the electrode potential of copper sulfate in contact with copper de- pends upon the oxidizing potential of the copper ion, that is, upon the ease with which it gives up its positive charges to some other substance. Hence the oxidizing potentials of the different oxidizing agents are proportional to the electrode potentials shown by these agents when they undergo a reaction in a galvanic cell. Fig. 59. Diagram of a Galvanic Cell PROCESSES INVOLVING OXIDATION 319 If a numerical value is arbitrarily assigned to some particular electrode and the electromotive force of the cells formed by com- bining this electrode with a number of other electrodes is deter- mined a series of numbers representing the comparative values of the electrode potentials of these electrodes can be calculated. In attempting to prepare electrodes, whose potential differences shall represent the oxidizing potentials of reagents which are not conductors of the metallic class and which do not yield conductors of the metallic class, it is necessary to make use of a metal like platinum which is a good conductor and whose action on the solution is so small that it can be neglected. Thus in measuring the oxidizing poten- tial of hydrogen it is necessary to use an electrode which measures the potential difference between gaseous hydrogen and a solution of the hydrogen ion. This can be effected by use of the device represented in Fig. 60.* It consists of a sheet of platinum foil bent like the letter S, which is sur- rounded by a bell-shaped glass tube of such a form that the lower half of the foil is in contact with the solution and the upper half with pure gaseous Fl &- ^ hydrogen, which is made to circulate through the drogen apparatus continuously. The potential difference shown by such an electrode also depends upon the oxidizing potentials of such reagents as may be added to the solution in contact with it, and hence it can be used to measure the oxidizing potentials of reagents like ferric salts or chromic acid. A Table of Electrode Potentials. In the table which appears below, the oxidizing agents whose formulae appear in the first column have been arranged with respect to the numerical value of the electrode potential to which they give rise when they react in a galvanic cell in the manner indicated in the second column. * Hildebrand, Jour, of Am. Chem. Soc., 36, 847. 320 QUANTITATIVE CHEMICAL ANALYSIS TABLE OF ELECTRODE POTENTIALS Oxidizing agent Reaction concerned Cone, of solution Electrode potentials KMnO 4 + acid MnO 4 > Mn < +1.640 C1 2 K 2 CrO 4 + acid Cr 2 0? > Cr (d)=i +1.640 <+l 270 Br 2 Br 2 ^2Br (B + r) = l +1.270 * Ag + ->Ag + Fe + -> Fe c^- 1 H (Fe") = (Fe) +1.076 +1.016 I 2 Cu + I,->2I Cu->Cu MZ\ +0.80 +0.606 (H) ("/ ^ H +0.277 (Pb) (Zn) (Pb) -^ Pb (Cd) ^ Cd (Zn) -> Zn (Pb) = l (Cd) = l (Z^) = l +0.129 -0.143 -0.493 (Mg) (Mg)^Mg (Mg) = l -1.273 (Na) (Na) -* Na (Na) = l -2.483 (Li) (Li) - Li (Li) = l -2.744 The figures given in the last column represent the electrode poten- tials when the concentration of the solution is that represented in the third column. In general, any reagent which appears in the upper part of the table should oxidize any reagent which appears below it, that is, if the two reagents are brought together the one which appears first in the table reacts in the manner indicated in the second column; that which appears later reacts in the reverse direction of that indicated in the second column. The value of the equilibrium constants between any two such reagents is large in proportion as the difference between the corresponding electrode potentials is large. Thus the very large equilibrium constant of reaction (1) accords with the difference between the electrode PROCESSES INVOLVING OXIDATION 321 + + potentials of the Cu > Cu and the Zn > Zn electrodes, that is, (+0.606) - (-0.493), or 1.099 volts. The smaller equilibrium con- stant of reaction (2) accords with the smaller difference be- + +++ ++ tween the Ag > Ag and the Fe > Fe electrodes, that is, (+1.076) - (+1.016), or 0.06 volt. The Recognition of End-Points. The oxidizing potentials of mixtures made by adding together equivalent amounts of two reagents which react completely is zero. If the reaction con- cerned was not absolutely complete such mixtures would show a slight positive or negative oxidation potential when equivalent amounts were present. It is possible to measure the electro- motive force of a galvanic cell, one electrode of which consists of a hydrogen electrode placed in a mixture containing equivalent proportions of two oxidizing agents, with great accuracy. If such a measurement has been made, the true end-points of titrations between solutions containing these reagents can be ascertained by carrying he titration to the point at which the electromotive force of the cell corresponds with that previously found. The electromotive force of such a cell also changes very greatly with very slight changes in the ratio between the quantities of the two reagents present in the neighbo hood of the point at which this ratio is one; therefore the true end-point can also be determined by noting the rate of change in the value of the electromotive force of the cell during the titration. These methods of determining the end-points of processes of this class are not widely used at present altho they possess decided advantages. In most cases the end-point is determined by means of an indicator. The number of indicators available is very limited and with but few exceptions they can only be used for one titration; hence their action will be considered in discussing the particular titration in which they are used. CHAPTER XLV DETERMINATIONS WITH POTASSIUM PERMANGANATE I. POTASSIUM PERMANGANATE AS AN OXIDIZING AGENT Oxidizing Potential and Oxidizing Capacity. This is a par- ticularly useful oxidizing agent since solutions of it act completely and instantaneously with a large number of reagents. Its oxi- dizing potential has not been measured accurately, but exceeds that of all the reagents listed in the table on page 320. Its reaction with a ferrous salt, which is typical of a large num- ber of oxidations effected by it in an acid solution, is represented by the expression: (1) 2 KMn0 4 + 10 FeS0 4 + 8 H 2 S0 4 -4 5 Fe 2 (S0 4 ) 3 + 2 MnS0 4 + K 2 SO 4 + 8 H 2 O. Assuming that the degree of oxidation of the potassium has a con- stant value of +1, and that of sulfur in sulfates is +6 the de- gree of oxidation of the manganese changes from (2 X 4) 1, or + 7, to (2X4) 6, or + 2, and hence the oxidizing capacity of one molecule of the permanganate is 5. Its behavior in all such reactions may also be represented by the expression: (2) 2 KMn0 4 -> K 2 O + 2 MnO + 50. This equation represents an ideal conception only and will not take place in an aqueous solution unless some acid is present, which can take up the oxides of potassium and manganese, and some reducing agent is present to take up the available oxygen. Its use in a neutral solution is illustrated by its reaction with a manganese salt according to the expression: (3) 2 KMn0 4 + 3 MnCl 2 + 2 H 2 -> 5 Mn0 2 + 2 KC1 + 4 HC1. 322 DETERMINATIONS WITH POTASSIUM PERMANGANATE 323 In this reaction the degree of oxidation of the manganese changes from (2 X 4) - 1, or + 7, to (2 X 2), or + 4, and the oxidizing capacity of one molecule of the permanganate is 3. Its behavior in reactions of this type is therefore correctly represented by the expression: (4) 2 KMn0 4 - K 2 + 2 Mn0 2 + 30. This reaction like (2) is an ideal conception and does not take place with appreciable velocity unless some agent which is capable of utilizing the available oxygen is present. It should be noted that the normal value of potassium permanganate is either one-fifth or one-third of its molecular weight according to whether it is used in an acid or in a neutral solution. Factors Which Affect Permanganate Reactions. When this reagent is used in an acid solution some judgment must be exer- cised with respect to the character and concentration of the acid present. Nitric acid is usually to be avoided, since it is itself a strong oxidizing agent, and many of the organic acids are ob- jectionable since some of them reduce potassium permanganate. Hydrochloric is often objectionable owing to the possibility of a reaction taking place, which is represented by the expression: (5) 2 KMn0 4 + 16 HC1 -> 2 KC1 + 2 MnCl 2 + 5 C1 2 + 8 H 2 0. In the presence of certain metallic ions, especially iron, gold, plati- num and cadmium, this reaction takes place even in moderately dilute cold solutions, and hence erroneous results and unsatisfac- tory end-points are obtained in the titration of such solutions. In the absence of these ions the presence of moderate concentra- tions of hydrochloric acid is not objectionable. Various theories have been advanced to explain this phenomenon, but the assump- tion that the ions named act as positive catalyzers is as satisfac- tory as any. The effect of these ions is largely inhibited by the addition of large amounts of a manganous salt, that is, the man- ganous ion seems to act as a negative catalyzer for reaction (5). Altho it is possible to counteract the effect of moderate concen- 324 QUANTITATIVE CHEMICAL ANALYSIS trations of hydrochloric acid, even when positive catalyzers are present, by the addition of manganous sulfate the conditions which make such an addition necessary should be avoided whenever possible. In view of the above statements sulf uric acid is usually employed in all titrations with potassium permanganate which are effected in acid solutions. The concentration of hydrogen ion necessary to make such reactions complete and instantaneous varies. Re- action (1) is found to be sufficiently complete even when 1 cc. of concentrated acid per 100 of solution is present; that is, where (H) = 0.35. If the amount of acid added exceeds 40 cc. per 100 of solution, especially if the temperature is much above 20, a further secondary reaction becomes possible which is expressed by the equation (6) 2 KMn0 4 + 3 H 2 S0 4 -i K 2 S0 4 + 2 MnS0 4 + 2.5 2 + 3 H 2 0. Determination of the End-Point. A single drop of a one-tenth normal ^solution of potassium permanganate, that is, one contain- ing 3.16 gm. per liter, imparts an easily recognizable pink color to 200 cc. of water. Since potassium and manganese sulfates impart no color to aqueous solutions no special indicator need be used, provided the compound which is oxidized yields products whose colorific value is sufficiently small. Thus the true end- point of reaction (1) can be easily and accurately recognized, since the yellow color imparted to the solution by the small concentra- tion of ferric ion present at the end-point of the titration is negli- gible, as compared with the pink color produced by one drop of the permanganate. In other reactions, such as the reaction by which ferrocyanides are oxidized to ferricyanides, the red color acquired by the solution before the end-point is reached leads to a large error. Possible Uses. The more important determinations which involve the use of a standard permanganate solution may be con- veniently classified under four groups. DETERMINATIONS WITH POTASSIUM PERMANGANATE 325 First, the direct oxidation of certain metallic elements from a lower to a higher degree of oxidation, including, in addition to iron and manganese, the elements copper, tin, arsenic, antimony, tita- nium, molybdenum, tungsten and uranium. Some of these proc- esses are unsatisfactory or are less convenient than other methods. Second, the direct oxidation of certain inorganic acids or their salts, including nitrous acid, which is oxidized to nitric; sulfurous acid, which is oxidized to sulfuric; sulfhydric acid, which is oxi- dized to sulfur and water; ferrocyanic acid, which is oxidized to ferricyanic acid; sulfocyanic acid, which is oxidized to hydro- cyanic and sulfuric acids, and hydrogen peroxide which is oxidized to oxygen and water. Third, the direct oxidation of certain organic substances such as oxalic and formic acids, and tannin. Fourth, a large number of indirect determinations. They would include elements which form insoluble compounds with the acids enumerated in the second and third groups, and which can there- fore be separated from solution, treated with a stronger acid and the liberated acid titrated. Of especial interest is a method for the determination of phosphorus which involves precipitating that element as ammonium phosphomolybdate, separating from the solution, redissolving and reducing the molybdenum in the solu- tion, and titrating the latter. II. PREPAKATION AND STANDARDIZATION OF A PER- MANGANATE SOLUTION Preparation. Nearly all " of the determinations commonly made with potassium permanganate are carried out in an acid solution. A solution of one-tenth normal strength, assuming that the oxidizing power is five, is usually prepared; it should contain 3.16 gm. per liter. If it becomes desirable to use such a solution for determinations which are carried out in the absence of an acid it should be remembered that it is only 0.06 normal for all such determinations. 326 QUANTITATIVE CHEMICAL ANALYSIS The potassium permanganate sold by dealers, even tho marked C.P., usually contains small amounts of manganese dioxide; further, when dissolved in water more manganese dioxide slowly separates owing to the reducing action of the small amount of organic matter usually present even in distilled water, and to the action of light. The insoluble dioxide seems to catalyze this action and leads to the production of further amounts of dioxide. Hence it is desir- able to allow the prepared solution to stand for twenty-four hours, that is, until the easily oxidizible organic matter is entirely con- sumed, then to remove the dioxide and other insoluble impurities by filtering thru asbestos, and to preserve the solution in a per- fectly clean bottle which is protected from strong sunlight. Under these conditions a solution can be preserved for many months without appreciable reduction in strength. Methods of Standardization. A large number of substances have been and are still used for the standardization of perman- ganate solutions. Pure metallic iron, which has been deposited on a weighed platinum dish by means of an electric current, has many advantages, but since this deposit contains small amounts of carbon, which has a large reducing power, the results are slightly in- accurate. Pure ferrous ammonium sulfate, FeSO^NH^SO^G H 2 0, is still more convenient but the purity of the salt sold under this name cannot be assured, and it is necessary to test each sample for its reducing power by some independent' process. Oxalic acid is sometimes used, but unless prepared under certain definite conditions its purity cannot be depended upon. The most satisfactory standard is sodium oxalate, which can be prepared to correspond with the formula Na2C 2 4 under conditions first determined by Sorensen.* The proper conditions for its prep- aration, and methods of ascertaining its purity were more carefully elaborated by Blum,t and samples of guaranteed purity can now be purchased from the Bureau of Standards at Washington. * Zeit. fiir analyt. Chemie, 42, 512 (1903). f Jour, of Am. Chem. Soc. 34, 123 (1912). DETERMINATIONS WITH POTASSIUM PERMANGANATE 327 Conditions for Titration of Sodium Oxalate. Oxalic acid can be completely oxidized by potassium permanganate according to the reaction: (7) 5 C 2 H 2 4 + 2 KMn0 4 + 3 H 2 S0 4 -* 10 C0 2 + K 2 S0 4 + 2MnS0 4 + 8H 2 0. At ordinary temperatures the velocity of this reaction is very small, but at 60 it proceeds almost instantaneously, and after the reaction has once been initiated it proceeds fairly rapidly, even if the temperature falls below 60. The concentration of hydro- gen ion necessary to make the reaction complete and instanta- neous is somewhat greater than that necessary for the oxidation of iron. Either sulfuric or hydrochloric acid can be used to sup- ply the necessary concentration of hydrogen ion. Outline of Method of Procedure. Weigh out 6.32 of pure crys- tallized permanganate into a 400 cc. beaker, add 250 cc. of water, warm slightly and stir for a few minutes, then pour the clear supernatant liquid into a 2000 cc. flask; again add water, warm, stir and pour into the flask, and continue this cycle of operations until all of the salt has been brought into solution. Altho the salt is highly soluble the rate of solution is low and some time can be saved by proceeding as directed. Finally, dilute to 2000 cc. and allow to stand for at least 24 hours. Prepare an asbestos filter and connect with a clean two-liter bottle as shown in Fig. 58, then filter the permanganate solution thru it. Keep the bottle in a dark closet or cover with opaque paper. Dry some pure sodium oxalate (Sorensen) for a half hour at a temperature of 250. Weigh out from 0.25 to 0.3 gm. into a 400 cc. beaker, add 200 cc. of water, then slowly add 5 cc. of con- centrated sulfuric acid. Heat the solution to 80 and titrate slowly, adding the permanganate solution until a faint but per- manent pink color appears. Divide the weight of sodium oxalate weighed out by the volume of permanganate solution used and then divide the quotient by 328 QUANTITATIVE CHEMICAL ANALYSIS the weight of sodium oxalate present in a normal solution of that reagent to determine the relation of the permanganate solution to normality. Since one molecule of sodium oxalate yields one of oxalic acid, and since the reducing power of the latter is two, 1 cc. of normal sodium oxalate should contain one two-thousandth of its molecular weight expressed in grams. III. DETERMINATION OF IRON IN CAST IRON Interfering Elements. Cast iron usually contains several per cent of silicon and carbon and smaller amounts of manganese, sul- fur and phosphorus. If dissolved in sulfuric acid the silicon forms silicic acid, the manganese forms manganous sulfate, the phos- phorus forms phosphorous acid and that part of the carbon which exists in the form of graphite separates as such, but that part which exists as iron carbide (FesC) yields more or less volatile hydrocarbons. Even if the resulting solution is heated to boiling it will be found to reduce more iron than would correspond to the iron present. The simplest method of overcoming this difficulty is to destroy these reducing substances by a preliminary treatment with potassium permanganate, reduce the iron necessarily oxidized by this treatment and again titrate with the permanganate solu- tion. If a slight excess of permanganate is used and the solution heated during the preliminary oxidation, a more complete oxida- tion of these reducing substances than is effected in the final titration can be assured, and experience shows that the products formed, which are in part carbon dioxide and water, are not reduced by the method used for the reduction of the iron. Methods of Reducing Iron. The reducing agents employed for this purpose must be slightly soluble solids or gases, otherwise the excess necessarily used cannot be removed. Of the possible solid reagents, metallic zinc, aluminum, magnesium and lead are most frequently used. The reactions concerned can be represented by the expression: (8) Fe 2 (S0 4 ) 3 + Zn -> 2 FeS0 4 + ZnS0 4 DETERMINATIONS WITH POTASSIUM PERMANGANATE 329 Reduction with these reagents is always effected in a solution strongly acidified with sulfuric acid, but the hydrogen which is also produced has no effect on the degree of oxidation of the iron, and reduction takes place only at the surface of the metal used. Of the metals named, aluminum acts somewhat more rapidly than zinc or magnesium, and is not acted upon to the same extent by the free sulfuric acid present; on the other hand, it is very difficult to obtain the metal sufficiently free from iron. Of the gaseous reducing agents, hydrogen sulfide, which is oxidized by ferric iron to sulfur and water, and sulfur dioxide, which is oxidized to sulfuric acid, are most fre- quently used. Both reagents reduce the iron rapidly and completely, and boiling for a few minutes expels the excess used completely. The finely divided sulfur which is formed when the former reagent is used is without appreciable action on the permanganate solu- tion unless the solution is hot. When sulfur dioxide is used the best results are obtained when the solution contains a very slight excess of free acid only. Use of the Jones Reductor. Since reduc- tion takes place only at the surface of the metal used, the process is a slow one, espe- cially if the solution has a large volume. If, however, the metal is reduced to a fine state of division and the iron solution passed slowly thru a tube filled with it, both the total amount of metal con- sumed and the time required for complete reduction are very greatly reduced. This principal is made use of in the Jones reductor represented in Fig. 61. Its use often decreases the tune Fig. 61. Jones Re- ductor 330 QUANTITATIVE CHEMICAL ANALYSIS needed for complete reduction from two hours to fifteen minutes. In using it care should be taken to prevent air from coming into contact with the zinc while the solution is being reduced, as it has been shown that a small amount of hydrogen peroxide, which is subsequently oxidized by the permanganate, may be formed under these conditions. Outline of Method of Procedure. Prepare the sample either by drilling out about 10 gm. of fine powder, or by turning off an equal amount of thin shavings from the metal to be analyzed. Weigh out 0.25 gm. of the powdered sample into a 200 cc. beaker, add 25 cc. of dilute sulfuric acid, warm gently and allow to stand until no more hydrogen is evolved, and only gelatinous silicic acid and graphite, which float in or on the solution, remain. Add sufficient permanganate solution to impart a deep red color to the mixture, even after it has been warmed to 50. Dissolve the precipitate of manganese dioxide, which usually separates, by heating and if necessary adding a very small amount of sodium sulfite and expelling the sulfur dioxide formed. Filter the mix- ture, using a 9 cm. filter and washing the latter free from iron, but endeavor to keep the total volume less than 100 cc. Prepare a Jones reductor as follows : Dissolve 5 gm. of metallic mercury in 50 cc. of dilute nitric acid and dilute the solution to 250 cc. Add 250 gm. of granulated zinc, which is fine enough to pass a 20- but not fine enough to pass a 30-mesh sieve. Stir the mix- ture for a few minutes, then pour off the solution and wash the residual metal until free from nitric acid and nitrates. Place a disk of perforated platinum foil in the bottom of the reductor tube, cover this with a thin layer of glass wool and finally fill with the amalgamated zinc as far as the cuplike enlargement at the top. Connect the tube with the flask and the latter with a suction pump. Rinse out the tube by passing thru it 250 cc. of dilute sulfuric acid (5 of cone, acid to 100 of water) being careful never to let the liquid get below the top of the zinc column. Next pass the iron solution thru the reductor, regulating the DETERMINATIONS WITH POTASSIUM PERMANGANATE 331 pump so as to require about fifteen minutes for the passage of the entire solution, and as soon as the latter reaches the top of the zinc column rinse out by the use of 200 cc. of dilute sulfuric acid. Remove the flask from the reductor tube and titrate the solution without delay. Calculate the percentage of iron present in the solution, noting that since its degree of oxidation is increased from two to three its reducing power is one. IV. DETERMINATION OF POTASSIUM NITRITE IN THE COM- MERCIAL SALT Theory of the Method. The action of potassium permanga- nate on nitrous acid is represented by the expression: (9) 5 HN0 2 + 2 KMn0 4 + 3 H 2 S0 4 -> 5 HN0 3 + K 2 SO 4 + 2 MnS0 4 + 3 H 2 0. When nitrous acid is titrated with potassium permanganate in a dilute solution the reaction is complete and instantaneous as long as either reagent is present in moderately large excess, but as the end-point is approached the rate of action becomes extremely slow, and it is not possible to determine the correct end-point with even approximate accuracy. If, however, an excess of perman- ganate is added to the nitrous acid solution the latter is rapidly and completely oxidized, and the excess of permanganate used can be determined by titrating with a standard solution of a ferrous salt, or by adding an excess of a ferrous salt and titrating back with the permanganate; there is little danger that reaction (9) will reverse, that is, that nitric acid will be reduced to nitrous acid by either the ferrous or manganous salt present, provided the solution is cold and dilute. Potassium nitrite is decidedly hygroscopic and an average sample cannot be obtained unless it is thoroughly mixed and unless several grams are weighed out. It does not ordinarily contain any other substances which interfere with the titration. 332 QUANTITATIVE CHEMICAL ANALYSIS Outline of Method of Procedure. Prepare a solution of ferrous sulfate by dissolving 28 gm. of the crystallized salt (FeSO^T H 2 0) in water, adding 10 cc. of concentrated sulfuric acid and diluting to one liter. Determine the volumetric relation between this and the permanganate solution by titrating 25 cc. Weigh out 2 gm. of the well-mixed sample in a weighing bottle, dissolve and dilute to 250 cc. in a graduated flask and mix thor- oughly. Remove 25 cc. of this solution to a 250 cc. beaker or Erlenmeyer flask, add exactly 50 cc. of the permanganate solution and allow to stand for a few minutes. Next add 5 cc. of dilute sulfuric acid and shake or stir for a few minutes, then add 25 cc. of the ferrous sulfate solution and finally titrate with the perman- ganate solution. Calculate the volume of permanganate solution which would be equivalent to the 25 cc. of ferrous sulfate solution used and subtract from the total volume of permanganate em- ployed. Calculate the weight of KN0 2 corresponding to this volume of permanganate, assuming that the reducing power of the KNO 2 is two. Report the per cent present in the sample. V. DETERMINATION OF CALCIUM IN LIMESTONE Theory of the Method. The insolubility of calcium oxalate and the ease with which oxalic acid can be titrated with potassium permanganate forms the basis of an exceedingly useful indirect method for the determination of this element. The accuracy of the method depends, first, upon the completeness with which the oxalate can be separated from the solution and from any other oxalates which may be occluded or co-precipitated with it; second, upon the completeness of the reaction: (10) CaC 2 4 + H 2 S0 4 -> CaS0 4 + H 2 C 2 4 , and third upon the equilibrium constant of reaction (7). The first of these factors is discussed in Chapter XXIV and it is there shown that even in the presence of magnesium the error involved in the separation can be made very small. The constant for DETERMINATIONS WITH POTASSIUM PERMANGANATE 333 reaction (10) is large since the dissociation constant of oxalic acid is much smaller than that of sulfuric acid. The constant for reaction (7) as shown in an earlier paragraph of this chapter is also very large. Outline of Method of Procedure. Weigh out 0.5 gm. of the sample into a 250 cc. beaker, cover with a watch glass and intro- duce 10 cc. of dilute hydrochloric and 5 of dilute nitric acid, and warm on a sand or steam bath until the decomposition seems to be complete, and fumes of NO and Cl are no longer given off. Rinse off and remove the watch-glass cover and bring the volumes of the solution to 100 cc. Heat the solution nearly to boiling, add a slight excess of am- monium hydroxide, digest for a few minutes, then filter on a 9 cm. filter and wash until free from soluble salts. If the volume of iron and aluminum hydroxide thus obtained is large, redissolve and precipitate and combine the two filtrates. Dilute the filtrate to 300 cc., add a drop of methyl orange indicator and dilute hydrochloric acid until the solution gives a neutral reaction. Heat to boiling, add 18 cc. of oxalic acid solu- tion and stir for a few minutes; if a precipitate does not separate add a single drop of ammonium hydroxide and stir rapidly. After about ten minutes add diluted (1:4) ammonium hydroxide slowly and with constant stirring until the solution is distinctly alkaline; finally allow the mixture to stand for at least an hour. Filter off the precipitate on a 9 cm. filter and wash both precip- itate and filter very thoroughly, that is, until the washings show no action on a drop of permanganate solution even after acidifying and heating to 80. Remove the filter from the funnel, open it out and flatten against the side of a 400 cm. beaker. Rinse the precipitate adhering to the filter into the bottom of the beaker and bring the total volume up to 200 cc. Add 5 cc. of concentrated sulfuric acid, heat to 80 and titrate with the permanganate as in the standardization. Calculate and report the percentage of CaO present, noting that 334 QUANTITATIVE CHEMICAL ANALYSIS since one atom of calcium precipitates one molecule of calcium oxalate and the latter yields one molecule of oxalic acid, which has a reducing power of two, the correct per cent is given by the formula: Mol. wt. CaO Ar vol. KMn0 4 , 2 X 1000 X N X wt. of sample X 10 = per Cent Ca > in which N represents the normality of the solution used. VI. QUESTIONS AND PROBLEMS. SERIES 23 1. Outline the method of reasoning by which you decide upon the reduc- ing capacity of the two metallic elements and the two acids oxidized by potassium permanganate according to the equations given below: 2 KMn0 4 + 5 Ti 2 (SO 4 ) 3 + 8 H 2 SO 4 -> 10 Ti(SO 4 ) 2 + K 2 SO 4 + 2 MnS0 4 + 8H 2 0, 2 KMnO 4 + 5 U (SO 4 ) 2 + 2 H 2 O - 5 (U0 2 )S0 4 + K 2 SO 4 + 2 MnSO 4 + 2H 2 S0 4 , 14 KMnO 4 + Mo 24 O 37 + 21 H 2 SO 4 - 24 MoO 3 + 14 MnSO 4 + 7 K 2 SO 4 + 21H 2 0, 12 KMnO 4 + 10 HCNS + 8 H 2 S0 4 - 10 HCN + 6 K 2 S0 4 + 12 MnSO 4 + 8H 2 O. 2. Write out the reactions in which potassium permanganate oxidizes tin from the divalent to the quadrivalent condition, and arsenic and antimony from the trivalent to the quinquivalent condition in acid solutions. 3. When water acts on calcium carbide C 2 H 2 is produced, when it acts on aluminum carbide CH 4 is produced, what are the probable formulae of the two carbides? 4. What weight of phosphorus would be represented by one cc. of a one- tenth normal solution of potassium permanganate assuming that the phos- phorus was precipitated as (NH 4 ) 3 PCV12 MoO 3 , the precipitate dissolved and reduced to Mo 24 O 37 , and the latter titrated by the reaction given in the first problem? 6. What weight of copper would be represented by one cc. of a one-tenth normal solution of potassium permanganate, assuming that the copper was precipitated as CuCNS and the precipitate oxidized to CuS0 4 , HCN and H 2 SO 4 by the permanganate solution? DETERMINATIONS WITH POTASSIUM PERMANGANATE 335 6. What weight of potassium permanganate should be present in one cc. of the solution in order that each cc. should represent three milligrams of manganese if precipitated by reaction (3)? 7. How much antimony would be represented by one cc. of a solution containing 3 gm. of KMnO 4 per liter, assuming that the antimony is pre- cipitated as sulfide, the sulfide added to a solution of ferric sulfate and the reduced iron titrated according to the reactions: 5 Fe 2 (SO 4 ) 3 + Sb 2 S 3 + 6 H 2 O - 2 HSbO, + 3 S + 10 FeS0 4 + 5 H 2 S0 4 , 2 KMnO 4 + 10 FeSO 4 + 8 H 2 S0 4 - 5 Fe 2 (SO 4 ) 3 + K 2 SO 4 + 2 MnSO 4 + 8H 2 8. In determining iron in a sample of cast iron which contained 95 per cent of iron and 3 per cent of carbon, one-tenth of the latter remains in solution as C 2 H 2 and is oxidized to carbon dioxide and water by the permanganate, what is the error in the determination of iron? 9. Suggest indirect methods for the determination of the elements arsenic cobalt and zinc in which potassium permanganate is used as the oxidizing agent. 10. In the determination of iron in cast iron, (a) why dissolve in H 2 SO 4 rather than HC1 or HN0 3 , how would the result be affected (b) if the pre- cipitate of MnO 2 was not dissolved, (c) if an excess of Na->SO 3 was used and the solution was not heated, (d) if the H 2 SO 4 used to wash out the reductor contained small amounts of HNO 3 , (e) if the sample contained small amounts of Cu, or Mn, or Cr or Al? CHAPTER XLVI DETERMINATIONS WITH POTASSIUM BICHROMATE I. POTASSIUM BICHROMATE AS AN OXIDIZING AGENT Oxidizing Potential. This reagent is used as an oxidizing agent in an acid solution, and altho in its general behavior it resembles potassium permanganate the data given in the table on page 320 shows that its oxidizing potential is somewhat less. The salts of certain metals which are completely oxidized from a lower to a higher degree of oxidation by the permanganate are only partially oxidized by the dichromate; further, the dichromate has but little action upon oxalic and other organic acids unless the solutions used are hot and concentrated. Its solutions are so stable that they can be preserved for months without loss of strength, even when exposed to strong sunlight. Oxidizing Capacity. The oxidizing capacity of this reagent is best shown in the reaction which takes place when it is brought into contact with a ferrous salt, and which can be expressed as follows : (1) K 2 Cr 2 7 + 6 FeCl 2 + 14 HC1 -> 6 FeCl 3 + 2 KC1 + 2 CrCl 3 + 7H 2 Since this reaction involves the reduction of the chromium from chromium trioxide, whose degree of oxidation is represented by + 6, to a salt of chromium, in which the degree of oxidation is represented by + 3, the oxidizing power of one molecule of the dichromate, which can be regarded as a combination of one mole- cule of potassium oxide with two of chromium trioxide, is two times the difference between six and three or six. The decomposi- tion of the dichromate may also be represented by the equation: (2) K 2 Cr 2 7 -> K 2 + Cr 2 3 + 30. 336 DETERMINATIONS WITH POTASSIUM DICHROMATE 337 The latter, like the corresponding equation for the permanga- nate, is an ideal conception only, and does not take place in solution unless it contains a sufficient amount of acid to take up the oxides of potassium and chromium, and a reducing agent of sufficient strength to utilize the available oxygen. Conditions Necessary for the Titration. Reaction (1) is both complete and instantaneous if a concentration of hydrogen ion corresponding to that represented by about 1 cc. of the concen- trated hydrochloric acid per 100 of solution is present. There is but little danger of interaction with the acid itself and consequent liberation of chlorine, unless the solution is hot, or unless the concentration of acid exceeds forty times the minimum value named. Sulfuric acid, if added in amounts sufficient to yield concentrations of hydrogen ion equal to that resulting from the minimum concentration of hydrochloric acid named, can also be used to acidify the solution. Determination of the End-Point. The intensity of the yellow color of solutions containing C^O? ions is much less than the red color of those containing corresponding concentrations of Mn04 +++ __ ions, and furthermore the Cr ions formed when Cr 2 07 or CrO4 are reduced, impart a very intense green color to the solution. In the titration of iron salts the end-point can be determined by the use of a test which distinguishes between ferrous and ferric ions; in the titration of other reducing agents it becomes necessary to add an excess of the dichromate solution, and to determine , the amount added in excess by titrating back with a standard solution of a ferrous salt. Potassium ferricyanide reacts with a ferrous salt as follows: (3) 2 K 3 Fe(CN) 6 + 3 FeCl 2 - Fe 3 [Fe(CN) 6 ] 2 + 6 KC1. The ferrous ferricyanide produced is insoluble even in acid solu- tions, and has a very intense blue color. It is possible to recognize by this test one part of ferrous ion in one hundred thousand of water. Ferric salts do not react with the reagent, but when the 338 QUANTITATIVE CHEMICAL ANALYSIS concentration of the ferric ions is sufficiently large and that of the ferrous ions small, the yellow color of the ferric ion masks the blue coloration normally produced by the indicator and gives a green coloration. If the indicator is added directly to the solution in which the titration is being made the ferrous ferricyanide precipitate pro- duced remains unaffected, even after an excess of potassium di- chromate has been added. It becomes necessary, therefore, to use this reagent as an " outside indicator," that is, to remove and test a drop of the solution from time to time during the titration. These tests will first yield a deep blue precipitate; slightly before the true end-point is reached they will show a green coloration; at the true end-point a clear yellow; and when an excess of di- chromate is present a slight brown. The accuracy of this method of determining the end-point is affected by a number of details. If the indicator solution used has stood for more than twenty-four hours in strong sunlight it will be found to contain some ferrocyanide and hence will give misleading results. If its concentration exceeds one-fifth of one per cent, the end-points are not clearly defined. Further, the size of the drop of indicator solution used, as compared with the size and concentration of the drop of solution which is tested affect the final color. Even those tests which show no reaction for ferrous iron at first, gradually develop a blue color, owing to the gradual reduction of some of the iron by the light, and hence a definite time interval should be observed in judging whether the true end- point has been reached. Special Advantages of Potassium Dichromate. This reagent does not oxidize hydrochloric acid, even in the presence of iron salts, and hence it can often be used when potassium perman- ganate cannot be employed. Since most of the ores of iron can- not be brought into solution without the use of hydrochloric acid, and since the iron in such ores can be reduced more rapidly by the use of stannous chloride than by any other method, the process is DETERMINATIONS WITH POTASSIUM BICHROMATE 339 peculiarly adapted to the determination of iron in iron ores. Altho it oxidizes a number of other metals by reactions which are both complete and instantaneous it is rarely used for the determina- tion of such metals, owing to the difficulty of ascertaining the end-point of these reactions. II. PREPARATION AND STANDARDIZATION OF A BICHROMATE SOLUTION Method. The potassium dichromate sold by dealers often contains small amounts of potassium sulfate, but can be easily purified by recrystallization. Since the salt is not appreciably hygroscopic an accurately standardized solution can be prepared by weighing out a definite amount, dissolving, and diluting to the proper volume. As the solution is most frequently used for the determination of iron it is convenient to prepare it according to the unitary system, that is, so that 1 cc. will oxidize exactly 0.005 gm. of Fe. As already noted there are a number of factors which affect the method used to determine the end-point of the reaction, and it is always advisable to check the theoretical value of the solution by titrating it against a known weight of a pure ferrous ammonium sulfate under definite conditions. Detailed Outline of Method. Weigh out exactly 4.39 gm. of the pure salt, dissolve in water and dilute to exactly one liter. Weigh out 1 gm. of pure ferrous ammonium sulfate, dissolve in 100 cc. of water, add 5 cc. of concentrated hydrochloric acid and titrate with the dichromate solution. Use as an indicator a freshly prepared solution of potassium ferricyanide made by dis- solving a crystal of the pure salt as large as a grain of wheat in 25 cc. of water. Add at once to the iron solution 26 cc. of the di- chromate solution, and then test the mixture for unoxidized iron by bringing a drop of it into contact with a drop of the indicator on a porcelain plate, or piece of glazed white paper. If the test shows an intense blue color continue adding the dichromate solu- tion in quantities of two-tenths of a cubic centimeter at a time 340 QUANTITATIVE CHEMICAL ANALYSIS until the test shows a light blue only, then continue adding in quantities of two drops at a time until, after passing thru various shades of blue and green, the tests show a clear yellow only which persists for at least two minutes. Calculate the weight of iron actually oxidized by 1 cc. of the solution. III. DETERMINATION OF IRON IN IRON ORES Decomposition. The more easily soluble ores of iron, includ- ing siderites, which are mainly ferrous carbonate, and many of the hematites and magnetites, which are mainly ferric oxide and fer- rous-ferric oxide respectively, are dissolved by treatment with warm concentrated hydrochloric acid. The action of this acid is greatly intensified by the addition of a small amount of stannous chloride. A small amount of insoluble residue resulting from treatment with these reagents is usually assumed to be free from iron and disregarded, provided it is of a pure white color; it may contain small amounts of iron in the form of an insoluble silicate. Many samples of limonite ores, which contain carbonates and sometimes organic matter, and many ores which contain sulfur, yield to the hydrochloric acid and stannous chloride, only after ignition in an open crucible; this treatment also oxidizes the organic matter, the presence of which might lead to high results. The more difficultly soluble ores, including many varieties of hematite, magnetite and limonite and all ores containing iron in the form of an insoluble silicate, are most easily and completely decomposed by fusion with sodium peroxide. This treatment yields ferrates and silicates of sodium, also aluminates, chromates and manganates if these elements are present, all of which com- pounds are easily decomposed by hydrochloric acid. The excess of sodium peroxide used, also the chromates and manganates, are completely reduced by heating with hydrochloric acid and any chlorine which may be liberated is either volatilized or is reduced by the stannous chloride used to reduce the iron. The action of the molten peroxide of sodium on platinum cru- DETERMINATIONS WITH POTASSIUM BICHROMATE 341 cibles is sufficiently energetic to render their use unadvisable; its action on nickel is also appreciable and both nickel and iron, small amounts of which are usually present in the metal of which such crucibles are made, are usually introduced into the resulting solu- tion in sufficient amounts to produce appreciable errors. Crucibles of silver may be used to advantage but well-glazed porcelain ones answer very well, for although the glaze is gradually disintegrated no error is introduced as it does not contain iron, and the crucible can usually be employed for several analyses. Reduction of Iron by Means of Stannous Chloride. Ferric salts can be reduced by stannous salts as represented by the equation (4) SnCl 2 + 2 FeCl 3 -> SnCl 4 + 2 FeCl 2 . This reaction is almost complete and instantaneous provided the solutions concerned are hot and concentrated, and provided a rather large concentration of hydrochloric acid is also present. Since solutions of ferric salts, especially when hot and when Cl ions are present, possess an intense red or yellow color, whereas solutions of ferrous salts show a slight greenish color only, the point at which sufficient stannous chloride has been added to com- pletely reduce the iron in a solution can be determined with suffi- cient accuracy by noting the color changes of the solution. It is scarcely possible to reduce all of the iron in a solution with- out introducing a slight excess of stannous chloride and since the latter reduces chromic acid, this excess must be oxidized before titration, without at the same time reoxidizing any of the iron. This can be effected by means of mercuric chloride which easily oxidizes the tin but not the iron, and is itself reduced to insoluble mercurous chloride, which compound is not affected by chromic acid. If, however, the solution is hot, and if its concentration with respect to stannous chloride is large as compared with that of the mercuric chloride the reduction may go farther and metallic mercury may be formed, which unlike mercurous chloride is 342 QUANTITATIVE CHEMICAL ANALYSIS capable of reducing chromic acid. For this reason care must be taken in using this process to add a slight excess of stannous chloride only, to cool or dilute before adding the mercuric chloride, and to add a relatively large amount of the latter. Effect of Other Elements on the Process. This method is not affected by the presence of even large amounts of aluminum, manganese, zinc, cadmium, calcium or magnesium. Cobalt and nickel in small amounts are not objectionable, but large amounts affect the accuracy of the end-point. Chromium, in large amounts, increases the difficulty of recognizing the point at which the proper excess of stannous chloride has been added, but in small amounts is not objectionable. Copper, since it is reduced to the cuprous form By stannous chloride and reoxidized to the cupric form by the dichromate, increases the amount of standard solution used almost in proportion to the amount present and also masks the end-point. Antimony and titanium are also reduced by stannous chloride and partly oxidized by the dichromate and hence yield high results. If solutions containing either copper, antimony or titanium are reduced by hydrogen sulfide instead of .stannous chloride, correct results can be obtained, since the two first- named elements are precipitated and can be removed by filtra- tion, and the last is not reduced. Outline of Method for an Easily Soluble Hematite or Magne- tite Ore. Weigh out 1 gm. of the finely ground sample into a covered beaker, introduce 20 cc. of concentrated hydrochloric acid and about five drops of stannous chloride solution, cover with a watch glass, and allow to digest on a sand bath until the residue is a pure white color. Rinse the cover and sides of the beaker and transfer the solution to a 100 cc. graduated flask. Cool to room temperature, dilute to exactly 100 cc. and mix thoroughly. Remove 25 cc. of the solution to a 200 cc. beaker by means of a pipet, add 5 cc. of dilute hydrochloric acid, heat to boiling, and then add stannous chloride solution a drop at a time until the solution is colorless, but carefully avoid adding more than one DETERMINATIONS WITH POTASSIUM BICHROMATE 343 drop in excess. Cool the solution slightly, add 50 cc. of water and then 10 cc. of a saturated solution of mercuric chloride. This should produce a white, crystalline, precipitate of mercurous chlo- ride; if it does not do so an insufficient amount of stannous chloride was used; if the precipitate is black or gray too much was used and the results will probably be too high. Titrate with the dichromate solution as in the standardization, adding it in quantities of 2 cc. until the tests show a change from a deep blue to a light blue, then add the titrating solution until the proper end-point has been reached. With some experience it is possible to obtain a good end-point with the first portion of solution used; beginners usually find it necessary to titrate a second portion, profiting by the experience previously gained. Calculate the per cent of iron present. Determination of Iron in a Difficultly-soluble Ore. Weigh out into a 20 cc. glazed porcelain crucible approximately 3 gm. of sodium peroxide, avoiding the white crust often found on the surface, which consists largely of sodium carbonate and which, in addition to being less efficient in its action on the ore, has a much higher melting point. Weigh out accurately 1 gm. of the finely powdered ore, add to the crucible and mix with the peroxide with a platinum wire or glass rod. Place the crucible on a gauze, heat slowly until its contents fuse and keep at that temperature for ten minutes; this should produce a clear but deeply colored molten mass. Allow the crucible to cool, distributing the molten mass over its inner surface by carefully tipping and rotating during solidification. Place the crucible in an evaporating dish, add 50 cc. of water and slowly introduce an excess of hydrochloric acid. Remove and rinse off the crucible, heat the solution to boiling to decompose the hydrogen peroxide formed, then transfer to a 100 cc. graduated flask and treat as in the analysis of easily soluble ores. The method outlined assumes that neither copper nor any of the other metals which affect the result are present. 344 QUANTITATIVE CHEMICAL ANALYSIS IV. DETERMINATION OP CHROMIUM IN CHROMITE Theory of the Process. The reaction between a soluble chro- mate and a ferrous salt can also be used for the determination of the former by using the method of back titration, that is, by adding an excess of a standard solution of ferrous salt and then titrating with a standard dichromate solution. Since all com- pounds of chromium are readily converted into soluble sodium chromate by fusing with sodium peroxide the method is widely applicable for the determination of this element. The mineral chromite consists of ferrous oxide combined with the sesquioxide of chromium, but many samples also contain magnesium, aluminum, silicon, and sometimes manganese and nickel. When fused with sodium peroxide, chromates, ferrates, aluminates, silicates and manganates of sodium, also oxide of magnesium and peroxide of nickel, if this element is present or if the fusion is made in a nickel crucible, are produced. The fused mass is readily disintegrated by treatment with water, especially if an excess of peroxide is present. The chromate and most of the silicate and aluminate dissolve readily; the permanganate also dissolves unless an excess of peroxide is present, the ferrate hy- drates and forms insoluble ferric oxide or hydroxide; the magne- sium and nickel oxides remain insoluble. Hence by digesting the fused mass, filtering off and washing the resulting precipitate a solution which contains all of the chromium as sodium chromate, and no substances which possess strong oxidizing or reducing properties except the excess of sodium peroxide used, is obtained. The peroxide is readily decomposed by heating the solution to boiling. There is evidently no objection to making the fusion in a nickel crucible. Outline of Method of Procedure. Weigh out about 4 gm. of sodium peroxide, which should not contain much carbonate, into a 30 cc. nickel crucible. Weigh out one-half gram of the finely ground ore, add to the crucible and mix thoroughly with the DETERMINATIONS WITH POTASSIUM DICHROMATE 345 peroxide by means of a glass rod. Place the crucible on a wire gauze, heat until the mass fuses to a liquid and keep at this tem- perature for ten minutes. Decomposition of the sample will be greatly facilitated by seizing the crucible with a pair of tongs and gently rotating the contents. The resulting liquid mass will be of a dark red color and contain much suspended nickel oxide. Allow the crucible to cool, distributing the contents around the sides during solidification, then place in a capacious evaporating dish and add 100 cc. of water. Heat slowly to boiling and stir until the fused mass is completely disintegrated; remove the crucible from the dish and rinse it off; filter the resulting mixture thru all cm. filter, receiving the filtrate into a 250 cc. graduated flask, and wash until the precipitate is free from soluble chromate. Cool the solution in the flask and dilute to exactly 250 cc. Measure out 50 cc. of the solution, acidify with hydrochloric acid, and add 5 cc. of the concentrated acid in excess; next add 50 cc. of an approximately one-tenth normal solution of ferrous sulfate, and finally titrate with the standard dichromate solution. Titrate also a second 50 cc. portion of the ferrous sulfate solution directly with the dichromate solution. The difference between the amounts of dichromate solution used in the two titrations corresponds to the chromic acid formed from one-fifth of the ore weighed out. Calculate the percentage of chromium present. V. QUESTIONS AND PROBLEMS. SERIES 24 1. In the standardization of a solution of potassium dichromate a solution of a ferrous salt, which has a volume of 100 cc. and contains 0.2 gm. of iron, is used. In titrating an ore with the same solution 0.2 gm. of iron is again present, but the solution has a volume of 600 cc. If the indicator used per- mits of the recognition of one part of ferrous iron in 100,000, what error results from the fact that the two titrations are made at different volumes? 2. What error might be expected in a determination of iron in an ore containing forty per cent of iron and two-tenths of a per cent of copper, assuming that the copper is completely reduced by the stannous chloride to the cuprous form and reoxidized by the dichromate? Ans. 0.17 per cent. 346 QUANTITATIVE CHEMICAL ANALYSIS 3. Write out all of the reactions involved in the determination of chromium in chromite which contains, in addition to iron and chromium, aluminum, manganese and nickel. 4. Outline an indirect volumetric method for the determination of lead which makes use of a standard solution of potassium dichromate. 5. If a solution of potassium dichromate is one-tenth normal when used as an oxidizing agent, what relation does it bear to normality when used as a precipitating agent? 6. What volume of tenth-normal potassium dichromate would be reduced by 0.1 gm. of iron, (a) when in the form of metallic iron, (b) when in the form of ferrous chloride, (c) when in the form of the magnetic oxide? 7. Why is the oxidizing potential of potassium permanganate greater in an acid than in a neutral solution ? 8. How could you decide from the method used for the determination of iron hi an ore whether potassium dichromate would oxidize a stannous salt completely? 9. If the equilibrium constant of reaction (2) of page 316 is 0.1, what weights of ferric and ferrous nitrate would be present in a solution which contained 1 gm. of ferric nitrate and had a volume of 479 cc., after an excess of metallic silver had been added? Ans. 0.073 and 0.689 gm. CHAPTER XLVII DETERMINATIONS WITH IODINE AND SODIUM THIOSULFATE I. GENERAL FEATURES OF IODOMETRIC PROCESSES Typical Reactions. Iodine acts directly as an oxidizing agent by taking up a negative charge and forming the iodine ion as rep- resented by (1) Sn + 2 Cl + I 2 - + SrT+ 2 Cl + 2 1 and (2) 4Na + 2S~ 2 6 3 + I 2 ->4Na + S 4 6 + 21, or indirectly, by reacting with water to form both iodine and hydrogen ions and thus rendering the oxygen of the water available as an oxidizing agent, as represented by: (3) 3H + As6 3 + l2 + H 2 O->5H + As04+2L Of these reactions (1) is practically complete, (2) is complete in a neutral solution and (3) can be made complete in either direc- tion by varying the concentration of hydrogen ion. In the presence of even small concentrations of a strong base iodine acts very differently since it is itself oxidized to IOs ions as represented by the equation (4) 6 K + 6 HO + 3 1 2 - 6 K + 5 1 + K) 3 + 3 H 2 0. The equilibrium constant of this reaction is small and altho it cannot be made the basis of a quantitative process it often pre- vents the use of iodine as an oxidizing agent in solutions which contain appreciable concentrations of hydroxyl ions. 347 348 QUANTITATIVE CHEMICAL ANALYSIS The table of electrode potentials on page 320 indicates that the oxidizing potential of iodine is decidedly less than that of per- manganates and chromates, and of chlorine and bromine. Ex- perience shows that in the presence of a sufficient concentration of hydrogen ion all of these reagents oxidize the iodine ion to free iodine according to reactions, similar to (5), which are practically complete. (5) 12 K + 2 Mn0 4 + 10 1 + 16 H + 16 Cl - 5 I 2 + 12 K + 16CH-2Mn lodometric Processes. The facts outlined above suggest two classes of reactions which could be used as the basis of volumetric processes. In the first class certain reactions which involve the use of a standard solution of iodine, which acts either directly or indirectly as an oxidizing agent in either a neutral or acid solution, are used for the determination of certain substances commonly classed as reducing agents. Since the degree of oxidation of the iodine in all of these reactions changes from to 1, its oxidiz- ing capacity is always 1. In the second class certain substances, which are usually classed as oxidizing agents, are determined indirectly by causing them to react with an acidified solution of a soluble iodide and titrating the iodine liberated with a solution of a reducing agent. Both classes of processes are included under the term "iodometric." Preparation of an Iodine Solution. The solubility of iodine in water is too small to make the preparation of even one-tenth nor- mal solutions possible. In the presence of an excess of potassium iodide an unstable but soluble periodide of the formula KIs is formed, which, in the presence of reducing agents, decomposes so readily into potassium iodide and free iodine that it can be used as though it were a simple solution of iodine. Solid iodine is readily dissolved by concentrated but not by dilute solutions of potassium iodide and when a solution of the periodide has been IODINE AND SODIUM THIOSULFATE 349 prepared in this manner it can be diluted up to a certain limit without causing free iodine to separate. The solution of iodine in potassium iodide probably contains in addition to normal iodine ions, ions of the formula la. Preparation of a Standard Reducing Agent. A standard solu- tion of a reducing agent, which reacts completely with the iodine solution can be used to advantage for the readjustment of the standard of this solution, as it is much less stable than potassium permanganate; it is also necessary for processes based upon re- actions similar to (5). Sodium thiosulfate is by far the most satisfactory reagent for this purpose, as it is comparatively stable if the solution is kept neutral altho it is slowly decomposed by the carbon dioxide absorbed from the air if left exposed. Determination of the End-Point. A single drop of one-tenth normal iodine solution imparts an appreciable color to 200 cc. of water and in many of the titrations made with this solution no indicator is necessary. If the solution titrated contains other color-yielding substances, or if greater accuracy is demanded, a solution of starch should be used as an indicator. Under favor- able conditions the presence of one part of free iodine in several million can be recognized, by this indicator, but the delicacy of the test and the character of the color produced are affected by a number of factors. It is decidedly less delicate when the concen- tration of iodine ions and of hydrogen ions is very small. If the con- centration of the free iodine present is large as compared with that of the starch, the solution has a green color; if this ratio is smaller it has a blue color; if the solution contains a large concentration of bicarbonates it has a reddish color. Standardization of the Iodine Solution. The iodine solution can be standardized by titrating against a previously standardized thiosulfate solution, or against a weighed amount of arsenious oxide or potassium antimonyl tartrate (tartar emetic). Owing to the ease with which it can be purified by sublimation the former substance is more generally used. 350 QUANTITATIVE CHEMICAL ANALYSIS Since the action of the iodine solution is actually due to the I 3 ions which it contains, the reaction upon which this method of standardization is based is properly represented by the expression (6) 3 H + As6 3 -f K + T 3 + H 2 -> 5 H + As6 4 + K + 3 1. The equilibrium constant for this reaction has been found* to have the value 0.07 at 25 and therefore that (As6 4 ) + (As0 3 ) = (0.07) - (la) + (H) 2 . (I) 3 . The only factor which can be varied for the purpose of displacing the equilibrium in the desired direction and making the ratio + + (AsO*) -T- (AsOa) very large is (H) . Evidently (H) must be made small as compared with 0.07 if the oxidation of all the arsenic present is to be made reasonably complete when an equivalent amount of iodine solution has been added. Since hydrogen ions are formed as the reaction progresses it is also necessary to intro- duce some reagent, like sodium bicarbonate, which will keep the concentration of hydrogen ions small and which does not yield sufficient concentrations of hydroxyl ions to cause reaction (4) to take place. Experience has shown that the proper conditions are maintained if the solution has a volume of 75 cc., if it is made neutral to phenolphthalein and if 2.5 gm. of pure sodium bicarbon- ate is added and the solution saturated with carbon dioxide. II. CLASSIFICATION OF IODOMETRIC PROCESSES Determination of Substances Oxidized by Iodine. Under this head are included the element tin, which is oxidized from the bi- to the quadrivalent condition even in the presence of acids, and arsenic and antimony, which are oxidized from the tri- to the quin- quivalent condition under the conditions noted in the preceding paragraph. Under the same head are included sulfurous acid which is oxidized to sulfuric acid in neutral or acid solutions; * Washburn, Jour, of Am. Chem. Soc., 30, 31 (1908). IODINE AND SODIUM THIOSULFATE 351 hydrogen sulfide, which is oxidized to sulfur and hydriodic acid under similar conditions; thiosulfuric acid, which is oxidized to tetrathionic acid (see reaction 2) under similar conditions; and salts of hydrocyanic acid, which are oxidized to cyanogen iodide and a salt of hydriodic acid in a neutral solution. Determination of Substances Reduced by Hydriodic Acid. Three factors can be varied for the purpose of making reactions similar to (5) sufficiently complete and rapid to make the deter- mination of oxidizing agents possible. First, a large amount of a soluble iodide may be added for the purpose of making the con- centration of the iodide ions large. Thus the reaction in which the ferric ion is reduced may be made complete to such an extent as to make it useful in the determination of ferric salts by the use of a large excess of potassium iodide. Second, the concentration of the hydrogen ion can be made large by the addition of a strong acid. Thus altho chlorine and bro- mine are completely reduced by moderate concentrations of sol- uble iodides, cupric salts, also permanganates and chromates, are not completely reduced unless a small concentration of hydrogen ion is also present and arsenates and antimonates are not com- pletely reduced unless this concentration is very large. Third, by increasing the temperature to the boiling point of the solution the iodine formed is volatilized and the equilibrium forced in the desired direction. Such determinations are necessarily carried out in a distilling apparatus, in which all of the iodine formed is distilled into a receiver before being titrated. This device has been successfully used in the determination of molyb- denum which can be reduced from the hexa- to the trivalent condition. Indirect lodometric Determinations. A number of insoluble oxidizing agents, such as the peroxides of manganese and lead, are completely reduced by concentrated hydrochloric acid at moderately high temperatures and the chlorine produced can be distilled into a solution of potassium iodide, and the resulting 352 QUANTITATIVE CHEMICAL ANALYSIS iodine titrated. This forms the basis of an indirect method for the determination of these oxides and in general of all oxidizing agents which are completely reduced under these conditions. A second series of indirect processes represents combinations of precipitation and oxidation processes. As already noted chromic acid and its salts can be determined by reducing with potassium iodide and titrating the resulting iodine; hence those metals which form insoluble chromates can be determined by adding a meas- ured volume of a standard solution of a soluble chromate, filtering off the precipitate formed and determining the soluble chromate left in the filtrate; the amount of metal present can then be cal- culated from the difference between the soluble chromate added and that found in the filtrate. III. OUTLINE OF METHOD FOR PREPARATION OF SOLUTION Preparation of Iodine Solution. Weigh out 12.7 gm. of pure iodine, place in a small beaker, add 20 gm. of potassium iodide and 20 cc. of water and stir occasionally until the iodine is com- pletely dissolved. Dilute the mixture slowly to one liter and place in a clean bottle made of colored glass or one which is covered with opaque paper. Preparation of Starch Solution. Place about a gram of starch in a small beaker, add about 20 cc. of water and stir until the mixture is smooth. Heat in a separate beaker 200 cc. of water to boiling, pour the starch mixture into it and boil the resulting mixture for three minutes, being careful to prevent any of the starch from settling to the bottom, for if it does so the beaker will crack. Allow the mixture to stand for several hours, then decant off the clear portion. Standardization of Iodine Solutions. Weigh out 0.2 gm. of pure arsenious oxide, dissolve in 20 cc. of an approximately normal solution of sodium hydroxide, add a drop of phenolphthalein and then dilute hydrochloric acid until the solution is just colorless. Dilute the solution to 75 cc., add 2.5 gm. of sodium bicarbonate, IODINE AND SODIUM THIOSULFATE 353 and pass carbon dioxide thru it until saturated. Add about 1 cc. of the starch solution, and titrate with the iodide solution added from a glass-stoppered buret until the mixture acquires a faint but permanent rose to purple color. Calculate the relation of the solution to normal strength, assuming that the reducing power of the arsenious oxide is four. Preparation of Thiosulfate Solution. Weigh out 24.8 gm. of pure crystallized sodium thiosulfate (Na^Os'SH^O), dissolve and dilute to one liter. Measure out by means of a pipet 25 cc. of the iodine solution, dilute to 75 cc. and titrate with the thiosulfate solution. It will be found desirable to add the latter until the mixture has a very faint yellow color before adding the starch indicator and then to continue the titration until the mixture changes from blue to colorless. Calculate the relation which the thiosulfate solution bears to normal strength. IV. DETERMINATION OF ARSENIC IN PARIS GREEN Composition of Sample. Paris green is an aceto-arsenite of copper which is largely used in combating insects injurious to cultivated plants. The composition of commercial samples varies and one of the factors which determine their value for the purpose indicated is the percentage of arsenic present. Theory of Method Used. Arsenic can be determined by oxidizing it from the tri- to the quinquivalent condition with a standard solution of iodine, or by reducing it from the quinqui- to the trivalent condition by means of hydriodic acid and titrat- ing the liberated iodine with a solution of sodium thiosulfate. When Paris green is treated with a solution of sodium hydroxide, cuprous oxide, sodium acetate, and a mixture of sodium arsenite and sodium arsenate are produced. The insoluble cuprous oxide can be filtered off and the arsenic determined in the filtrate by reducing it to the trivalent condition with hydriodic acid in a strongly acidified solution, reducing the liberated iodine, neu- tralizing the solution and titrating with an iodine solution. 354 QUANTITATIVE CHEMICAL ANALYSIS Outline of Method of Procedure. Weigh out 2 gm. of the sample into a small beaker, add 25 cc. of 2-normal solution of sodium hydroxide, heat cautiously for some five minutes or until converted into bright red cuprous oxide. Rinse the mixture into a 100 cc. graduated flask, cool and dilute to exactly 100 cc. and then filter thru a dry filter, rejecting the first 10 cc. of filtrate. Remove 25 cc. of the filtrate to a 300 cc. beaker, add 15 cc. of concentrated hydrochloric acid and 2 gm. of potassium iodide and then add one-tenth normal sodium thiosulfate solution until the mixture is just colorless. As the volume is small it is not neces- sary to use an indicator. Next add 40 cc. of water and one drop of phenolphthalein, then add slowly a 20 per cent solution of sodium hydroxide until the mixture shows a faint pink color. Acidify with a drop of dilute hydrochloric acid, add 2.5 gm. of sodium bicarbonate, saturate with carbon dioxide and titrate with iodine solution as in the standardization. Calculate the percent- age of As2Os present. V. DETERMINATION OF COPPER IN BRASS Theory of Method. All soluble cupric salts react with potas- sium iodide in neutral or slightly acid solutions as represented by (7) 2 CuS0 4 + 4 KI -> 2 Cul + 2 K 2 S0 4 + I 2 . The fact that cuprous iodide is very insoluble and that cupric iodide is very unstable gives the equilibrium constant of this reac- tion a large value. The most favorable conditions are the presence of from 3 to 5 per cent of potassium iodide and about 3 per cent by volume of concentrated hydrochloric acid. With a smaller concentration of hydrogen ion the reaction is slower and the end- points less distinct. The presence of large concentrations of soluble salts especially of acetates seem to retard the reaction; the reason for this is not apparent. When brass is dissolved in nitric acid small amounts of nitrous acid are produced; as this reagent slowly liberates iodine from IODINE AND SODIUM THIOSULFATE 355 potassium iodide it must be expelled by evaporation or oxidized by bromine or hydrogen peroxide before making the titration. Outline of Method of Procedure. Weigh out 0.3 gm. of sample into a 200 cc. beaker, add 10 cc. of dilute nitric acid, cover with a watch glass and warm gently until the metal dissolves. Remove the cover, rinse its under side with water and evaporate the solution to about 3 cc. Dissolve basic salts if such have separated with a few drops of nitric acid and dilute to 50 cc. Add sufficient ammonium hydroxide to produce a clear bright blue solution, then neutralize with hydrochloric acid and add 3 cc. of the dilute acid in excess. Cool the solution to 25, add 3 gm. of potassium iodide and stir until dissolved. Titrate with the thiosulfate solution until the mixture has a light yellow color only, then add starch solution and continue the titration until the light blue or lilac color of the mixture fades to a nearly pure white and does not regain a per- ceptible blue color after three minutes. Calculate the percentage of copper present. VI. DETERMINATION OF COPPER IN A CHALCOPYRITE ORE Interfering Elements. These ores usually contain in addition to copper and iron sulfides small amounts of lead, zinc and arsenic sulfides. When dissolved in nitric acid the iron is oxidized to the trivalent and the arsenic to the quinquivalent condition. As both elements are reduced by hydriodic acid it is necessary to separate the copper before using this method. Small amounts of lead and even large amounts of zinc have no effect upon the process. Separation of Copper by Metallic Aluminum. The oxidizing potential of cupric salts is large as compared with that of metals like zinc, magnesium and aluminum, and under certain conditions it is possible to separate copper from such solutions completely by means of these metals. Aluminum is to be preferred for this pur- pose owing to the slowness with which it is attacked by moderately 356 QUANTITATIVE CHEMICAL ANALYSIS strong solutions of sulfuric acid. The separation of copper by this metal is retarded by ferric iron, which is reduced to the ferrous condition before the copper begins to separate. It is rendered incomplete by the presence of even small concentrations of nitric acid. It is most rapid when the solution is kept hot and enough sulfuric acid is present to cause the formation of sufficient hydro- gen to stir the solution vigorously. Under these conditions all of the copper, most of the lead and a part of the arsenic but none of the zinc and iron are precipitated. The small amount of arsenic which may separate with the copper does not affect the final titra- tion appreciably if the solution is acidified with acetic instead of hydrochloric acid. Outline of Method of Procedure. Weigh out 1 gm. of the ore into a 200 cc. Erlenmeyer flask, add 5 cc. of concentrated nitric acid and warm until violent action is over, next add 10 cc. of concentrated hydrochloric acid and evaporate until the volume has been reduced to one-half, then cool, add very cautiously 8 cc. of concentrated sulfuric acid, and evaporate until the flask is filled with dense white fumes of sulfur trioxide. Cool the flask, add 30 cc. of water and allow to stand with occasional shaking until all the soluble salts have been brought into solution. Transfer the solution to a 200 cc. beaker, retaining the insoluble matter as far as possible in the flask but washing the latter thoroughly; the final volume should not exceed 70 cc. Add to the solution a strip of aluminum foil 3 cm. wide and 15 cm. long, which has been bent into the form of the letter S, heat to 80 and set aside in a warm place until the copper has been completely precipitated, which usually requires ten minutes more than the time necessary to decolorize the solution. Next add 10 cc. of water saturated with hydrogen sulfide, and if the solution remains colorless or acquires a faint brown coloration only filter at once, using a small filter and retaining as much of the precipitated copper in the beaker as possible. Wash the precipitate three times with 10 cc. portions of hydrogen sulfide. IODINE AND SODIUM THIOSULFATE 357 Place the beaker containing the precipitate under the funnel and pour over the filter about 10 cc. of warm dilute nitric acid, moving the beaker in such a manner as to cause the acid solution to flow over the surface of the aluminum plate and dissolve the small amount of adhering precipitate. Replace the beaker by the flask used to dissolve the ore which has in the meantime been cleaned. Warm the solution in the beaker until all of the pre- cipitate has been dissolved, then remove and rinse the aluminum plate, pour the solution thru the filter and wash free from copper. Add 10 cc. of bromine water to the flask and boil vigorously until the excess added is expelled. Cool the solution, make alka- line with ammonium hydroxide, acidify with acetic acid and then add 3 cc. of the dilute acid in excess. The solution should have a volume not greatly exceeding 60 cc. Add 3 gm. of potassium iodide and titrate as in the previous determination, remembering that slightly more time must be allowed for the mixture to come to equilibrium owing to the smaller concentration of hydrogen ion present. VII. QUESTIONS AND PROBLEMS. SERIES 25 % 1. A solution contains 0.1 gm. of HsAsO4 and 1 gm. of HC1, and has a volume of 100 cc.; if 3 gm. of potassium iodide is added and it is assumed that the potassium iodide and the three acids are completely dissociated, what fraction (calculated approximately) of the HsAsO4 is reduced? Ans. 0.6. 2. Write out all of the reactions involved in the determination of arsenic in Paris green. 3. Outline the changes resulting from the addition to water of (a) Na^COa, (b) NaHC0 3 , (c) NaHCO 3 + CO 2 . What other reagents could be sub- stituted for NaHCO 3 in the standardization of the iodine solution? 4. Show how you could standardize a solution of iodine from a standard solution of (a) KMnO 4 , (b) K 2 Cr 2 O 7 . SECTION X PHYSICO-CHEMICAL PROCESSES CHAPTER XLVIII THEORY OF PHYSICO-CHEMICAL METHODS Uses of Physical Constants. The analyst often finds it de- sirable to determine certain physical constants of substances sub- mitted to him, usually with one of three objects in view. First, for the purpose of identifying or characterizing such substances. Use is here made of the well-established principle that the physical constants of every pure substance are definite magnitudes, whose values are often changed materially by the presence of small amounts of impurities; the extended uses made of the melting- points of solids and of the boiling-goints of liquids for this purpose are good illustrations. Second, to determine whether the com- position of the substance lies within the limits which characterize- the class of substances to which it is supposed to belong; especially for the detection of adulterations in certain food products, or other substances of natural origin, which are complex mixtures. Third, for the determination of the percentage composition of certain mixtures, which can be analyzed by such methods more easily or more accurately than by methods which are purely chemical. Analysis of Mixtures With Additive Properties. The quanti- tative analysis of mixtures by physico-chemical methods involves an accurate measurement of some physical property of the sample, and comparison of this result with the corresponding physical constants of the pure components of the mixture, or with a series 358 THEORY OF PHYSICO-CHEMICAL METHODS 359 of constants representing similar mixtures of known composition. If the sample is a simple mechanical mixture of two components an additive relation may exist between certain of its physical con- JET stants and those of the two components, that is, -7^ is a constant where dE and dP represent correlated changes in the constant concerned, and the percentage of one of the constituents in the mixture. In some cases the expression has a constant value only when P represents the relation between the number of molecules, of one constituent and the total number of molecules in the mixture; in other cases it is constant when P represents con- centration, that is, the weight of one constituent per unit volume of mixture. If the constant found for such a mixture is represented by E, and the corresponding constants of its two components A and B are represented by Ei and E 2 , the additive relationship \vould require that xE + (100 - x) E 2 = 100 E where x and (100 - x) represent the percentages of A and B respectively. The value of x can then be easily calculated by the use of the derived formula 100 (E - E 2 ) The accuracy of such a process clearly depends, not only upon the accuracy with which the three constants E, EI and E 2 are deter- mined, but also upon the value (Ei E 2 ). Such methods cannot be used for the analysis of mixtures con- taining more than two components unless one or more of the components is without effect upon the property concerned. Theoretically it is possible to analyze a mixture containing three components by measuring two of its physical constants, formulat- ing two equations similar to that already given, and solving these in the customary manner. Mixtures Whose Properties Are Not Additive. Mixtures which possess purely additive properties are rare, altho the de- 360 QUANTITATIVE CHEMICAL ANALYSIS Melting Points partures from pure additive relationships are not infrequently so small that they can be disregarded. Considering first solid mixtures, three types of structural units are possible. First, the two substances may themselves exist as distinct independent structural units; second, they may form one or more series of solid solutions with each other, each with definite saturation limits ; and third, they may form one or more chemical compounds, often when the appearance of the mixture gives no evi- dence of chemical changes having taken place. Mixed types are also possible, that is, the pure components may form solid solutions with the compounds and the com- pounds may form solid solu- tions with each other. The significance of these three types of structure in the interpretation of the physical constants of mixtures is illus- trated by the curves shown in Fig. 62. The abscissas here represent the relative amounts of the two components A and B in the mixture, and the ordinates the temperatures at which they begin to solidify when cooled from the molten condition. Curve I illustrates mixtures which form neither solid solutions nor compounds, and is characterized by a distinct break, which represents the so-called eutectic point. Curve II illustrates mixtures which form a con- tinuous series of solid solutions ; it is characterized by a minimum, altho certain mixtures of this type show a maximum. Curve III illustrates mixtures which form a single stable compound ; it shows a well-defined cusp at the point which represents the composition Composition of Mixture Fig. 62. Melting Points of Mixtures of Two Solids THEORY OF PHYSICO-CHEMICAL METHODS 361 of the compound. The corresponding curves for mixtures which show mixed types of structure are still more complex, but can be easily interpreted from the relations found in the simpler cases. The factors which affect the physical properties of liquid mix- tures are the possible association of the molecules of the solvent, the formation of molecular complexes, especially hydrates and double salts, and the electrolytic dissociation of the solute. The relations are decidedly simpler than where solid mixtures are con- cerned, and the curves representing many of the physical con- stants of liquid mixtures, especially where there is no dissociation, or where the dissociation is nearly complete, are straight or slightly curved lines. Use of Interpolation Methods. In all cases in which the con- stant measured is not an additive function of its two components, it becomes necessary to measure this property for a sufficient num- ber of mixtures containing known proportions of these components before it can be used for the analysis of unknown mixtures. The composition of the unknown mixture is then determined by inter- polating the value found between the proper interval in the table which has been prepared. If the relation made use of is repre- sented by a curve which shows a maximum or a minimum, certain of the determinations made may correspond to two different points on it, and therefore to either of two mixtures whose percentage composition may differ greatly. If the mixture is a solid this is a serious difficulty, but if it is a liquid the composition of the mixture under examination can be inferred from the effect produced upon the constant by increasing the dilution. If the curve shows a maximum, and increasing the dilution increases the value of the constant employed, the mixture represents the more concen- trated of the two in question; if it shows a minimum the reverse relationship must hold. The error involved in the interpolation depends upon the form of the curve at different intervals; the most favorable condition is where the curve forms an angle of 45 with the horizontal axis. 362 QUANTITATIVE CHEMICAL ANALYSIS Physical Constants Most Largely Used. The physical con- stants largely used for quantitative determinations are the specific gravity, specific volume, colorific absorption, index of refraction, and optical activity. A number of others, such as the conduc- tivity for electrical energy, are used more rarely. The three first named will be considered in detail in the subsequent chapters. Index of Refraction. This is defined as the ratio of the sine of the angle of incidence to that of the angle of refraction, when a beam of light passes from air to a layer of the medium under con- sideration. It is used especially for the analysis of liquid solutions. The refractometer devised by Abbe is largely used for such deter- minations; it is based upon the measurement of the angle at which an incident beam of light is totally reflected when it passes thru a double prism which is made of glass but has the form of a Nicol prism. The determination consists in placing a drop of the liquid between the two parts of the prism and rotating its position in a vertical plane until a shadow is cast at a particular position, that is, corresponds to the cross-bar of a telescope, with which the in- strument is provided. The angle thru which the prism is turned is read on a scale by means of a magnifying glass in terms of re- fraction index directly. It can be used for liquids varying from 1.3 to 1.7 with a maximum error which is less than 1 in the third decimal place. This instrument is used especially for the exami- nation of fats and oils and was found especially satisfactory for the detection of adulterants in olive oil and butter. The instrument of Zeiss is based on the same principle, altho the mechanical construction and method of making the measure- ment are totally different. The single glass prism used is immersed in a small beaker containing the liquid to be tested, and the ob- served results are expressed on an arbitrary scale, which corre- sponds to a range in refractive index of from 1.325 to 1.366. The refractive indices of aqueous solutions of a large number of organic and inorganic compounds have been found to bear a simple relation to their concentration, and the percentage com- THEORY OF PHYSICO-CHEMICAL METHODS 363 te vo o N position of a large number of such solutions can be determined with the aid of the tables showing this relation. It is possible to analyze by this method certain mixtures which are extremely difficult to analyze by any other method. Mixtures of methyl and ethyl alcohol are good illustrations. The curves representing the re- fraction indices of aqueous solutions of these compounds show the wide divergence rep- resented in Fig. 63. It so hap- pens that the specific gravities | of aqueous solutions of the two 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 334 5 5 6 66 67 63 ^69 70 71 8195 8261 8325 8202 8267 8331 8209 8274 8338 8215 8280 8344 8222 8287 8228 8293 8357 8235 8299 8363 8241 8306 8370 8248 8312 8376 8254 8319 8382 334 334 334 5 5 6 5 5 6 4 5 6 co m M en T m CO CO CO 8395 8457 8519 8401 8463 8525 8407 8470 853i 8414 8476 8537 8420 8482 8543 8426 8488 8549 8432 8494 8555 8439 8500 8561 8445 8506 8567 234 234 234 456 45^ 455 72 73 74 75 76 77 78 79 80 81 82 83 84 85 8573 8633 8692 8579 8639 8698 8585 8645 8704 859 1 8651 3710 8597 8657 8716 8603 8663 8722 8609 8669 8727 8615 8675 8733 8621 8681 8739 8627 8686 8745 234 234 234 455 4 5 5 455 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 233 455 8808 8865 8921 8814 8871 8927 8820 8876 8932 8825 8882 8938 8831 8887 8943 8837 8893 8949 8842 8899 8954 8848 8904 8960 8854 8910 8965 8859 8915 8971 233 233 233 455 445 445 8976 9031 9085 8982 9036 9090 8987 9042 9096 8993 9047 9101 8998 953 9106 9004 9058 9112 9009 9063 9117 9015 9069 9122 9020 9074 9128 9025 9079 9*33 233 233 233 445 445 445 9138 9191 9243 9M3 9196 9248 9149 9201 9253 9*54 9206 9258 9 r 59 9212 9263 9i 6 5 9217 9269 9170 9222 9274 9175 9227 9279 9180 9232 9284 9186 9238 9289 233 233 233 445 445 445 929/1 9299 9304 9309 9315 9320 9325 9330 9335 9340 233 445 86 87 88 9345 9395 9445 9350 9400 9450 9355 9405 9455 9360 9410 9460 9365 9415 9465 9370 9420 9469 9375 9425 9474 938o 9430 9479 9385 9435 9484 939 9440 9489 233 2 3 2 3 445 344 344 89 90 91 9494 9542 959 9499 9547 9595 9504 9552 9600 9509 9557 9605 9513 9562 9609 95i8 9566 9614 9523 9619 9528 9576 9624 9533 958i 9628 9538 9586 9633 2 3 2 3 2 3 344 344 344 92 93 94 9638 9685 9731 9 6 43 9689 9736 9647 9694 9741 9652 9699 9745 9657 9703 9750 9661 9708 9754 9666 9713 9759 9671 9717 9763 9675 9722 9768 9680 9727 9773 2 3 2 3 2 3 344 344 344 95 96 97 98 99 tn 9777 9782 9786 979 1 9795 9800 980=; 9809 9814 9818 2 3 344 9823 9868 9912 9827 9872 9917 9832 9877 9921 9836 9881 9926 9841 9886 9930 9845 9890 9934 9850 9894 9939 9854 9899 9943 9859 9903 9948 9863 9908 9952 2 3 2 3 2 3 344 344 344 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 Oil 223 3 3 4 APPENDIX II 391 SPECIFIC GRAVITIES OF SULFURIC ACID Lunge and Isler Specific gravity 15 4 in vacuo 100 parts by weight correspond to H|O. Specific gravity 15 4 in vacuo 100 parts by weight correspond to H|O, Specific gravity 15 4 in vacuo 100 parts by weight correspond to H|O. .000 0.09 1.205 27.95 1.410 51.15 .005 0.83 1.210 28.58 .415 51.66 .010 1.57 .215 29.21 .420 52.15 .015 2.30 .220 29.84 .425 52.63 .020 3.03 .225 30.48 .430 53.11 .025 3.76 .230 31.11 .435 53.59 .030 4.49 .235 31.70 .440 54.07 .035 5.23 .240 32.28 .445 54.55 .040 5.96 .245 32.86 .450 55.03 .045 6.67 .250 33.43 .455 55.50 .050 7.37 .255 34.00 .460 55.97 ,055 8.07 .260 34.57 1.465 56.43 .060 8.77 .265 35.14 .470 56.90 .065 9.47 .270 35.71 1.475 57.37 .070 10.19 .275 36.29 1.480 57.83 .075 10.90 .280 36.87 1.485 58.28 .080 11.60 .285 37.45 1.490 58.74 1.085 12.30 .290 38.03 1.495 59.22 1.090 12.99 .295 38.61 1.500 59.70 1.095 13.67 .300 39.19 1.505 60.18 .100 14.35 .305 39.77 1.510 60.65 .105 15.03 .310 40.35 1.515 61.12 .110 15.71 .315 40.93 1.520 61.59 .115 16.36 .320 41.50 1.525 62.06 .120 17.01 .325 42.08 1.530 62.53 .125 17.66 .330 42.66 1.535 63.00 .130 18.31 .335 43.20 1.540 63.43 1.135 18.96 .340 43.74 1.545 63.85 1.140 19.61 .345 44.28 1.550 64.26 1.145 20.26 .350 44.82 1.555 64.67 1.150 20.91 .355 45.35 1.560 65.08 1.155 21.55 .360 45.88 1.565 65.49 1.160 22.19 .365 46.41 1.570 65.90 .165 22.83 .370 46.94 1.575 66.30 .170 23.47 .375 47.47 1.580 66.71 .175 24.12 .380 48.00 1.585 67.13 .180 24.76 .385 48.53 1.590 67.59 .185 25.40 .390 49.06 1.595 68.05 .190 26.04 .395 49.59 1.600 68.51 .195 26.68 .400 50.11 1.605 68.97 .200 27.32 .405 50.63 1.610 69.43 392 QUANTITATIVE CHEMICAL ANALYSIS i SPECIFIC GRAVITIES OF SULFURIC ACID (Continued) Specific gravity lo T in vacuo 100 parts by weight correspond to H!O. Specific gravity 15 4 in vacuo 100 parts by weight correspond to % H 2 S0 4 Specific gravity 4* in vacuo 100 parts by weight correspond to H 2 SO 4 1.615 69.89 1.735 80.24 1.827 91.50 1.620 70.32 1.740 80.68 1.828 91.70 1.625 70.74 1.745 81.12 1.829 91.90 1.630 71.16 1.750 81.56 1.830 92.10 1.635 71.57 1.755 82.00 1.831 92.30 1.640 71.99 1.760 82.44 1.832 92.52 1.645 72.40 1.765 82.88 1.833 92.75 1.650 72.82 1.770 83.32 1.834 93.05 1.655 73.23 1.775 83.90 1.835 93.43 1.660 73.64 1.780 84.50 1.836 93.80 1.665 74.07 1.785 85.10 1.837 94.20 .670 74.51 1.790 85.70 1.838 94.60 .675 74.97 1.795 86.30 1.839 95.00 .680 75.42 1.800 86.90 1.840 95.60 .685 75.86 1.805 87.60 .8405 95.95 .690 76.30 1.810 88.30 .8410 97.00 .695 76.73 1.815 89.05 .8415 97.70 .700 77.17 1.820 90.05 .8410 98.20 .705 77.60 1.821 90.20 .8405 98.70 .710 78.04 1.822 90.40 .8400 99.20 .715 78.48 1.823 90.60 .8395 99.45 1.720 ' 78.92 1.824 90.80 .8390 99.70 1.725 79.36 1.825 91.00 .8385 99.95 1.730 79.80 1.826 91.25 APPENDIX III 393 LIST OF APPARATUS NEEDED The articles which are named in the following list represent the apparatus with which it is desirable that each student should be provided; it can be modified in many particulars without jeopardizing the success of his work. For many of the determinations which are described, especially those out- lined in Chapters XII, XIII, XIV, XV, XXII, XXVII, XXX, XXXI, XXXIII, XXXIV, XLIX and L, additional apparatus is necessary. It will be found desirable to prepare a series of boxes containing all of the special articles needed for each of these determinations and give them out to the different students as called for. 6 Beakers of Jena glass with lips, 2-100 cc., 2-260 cc., 2-400 cc., 1-600 cc., 1-800 cc. 2 Bottles with glass stoppers, 2000 cc. 2 Burets, 50 cc. (1 Mohr form and 1 Geissler form.) 1 Bunsen burner with rubber tubing. 1 Camel's hair brush. 2 Clamps to hold burets. 1 Desiccator with support for crucibles. 4 Erlenmeyer flasks, 2-100 cc., 2-250 cc. 1 Filter flask with rubber stopper, 500 cc. 2 Filter holders (to fit cleats on desk). 1 Package washed filters, 25-11 cm., 20-9 cm.. 10-7 cm. 1 Flask of Jena glass, 750 cc., with 2-hole rubber stopper for wash bottle. 1 Flask of Jena glass, 250 cc., with 2-hole rubber stopper for wash bottle. 1 Pair forceps of nickel or brass. 4 Funnels, 2-5 cm., 2-8 cm. 1 Glass filter tube. 4 Feet glass tubing, 6 mm. in diameter. 3 Glass rods, 20 cm. long, 6 mm. in diameter. 1 Piece glazed paper, 30 cm. square. 1 Graduated cylinder, 50 cc. 1 Iron stand with two rings. 2 Keys, 1 for desk and 1 for drawer to balance. 3 Pipets, 1-5 cc., 1-10 cc., 1-25 cc. 1 Piece platinum wire, 20 cm. long and 0.2 mm. in diameter. 4 Porcelain crucibles, 2-No. 000 (8 cm.) ? 2-No. 00 (12 cc.). 1 Porcelain Gooch crucible, 25 cc. 1 Porcelain plate. 2 Porcelain casseroles or evaporating dishes, 250 cc. 1 Piece fine rubber tubing, 20 cm. long and 6 mm. in diameter. 4 Reagent bottles, for dilute acids and ammonium hydroxide. 4 Test tubes, 15 cm. 2 Triangles of nichrome wire. 2 Weighing bottles, 10 cm. and 30 cm. 2 Pieces of wire gauze. 1 Witt filter plate, 23 mm. INDEX Absorption method for gas-evolution processes, 85. Acetic acid in vinegar, determination of, 306. Acids, distillation of, 72; dissociation constants of, 295; evaporation of, 72; titration with an acid indicator, 285. Acid salts, titration of, 294. Activity, of acids, 51; of bases, 52; of salts, 53. Adsorption, 133. Alkalies, commercial, analysis of, 309. Alloys of lead and tin, analysis of, 184, 374. Alundum, use of, 123. Ames extraction apparatus, 204. Apparatus, list of, for quantitative work, 393. Arsenious acid in Paris green, determination of, 353. Asbestos, use of, for filtration, 123. Atomic weights, table of, 76. Baking powder, determination of carbon dioxide in, 107. Balance, construction of, 9; rules for use of, 22. Ball mill for grinding, 28. Barium sulfate, ignition of, 171; properties of, 170. Bases, titration of, with an acidic indicator, 295. Basic salts, titration of, 296. Black powder, composition of, 218; analysis of, 218. Boric anhydride in borates, determination of, 308. Brass, analysis of, 189; determination of copper in, 354. Bumping, cause of, 68. Bunsen apparatus, description of, 103. Buoyancy, correction for, 20. Burets, forms of, 240. Caffeine in tea, determination of, 231. Calcium carbonate, decomposition of, 81. 395 396 INDEX Calcium chloride, properties of, 97. Calcium oxalate, properties of, 177. Calcium in limestone, determination of, 332; separation of, from magnesium^ 175; theory of separation of, 179. Calculations, abbreviation of, 77; of volumetric determinations, 254. Calibration of burets, 248; of flasks, 249; of pipets, 249. Carbon dioxide, determination of, in limestone, 103; in baking powder,, 107. Catalizers, action of, 48. Chaddock burner, 66. Chalcopyrite, determination of copper in, 355. Chemical factors, calculation of, 74. Chemical formulae, calculation of, 79. Chlorine, determination of, in sodium chloride, 154; titration of, with silver solution, 256-259. Chromate indicator, use of, 257. Chromium in chromite, determination of, 344. Cleaning graduated apparatus, 247. Cochineal, use of, 291. Colorimetric processes, principles of, 378; methods of making, 379; limita- tions of, 382. Colorimeters, 379. Combustion method, theory of, 87. Compensating errors, principle of, 238. Complex ions, reactions involving formation of, 60. Concentration, definition of, 32. Consolute li quids, 220; separation of, 222. Continuous extraction, 202. Copper, determination of, in slag, 386; in brass, 354; in chalcopyrite, 355. Copper, separation of, by electrolysis, 192; by aluminum, 355. Copper sulfate, dehydration of, 84; determination of water in, 96. Counterpoise, use of, in weighing, 21. Crude fat, meaning of, 214; determination of, in peanuts, 216. Crude protein, meaning of, 311; determination of, in flour, 310. Cyanides, reaction of, with silver salts, 261. Dalton's Law, 82. Decantation, 131. Decomposition voltage, meaning of, 142; of metals, 143. Dehydration of salts, 83. Dehydrating agents, efficiency of, 96. Departure, meaning of, 93. INDEX 397 Desiccator, use of, 30. Displacement processes, end-points of, 281. Displacement reactions, 59. Dibasic acids, titration of, 293. Dissociation pressures of carbonates, 83. Dissociation of electrolytes, factors affecting, 39. Dissociation constants, 53; of acids, 295. Distribution coefficient, 221. Double precipitation, 140. Double weighing, 12. Drainage, error from, 244. Drying, devices for, 63; methods of, 30 Electric furnace, 67. Electro-neutrality, law of, 49. Electrodes, efficiencies of different, 146; forms of, 144-145. Electrode potential, determination of, 318; table of, 320. Electrolytic dissociation theory, development of, 36; importance of, 41. Electrolytic precipitation, effect of current strength on, 146; effect of con- centration on, 148. End-point, meaning of, 235; recognition of, in processes involving neutral- ization, 283; oxidation, 321; in titrations with silver, 257. Equilibrium, 42; effect of temperature on, 45; of pressure on, 45. Equilibrium constant, 44. Ether, purification of, 215. Evaporation, devices for, 62. Evolution method, 85. Extraction processes, 201. Factor weights, use of, 77. Faraday, law of, 146. Fat, chemical nature of, 214; determination of, 216. Filtering tube, use of, 126. Filtration, devices for, 123; media used for, 122. Gas volumes, calculation of, 80. Gangue matter, meaning of, 175. Gooch crucible, 126. Gypsum, determination of water in, 92; properties of, 90. Hematite, determination of iron in, 342. Heterogeneous equilibrium, 42. 398 INDEX Homogeneous equilibrium, 42. Hydriodic acid, substances reduced by, 351. Hydrocyanic acid, indirect determination of, 298. Hydrolysis, reactions involving, 58. Hydrometers, calibration of, 370. Hygroscopic water, 20. Ignition of precipitates, 131. Index of refraction, uses of, 362. Indicator constant, 285. Indicator theory, first case, 236; second case, 237. Indirect determinations, 78, 297, 351. Intermittent extraction, 203. Interpolation methods, use of, 361. Iodine, as an oxidating agent, 347; substances oxidized by, 350. Iodine solution, preparation of, 348; standardization of, 349. lodometric processes, 348. Ions, 37; formation of complex, 60. Iron, determination of, in cast iron, 328; in ferrous ammonium sulfate, 163; in ores, 342; errors in determination of, 176. Iron, methods of reducing, 328; separation of by ammonium hydroxide, 176; separation from nickel, 225. Iron ores, decomposition of, 340. Isohydric solutions, 55. Jones reductor, 329; use of, 330. Kainite, determination of chlorine in, 264. Kjeldahl method, 311. Knorr extraction apparatus, 204. Lead sulfate, properties of, 185. Lead tin alloy, analysis of, 184, 374. Limestone, analysis of, 175; determination of carbon dioxide in, 103. Lindo-Gladding method for potassium, 210. Logarithms, table of, 389-390. Magnesium ammonium phosphate, precipitation of, 159; ignition of, 160. Magnesium in magnesium sulfate, determination of, 159. Magnesium oxalate, properties of, 178. Manganese, determination of, in cast iron, 385; colorimetric method for, 383. Mass action, law of, 43. INDEX 399 Measurement of volumetric solutions, 240. M6ker burner, 65. Metastannic acid, properties of, 184. Mercury, determination of, 111. Methyl orange, use of, 290. Mixing of samples, 28. Mixtures with additive properties, 358. Modulus of hydrometers, 370. Moisture, determination of, 28. Monobasic acids, titration of, 292. Muffle, use of, 63; for heating tubes, 86. Multiple extraction apparatus, 206. Nessler's cylinders, 381. Neutralization, reactions involving, 278. Nickel, determination of, in nickel steel, 227. Normal system for standard solutions, 252; advantages of, 254. Occlusion, factors affecting, 134, 137; methods of avoiding errors from, 139; theories of, 133. Oxidation and reduction, 314. Oxidation and theory of the galvanic cell, 317. Oxidizing agents, normal values of, 316. Oxidizing capacity, 314. Oxidizing potential, 317. Paralax, errors from, 242. Para-nitro-phenol, use of, 291. Paris green, determination of arsenic in, 353. Partition processes, theory of, 223. Peanuts, composition of, 215; determination of fat in, 216. Petroleum, determination of specific gravity of, 376. Percentage error, 93. Permanganates, formation of, 383. Phase, definition of, 3. Phenolphthalein, color changes of, 284; uses of, 291. Phosphoric acid, indirect determination of, 298. Physical constants, uses of, 358. Pipets, forms of, 241; errors in using, 244. Point of rest of balance, 14; method of determining, 23. Potassium in potassium sulfate, determination of, 209. 400 INDEX Potassium bitartrate, determination of, 307. Potassium cyanide, determination of, 265. Potassium chloroplatinate, formation of, 209; properties of, 210. Potassium dichromate, end-points with, 337; factors affecting reaction with, 337; oxidizing capacity of, 336; oxidizing potential of, 336; preparation of standard solutions of, 339. Potassium ferrocyanide, factors affecting reaction with zinc, 270; preparation of a standard solution of, 273. Potassium nitrite, determination of, 331. Potassium permanganate, factors affecting reactions with, 323; oxidizing potential, 322; oxidizing capacity, 322; standardization of, 326; uses of, 325. Precipitation processes, general theory of, 115. Precipitates, classes of, 126; solubility of, 115. Pycnometer, use of, 367. Quantitative processes, classes of, 2. Reaction constant, 44. Reading burets, 248. Reduction of iron, methods of, 328; by stannous chloride, 341. Repression of ionization, T6. Reversible reactions, 46. Rosolic acid, use of, 291. Sampling, theory of, 26. Selection, methods of, 28. Sensitiveness of balance, 13; of indicators, 288. Separatory funnel, use of, 222. Separation of closely related ions, 119. Silicates, decomposition of, 194. Silica in hornblende, determination of, 194. Silicic acid, dehydration of, 195. Silver chloride, properties of, 154; theory of precipitation of, 117. Silver nitrate, preparation of standard solution of, 262. Size of particle, calculation of, 27. Slags, decomposition of, 386. Soda lime, properties of, 107. Sodium oxalate, uses of, 327. Solder, analysis of, 184. Solid mixtures, analysis of, 373. INDEX 401 Solubility, 32; effect of size of particles on, 34; of gases, 32. Solubility product, 116. Solutions, 31. Solution processes, theory of, 199. Solvent, 31. Soxhlet tube, 203. Specific gravity, 365; determination of, 366-367. Specific rotary power, 363. Specific volume, 365. Splitting a watch glass, 164. Stammar's colorimeter, 380. Standard solution, 234. Stirring devices in electrolytic precipitations, 153. Strength of acids and bases, 40. Sulfides, methods of oxidizing, 168. Sulfur in pyrites, determination of, 168. Sulfuric acid, determination of, 306; specific gravity of, 391. Superheating, 69. Supersaturation, 33. Tap water, determination of chlorine in, 264. Tea leaves, composition of, 230; determination of caffeine in, 231. Temperature changes in measuring solutions, 245. Temperature attainable with burners, 65. Thiosulfate solution, preparation of, 353. Titration, 234. Unit of volume, 246. Unitary system for standard solutions, 251. Valence, positive and negative, 314. Van't Hoff, law of, 35. Vapor pressures of mixed liquids, 70. Volumetric processes, advantages of, 238; reactions suitable for, 235; theory of, 234. Wash bottle, preparation of, 155. Washing precipitates, theory of, 129. Water, determination of, in copper sulfate, 100; in gypsum, 92; reactions involving formation of, 57. Weighing, abbreviated method of, 17; accurate method of, 16. 402 INDEX Weights, calibration of, 19, 25. Westphal balance, 371. Whitton's apparatus, 112. Wiley extraction apparatus, 203. Wiring of bench for electrolytic determinations, 152. Witt filter plates, 125. Wolff's colorimeter, 380. Zinc, determination of, as phosphate, 190; determination of, in an ore, 274, 276; effect of temperature on titration of, 270; effect of acid on titration of, 272; effect of concentration on titration of, 271. D. VAN NOSTRAND COMPANY 25 PARK PLACE NEW YORK SHORT-TITLE CATALOG OF Publications i Importations OF SCIENTIFIC AND ENGINEERING BOOKS This list includes the technical publications of the following English publishers: SCOTT, GREENWOOD & CO. JAMES MUNRO & CO., Ltd. CONSTABLE & COMPANY, Ltd. TECHNICAL PUBLISHING CO. BENN BROTHERS, Ltd. for whom D. Van Nostrand Company are American agents Descriptive Circulars sent on request. 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