AN INTRODUCTORY COURSE 
 
 OF 
 
 QUANTITATIVE 
 CHEMICAL ANALYSIS, 
 
 WITH 
 
 EXPLANATORY NOTES 
 
 AND 
 
 STOICH10METRICAL PROBLEMS. 
 
 HENRY P. TALBOT, PH.D., 
 
 ASSOCIATE PROFESSOR OF ANALYTICAL CHEMISTRY IN THE 
 MASSACHUSETTS INSTITUTE OF TECHNOLOGY. 
 
 NEW YORK: 
 THE MACMILLAN CO. 
 
 LONDON : MACMILLAN & Co., Ltd. 
 1897. 
 
T3 
 
 COPYRIGHT, 1897, 
 BY HENRY P. TALBOT. 
 

 ^ 
 
 ; 
 
 PREFACE. 
 
 THIS Introductory Course of Quantitative Analysis has been 
 prepared to meet the needs of students who are just entering 
 upon the subject, after a course of qualitative analysis. It is 
 primarily intended to enable the student to work successfully 
 and intelligently, without the necessity for a larger measure 
 of personal assistance and supervision than can reasonably be 
 given to each member of a large class. To this end the direc- 
 tions are given in such detail that there is very little oppor- 
 tunity for the student to go astray; but the manual is not, the 
 author believes, on this account less adapted for use with small 
 classes, where the instructor, by greater personal influence, can 
 stimulate independent thought on the part of the pupil. 
 
 The method of presentation of the subject is that suggested 
 by Prof. A. A. Noyes' excellent manual of Qualitative Analysis. 
 For each analysis the procedure is given in considerable detail, 
 and this is accompanied by explanatory notes, which are believed 
 to be sufficiently expanded to enable the student to understand 
 fully the underlying reason for each step prescribed. The use 
 of the book should nevertheless be supplemented by classroom 
 instruction, mainly of the character of recitations, and the student 
 should be taught to consult the larger works, such as those of 
 Fresenius, Mohr, and Sutton. The general directions of Part I 
 are intended to emphasize those matters upon which the begin- 
 ner in quantitative analysis must bestow special care, and to 
 offer some helpful suggestions. The student can hardly be ex- 
 pected to appreciate the force of all the statements contained in 
 these directions, or, indeed, to retain them all in the memory, 
 after a single reading, but the instructor, by frequent reference 
 
4 PREFACE. 
 
 to special paragraphs as suitable occasion presents itself, can 
 soon render them familiar to the student. 
 
 The analyses selected for practice are those comprised in the 
 course of " preliminary quantitative analysis " at the Massachu- 
 setts Institute of Technology, and have been chosen, after an 
 experience of some years, as affording the best preparation for 
 more advanced work, and as satisfactory types of gravimetric 
 and volumetric methods. From the latter point of view, they 
 also seem to furnish the best insight into quantitative analysis 
 for those students who can devote but a limited time to the sub- 
 ject, and who may never extend their study beyond the field cov- 
 ered by this manual. The author has had opportunity to te^t the 
 efficiency of the course for use with such students, and has 
 found the results satisfactory. 
 
 In place of the usual custom of selecting simple salts as mate- 
 rial for preliminary practice, it has been found advantageous to 
 substitute, in most instances, approximately pure samples of ap- 
 propriate minerals or industrial products. The difficulties are 
 not greatly enhanced, while the student gains in practical 
 experience. 
 
 It has been found expedient with large classes, to allow the 
 whole class to work simultaneously upon the same procedure, for 
 example, that for the determination of chlorine in sodium chlo- 
 ride, since classroom instruction can then be made more effective. 
 Each individual is, however, permitted to work as rapidly as his 
 capacity admits, and to such students as exhibit unusual facility in 
 manipulation, extra analyses are assigned. 
 
 The author has been unable to find any work in which such 
 stoichiometrical problems as are constantly met with in the experi- 
 ence of an analyst are dealt with in such detail as to enable the 
 student to fully understand the underlying principles. A chap- 
 ter has therefore been added in which such problems are pre- 
 sented, and the solutions of certain typical cases are explained. 
 A table of atomic weights and a table of four-place logarithms are 
 appended for convenience. 
 
PREFACE. 5 
 
 The analytical procedures, as detailed in this manual, are those 
 dictated by experience in the laboratories of the Institute. The 
 author has received many suggestions from standard works, but 
 no attempt has been made to enumerate these in full ; nor, on 
 the other hand, is any considerable credit claimed for originality. 
 Criticisms or corrections will be welcomed. 
 
 The author desires to express his obligation to Drs. W. H. 
 Walker and F. J. Moore, Instructors in Analytical Chemistry at 
 the Institute, for helpful suggestions, and much kind assistance in 
 the preparation of this work. 
 
 HENRY P. TALBOT. 
 
 MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 
 February, 1897. 
 

PART I. 
 
 INTRODUCTION. 
 
 A COMPLETE chemical analysis of a body of unknown 
 composition involves the recognition of its component parts 
 by the methods of qualitative analysis, and the determina- 
 tion of the proportions in which these components are pres- 
 ent by the processes of quantitative analysis. The quali- 
 tative examination is indispensable if intelligent and proper 
 provisions are to be made for the separation of the various 
 constituents, under such conditions as shall insure accurate, 
 quantitative estimations. 
 
 It is assumed that the operations of qualitative analysis 
 are familiar to the student, who will find that the reactions 
 made use of in quantitative processes are not infrequently 
 those employed for the qualitative detection of the same 
 element ; but it should be noted that the conditions must 
 now be regulated with greater care, and in such a manner 
 as to insure the most complete separations possible. For 
 example, in the qualitative detection of sulphates by pre- 
 cipitation as barium sulphate from acid solution, it is not 
 necessary, in most instances, to regard the solubility of the 
 sulphate in hydrochloric acid, while in the quantitative de- 
 termination of sulphates by this reaction, this solubility be- 
 comes an important consideration. The operations of qual- 
 itative analysis are, therefore, the more accurate, the nearer 
 they are made to conform to quantitative conditions. 
 
 The methods of quantitative analysis are sub-divided, ac- 
 cording to their nature, into those of gravimetric and vol- 
 iimetric analysis. In gravimetric processes the constituent 
 to be determined is isolated in the form of some compound 
 possessing a well-established and definite composition, which 
 can be readily and completely separated by filtration, and 
 
8 GENERAL DIRECTIONS. 
 
 weighed either directly, or after ignition. From the weight 
 of this body the amount of the constituent in question is 
 determined. 
 
 In volumetric analysis, instead of the final weighing of a 
 definite body, a well-defined reaction is caused to take place, 
 wherein the reagent is added in the form of a solution, of 
 which the strength (and hence the value for the reaction in 
 question) is accurately known. The volume of -this solution 
 required to complete the reaction then becomes a measure 
 of the substance acted upon. An example will make the 
 distinction clear. The percentage of chlorine in a sample of 
 sodium chloride may be determined by precipitation of the 
 chlorine from a weighed portion as silver chloride, which 
 is separated by filtration, ignited, and weighed (a gravime- 
 tric process) ; or the sodium chloride may be dissolved in 
 water, and a solution of silver nitrate, containing an accu- 
 rately known amount of the silver salt in each cubic centi- 
 meter, may be cautiously added until precipitation is com- 
 plete, when the amount of chlorine may be calculated from 
 the number of cubic centimeters of the silver nitrate solu- 
 tion involved in the reaction. This is a volumetric process 
 and is equivalent to weighing without the use of a balance. 
 
 Volumetric methods are generally more rapid, and fre- 
 quently capable of greater accuracy, than gravimetric methods. 
 
 GENERAL DIRECTIONS FOR QUANTITATIVE WORK. 
 
 The following suggestions should be carefully and thought- 
 fully read ; their adoption will lead to work of a high grade 
 of excellence, while their rejection may often lead to unsat- 
 isfactory or careless work. 
 
 NEATNESS. 
 
 The laboratory desk, and all apparatus, should be scrupu- 
 lously neat and clean at all times. A sponge should always 
 be ready at hand, and desk and filter-stands should be dry 
 and in good order. Funnels should never be allowed to 
 drip upon the base of the stand. Glassware should always 
 be wiped with a clean, lintless towel just before use. 
 
WASH-BOTTLES AND DESICCATORS. g 
 
 WASH-BOTTLES. 
 
 Wash-bottles, for distilled water, should be made from 
 flasks of about 750 cc. capacity and be provided with grace- 
 fully bent tubes, which should not be too long. The jet 
 should be connected with the tube entering the wash-bottle 
 by a short piece of rubber tubing, in such a way as to be 
 flexible, and should deliver a stream about one millimeter 
 in diameter. The neck of the flask may be wound with 
 twine, or covered with wash leather for greater comfort 
 when hot water is used. It is well to provide several 
 small wash-bottles for liquids other than distilled water, 
 which should invariably be clearly labelled. 
 
 DESICCATORS. 
 
 Desiccators should be filled with fused, anhydrous calcium 
 chloride, over which is placed an iron triangle wound with 
 platinum foil at those points which come into contact with 
 a hot crucible. The cover of the desiccator should be made 
 air-tight by the use of a thin coating of tallow. 
 
 Pumice moistened with sulphuric acid may be used in 
 place of the calcium chloride, and is essential in^ special 
 cases, but for most purposes the calcium chloride, if re- 
 newed occasionally and not allowed to cake together, is 
 equally efficient. 
 
 Desiccators should never remain uncovered for any length 
 of time. The dehydrating agents rapidly lose their efficiency 
 on exposure to the air. 
 
 CRUCIBLES. 
 
 Platinum crucibles should be employed for all ignitions . 
 and fusions, when possible. All crucibles, whether of plat- 
 inum or porcelain, must be heated and cooled in a desic- 
 cator before use. This is to insure parallel conditions in 
 separate weighings, which could not be obtained if the cru- 
 cible were cooled in contact with the air, since a layer of 
 moisture is then condensed on its surface, the amount vary- 
 ing with the humidity of the atmosphere. In the dry air 
 of the desiccator this difficulty is avoided. 
 
io GENERAL DIRECTIONS. 
 
 Crucibles should be cleaned, heated, and weighed before 
 each analysis. 
 
 Platinum crucibles should be frequently scoured, either 
 with sea sand or some preparation of the general character 
 of "sapolio." Constant heating causes a slight crystalliza- 
 tion of the surface of the platinum, which, if not removed, 
 penetrates into the crucible. Gentle abrasion of the sur- 
 face destroys the crystalline structure and prevents further 
 damage. If sea sand is used great care is necessary to 
 keep it from the desk, since beakers are easily scratched 
 by it, and subsequently broken on heating. 
 
 Platinum crucibles stained by iron may often be cleaned 
 by the use of potassium acid sulphate, or by heating with 
 ammonium chloride. If the former is used, care should be 
 taken not to heat so strongly as to expel all of the sul- 
 phuric acid, since the normal sulphate expands so rapidly 
 on cooling as sometimes to burst the crucible. 
 
 Bodies containing metals which might be reduced, with 
 the formation of metallic buttons, must not be treated in 
 platinum crucibles. Fusible alloys of platinum may be 
 formed which ruin the crucible. Compounds of phospho- 
 rus or arsenic must not be heated under reducing condi- 
 tions, since these elements, by contact with the platinum, 
 render it brittle. 
 
 Liquids containing free chlorine, aqua regia, or ferric chlo- 
 ride all exert a solvent action upon platinum, the ferric chlo- 
 ride to a lesser degree than the others. Care must be taken 
 to prevent the introduction' of platinum into analyses by a 
 disregard of these facts. 
 
 Caustic alkalies and peroxides of the alkalies attack plat- 
 inum freely. Fusions with these fluxes should be made in 
 silver crucibles. 
 
 EVAPORATION OF LIQUIDS. 
 
 Too great care cannot be taken to prevent loss of solu- 
 tions during processes of evaporation, either from too vio- 
 lent ebullition, from evaporation to dryness and spattering, 
 or from the evolution of gas during the heating. It may be 
 
REAGENTS. II 
 
 stated in general that evaporation upon the steam bath is 
 to be preferred to other methods on account of the im- 
 possibility of loss by spattering. If the steam baths are 
 well protected from dust, solutions should be left without 
 covers during evaporation, but solutions which are boiled 
 upon the hot plate, or' from which gases are escaping, should 
 invariably be covered. In any case a watch-glass may be 
 supported above the vessel by means of a glass triangle, or 
 other similar device, and the danger. of loss of material or 
 contamination by dust be thus avoided. 
 
 It is obvious that evaporation is promoted by the use of 
 vessels which admit of the exposure of a broad surface to 
 the air. 
 
 Liquids which contain suspended matter (precipitates) 
 should always be cautiously treated, since the presence of 
 the solid matter is frequently the occasion of violent " bump- 
 ing," with consequent risk to apparatus and analysis. 
 
 Liquids should never be transferred from one vessel to 
 another, nor to a filter, without the aid of a stirring rod 
 held firmly against the side or lip of the vessel. When the 
 vessel is provided with a lip it is not usually necessary to 
 use tallow or vaseline to prevent the loss of liquid by run- 
 ning down the side ; whenever this seems imminent a very 
 thin layer of tallow, applied with the finger to the edge of 
 the vessel, will suffice. The stirring rod, down which the 
 liquid runs, should never be drawn upward in such a way 
 as to allow the solution to collect on the under side of the 
 rim of a beaker. 
 
 REAGENTS. 
 
 All reagents should be measured, and a record of the 
 amounts used should be made in the notebook. 
 
 Whenever it is practicable, the amount of the reagent 
 required should be calculated, and a large excess avoided. 
 Many analyses are spoiled by a neglect of this precaution. 
 
 Reagents should be carefully examined for impurities. If 
 these are found, blank analyses must be made, using only 
 the reagents, and the amounts thus found deducted from 
 the weights of contaminated precipitates. Under these cir- 
 
I2 GENERAL DIRECTIONS. 
 
 cumstances, the value of the first suggestion in this para- 
 graph is obvious. 
 
 The stoppers of reagent bottles should never be laid upon 
 the desk, unless upon a clean watch-glass or paper. The 
 neck and mouth of all such bottles should be kept scru- 
 pulously clean, and care taken that no confusion of stoppers 
 occurs. 
 
 PRECIPITATION. 
 
 From theoretical considerations it appears that no sub- 
 stance is to be regarded as absolutely insoluble in a spe- 
 cific medium, although the solubility of many, which we 
 term insoluble bodies, is less than can be measured by the 
 means at our disposal. Successful precipitation must in- 
 volve conditions which insure the nearest approximation to 
 insolubility of the precipitated body, and the precipitate must 
 also be in a form favorable for filtration and washing. For 
 crystalline precipitates, the latter condition is fulfilled when 
 the crystals are relatively large. This is often attained by 
 allowing the. fine crystals, which first separate, to digest in 
 contact with the hot liquid from which they have fallen. 
 During this digestion the smaller crystals, which are very 
 slightly more soluble than the larger ones, redissolve, and 
 the solution, which is supersaturated as regards the larger 
 crystals, allows the latter to separate. This transfer is fur- 
 ther promoted by the influence of surface tension, which 
 tends to reduce the surface of the solid, i. e., to increase 
 the size of the individual crystals. 
 
 Certain amorphous bodies, such as ferric hydroxide, alu- 
 minum hydroxide, and silicic acid may pass into a colloidal 
 state, in which they form semi-solutions. This may happen 
 if an attempt is made to precipitate them from solutions 
 which are free from other salts. These rarely occur in anal- 
 ysis, but during the washing of these precipitates such semi- 
 solutions may sometimes be formed, unless some salt is 
 added to the wash water. In cases where the addition of 
 a salt to the wash water is impracticable, the precipitate 
 should be digested for some time on the steam bath with 
 the original solution, a procedure which lessens its ten- 
 dency to pass into the colloidal state. 
 
 
FILTRATION. 13 
 
 In all precipitations the reagent should be added slowly, 
 with constant stirring, and should be hot when circumstances 
 permit. The slow addition is less likely to occasion contam- 
 ination of the precipitate by the inclosure of other substances 
 which may be in the solution, or of the reagent itself. 
 
 For the complete removal of precipitates from containing 
 vessels, it is often necessary to rub the sides of these ves- 
 sels to loosen the adhering particles. This can best be done 
 by slipping over the end of a stirring rod a piece of soft 
 rubber tubing, which has been well washed to remove loose 
 fragments, or by using a piece of sheet rubber, which may 
 be folded over the rod and cemented together by moisten- 
 ing the surfaces with benzene. The sides of the beaker can 
 
 o 
 
 then be rubbed with the covered rod. 
 
 All stirring rods should have the ends rounded in the 
 flame to avoid scratching the beakers. 
 
 FILTRATION, AND THE TESTING OF FILTRATES AND 
 WASHINGS. 
 
 Distilled water should be employed in all quantitative work, 
 and nitration should be made only through " washed filters," 
 i. e., those which have been treated with hydrochloric and 
 hydrofluoric acids, and which, on incineration, leave a small 
 and definitely known weight of ash. Such filters are read- 
 ily obtainable in the market. , 
 
 Funnels should be selected which have an angle as near 
 60 as possible, and with a narrow stem about six inches in 
 length. The- filter should be accurately folded to fit the 
 funnel, and placed so that the top of the filter is about one- 
 fourth inch below the top of the funnel. Under no cir- 
 cumstances should the filter ever extend above the edge of 
 the funnel, as it is then utterly impossible to effect com- 
 plete washing. 
 
 To test the efficiency of the filter, fill it with distilled 
 water ; this water should soon fill the neck completely, 
 forming a continuous column of liquid which, by its hydro- 
 static pressure, produces a gentle suction, materially pro- 
 moting the rapidity of filtration. Unless the filter allows 
 
14 GENERAL DIRECTIONS. 
 
 a free passage of water under these conditions, its use is 
 likely to prove a source of annoyance. 
 
 The use of a vacuum pump to promote nitration is rarely 
 altogether advantageous in quantitative analysis, if paper fil- 
 ters are employed. The tendency of precipitates to pass 
 through the pores of the filter is increased, and this source 
 of danger more than compensates for the possible gain in 
 time. Exception may be made in the case of such precip- 
 itates as the hydroxides of chromium, aluminum, or iron, and 
 of silicic acid, but whenever suction is applied, the point of 
 the paper filter must be supported by a perforated platinum 
 cone or a small " hardened filter " of parchment. The rate 
 of filtration is often greater when an asbestos felt (Gooch 
 filter) is used (see page 27 for a description), and the pos- 
 sibility of a substitution of this for the paper filter should 
 always be considered. 
 
 When the filtrate is received in a beaker, the stem of the 
 funnel should touch the side of the receiving vessel to avoid 
 loss by spattering. Neglect of this precaution is a frequent 
 source of error. 
 
 The vessels which contain the initial filtrate should always 
 be replaced by clean ones, properly labelled, before the wash- 
 ing of a precipitate begins. In many instances a finely di- 
 vided precipitate, which shows no tendency to pass through 
 the filter at first, while the solution is relatively dense, ap- 
 pears at once in the washings. Under such conditions the 
 advantages accruing from the removal of the first filtrate 
 are obvious, both as regards the diminished volume requir- 
 ing refiltration, and also the lesser amount of washing sub- 
 sequently required. 
 
 Much time may often be saved by washing precipitates 
 by decantation, /'. e. t by .pouring over them, while still in the 
 original vessel, considerable volumes of wash-water and al- 
 lowing them to settle. The supernatant, clear wash-water 
 is then decanted through the filter, so far as is practicable 
 without disturbing the precipitate, and a new portion of 
 wash-water is added. This procedure can be employed to 
 special advantage with gelatinous precipitates, which fill up 
 the pores of the filter paper. As the medium from which 
 
IGNITION OF PRECIPITATES. 15 
 
 
 
 the precipitate is to settle becomes less dense, it subsides 
 less readily, and it becomes necessary to transfer it to the 
 filter and complete the washing there. 
 
 A precipitate should never fill the filter completely, and 
 the wash-water should be applied at the top of the filter, 
 above the precipitate. It may be shown mathematically 
 that the washing is most rapidly accomplished by filling the 
 filter well to the top with wash-water each time, and allow- 
 ing it to drain completely after each addition, but that when 
 a precipitate is to be washed with the least possible volume 
 of liquid the latter should be applied in repeated small quan- 
 tities. For a discussion of this matter and the phenomena 
 of adsorption, the student is referred to Ostwald's Founda- 
 tions of Analytical Chemistry, page 15, et seq. 
 
 Gelatinous precipitates should not be allowed to dry be- 
 fore complete removal of foreign matter is effected. They 
 are likely to shrink and crack, and subsequent additions of 
 wash-water pass through these channels only. 
 
 Solutions should be filtered while hot, as far as possible, 
 since the motion of the liquid through the pores of a filter 
 is retarded by internal friction, and this, for water at 100 
 C., is less than one sixth of the resistance at o C. 
 
 All filtrates and wash-waters without exception should be 
 properly tested. In testing the latter an amount not less 
 than 3 cc. should be taken for the final test. 
 
 It is impossible to trust to one's judgment with regard to 
 the washing of precipitates ; the washings from each pre- 
 cipitate of a series simultaneously treated must be tested, 
 since the rate of washing will often differ materially under 
 apparently similar conditions. No exception can ever be made 
 to this rule. 
 
 The habit of placing a clean filter paper under the receiv- 
 ing .beaker during filtration, is one to be commended. On 
 tnis paper a record of the number of washings can very well 
 be made as the portions of wash-water are added. 
 
 IGNITION OF PRECIPITATES. 
 
 The larger number of precipitates may, if proper precau- 
 tions are taken, be ignited without previous drying. If, how- 
 
T 6 GENERAL DIRECTIONS. 
 
 ever, such precipitates can be dried without loss of time to 
 the analyst (as,. for example, over night), it is well to submit 
 them to this process. It should, nevertheless, be remem- 
 bered that a partially dried precipitate requires as much, or 
 more care during ignition than a thoroughly moist one. 
 
 The precipitate, with the filter folded over it, should be 
 placed well at the base of the crucible, which should then 
 be placed so far above the flame of the lamp that no vio- 
 lent escape of steam is possible. When the filter and con- 
 tents have dried, the crucible should be placed on its side 
 without the cover, and the heat should be gently increased 
 until the filter chars, but should never be increased beyond 
 this point until all volatile matter from the dry distillation 
 of the filter paper has been expelled without taking fire. 
 Much annoyance will be avoided by observing this point. 
 
 During this preliminary heating the flame should be placed 
 near the mouth of the crucible, but in all subsequent heat- 
 ing the flame of the lamp should be well at the base of the 
 crucible, as it is inclined upon its side, to allow a ready 
 access of oxygen and to avoid the entrance of unburned 
 (reducing) gases. When the filter has charred, the heat 
 should be raised to redness until ignition is complete. 
 The heating of precipitates over the blast lamp is to be 
 avoided unless specially directed. 
 
 The limited number of instances in which the precipitate 
 must be separated from the filter preliminary to ignition 
 will be treated of as they occur. 
 
 USE AND CARE OF BALANCES. 
 
 The analytical balance is a delicate instrument, which will 
 perform excellent service under careful treatment, but such 
 treatment is an essential condition if its accuracy is to be 
 depended upon. The following rules may be regarded as 
 embodying the important points involved in the use of a bal- 
 ance, but no rules can do away with the necessity for a 
 sense of personal responsibility on the part of each student, 
 since by carelessness he can render inaccurate not only his 
 own analyses, but those of other students using the balance : 
 

 USE OF BALANCES. 17 
 
 1. The balance pans should be brushed off and the ad- 
 justment of the balance tested before use, particularly where 
 several persons use the same instrument. 
 
 To determine whether or not the balance is in adjust- 
 ment, note (i) whether it is level; (2) whether the pointer 
 rests at zero when the beam is lifted from its knife-edges, 
 and also when lowered so that the pan arrests touch the 
 scale pans ; (3) that the mechanism for raising and lowering 
 the beams works smoothly; (4) that the pan arrests touch 
 the pans when the beam is lowered ; and (5) that the needle 
 swings equal distances on either side of the zero-point when 
 set in motion without any load on the pans. If the latter 
 condition is not absolutely fulfilled, the balance should be 
 adjusted, unless the variation is not more than one division 
 on the scale ; it is often better to make a proper allowance 
 for this zero error rather than to disturb the balance by an 
 attempt at correction. 
 
 Unless a student thoroughly understands the construction 
 of a balance he should never attempt to make adjustments, 
 but should apply to the instructor in charge. For a dis- 
 cussion of the construction and essential characteristics of 
 a balance the student is referred to Fresenius Quantitative 
 Analysis. 
 
 2. The beam should never be set in motion by lowering 
 it forcibly upon the knife-edges, nor by touching the pans, 
 but rather by means of the rider (unless the balance be 
 provided with some of the newer devices for the pur- 
 pose), and the swing should be arrested only when the 
 needle passes the zero on the scale, otherwise the knife- 
 edges become dull. For the same reason the beam | 
 should never be left upon its knife-edges, "nor should 
 weights be removed from, or placed on the pans without 
 supporting the beam, except in the case of the small frac- 
 tional weights. 
 
 3. In testing the weight of a body, the weights should be 
 applied in the order in which they occur in the weight-box 
 (not at haphazard), and the weight should be recorded first 
 by noting the weights missing from the weight-box, and 
 that record subsequently checked as th'ese weights are 
 
1 8 GENERAL DIRECTIONS. 
 
 taken from the pan. This practice will often avoid or 
 detect errors. 
 
 4. The balance-case should always be closed during the 
 final weighing, when the rider is used, to protect the pans 
 from the influence of air currents. 
 
 Before the final determination of an exact weight the 
 beam should always be lifted from the knife-edges and 
 again lowered into place, as it frequently happens that 
 the scale pans are twisted by the impact of the weights, the 
 beam being virtually lengthened or shortened. Lifting the 
 beam restores the proper alignment. 
 
 After the weighing is finished, the weights should always 
 be replaced in their proper places in the weight-box and 
 the rider taken from the beam. 
 
 5. No chemical substance should ever be placed directly 
 upon the balance-pan. Every substance or vessel weighed 
 should be dry and cold. A warm object occasions the for- 
 mation of air currents, which vitiate the accuracy of the 
 weight. 
 
 6. Above all, if any damage be done to a balance, if any 
 substance be spilled upon the pans, or if the mechanism 
 appear to be deranged, the matter should receive imme- 
 diate attention, and should be reported at once to the in- 
 structor in charge. In the majority of instances serious 
 damage can be averted by prompt action, when delay might 
 ruin the balance. 
 
 
 NOTEBOOKS. 
 
 Notebooks should contain, beside the record of observa- 
 tions, descriptive notes. All records of weights should be 
 placed upon the right-hand page, while that on the left is 
 reserved for the notes, calculations of factors, or the amount 
 of reagents required. 
 
 The neat and systematic arrangement of the records of 
 analyses is of the first importance, and is an evidence of 
 careful work and an excellent credential. Of two notebooks 
 in which the results may be, in fact, of equal value as legal 
 
ECONOMY OF TIME. 19 
 
 _ 
 
 evidence, that one which is neatly arranged will carry with 
 it greater weight. 
 
 All records should be dated, and all observations should 
 be recorded at once in the notebook. The making of rec- 
 ords upon loose paper is a practice to be deprecated, as is 
 also that of copying original entries into a second notebook. 
 The student should accustom himself to orderly entries at 
 the time of observation. 
 
 The descriptive notes should mention any special diffi- 
 culties encountered in the analyses and the remedies applied, 
 and also incidents in the course of the analysis, if any, which 
 may possibly influence the results injuriously. All analyses 
 should be made in duplicate, and in general a close agree- 
 ment in results should be expected. It should, however, be 
 remembered that a close concordance of results in "check 
 analyses " is not conclusive evidence of the accuracy of those 
 results, although the probability that such is the case is, of 
 course, considerably enhanced. The satisfaction in obtain- 
 ing " check results " in such analyses must never be allowed 
 to interfere with the critical examination of the procedure 
 employed, nor must they ever be regarded as in any meas- 
 ure a substitute for absolute truth and accuracy. 
 
 ECONOMY OF TIME. 
 
 An economical use of laboratory hours is best secured by 
 acquiring a thorough knowledge of the character of the work 
 to be done before undertaking it, and then by so arranging 
 the work that no time shall .be wasted during the evapora- 
 tion of liquids and like time-consuming operations. To this 
 end the student should read thoughtfully not only the pro- 
 cedure, but the explanatory notes as well, before any step is 
 taken in the analysis. 
 
 Several analyses should be in progress at once and con- 
 fusion carefully guarded against by a free use of labels. 
 
 In general, economy of time results from the filtration of 
 several solutions at once, since the washing of five or more 
 precipitates may frequently be accomplished in the time re- 
 quisite for any one, if taken alone. 
 
20 GENERAL DIRECTIONS. 
 
 ACCURACY AND INTEGRITY DEMANDED. 
 
 The fundamental conception of . ..rmtitative analysis im- 
 plies a necessity for all possible care in guarding against 
 loss of material, or the introduction of foreign matter. All 
 filters and solutions should be covered to protect them from 
 dust, just as far as is practicable, and every particle of solu- 
 tion or precipitate must be regarded as invaluable for the 
 success of the analysis. 
 
 In this connection it must also be emphasized that only 
 the operator himself can know the whole history of an an- 
 alysis, and only he can know whether his work is worthy of 
 full confidence. No work should be continued for a moment 
 after such confidence is lost, but should be resolutely dis- 
 carded as soon as a cause for distrust is fully established. 
 The student should determine to put forth his best efforts 
 in each analysis ; it is well not to be too ready to condone 
 failures and to "begin again," as much time is lost in these 
 fruitless attempts. Nothing less than absolute integrity is or 
 can be demanded of a quantitative Analyst, and any disregard 
 of this principle, however slight, is as fatal to success as lack 
 of chemical knowledge or inaptitude at manipulation can pos- 
 sibly be. 
 
 
 
 ' * * 
 
 -BF -" 
 
 
 
* 
 
 PART II. 
 
 
 t 
 GRAVIMETRIC , TALYSIS. 
 
 -- 
 
 DETERMINATION OF CHLORINE IN SODIUM CHLORIDE. 
 
 PREPARATION. 
 
 ; 
 
 THE preparation of chemically pure sodium chloride from 
 the commercial article may be effected as follows : 
 
 Procedure. Weigh out, upon rough balances, about 50 
 grams of a sample of "table salt," cover this with 129 cc. 
 of distilled water, stir until the water is saturated, and filter. 
 To the filtrate add concentrated hydrochloric acul (sp. gr. 
 i. 20) until the chloride begins to separate, then pass into 
 the solution gaseous hydrochloric acid. This acidithould be 
 generated in a flask, from rock salt and commercial sulphu- 
 ric acid. The gas should be washed, by passing it through 
 concentrated, aqueous hydrochloric acid, and the delivery- 
 tube should terminate in a 2-inch funnel, placed mouth 
 downward, to prevent the clogging of the delivery-tube 
 by the separated salt. When the separation of ''the salt 
 has apparently ceased, remove it by filtration upon a 
 paper disc placed upon a perforated porcelain plate (a 
 Witt filter), and drain by suction. Wash the chloride with 
 25 cc. of hydrochloric^ acid (sp. gr. 1.12) in successive small 
 portions, allowing the precipitate to drain completely after 
 each addition. Wash finally wfth a small quantity (5 cc.) of 
 water, and test this wash-water for sulphates. If sulphates 
 are found, the washing with hydrochloric acid must be con- 
 tinued. When freed f n sulphates, transfer. the precipitate 
 to a porcelain or platinum dish, or crucible, and heat until 
 decrepitation ceases. The chloride should then be allowed 
 
 
 
22 GRAVIMETRIC ANALYSIS, 
 
 to cool in a desiccator, and be placed in a weighing-tube (like 
 a small test-tube), which should be kept tightly stoppered. 
 
 Notes. i. The commercial grades of table salt contain, 
 beside sodium chloride, chlorides or sulphates of magnesium, 
 calcium, or potassium, the two first-named causing the salt to 
 absorb moisture. When hydrochloric acid is added to a 
 saturated solution of the salt, sodium chloride is thrown 
 down, leaving the impurities in solution. The principle un- 
 derlying this separation may be briefly stated by saying 
 that the solution is saturated with respect to chlorine radi- 
 cals (chlorine ions, more properly), and when more of these 
 chlorine ions are added, in the form of the readily soluble 
 hydrochloric acid, some of those in combination with sodium 
 are forced out of solution in the form of the relatively insol- 
 uble sodium chloride. 
 
 2. The precipitation of the sodium chloride might be ef- 
 fected more quickly by the addition of liberal quantities of 
 concentrated aqueous hydrochloric acid, but its purity is less 
 certain under those conditions. The slow separation, caused 
 by the absorption of the gas, is more favorable to the isola- 
 tion of a pure product, and the process is also somewhat 
 more economical. 
 
 3. Since the sodium chloride is not insoluble in either 
 the acid or the water used for washing, it is essential that 
 these should be used in as small quantities as is practicable. 
 Note the statement on page 15 concerning the most efficient 
 method of washing a precipitate with a limited quantity of 
 liquid. 
 
 4. The heating of the chloride is essential to expel any 
 excess of hydrochloric acid held by the salt, and to remove 
 moisture inclosed, between crystal surfaces. The escape of 
 this moisture is the cause of decrepitation. Even the pure 
 salt is slightly hygroscopic ; hence the necessity for cooling 
 in the dry air of the desiccator and for preservation in stop- 
 pered tubes. 
 
 ANALYSIS. 
 
 The sodium chloride, prepared as above, is ready for analy- 
 sis, and if the preparation has been carefully made, the per- 
 centage of chlorine found on analysis should agree closely 
 with that calculated from the symbol. 
 
DETERMINATION OF CHLORINE. 23 
 
 Procedure. Carefully clean the weighing-tube containing 
 the sodium chloride, handling it as little as possible with the 
 moist fingers, and weigh it accurately to o.oooi gram, re- 
 cording the weight at once in the notebook. Hold the tube 
 over the top of a No. 3 lipped beaker, and cautiously remove 
 the stopper, noting carefully that no particles fall from it, 
 or from the tube, elsewhere than into the beaker. Pour out 
 a small portion of the chloride, replace the stopper, and de- 
 termine by approximate weighing how much has been re- 
 moved. Continue this procedure until 0.25-0/30' gram has 
 been taken from the tube, then weigh accurately and record 
 the weight beneath the first in the notebook. The differ- 
 ence of the two weights represents the weight of the chlo- 
 ride taken for analysis. Again weigh a second portion of 
 0.25-0.30 gram into a second beaker of the same size as 
 the first. The beakers should be plainly marked to corre- 
 spond with the entries in the notebook. Dissolve each 
 portion of the chloride in 150 cc. of distilled water, and add 
 about ten drops of nitric acid (sp. gr. 1.20). Calculate .the 
 volume of a silver nitrate solution required to effect com- 
 plete precipitation in each case, and add slowly about 5 cc. 
 in excess of that amount, with constant stirring. Heat the 
 solutions cautiously to boiling, stirring occasionally, and con- 
 tinue the heating and stirring until the precipitates settle 
 promptly, leaving a nearly clear supernatant liquid. This 
 heating should not take place in direct sunlight. The 
 beaker should be covered with a watch-glass, and both 
 boiling and stirring so regulated as to preclude any possi- 
 bility of loss of material. Add to the clear liquid one or 
 two drops of silver nitrate solution, to make sure that an 
 excess of the reagent is present. Prepare two washed fil- 
 ters (9 cm. in diameter), bearing in mind the precautions 
 mentioned on pages 13 and 14, and pass the liquid through 
 the filter, leaving the chloride in the beaker as far as pos- 
 sible. Wash the precipitates two or three times with 
 hot water, by decantation, transfer them to the filter by 
 means of a stream from the wash-bottle, with the aid of a 
 feather or a rubber tip on a stirring rod, if need be. Fi- 
 nally remove the main filtrate, replace by a clean beaker, 
 
2 4 
 
 GRA VI ME TRIG ANAL YS1S. 
 
 and wash the filters and precipitates until 3 cc. of the wash- 
 ings show no cloudiness with a drop of hydrochloric acid. 
 The funnels should then be covered with a filter paper 
 which has been previously moistened and stretched over 
 the sides of the funnel, to which it will adhere on drying. 
 It should be properly labelled with the student's name and 
 desk number, and then placed in a drying closet, at a tem- 
 perature of about 100-110 C., until completely dry. Put 
 the filtrate containing the silver nitrate aside in a suitable 
 receptacle for "silver residues," from which the silver can 
 be recovered. 
 
 The perfectly dry filter is then opened over a circular 
 piece of clean, smooth, glazed paper about six inches in di- 
 ameter, placed upon a larger piece about twelve inches in 
 diameter. The precipitate is removed from the filter as 
 completely as possible, by rubbing the sides gently to- 
 gether, or by scraping them cautiously with a feather, 
 which has been cut close to the quill and is slightly stiff. 
 In either case, care must be taken not to rub off any con- 
 siderable quantity of the paper, nor to lose silver chloride 
 in the form of dust. Cover the precipitate on the glazed 
 paper with a watch-glass, to prevent loss of fine particles 
 and to protect it from dust. Fold the filter paper care- 
 fully, as it was when it came from the funnel, roll it into a 
 small cone, and wind loosely around the top a piece of small 
 platinum wire. Hold the filter by the wire over the proper 
 porcelain crucible, ignite it, and allow the ash to fall into 
 the crucible. Place the crucible upon a clean clay triangle, 
 on its side, and ignite, with the flame well at its base un- 
 til all the carbon of the filter has been consumed. Allow 
 the crucible to cool, add two drops of nitric acid and one 
 drop of hydrochloric a,cid, and heat very cautiously, to avoid 
 spattering, until the acids have been expelled ; then trans- 
 fer the main portion of the precipitate from the glazed 
 paper to the cooled crucible, placing the latter, for the pur- 
 pose, on the larger piece of glazed paper and brushing the 
 precipitate from the smaller piece into it, sweeping up all 
 particles belonging to the determination. 
 
 Moisten the precipitate with two drops of nitric acid and 
 
DETERMINATION OF. CHLORINE. 25 
 
 one drop of hydrochloric acid, and again heat with great 
 caution until the acids are expelled and the precipitate is 
 white, after which the temperature is gradually raised until 
 the silver chloride begins to fuse. The crucible is then 
 cooled in a desiccator and weighed, after which the heat- 
 ing (without the addition of acids) is repeated, and it is 
 again weighed. This must be continued until the weight 
 is constant within 0.0003 gram in two consecutive weigh- 
 ings. Deduct the weight of the crucible, and calculate the 
 weight of chlorine in the silver chloride, and subsequently 
 the percentage in the sample of sodium chloride taken for 
 analysis. Consult Part IV, page 105. 
 
 Notes. i. The nitric acid is added before precipitation 
 to lessen the tendency of the silver chloride to carry down 
 with it other substances which may be present in the solu- 
 tion. A large excess of the acid would exert a slight solvent 
 action upon the chloride. 
 
 2. The solution should not be boiled after the addition of 
 the nitric acid, before the presence of an excess of silver 
 nitrate is assured, since a slight interaction between the nitric 
 acid and the sodium chloride is possible, by which a loss of 
 chlorine, either as such or as hydrochloric acid, might ensue. 
 The presence of an excess of the precipitant can usually be 
 recognized at the time of its addition, by the increased readi- 
 ness with which the precipitate clots together and settles. 
 
 3. The precipitate should not be exposed to strong sun- 
 light, since by its action a reduction of the silver chloride 
 is effected, accompanied by a loss of chlorine. The superfi- 
 cial alteration which the chloride undergoes in diffused day- 
 light is not fatal to the accuracy of the determination, since 
 the slight loss of chlorine may be counteracted by the treat- 
 ment of the precipitate with nitrohydrochloric acid, as noted 
 below. 
 
 4. The precipitate must be washed with hot water until it 
 is absolutely free from silver and sodium nitrates. It may be 
 assumed that the sodium is also completely removed when the 
 wash-water shows no evidence of silver. It must be borne 
 in mind that silver chloride is somewhat soluble in hydro- 
 chloric acid, and only a single drop, should be added. The 
 
26 GRAVIMETRIC ANALYSIS. 
 
 washing should be continued until no cloudiness whatever 
 can be detected in 3 cc. of the washings. 
 
 5. The separation of the silver chloride from the filter is 
 essential, since the burning carbon of the paper would reduce 
 a considerable quantity of the precipitate to metallic silver, 
 and its complete reconversion to the chloride within the cru- 
 cible, by means of acids, would be accompanied by some un- 
 certainty. The small amount of precipitate which adheres 
 to the filter is partially reduced to metallic silver during the 
 ignition, but this small quantity can be dissolved in the nitric 
 acid which is added, and completely reconverted to chloride 
 by the hydrochloric acid. The subsequent addition of these 
 two acids to the main portion of the precipitate restores the 
 chlorine to the chloride reduced by the sunlight. 
 
 The platinum wire is wrapped around the top of the filter 
 during its incineration, to avoid contact with any reduced sil- 
 ver which might come from the reduction of the precipitate. 
 If the wire was placed nearer the apex, such contact could 
 hardly be avoided. 
 
 6. Silver chloride should not be heated to complete fu- 
 sion, since a slight loss by volatilization is possible at higher 
 temperatures. The temperature of fusion is not always 
 sufficient to destroy filter shreds ; hence these should not 
 be allowed to contaminate the precipitate. 
 
 7. The ignited precipitate of silver chloride should be 
 placed in the jar for "silver residues." The crucible may 
 be cleaned by placing in it some granulated zinc and sul- 
 phuric acid. The chloride is soon loosened, and may be 
 detached. 
 
 8. Silver chloride is practically insoluble in water and di- 
 lute nitric acid, slightly soluble in strong nitric acid, and ap- 
 preciably so in strong hydrochloric acid. It is also slightly 
 soluble in hot concentrated solutions of silver nitrate. The 
 chloride is readily soluble in aqueous ammonia and in solu- 
 tions of potassium cyanide and sodium thiosulphate. 
 
 9. Stoppers in weighing-tubes are likely to change in 
 weight from the varying amounts of moisture absorbed 
 from the atmosphere. It is, therefore, necessary to confirm 
 the recorded weight of a tube which has been unused for 
 some time, before weighing out a new portion of substance 
 from it. 
 
DETERMINATION OF CHLORINE. 27 
 
 DETERMINATION OF CHLORINE IN SODIUM CHLORIDE, WITH 
 THE USE OF A GOOCH FILTER. 
 
 A commercial sample of table salt may advantageously be 
 substituted for the pure sodium chloride, if the latter has 
 already been examined. The table salt should be heated 
 until decrepitation ceases, and cooled in a desiccator. 
 
 Procedure. (&) Weigh out two portions of the sub. 
 stance, each weighing about 0.25 gram, and precipitate 
 the silver chloride as described in procedure (a). Mean- 
 while prepare a Gooch filter as follows : Select a small 
 glass funnel, I to ij inches in diameter, and stretch over 
 its mouth a piece of rubber-band tubing (" bill-tie tubing") 
 about i inch wide and ij. inches long. This should be 
 drawn down on the sides of the funnel until it holds firmly, 
 leaving an opening at the center of the mouth of the funnel, 
 into which a perforated porcelain crucible (Gooch crucible) 
 is fitted. The rubber should be drawn up around the sides 
 of the crucible until it is air-tight. Fit the glass funnel 
 into the stopper of a filter bottle, and connect it with the 
 vacuum pump. Suspend some finely divided asbestos, which 
 has been washed with acid, in 20 to 30 cc. of water ; allow 
 this to settle, pour off the very fine particles, and then 
 pour the rest cautiously into the crucible until an even felt 
 of asbestos, not over -fa inch in thickness, is formed. A 
 gentle suction must be applied while preparing this felt. 
 Wash the felt thoroughly with distilled water until all 
 fine or loose particles are removed, then place the cruci- 
 ble in a small beaker, and place both in a drying closet at 
 130 C. for 30 to 40 minutes. Cool the crucible in a des- 
 iccator, and weigh. Heat again for 20 to 30 minutes, cool, 
 and again weigh, repeating this until the weight is constant 
 within 0.0003 gram. The filter is then ready for use. 
 
 Replace the crucible in the funnel, and apply a gentle 
 suction, after which, pour in the solution to be filtered, with- 
 out disturbing the asbestos felt. When pouring liquid into 
 a Gooch filter, hold the stirring rod well down in the cru- 
 
2 8 GRAVIMETRIC ANALYSIS. 
 
 cible, so that the liquid does not fall with any force upon 
 the asbestos. 
 
 Transfer the whole of the precipitate to the filter, and 
 wash thoroughly with hot water until free from soluble sil- 
 ver salts, then dry, at 130 C, to a constant weight. The 
 percentage of chlorine may be calculated from the weight 
 of silver chloride. 
 
 Notes. i. The asbestos should be of the finest quality 
 and capable of division into minute fibrous particles. A 
 coarse felt is not satisfactory. 
 
 The use of the Gooch filter commends itself strongly when 
 a considerable number of halogen determinations are to be 
 made, since successive portions of the silver halides may be 
 filtered o.n the same filter, without the removal of the pre- 
 ceding portions, until the crucible is about two thirds filled. 
 The use of a perforated disc of porcelain or platinum, which 
 may be placed upon the top of the asbestos felt, serves to 
 protect it in some measure, but it is obvious that care should 
 be taken to avoid loosening the felt at the edges as the liquid 
 is poured upon it. If the felt is properly prepared, filtration 
 and washing are rapidly accomplished on this filter, and this 
 factor, combined with possibility of collecting several precip- 
 itates on the same filter, are strong arguments in favor of 
 its use with any but gelatinous precipitates. If perforated 
 platinum crucibles are employed, which can be fitted into a 
 platinum cap after removal from the funnel, the precipitates 
 can be ignited over the flame of a lamp as in an ordinary 
 platinum crucible. The asbestos is apt to curl away from the 
 edges during such heating, and if the same filter be used for 
 a second time, great care is required to prevent loss of asbestos. 
 
 2. A funnel tube, made from stout glass tubing about 
 ij inch inside diameter and 3 inches long, to which is at- 
 tached a tube of suitable size and length to pass through a 
 rubber stopper, may be substituted for the glass funnel 
 above prescribed. It is then only necessary to cover the 
 upper edges of this tube with rubber. The crucible may be 
 pressed into it, and makes air tight connections. 
 
FERROUS AMMONIUM SULPHATE. 29 
 
 DETERMINATION OF IRON AND OF SULPHUR IN 
 FERROUS AMMONIUM SULPHATE. 
 
 FeSO 4 . (NH 4 ) 2 SO 4 . 6H 2 O. 
 
 DETERMINATION OF IRON. 
 
 Procedure. Select a quantity of perfectly clear crystals 
 of the salt sufficient to fill a weighing tube. Weigh out, 
 into two No. 4 lipped beakers, two portions of about i gram 
 each, and dissolve these in 50 cc. of water, to which I cc. 
 of hydrochloric acid (sp. gr. 1.12) has been added. Heat the 
 solution to boiling, and while at the boiling point add nitric 
 acid (sp. gr. 1.42), drop by drop (noting the quantity used), 
 until the brown coloration, which appears after the addition 
 of a part of the nitric acid, gives place to a yellow or red. 
 Avoid a large excess of nitric acid, but be sure that the ac- 
 tion is complete. Pour this solution cautiously into about 
 200 cc. of water, containing a slight excess of ammonia. 
 Calculate for this purpose the amount of aqueous ammonia 
 required to neutralize the acids added, and also to precipitate 
 the iron as ferric hydroxide from the weight of the ferrous 
 ammonium sulphate taken for analysis. The volume" thus 
 calculated will be a slight excess over that actually required, 
 since a part of .the acids are consumed in the oxidation proc- 
 ess, or are volatilized. Heat the solution to boiling, and 
 allow the precipitated ferric hydroxide to settle. Decant 
 the clear liquid through a washed filter (9 cm.), keeping as 
 much of the precipitate in the beaker as possible. Wash 
 once by decantation with 100 cc. of hot water, and then 
 transfer the bulk of the precipitate to the filter. Dissolve 
 the iron from the filter with hot hydrochloric acid, and col- 
 lect the solution in the beaker in which precipitation took 
 place. Add 3 cc. of nitric acid (sp. gr. 1.42), boil for a few 
 moments, and again pour into an excess of ammonia. Wash 
 the precipitate twice by decantation, and finally throw it on 
 the filter, and wash continuously with hot water until 3 cc. 
 of the washings show no evidences of the presence of chlo- 
 rides when tested with silver nitrate, acidified with nitric 
 
3 
 
 GRAVIMETRIC ANALYSIS. 
 
 acid. The filtrate and washings are combined with those 
 from the first precipitation. 
 
 The moist precipitate is placed in a platinum crucible 
 which has been previously heated, cooled in a desiccator, 
 and weighed. It is then treated according to the directions 
 for "Ignition of Precipitates," page 16. When the volatile 
 matter of the filter has been expelled, raise the temperature 
 to the full heat of the burner for fifteen minutes, and finally 
 heat over the blast lamp, with the crucible covered, for three 
 minutes. Cool and weigh. Repeat the strong heating 
 until the weight is constant within 0.0003 gram. Exercise 
 great care when heating over the blast lamp that a small 
 flame is used, and that this is directed against the bottom 
 of the crucible in such a way as to preclude the entrance 
 of unburned or reducing gases into it, by reflection from 
 the edges of the cover. From the weight of ferric oxide 
 (Fe 2 O 3 ) calculate the weight of iron (Fe) and the percent- 
 age of the latter in the sample. 
 
 Notes. i. If a selection of pure material for analysis is 
 to be made, those crystals which are cloudy are to be avoided, 
 on account of loss of water of crystallization ; and also those 
 which are red, indicating the presence of ferric iron. If, on 
 the other hand, the value of an average sample of the material 
 is desired, it is preferable to grind the whole together, mix 
 thoroughly, and take from the mixture a sample for analysis. 
 
 2. The hydrochloric acid is added to prevent the precipi- 
 tation of basic ferric salts during solution, as a result of a par- 
 tial oxidation o*f the iron in the absence of free acid. The 
 nitric acid oxidizes the ferrous iron, after attaining a mod- 
 erate strength, with the formation of an intermediate nitroso- 
 compound similar in character to that formed in the "ring- 
 test" for nitrates.' The nitric oxide is driven out by heat, 
 and the solution then shows by its color the presence of ferric 
 chloride. A drop of the oxidized solution may be tested on a 
 watch-glass with potassium ferricyanide, to insure the absence 
 of ferrous salts. This oxidation of the iron is necessary, since 
 ferrous salts are not completely precipitated by ammonia. 
 
 3. The ferric hydroxide tends to carry down some sul- 
 phuric acid in the form of basic ferric sulphate. This ten- 
 
DETERMINATION OF IRON. 31 
 
 dency is lessened if the solution of the iron is added to an 
 excess of ammonia, since under these conditions immediate 
 and complete precipitation of the hydroxide ensues ; whereas, 
 by the gradual neutralization with ammonia, the opportunity 
 for the local formation of a neutral solution within the liquid, 
 and consequent deposition of a basic sulphate, is favored. 
 Even with this precaution the entire absence of sulphates 
 from the first iron precipitate is not assured. It is, there- 
 fore, redissolved and again thrown down by ammonia. The 
 organic matter of the filter paper may occasion a partial re- 
 duction of the iron during solution, with consequent possibil- 
 ity of incomplete precipitation with ammonia. The nitric 
 acid is added to reoxidize this iron. 
 
 4. By the ignition of ferric oxide with ammonium chlo- 
 ride, volatile ferric chloride is formed, with consequent loss 
 of iron. The precipitate must, therefore, be completely 
 washed. The washings are acidified with nitric acid, before 
 testing with silver nitrate, to destroy the ammonia, which is 
 a solvent of silver chloride. 
 
 The use of suction to promote filtration and washing is 
 permissible, though not prescribed. The precipitate should 
 not be allowed to dry during the washing, for reasons stated 
 on page 15. 
 
 5. To avoid errors arising from the solvent action of 
 ammoniacal liquids upon glass, the iron precipitate should 
 be filtered without unnecessary delay. 
 
 6. The directions for the ignition of precipitates must be 
 closely followed. A ready access of atmospheric oxygen 
 is of special importance, to insure the reoxidation to ferric 
 oxide of any iron which may be reduced to magnetic oxide 
 during the combustion of the filter. The final heating over 
 the blast lamp is essential for the complete expulsion of the 
 last traces of water from the hydroxide. 
 
 7. Ignited ferric oxide is somewhat hygroscopic, on which 
 account the weighings must be promptly completed after re- 
 moval from the desiccator. In all weighings after the first, 
 it is well to place the weights upon the balance pan before 
 removing the crucible from the desiccator. It is then only 
 necessary to move the rider to obtain the weight. 
 
 8. Ferric hydroxide is practically insoluble in ammoniacal 
 liquids, in the presence of ammonium salts, but the corre- 
 
32 GRAVIMETRIC ANALYSIS. 
 
 spending hydroxides of aluminum and chromium are partially 
 redissolved by an excess of ammonia. Chromium hydroxide 
 is much the most soluble of the three. In other respects 
 the gravimetric determination of these two metals is compar- 
 able with that of iron. 
 
 For a further statement of the properties of these bodies 
 the student is referred to Fresenius* Quantitative Analysis, 
 under "Forms." 
 
 DETERMINATION OF SULPHUR. 
 
 Procedure. Add to the combined filtrates from the ferric 
 hydroxide, hydrochloric acid in moderate excess, and evapo- 
 rate to dryness on the water bath. Add 10 cc. of hydro- 
 chloric acid (sp. gr. 1.12) to the residue, and again evaporate 
 to dryness on the bath. Dissolve the residue in water, fil- 
 ter if not clear, transfer to a No. 5 lipped beaker, dilute to 
 about 400 cc., and cautiously add hydrochloric acid until the 
 solutiolTsriows a distinctly acid reaction. Heat the solution 
 to boiling, and add very slowly, and with constant stirring, 
 20 cc. in excess of the calculated amount of hot barium chlo- 
 ride solution (which should contain about 20 grams BaCL 2 , 
 2H 2 O per liter). Continue the boiling for about two min- 
 utes, allow the precipitate to settle, and decant the liquid at 
 the end of a half hour. Replace the beaker containing the 
 original filtrate by a clean beaker, wash the precipitated 
 sulphate by decantation with hot water, and subsequently 
 upon the filter, until it is freed from chlorides. The filter is 
 then transferred to a platinum crucible and ignited, as de- 
 scribed on page 16, until the weight is constant. 
 
 To test the purity of the precipitates, mix each, in the cru- 
 cible, with five to six times its weight of sodium carbonate. 
 This can best be done by placing the crucible on a piece of 
 glazed paper and stirring the mixture with a clean, dry stir- 
 ring rod, which may finally be wiped off with a small frag- 
 ment of filter paper, the latter being placed in the crucible. 
 Cover the crucible and heat over a Bunsen or Tirrill burner 
 until a quiet liquid fusion ensues. As the fused mass cools, 
 insert in it a piece of platinum wire, colled so that it will 
 hold securely in the solidified mass. When solidification is 
 
v\ 
 
 DETERMINATION OF SULPHUR. 33 
 
 complete, replace the lamp under the crucible and heat only 
 long enough to cause the outside of the mass to fuse. Now 
 allow the crucible to cool completely, when the mass may 
 frequently be at once drawn out of the crucible by the wire. 
 If it still adheres, a cubic centimeter or so of water may be 
 placed in the cold crucible and cautiously brought to boiling, 
 when the cake will become loosened, and may be removed on 
 the wire and suspended in about 250 cc. of distilled water 
 to dissolve. 
 
 Extract the residue of barium carbonate thoroughly with 
 water, taking care to clean the crucible completely. Filter 
 off the carbonate, and wash it with hot water, testing the 
 washings for sulphate, and preserving any precipitates 
 which appear in these tests. Acidify the filtrate with hy- 
 drochloric acid until just acid, bring to boiling, and add hot 
 barium chloride solution slowly, as before. Add also any 
 tests from the washings in which precipitates have appeared. 
 Filter, wash, ignite, and weigh. Compare the results with 
 those first obtained, and calculate the weight of sulphur in 
 the barium sulphate, and from that the percentage in the 
 ferrous ammonium sulphate. 
 
 Notes. i. Barium sulphate, in a larger measure than 
 most substances, tends to carry down other bodies which are 
 present in the solution from which it separates, even when 
 these other bodies are relatively soluble. This is notably 
 true in the case of nitrates and chlorates of the alkalies, and 
 of iron, and, since in this analysis ammonium nitrate has re- 
 sulted from the neutralization of the excess of nitric acid 
 added to oxidize the iron, it is essential that this should 
 be destroyed by repeated evaporation with a relatively large 
 quantity of hydrochloric acid. During evaporation a mutual 
 decomposition of the two acids takes place, and the nitric 
 acid is finally decomposed and expelled by the excess of 
 hydrochloric acid. 
 
 2. The precipitation of the sulphur as barium sulphate 
 might take place in the presence of the iron, but under these 
 conditions the likelihood of contamination of the sulphate by 
 iron would be considerable, and a purification of the precip- 
 itate would be unavoidable. On the other hand, ferric chlo- 
 
34 GRAVIMETRIC ANALYSIS, 
 
 ride exerts a slight solvent action upon the barium sulphate. 
 For these reasons it is preferable to precipitate the iron be- 
 fore proceeding to the determination of the sulphur. 
 
 3. Barium sulphate is slightly soluble in hydrochloric acid, 
 even dilute ; hence only the smallest excess should be added 
 over the amount required to acidify the solution. Recent 
 investigations show that the presence of an excess of the ba- 
 rium chloride lessens the solubility of the sulphate in the 
 acid. An addition of 20 cc. of solution in excess is, there- 
 fore, prescribed, but, for the reasons stated in Note i, this 
 excess of chloride should not be too large, and for the same 
 reasons the reagent should be added very slowly, and with 
 constant stirring. It has been shown that the rapid addition 
 leads to a slight co-precipitation of the chloride, which can- 
 not be washed out of the sulphate. 
 
 4. The precipitation of the barium sulphate is probably 
 complete at the end of a half-hour, and the solution may 
 safely be filtered at the expiration of that time, if it is desired 
 to hasten the analysis. 
 
 As noted on page 12, many precipitates of the general char- 
 acter of this sulphate tend to grow more coarsely granular if 
 digested for some time with the liquid from which they have 
 separated. It is, therefore, well to allow the precipitate to stand 
 in a warm place for several hours befpre filtration, whenever 
 practicable, to promote ease of filtration. The filtrate and 
 washings should, however, always be carefully examined for 
 minute quantities of the sulphate which may pass through 
 the pores of the filter. This is best accomplished by impart- 
 ing to the liquid a gentle rotary motion, when the sulphate, 
 if present, will collect in the center of the beaker. All fil- 
 trates in this, and other determinations, must be tested for 
 complete precipitation, by adding to them a small quantity of 
 the reagent and allowing them to stand. 
 
 5. A reduction of barium sulphate to the sulphide may be 
 caused by the reducing action of the burning carbon of the 
 filter, but subsequent ignition, with ready access of air, re- 
 converts the sulphide to sulphate, unless a considerable reduc- 
 tion has occurred. In the latter case it is expedient to add 
 one or two drops of sulphuric acid, and to heat cautiously 
 until the excess of acid is expelled. 
 
 6. Most impurities which are inclosed by the sulphate 
 
DETERMINATION- OF SULPHUR. 35 
 
 cannot be removed by washing with water ; treatment with 
 hydrochloric acid, even if it accomplishes the removal of these 
 impurities, dissolves some of the sulphate-, which must be re- 
 covered. It is advisable, then, in any case, and essential when 
 the contamination is due to iron, alumina, or silica, to purify 
 by fusion with sodium carbonate, as described in the proce- 
 dure. By this process the impurities are either rendered in- 
 soluble, and are removed by filtration with the barium carbon- 
 ate, or, if they pass into solution with the sodium sulphate, 
 they are present in such small amounts relatively, that they 
 fail to be carried down by a second precipitation of the sul- 
 phate. It is obvious that the excess of alkaline carbonate 
 must be destroyed by hydrochloric acid, and that the same 
 care must be taken in the addition of the barium chloride 
 the second time, as was taken at first. The reaction during 
 fusion is the following : 
 
 BaSO 4 + Na 2 CO 3 = Na 2 SO 4 -f BaCO 3 . 
 
 7. The removal of the fused mass from the crucible is fa- 
 cilitated by the procedure outlined, because, after the second 
 short heating, the crucible, by its more rapid cooling, springs 
 away from the mass inside. The boiling with water is some- 
 times necessary to dissolve a slight ring of carbonate, which 
 solders the mass to the crucible at its upper edge. 
 
 For a further statement of the properties of barium sul- 
 phate, the student is referred to Fresenius' Quantitative Analy- 
 sis, under " Forms." 
 
3 6 , GRAVIMETRIC ANALYSIS. 
 
 DETERMINATION OF PHOSPHORIC ANHYDRIDE IN 
 
 APATITE. 
 
 The sample of apatite selected for analysis should be as 
 nearly pure as possible. Specimens of the mineral which 
 leave but a slight siliceous residue are not difficult to secure. 
 
 Procedure. Grind the mineral in an agate mortar until 
 no grit is perceptible. Transfer the substance to a weigh- 
 ing tube, and weigh out two portions, not exceeding 0.20 
 gram each, into two No. 2 lipped beakers. Pour over them 
 20 cc. of nitric acid (sp. gr. 1.2), and warm gently until sol- 
 vent action has apparently ceased. Unless the absence of 
 soluble silicates is assured, evaporate the solution cautiously 
 to dryness, heat the residue, for about two hours, to 130 C, 
 and treat it again with nitric acid,. as described above; sep- 
 arate the residue of silica by nitration on a small filter (7 cm.) 
 and wash with warm water, using as little as possible (see p. 
 1 5). Receive the filtrate in a No. 3 or No. 4 lipped beaker. 
 Test the washings with ammonia for calcium phosphate, but 
 add all such tests, in which a precipitate appears, to the 
 original filtrate. The filtrate and washings should not ex- 
 ceed 100 cc. in volume. Add aqueous ammonia until the 
 precipitate of calcium phosphate first produced just fails to 
 redissolve, and then add a few drops of nitric acid until 
 this is again brought into solution. Warm the solution until 
 it cannot be comfortably held in the hand, and, after re- 
 moval from the lamp, add 75 cc. of ammonium molybdate 
 solution (68 grams MoO 3 per liter), which has been gently 
 warmed, but which must be perfectly clear. Allow the mix- 
 ture to stand at a temperature of about 50 to 60 C. for 
 twelve hours. Filter off the yellow precipitate on an 9 cm. 
 filter, and wash by decantation with a solution of ammonium 
 nitrate made acid with nitric acid.* Allow the precipitate 
 to remain in the beaker as far as possible. Test the wash- 
 ings for calcium with ammonia and ammonium oxalate. 
 
 * This solution is prepared as follows: Mix 100 cc. of ammonia solution 
 (sp. gr. 0.96) with 325 cc. of nitric acid (sp. gr. 1.2), and dilute with 100 cc. of 
 water. 
 
DETERMINATION OF PHOSPHORIC ANHYDRIDE. 37 
 
 Add 10 cc. of molybdate solution to the filtrate, and leave 
 it for a few hours. It should then be carefully examined 
 for a yellow precipitate ; a white precipitate may be neg- 
 lected. The filtrate should not be thrown away, but should 
 be placed in a suitable receptacle for "molybdenum resi- 
 dues," from which the molybdic acid may be recovered. 
 
 Dissolve the precipitate upon the filter, by pouring through 
 it dilute aqueous ammonia (one volume of ammonia (sp. gr. 
 0.96) and three volumes water, which should be ckrefully 
 measured}, and receive the solution in the beaker containing 
 the bulk of the precipitate. The total volume of filtrate 
 and washings must not exceed 75 cc. 
 
 Calculate the volume of magnesium ammonium chloride 
 solution ("magnesia mixture") required to throw out the 
 phosphoric acid, assuming 40 per cent. P 2 O 5 in the apatite. 
 Measure out not more than 2 cc. in excess, and add this 
 quantity to the cold ammoniacal solution, by dropping it 
 from a glass tube, stirring the solution constantly. The 
 rate of addition must not be greater than 10 cc. in a min- 
 ute. Continue the stirring for a few moments, and set the 
 solution aside, at the temperature of the laboratory, over 
 night. (Or it may be stirred constantly for a half-hour, 
 when the precipitation should be complete.) The magne- 
 sium ammonium phosphate is then removed by filtration and 
 washed with a mixture of one part ammonia (sp. gr. 0.96), 
 one part alcohol, and three parts water, until 3 cc. of the 
 washings show no evidence of chlorides. The washings 
 must be acidified with nitric acid before the silver nitrate 
 is added. Test the filtrate carefully for complete precipi- 
 tation by adding more magnesia mixture and allowing it to 
 stand. 
 
 Cover the funnel with a paper, dry the filter completely 
 in the drying closet, and then ignite, using great care to 
 insure the presence of plenty of oxygen during the com- 
 bustion of the filter paper, thus guarding against a possible 
 reduction of the phosphate, with disastrous consequences 
 both to crucible and analysis. Do not raise the tempera- 
 ture above moderate redness until the precipitate is white. 
 (Keep this precaution well in mind.) Ignite finally at the 
 
3 8 GRAVIMETRIC ANALYSIS. 
 
 highest temperature of the Tirrill burner, and repeat the 
 heating until the weight is constant. From the weight of 
 magnesium pyrophosphate (Mg 2 P 2 O 7 ) obtained, calculate the 
 weight of phosphoric anhydride (P 2 O 5 ), and the percentage 
 of the latter in the sample of apatite. 
 
 Notes. i. Apatite may contain, beside calcium phos- 
 phate, either calcium fluoride or chloride. It is evident that 
 the direct precipitation of the phosphoric acid in combination 
 with magnesium is impracticable in the presence of any metal 
 which forms compounds with phosphoric acid which are insol- 
 uble in ammoniacal liquids; such, for example, as iron, alumi- 
 num, chromium, and the alkaline earths. The previous isola- 
 tion of the phosphoric acid in combination with molybdenum, 
 which can be effected in nitric acid solution, is then neces- 
 sary. The phospho-molybdate is soluble in ammonia, and 
 from this solution the phosphoric acid may be separated as 
 magnesium ammonium phosphate. 
 
 2. As a result of the slight solubility of magnesium am- 
 monium phosphate, as noted below, the unavoidable errors of 
 analysis are greater in this determination than in those which 
 have preceded it, and some divergence may be expected in 
 duplicate analyses. It is obvious that the larger the amount 
 of substance taken for analysis, the less will be the relative 
 loss or gain due to experimental errors ; but in this instance a 
 check is placed upon the amount of material which may be 
 taken, both by the bulk of the resulting precipitate of am- 
 monium phospho-molybdate, and by the excessive amount of 
 ammonium molybdate required to effect complete separation 
 of the phosphoric acid, since a liberal excess above the theo- 
 retical quantity is demanded. Molybdic acid is one of the 
 more expensive reagents. 
 
 3. Soluble silicic acid might, if present, partially separate 
 with the phospho-molybdate, although not in combination 
 with molybdenum. Its previous removal by dehydration is 
 therefore advisable. 
 
 4. Nitric acid is chosen as a solvent because the phospho- 
 molybdate is slightly soluble in hydrochloric acid. An excess 
 of nitric acid also exerts a slight solvent action, while ammo- 
 nium nitrate lessens the solubility; hence the neutralization 
 of the former by ammonia. 
 
DETERMINATION OF PHOSPHORIC ANHYDRIDE. 39 
 
 5. The composition of the "yellow precipitate" undoubt- 
 edly varies slightly with varying conditions at the time of its 
 formation, and on this account the precipitate is not com- 
 monly separated and weighed as such. Its structure may 
 probably be represented by the symbol, (NH 4 ) 3 PO 4 . 12 MoO 3 . 
 H 2 O, when precipitated under the conditions prescribed in 
 the procedure. Whatever other variations may occur in its 
 composition, the ratio of 12 MoO 3 : i P seems to hold, and 
 this fact is utilized in volumetric processes for the determina- 
 tion of phosphorus, in which the molybdenum is reduced to a 
 lower oxide and re-oxidized by a standard solution of potas- 
 sium permanganate. 
 
 6. The precipitation of the phospho-molybdate takes place 
 more promptly in warm than in cold solutions, the tempera- 
 ture should not exceed 60 C. during precipitation ; a higher 
 temperature tends to separate molybdic acid from the solu- 
 tion. This acid is nearly white, and its deposition in the 
 filtrate on long standing should not be mistaken for a second 
 precipitation of the yellow precipitate. 
 
 The addition of 75 cc. of ammonium molybdate solution 
 insures the presence of a liberal excess of the reagent. 
 
 7. When washing the siliceous residue, the filtrate may be 
 tested for calcium by adding ammonia alone, since that re- 
 agent neutralizes the acid which holds the calcium phosphate 
 in solution and causes precipitation ; but after the removal of. 
 the phosphoric acid in combination with the molybdenum, the 
 addition of an oxalate is required to show the presence of 
 calcium. 
 
 8. Magnesium ammonium phosphate is not a wholly insol- 
 uble body, even under the most favorable analytical condi- 
 tions. It is least soluble in a liquid containing one fourth of 
 its volume of aqueous ammonia (sp. gr. 0.96), and this pro- 
 portion should be carefully preserved, as prescribed in the 
 procedure. On account of this slight solubility, the volume 
 of solutions should be kept as small as possible, and the 
 amount of wash-water limited to that absolutely required. 
 The addition of alcohol to the wash-water lessens the sol- 
 ubility of the magnesium compound in it. 
 
 9. A large excess of the magnesium solution tends both to 
 throw out magnesium hydroxide (shown by a flocculent pre- 
 cipitate), and to cause the phosphate to carry down molybdic 
 
40 GRAVIMETRIC ANALYSIS. 
 
 acid. The latter, if its presence be suspected, may be 
 removed from the phosphate by dissolving the precipitate in 
 hydrochloric acid, and passing sulphuretted hydrogen through 
 the warm solution from three to four hours. 
 
 10. The magnesium ammonium phosphate should be per- 
 fectly crystalline, and will be so if the directions are followed. 
 The slow addition of the reagent is essential, and the stirring 
 not less so. Stirring promotes the separation of the precip- 
 itate and the formation of larger crystals, and may therefore 
 be substituted for digestion in the cold. The stirring rod 
 must not be allowed to scratch the glass, as the crystals ad- 
 here to such scratches and are removed with difficulty. 
 
 The remarks on page 12, regarding the formation of large 
 crystals by digestion with the solution, have peculiar force in 
 connection with the magnesium ammonium phosphate, which 
 is a relatively soluble body. 
 
 11. During ignition, the magnesium ammonium phosphate 
 loses ammonia and water, and is converted into magnesium 
 pyrophosphate. 
 
 2 NH 4 MgP0 4 = Mg 2 P 2 7 + 2 NH 3 +.H 2 O. 
 
 The precautions mentioned on page 16 must be observed 
 with great care during the ignition of this precipitate. The 
 danger here lies in a possible reduction of the phosphate. 
 The phosphorus then attacks and injures the crucible, and the 
 determination is valueless. 
 
 If extreme care is employed, it is possible to safely ignite 
 this precipitate without previous drying, but the student is not 
 advised to attempt this until some general experience has 
 been gained. 
 
 For a further statement of the properties of ammonium 
 phospho-molybdate, magnesium ammonium phosphate, and 
 magnesium pyrophosphate, the student is referred to Fre- 
 senius* Quantitative Analysis, under " Forms." 
 
DOLOMITE. 41 
 
 DETERMINATION OF CALCIUM AND MAGNESIUM 
 IN DOLOMITE. 
 
 The sample of dolomite chosen for practice should leave 
 little or no residue insoluble in hydrochloric acid. 
 
 DETERMINATION OF CALCIUM. 
 
 Procedure. Grind the mineral to a fine powder. Weigh 
 out, into 1 50 cc. casseroles, two portions of about one gram 
 each. Pour over them 30 cc. of hydrochloric acid (sp. gr. 
 1.12), first having covered the casseroles; add i cc. of ni- 
 tric acid (sp. gr. 1.20) and boil five minutes. Filter off the 
 residue on a small filter, wash it with hot water until free 
 from chlorides, and ignite the filter in a platinum crucible. 
 Cover the filter ash and residue with a small quantity (per- 
 haps 0.5 gram) of sodium carbonate, heat to fusion, and dis- 
 integrate with a- little water, by cautiously boiling it in the 
 crucible. Add this solution, with any suspended matter, to 
 the main filtrate from the insoluble residue; evaporate the 
 solution to dryness, and heat the residue in the hot closet for 
 two hours at 130 C., to dehydrate any soluble silicic acid. 
 Moisten the residue with hydrochloric acid, warm gently, 
 dilute, and bring to boiling. Add aqueous ammonia in slight 
 excess, and, if the qualitative analysis has shown manganese 
 to be present, add 5 cc. of bromine water and boil for five 
 minutes, adding more ammonia, if need be. If manganese 
 is absent, omit the bromine. In either case, finally neutral- 
 ize the excess of ammonia until a faint odor only can be 
 detected, and filter off the silicic anhydride, together with 
 the iron, aluminum, and manganese hydroxides. The filtra- 
 tion must take place promptly after the addition of the am- 
 monia. Without washing the precipitate, re-dissolve it on 
 the filter in hydrochloric acid, receiving the solution in a 
 clean beaker. Wash the filter five times with water, and 
 throw down the hydroxides from the solution as before. 
 Wash this precipitate with hot water until free from chlo- 
 rides. The precipitate may then be discarded. 
 
 Treat one of the filtrates as follows : (a) To the filtrate, 
 concentrated to 250 cc. and heated to boiling, add ammo- 
 
42 GRAVIMETRIC ANALYSIS. 
 
 nium oxalate solution in moderate excess, stirring well, and 
 adding the reagent slowly. Boil for two minutes, allow the 
 precipitated calcium oxalate to settle for a half-hour, and 
 decant through a filter. Test the filtrate for complete pre- 
 cipitation by adding a few drops of the precipitant. If no 
 precipitate forms, make the solution slightly acid with hydro- 
 chloric acid, and proceed with the magnesium determination. 
 
 Re-dissolve the calcium oxalate in the beaker, and from 
 the filter, with hydrochloric acid, washing the filter five 
 times, and finally pouring through it aqueous ammonia. 
 Dilute the solution to 250 cc., bring to boiling, add i cc. 
 ammonium oxalate solution and ammonia in slight excess; 
 boil for two minutes, and set aside for a half-hour. Filter 
 off the calcium oxalate upon the filter first used, and wash 
 free from chlorides. The filtrate should be made barely acid 
 and combined with the first filtrate. 
 
 The precipitate of calcium oxalate may be ignited without 
 drying. It should be ignited at the highest heat of the Bun- 
 sen or Tirrill burner, after destroying the filter, and finally 
 for three minutes at the blast lamp. Repeat until the 
 weight is constant. As the calcium oxide absorbs moisture 
 from the air, it must be weighed as rapidly as possible- 
 (Compare Note 7, on p. 31.) From the weight of the oxide* 
 calculate the weight of calcium, and the percentage of the 
 latter in the dolomite. 
 
 Treat the second filtrate from the iron precipitate as fol- 
 lows : (b) Add hydrochloric acid to decided acid reaction. 
 Calculate the volume of ammonium oxalate solution required 
 to combine with both the calcium and magnesium, assuming 
 the presence of 20 per cent, of each. Add this volume to 
 the solution and, if a precipitate forms, dissolve it in hydro- 
 chloric acid. Dilute the whole to 1000 cc. and bring it to 
 boiling. Remove it from the hot plate and slowly add 
 ammonia in moderate excess, with constant stirring. Allow 
 the solution to stand for a half-hour, filter off the calcium 
 oxalate, and wash the precipitate with hot water until freed 
 from chlorides. Treat this precipitate as described in pro- 
 cedure (a). 
 
 Barely acidify the filtrate from the calcium oxalate with 
 
DETERMINATION OF MAGNESIUM, 43 
 
 hydrochloric acid, and proceed with the magnesium deter- 
 mination. 
 
 DETERMINATION OF MAGNESIUM. 
 
 Procedure. Evaporate the acidified filtrates from the cal- 
 cium precipitates until salts begin to crystallize, but do not 
 evaporate to dryness. Dilute until these salts are brought 
 into solution. Add a volume of aqueous ammonia (sp. gr. 
 0.96) equal to one third the volume of the solution. (To do 
 this, measure into a beaker of equal size a volume of water 
 equal to the volume of the solution. Note the number of 
 cubic centimeters and take one third as many of ammonia.) 
 Calculate the volume of hydrogen sodium phosphate solution 
 required to precipitate the magnesium, assuming 20 per 
 cent, to be present. Add the sodium phosphate to the cold 
 solution drop by drop from a glass tube, at a rate not greater 
 than 10 cc. per minute; stir thoroughly, set aside for some 
 hours, and treat the precipitate of magnesium ammonium 
 phosphate as prescribed for the determination of phosphoric 
 anhydride, on page 37. 
 
 Notes. i: The mineral Dolomite is a native isomorphous 
 mixture of calcium and magnesium carbonates, in which the 
 relative proportions may vary widely, ferrous iron and man- 
 ganese are not infrequently present, and most specimens leave 
 a larger or smaller residue on treatment with hydrochloric 
 acid. Since this residue may contain calcium or magnesium, 
 it must be rendered soluble by fluxing, and brought into solu- 
 tion. This may be quickly accomplished, if the directions 
 are closely followed with regard to the use of a small quan- 
 tity of the sodium carbonate and disintegration of the small 
 fused mass within the crucible. 
 
 If it is definitely known, from a qualitative examination, 
 that the residue insoluble in hydrochloric acid contains no 
 calcium or magnesium, its treatment may be omitted, and the 
 solution may be at once evaporated for the dehydration of 
 the silica, without filtration. The insoluble residue may be 
 filtered off with the hydroxide precipitate. 
 
 2. The addition of nitric acid is necessary to oxidize fer- 
 rous iron to ferric, and to insure its complete precipitation by 
 
44 
 
 GRAVIMETRIC ANALYSIS. 
 
 ammonia. Manganese is not oxidized by nitric acid, but is 
 oxidized by bromine in ammoniacal solution to a hydrated 
 dioxide, in which form it is precipitated and removed with 
 the iron and alumina. The possible presence of alumina 
 makes it necessary to finally neutralize all but a slight excess 
 of ammonia before filtration. (Compare Note 8, p. 31.) 
 
 3. The iron precipitate should be filtered off promptly, 
 since the alkaline solution absorbs carbon dioxide from the 
 air, with consequent precipitation of the calcium as carbon- 
 ate. This is possible even under the most favorable condi- 
 tions, and for this reason the iron precipitate is re-dissolved 
 and thrown out again, to free it from calcium. 
 
 4. The separation of calcium and magnesium as oxalates 
 requires special precautions. It is necessary either to re- 
 dissolve the first precipitate of calcium oxalate, and make a 
 second precipitation, as in procedure (0), or to separate in 
 dilute solution and in the presence of sufficient ammonium 
 oxalate to combine with both metals, as in procedure (). In 
 (0), the first calcium precipitate contains magnesium, but 
 when dissolved, the proportion of magnesium to the calcium 
 in solution is small, and the second calcium precipitate may 
 be considered to be pure. In (b\ it is sought to accomplish 
 the same end by liberal dilution in the presence of an excess 
 of ammonium oxalate, lessening in this way the tendency of 
 the magnesium to separate with the calcium. Method (a) 
 probably yields results which are more certainly accurate 
 than (b\ for large amounts of the two metals, while (b*) is 
 accurate for small quantities. 
 
 5. The small quantity of ammonium oxalate solution is 
 added before the second precipitation of the calcium oxalate, 
 to insure the presence of a slight excess of the reagent, which 
 promotes the separation of the calcium compound. 
 
 6. On ignition the calcium oxalate loses carbon dioxide 
 and carbon monoxide, leaving calcium oxide. 
 
 CaC 2 O 4 = CaO + CO 2 + CO. 
 
 For small weights of the oxalate (0.5 gram or less), this 
 reaction may be brought about at the highest temperature of 
 a Tirrill burner, but it is well to ignite larger quantities than 
 this over the blast lamp until the weight is constant. 
 
 7. The calcium oxide tends to absorb moisture to form the 
 hydroxide ; hence the necessity for rapid weighing. 
 
AZOTES. 45 
 
 8. The filtrate from the calcium oxalate should be made 
 slightly acid immediately after filtration, in order to avoid the 
 solvent action of the alkaline liquid upon the glass. 
 
 9. The precipitation of the magnesium should be made in 
 as small volume as possible, and the ratio of ammonia to the 
 total volume, of solution should be carefully provided for, 
 on account of the slight solubility of the magnesium ammo- 
 nium phosphate. This matter has been fully discussed in 
 connection with the phosphoric anhydride determination. 
 (Compare Note 8, p. 39.) 
 
 to. If the magnesium ammonium phosphate precipitate is 
 not wholly crystalline, as it should be, the difficulty may some- 
 times be remedied by filtering the precipitate and. without 
 washing it, re-dissolving in a small quantity of hydrochloric 
 acid, from which it may be again thrown down by ammonia, 
 after adding a few drops of sodium phosphate solution. If 
 the flocculent character was occasioned by the presence of 
 magnesiutu hydroxide, the second precipitation, in a smaller 
 volume, containing fewer salts, will often result more, favor- 
 ably. The removal of iron or alumina from a contaminated 
 precipitate is a matter involving a long procedure, and a re- 
 determination of the magnesium from a new sample, with 
 additional precautions, is usually to be preferred. 
 
 For a further statement of the properties of calcium oxalate 
 and calcium oxide, the student is referred to Frcs&iiuJ Qua*- 
 titatn* Analysis, under " Forms." 
 
4 6 GRAVIMETRIC ANALYSIS. 
 
 DETERMINATION OF LEAD, COPPER, AND 
 ZINC IN BRASS. 
 
 DETERMINATION OF LEAD. 
 
 Procedure. Select clean, bright chips or borings, or, if 
 the brass is in the form of wire, polish a piece of suitable 
 size by rubbing with emery, cleaning it carefully afterward. 
 Weigh out two portions of about 5 grams each, and dissolve 
 them in covered casseroles in 30 cc. of nitric acid (sp. gr. 
 1.2). When the solution is complete, cool, wash off the 
 cover glass,, and add slowly 10 cc. of sulphuric acid (sp. gr. 
 1.84). Evaporate under a hood until heavy white fumes of 
 sulphuric anhydride are evolved, keeping the casserole well 
 covered meanwhile; cool, add 125 cc. of water, and boil 
 until the sulphates of copper and zinc have dissolved, and set 
 the solution aside until perfectly cold. Filter off the lead 
 sulphate, wash it by decantation with dilute sulphuric acid 
 (one volume of concentrated acid to twenty volumes of 
 water) until the washings are free from copper, as shown by 
 the ferrocyanide test. Set the filtrate aside for the deter- 
 mination of copper and zinc, and transfer the lead sulphate 
 to the filter, finally washing the filter free from sulphuric 
 acid, with alcohol diluted with an equal volume of water. 
 Be sure that all the sulphate is removed from the casserole. 
 Discard the alcoholic washings, if they are entirely clear. 
 Dry the filter, and, if practicable, separate the lead sul- 
 phate from it, as described on page 24. Prepare a No. 7 
 porcelain crucible for use, by heating and weighing, burn 
 the filter on a platinum wire, as described on page 24, and 
 when cold, add to the ash two drops of nitric acid and one 
 drop of sulphuric acid. Ignite with great care until the 
 acids are expelled. Transfer the precipitate which was 
 separated from the filter, to the crucible, and ignite at a 
 moderate red heat. Repeat the heating until the weight is 
 constant. 
 
 From the weight of the lead sulphate, calculate the weight 
 of lead, and the percentage of the latter in the brass. 
 
DETERMINATION OF LEAD. 47 
 
 Notes. i. It is obvious that the brass taken for analysis 
 should be untarnished, which can be easily assured when wire 
 is used, by scouring with emery. If chips or borings are used, 
 they should be well mixed, and the sample for analysis taken 
 from different parts of the mixture. 
 
 2. The small percentage of lead usually found in brasses 
 makes it necessary to weigh out a considerable quantity in 
 order to secure accuracy. The amount taken, 5 grams, is too 
 large to use directly for the determination of copper and zinc, 
 on account of the bulk of the precipitates which would then 
 have to be handled. An aliquot part of this filtrate is, there- 
 fore, used for these analyses, as noted under the determina- 
 tion of copper. 
 
 3. Lead sulphate is slightly soluble in nitric acid; hence 
 the latter is removed by heating with sulphuric acid until the 
 more volatile acid is expelled. This point is indicated by the 
 appearance of the heavy, white fumes. 
 
 4. Lead sulphate is least soluble in dilute sulphuric acid 
 (i : 20). The sulphuric acid solution is, therefore, diluted to 
 secure this ratio, and a wash-water of the same strength is 
 used. 
 
 The sulphuric acid of the wash-water, if allowed to remain 
 on the filter, would char it during the drying, making subse- 
 quent handling difficult or impossible. It is accordingly 
 removed by washing with dilute alcohol ; but the alcohol is not 
 added to the main filtrate, as its presence is not advantageous 
 during the subsequent operations. 
 
 5. The lead sulphate must be separated from the filter for 
 the same reasons which apply in the case of silver chloride. 
 (Compare p. 26.) The addition of nitric acid to the ash dis- 
 solves any reduced lead, and the sulphuric acid converts it to 
 sulphate. A slight loss of lead is possible if the reduction of 
 any considerable quantity of the precipitate takes place, and 
 it is evident that the ignition of this precipitate in platinum 
 is 'impracticable. 
 
 6. It is possible to determine the percentage of lead in 
 the brass by solution in nitric acid, partial neutralization of 
 the excess of acid, and deposition of the lead by an electric 
 current as peroxide (PbO 2 ) on the anode ; but the relatively 
 large percentage of copper makes the simultaneous deter- 
 mination of that element difficult, if a sufficiently large quan- 
 
4 g GRAVIMETRIC ANALYSIS. 
 
 tity of the brass be taken for analysis to also secure an accu- 
 rate determination of the lead. For the determination of 
 small quantities of lead alone, this method might be employed. 
 For a further statement of the properties of lead sulphate, 
 the student is referred to Fresenius' Quantitative Analysis, 
 under " Forms." 
 
 DETERMINATION OF COPPER. 
 
 Procedure. Transfer the filtrate from the lead sulphate 
 to a 500 cc. graduated flask, washing out the beaker care- 
 fully. Fill the flask with distilled water until the lowest 
 point of the meniscus is exactly level with the mark on the 
 neck of the flask. Carefully remove, with a strip of filter 
 paper, any drops of water which are on the inside of the 
 neck of the flask above the graduation ; make the solution 
 thoroughly uniform by pouring it out into a dry beaker, and 
 back into the flask several times, and finally stopper the 
 flask. Measure off one tenth of this solution as follows : 
 Pour into a 50 cc. graduated flask about 10 cc. of the so- 
 lution, shake the liquid thoroughly over the inner surface 
 of the small flask and pour it out. Repeat the same op- 
 eration. Fill the 50 cc. flask until the lowest point of 
 the meniscus is exactly level with the mark on its neck, 
 remove any drops of solution from the upper part of the 
 neck with filter paper, and pour the solution into a plain 
 beaker of about 80 cc. capacity, of rather tall form. Wash 
 out the flask with small quantities of water until it is clean, 
 adding these to the main solution. (Consult also note on p. 
 62.) When the second portion of 50 cc. is measured out, re- 
 member that the flask must be twice rinsed out with solution 
 "as prescribed above, before the final measurement is made. 
 
 Add to the copper solution I gram of .ammonium nitrate. 
 The solution is then ready for the electrolytic deposition of 
 the copper. 
 
 Meanwhile, four platinum electrodes, two anodes and two 
 cathodes, should be cleaned by scouring with sapolio and 
 treatment with acid, and the two cathodes ignited gently and 
 cooled in a desiccator. Weigh them carefully, and place one 
 anode and one cathode in each solution. The connections 
 
DETERMINATION OF COPPER. 49 
 
 should then be made with the binding posts (or other device 
 for connection with the electric circuit), in such a way that 
 the copper will be deposited upon the larger electrode. If a 
 gravity battery is used, this electrode should be connected 
 with the zinc pole ; if a dynamo-current is used, a previous 
 qualitative experiment is necessary to determine the nega- 
 tive pole. Subject the solution to the action of the cur- 
 rent from eight to fifteen hours, as indicated by the rate of 
 deposition. It is well to leave the solution over nfght, if 
 practicable. 
 
 When the solution is colorless, and the deposition of copper 
 seems to be complete, break the circuit as follows : Lift the 
 cathode in the binding post until it is nearly, but not wholly, 
 out of the liquid, and wash the exposed portion with distilled 
 water. Then break the circuit by removing the electrode 
 entirely, and complete the washing promptly. Pour over 
 the electrode and copper enough alcohol to remove adhering 
 water, and dry for a few moments at 105 C. Cool in a des- 
 iccator and. weigh. Test the solution for copper by the addi- 
 tion of ammonia in excess, to about 5 cc. of the solution. If 
 copper is found, clean the electrodes and place the solution 
 in the circuit a second time. Whether copper is found or 
 not, return the test portion to the main solution. 
 
 The increase in weight of the electrode represents directly 
 the weight of copper from one tenth of the solution, from 
 which the percentage in the brass may be calculated. 
 
 Notes. i. The removal of one tenth of the solution for 
 the determination of copper and zinc is necessitated by the 
 difficulties which would be encountered if the precipitation of 
 such large quantities of these metals as would come from 
 5 grams of the brass, was attempted. The solution is, 
 therefore, diluted to a definite volume (500 cc.), and exactly 
 one tenth (50 cc.) is measured off. To attain, this end 
 it is evident that the solution must be thoroughly uniform, 
 which is brought about by careful mixing, and that it must 
 not be diluted by water adhering to the small flask. This is 
 insured by rinsing out this flask several times with the solu- 
 tion, instead of drying it, which would consume much time. 
 The two flasks must be graduated at the same temperature, 
 
5 
 
 GRAVIMETRIC ANALYSIS. 
 
 and if, as is usual, the small flask is graduated to contain 50 
 cc., it must be rinsed out with water before all the copper and 
 zinc belonging to one tenth of the solution are obtained. 
 This, and other kindred considerations, are discussed under 
 Volumetric Analysis, page 62. A pipette might properly be 
 substituted for the small flask, if desired. 
 
 2. The presence of sufficient ammonium nitrate to react 
 with the sulphuric acid in the solution, lessens the tendency of 
 the copper to deposit on the cathode in a spongy condition. 
 The amount of the nitrate added should not greatly exceed 
 i gram. 
 
 3. The electrodes should be freed from all greasy matter 
 before using, and after scouring, those portions upon which 
 the metal will deposit should not be touched with the fingers. 
 
 4. Under the conditions named in the procedure, the cop- 
 per may be deposited in satisfactory condition by a current 
 from three cells of a "gravity battery," in series, or by the 
 current which passes through three lo-candle Edison lamps, 
 in series, on a tio-volt circuit. The deposition is usually 
 complete after ten to twelve hours. 
 
 It is not well to leave the solution in the circuit for an ex- 
 cessive length of time, since, after the deposition of the cop- 
 per, the nitric acid is slowly reduced to ammonia by the 
 nascent hydrogen, with the possible production of an alkaline 
 solution from which zinc may be thrown down. 
 
 5. The electrodes should be washed as far as possible 
 before the current is broken, to prevent re-solution of the 
 copper. If several solutions are connected in the same cir- 
 cuit, some provision must be made by which the breaking of 
 the current shall be avoided when the electrodes in any one 
 solution are removed. This can be easily accomplished by 
 springing a piece of brass between the binding posts, before 
 removing the electrodes. The current at first passes through 
 both spring and solution, and when the current is broken in the 
 latter, it passes through the spring instead, and no copper is 
 dissolved from the electrodes in other solutions. 
 
 6. The electrode is washed with alcohol to promote rapid- 
 ity of drying. The copper should not remain in the hot closet 
 a moment longer than is necessary, as it tends to oxidize at 
 the higher temperature. 
 
 7. A dark deposit on the anode indicates a precipitation 
 
DETERMINATION OF ZINC. 
 
 5 1 
 
 of lead as peroxide. Such deposition is not infrequent, as the 
 lead sulphate is not absolutely insoluble in the acid liquid 
 from which it separates. This electrode may be weighed 
 with the precipitate, then cleansed and again weighed, and 
 the amount of lead calculated from the weight of the perox- 
 ide added to that found as sulphate in the corresponding 
 solution. 
 
 For a further statement of the properties of copper and of 
 lead peroxide, the student is referred to Fresenius* Quantita- 
 tive Analysis, under " Forms." 
 
 DETERMINATION OF ZINC. 
 
 Procedure. Transfer the solution, from which the copper 
 has been removed, to large porcelain casseroles (500 cc. 
 capacity or more). Cover these casseroles and add sodium 
 carbonate solution to distinctly alkaline reaction ; boil until 
 no odor of ammonia can be detected from the hot solution. 
 Again add I cc. or 2 cc. of the sodium carbonate solution 
 and boil to insure complete removal of the ammonia. Fil- 
 ter off the basic zinc carbonate, using two filters for each 
 determination, if the precipitate is too bulky to be properly 
 held by one ; wash the precipitates three times by decanta- 
 tion with hot water, and finally on the filter until freedlrom 
 carbonate. 
 
 Test the filtrate and washings for complete precipitation 
 by the addition of a few drops of ammonium sulphide, and 
 allow it to stand ; if zinc sulphide separates, collect it on a 
 filter, wash with water containing a very little ammonium 
 sulphide, ignite in a porcelain crucible, and weigh as oxide. 
 
 Dry the precipitated basic carbonate in the drying closet, 
 and separate the carbonate as completely as possible from 
 the filter, as described on page 24. Clean, heat, and weigh 
 a No. 7 porcelain crucible, burn the filter on a wire above it, 
 allow the ash to fall into the crucible, and ignite until the 
 carbon is all destroyed. Transfer the main portion of the 
 precipitate to the crucible and ignite at a red heat, until 
 the weight is constant. From the weight of zinc oxide, cal- 
 culate the weight of zinc and the percentage of the latter in 
 the brass, remembering that but one tenth of the solution 
 was used for this determination. 
 
GRAVIMETRIC ANALYSIS. 
 
 Notes. i. Porcelain or platinum vessels are required 
 when strongly alkaline solutions are to be boiled, as in this 
 determination, to prevent the introduction of silica from the 
 glass into the solution. 
 
 2. Sodium carbonate throws down a basic zinc carbonate, 
 the exact composition of which probably varies with varying 
 conditions. This precipitate is partially soluble in the pres- 
 ence of either ammonia or ammonium salts, and in the pres- 
 ence of carbon dioxide. Both of these may be removed by 
 continued boiling with an excess of sodium carbonate. 
 
 The precipitate is frequently very voluminous, though it 
 varies widely in this respect under apparently similar condi- 
 tions. The student is therefore not to suppose that errors 
 have been made if one precipitate should appear much larger 
 than the other. 
 
 3. The filtrate should always be tested for zinc by the ad- 
 dition of ammonium sulphide ; but when the boiling before 
 filtration is sufficiently prolonged, no weighable quantity of 
 zinc should be found in the filtrate. The zinc sulphide, if 
 any appears, must be washed with water containing ammo- 
 nium sulphide to prevent oxidation. 
 
 4. The basic zinc carbonate loses water and carbon diox- 
 ide on ignition, leaving the zinc oxide. This oxide may be 
 reduced to metallic zinc by contact with burning carbon, and 
 the zinc may volatilize ; a separation of the main portion of 
 the precipitate from the filter is, therefore, necessary. This 
 separation should be made as complete as possible, without 
 an admixture of shreds from the filter paper. 
 
 It is well to .test the ignited zinc oxide, after weighing, with 
 moist litmus paper for alkaline reaction. If this is found, 
 the presence of alkali in the precipitate is indicated. It 
 should then be boiled with water and again ignited, with the 
 same precaution as before. 
 
 For a further statement of the properties of basic zinc car- 
 bonate and of zinc oxide, the student is referred to Fresenius 1 
 Quantitative Analysis, under " Forms." 
 
PART III. 
 
 VOLUMETRIC ANALYSIS. 
 
 GENERAL DISCUSSION. 
 
 IT has already been pointed out in Part I, that the meas- 
 urement of the volume of a solution required for a definite 
 reaction, takes the place in Volumetric Analysis which is 
 occupied by the weighing of the precipitated body in Gravi- 
 metric Analysis. 
 
 It is plain that the analytical balance is equally requisite 
 as a starting point for both systems ; and it will be seen that 
 the processes of volumetric analysis demand, beside an ac- 
 curate balance, standard solutions ; i.e., solutions of accu- 
 rately known value ; graduated instruments in which to 
 measure the volume of such solutions ; and finally, some 
 means which shall furnish an accurate indication of the point 
 at which the desired reaction is completed. Those sub- 
 stances which furnish such information are called indicators. 
 The last-named will be treated of in connection with the dif- 
 ferent analyses. 
 
 The process whereby a standard solution is brought into 
 reaction is called tif ration, and the point at which the re- 
 action is exactly completed is called the end-point. The 
 indicator should show the end-point of the titration. 
 
 The processes of Volumetric Analysis are easily classified, 
 according to their character, into : 
 
 I. Saturation Methods ; such, for example, as those of 
 acidimetry and alkalimetry. 
 
 II. Oxidation Processes ; as exemplified in the determina- 
 tion of ferrous iron, by its oxidation with potassium bichro- 
 mate. 
 
 III. Precipitation Methods ; of which the titration for 
 silver with potassium sulphocyanate solution is an illustration. 
 
54 VOLUMETRIC ANALYSIS. 
 
 From a somewhat different standpoint the methods may 
 be sub-divided into (a) Direct Methods, in which the sub- 
 stance sought is directly determined by titration with a 
 standard solution to an end-point ; and (b) Indirect Methods^ 
 in which the substance itself is not measured, but a quantity 
 of reagent known to be an excess, with respect to a specific 
 reaction, is added, and the unused excess determined by 
 titration. Examples of the latter class will be pointed out 
 as they occur in the procedures. 
 
 Volumetric processes are, as a rule, more rapid and fre- 
 quently more accurate than gravimetric processes having the 
 same ends in view. The number of reactions capable of 
 adaptation as volumetric methods is, however, somewhat 
 limited. 
 
 STANDARD SOLUTIONS. 
 
 The strength or value of a solution for a specific reaction 
 is determined by a procedure called Standardization, in 
 which the solution is brought into reaction with a definite 
 weight of a substance of known purity. For example, a 
 definite weight of pure sodium carbonate may be dissolved 
 in water, and the volume of a solution of hydrochloric acid 
 necessary to exactly neutralize the carbonate, accurately de- 
 termined. From these data the strength or value of the 
 acid is known. It is then a standard solution. 
 
 Standard solutions may be made of a purely empirical 
 strength, dictated solely by convenience of manipulation, or 
 the concentration may be chosen with reference 'to a system 
 which is applicable to all solutions, and based upon chemical 
 equivalents. Such solutions usually bear some simple rela- 
 tion to a Normal Solution of the specific reagent ; i. e., they 
 are, for example, deci-normal or centi-normal solutions. 
 
 A Normal Solution, as defined by Mohr (Titrirmethode, 
 p. 56), contains in one liter " one equivalent of the active re- 
 agent in grams." The " equivalent in grams " may be 
 defined as " that quantity of the active reagent which con- 
 tains, replaces, unites with, or in any way, directly or indi. 
 rectly, brings into reaction one gram of hydrogen." 
 
 The application of this general statement to specific cases 
 is pointed out below. 
 
NORMAL SOLUTIONS. 55 
 
 A liter of normal acid sohition should contain such a 
 quantity of the reagent as will furnish I gram of hydrogen 
 replaceable by a base. Accordingly, the normal solution of 
 hydrochloric acid (HC1) should contain 36.45 grams of the 
 gaseous compound, since that amount furnishes the requisite 
 i gram of hydrogen. On the other hand, the normal solu- 
 tion of sulphuric acid (H 2 SO 4 ) should contain only 49.04 
 grams, one half of its molecular weight. 
 
 A normal alkali solution should contain sufficient alkali in 
 a liter to replace I gram of hydrogen in an acid. This quan- 
 tity is represented by the molecular weight in grams (40.05) 
 of sodium hydrate (NaOH), while a sodium carbonate solu- 
 tion (Na 2 CO 3 ) should contain but one half the molecular 
 weight in grams (i.e., 53.05 grams) in a normal solution. 
 
 A normal solution of an oxidizing agent should contain 
 one equivalent of available oxygen ; that is, sufficient oxygen 
 to unite with i gram of hydrogen to form water. The 
 amount, for example, of potassium bichromate (K 2 Cr 2 O 7 ), 
 which will furnish one equivalent of available oxygen is 
 seen from the following considerations : The bichromate 
 yields on reduction, a salt of potassium, corresponding to the 
 oxide K 2 O, and a salt of chromium, corresponding to the 
 oxide Cr 2 O 3 . The residual and available oxygen is repre- 
 sented by three atoms (K 2 Cr 2 O 7 = K 2 O + Cr 2 O 3 -f O 3 ). 
 Accordingly, i gram-molecule of the bichromate will fur- 
 nish six equivalents of oxygen, or enough to oxidize 6 grams 
 of hydrogen to water, as seen from the equation 6H 2 + 3O 2 
 = 6H 2 O. The definition, therefore, demands only one sixth 
 of the molecular weight (or 49.08 grams) for a normal 
 solution. 
 
 A liter of a normal solution of a reducing agent must 
 have the same reducing power as i^grarn^ of hydrogen. For 
 example, a solution of stannous crTTonde" must contain one 
 half of its molecular weight in grams per liter (99.97 grams), 
 as indicated by the equations, SnCl 2 -f- 2FeCl 3 = SnCl 4 -f- 
 2FeCl 2 and H 2 + 2FeCl 3 = 2HC1 + 2FeCl 2 . One gram- 
 molecule of the stannous chloride is plainly equivalent to 2 
 grams of hydrogen. 
 
 Normal solutions, since they rest upon a common founda- 
 
5 6 VOLUMETRIC ANALYSIS. 
 
 tion, have the advantage of uniformity. A liter of a normal 
 solution of an acid must, of necessity, exactly neutralize a 
 liter of normal alkali solution, and one of an oxidizing agent 
 exactly react with a liter of a normal reducing solution, and 
 so on. It must at the same time be remembered that the 
 same substance may have different equivalents when used 
 under varying conditions ; as, for example, potassium perman- 
 ganate, two molecules of which yield three atoms of availa- 
 ble oxygen (equivalent to six hydrogen atoms) in neutral 
 solution, and five atoms of oxygen (equivalent to ten atoms 
 of hydrogen) when used in acid solution. These facts must 
 be considered when reference is made to a normal solution 
 of that reagent, and the statement must specify the condi- 
 tions of use. 
 
 Beside the advantage of uniformity, the use of normal 
 solutions simplifies the calculations of the results of analyses. 
 This is particularly true if, in connection with the normal 
 solution, the weight of substance for analysis be chosen with 
 reference to the molecular weight of the constituent to be 
 determined. For illustrations of this, consult Part JV, 
 page 107. 
 
 The preparation of an exactly normal, half normal, or deci- 
 normal solution requires considerable time and care, as noted 
 on page 68, and is usually carried out when a large number 
 of analyses are to be made, or when the analyst has some 
 other specific purpose in view. It is, however, a compara- 
 tively easy matter to prepare standard solutions which differ 
 but slightly from the normal or half normal solutions, and 
 these have the advantage of practical equality. That is, two 
 approximately half normal solutions are more convenient to 
 work with, than two which are widely different in strength. 
 It is, however, true, that whatever advantage pertains to the 
 use of normal solutions as regards simplicity of calculations 
 is, to a considerable extent, lost when using these approxi- 
 mate solutions. 
 
 GRADUATED INSTRUMENTS. 
 
 A burette consists of a glass tube which is made as uni- 
 formly cylindrical as possible, and of such a bore that the 
 
CALIBRA TION. 
 
 57 
 
 divisions which are etched upon its surface shall correspond 
 to actual contents as far as is practicable. 
 
 The tube is contracted at one extremity, and terminates 
 in either a glass stopcock and delivery tube (a Giessler bu- 
 rette), or in such a manner that a piece of rubber tubing 
 may be firmly attached, connecting a delivery tube of glass. 
 The rubber tubing is closed by means of a pinchcock or by 
 a glass bead (Mohr burette). 
 
 The graduations are usually numbered in cubic centime- 
 ters, and the latter are subdivided into tenths. 
 
 A pipette may consist of a narrow tube, in the middle of 
 which is blown a bulb of a capacity a little less than that 
 which it is desired to measure by the pipette ; or it may be a 
 miniature burette, without the stopcock or rubber tip at the 
 lower extremity. In either case, the flow of liquid is regu- 
 lated by the pressure of the finger on the top, which pre- 
 vents the admission of the air. 
 
 Graduated, or measuring flasks are similar to the ordinary 
 flat-bottomed flasks, but are provided with long, narrow 
 necks in order that slight variations in the position of the 
 meniscus with respect to the graduation, shall represent a 
 minimum volume of liquid. The flasks must be of such a 
 capacity that, when filled with the specified volume, the 
 liquid rises well into the neck. 
 
 CALIBRATION OF INSTRUMENTS. 
 
 If accuracy of results is to be attained, the correctness of 
 all measuring instruments must be tested. None of the ap- 
 paratus offered for sale can be implicitly relied upon, unless 
 it be those more expensive instruments which are accompa- 
 nied by a certificate from the Physikalische Reichsanstalt in 
 Berlin, or other equally authentic source. 
 
 The bore of burettes may readily vary, and as the gradua- 
 tions must be applied without regard to such variations of 
 bore, local errors are the result. The same consideration ap- 
 plies to pipettes, while even the graduations upon flasks are 
 often incorrect for the temperatures given. It is the custom 
 in most laboratories to purchase the flasks ungraduated, and 
 to graduate them for the standard in use. 
 
5 8 VOL UME TRIG ANAL YSIS. 
 
 The process of testing these instruments is called Calibra- 
 tion. It is usually accomplished by comparing the actual 
 weight of water contained in the instrument, with its appar- 
 ent volume. 
 
 The unit of volume commonly adopted for volumetric 
 work is the so-called " Mohr liter," which is the volume 
 occupied by 1000 grams of water at 17.5 C., and the cubic 
 centimeter represents one thousandth of that volume. This 
 varies somewhat from the true liter, which is the volume of 
 1000 grams of water at 4 C. The objection to the latter 
 lies in the fact that the temperature at which the instru- 
 ments would be correct by this standard, differs essentially 
 from laboratory temperatures. The maintenance of a tem- 
 perature of 4 C. during calibration would be accompanied 
 by no little annoyance, and an attempt to calibrate at ordi- 
 nary temperatures, by making allowance for the expansion of 
 the water, is accompanied by some uncertainty. On the 
 other hand, the temperature at which the Mohr liter is the 
 standard does not differ greatly from the laboratory temper- 
 ature and, except when extreme accuracy is essential, no 
 corrections are necessary. The calibrations are also easily 
 effected. 
 
 It is obvious that some temperature must be chosen at 
 which all measuring instruments in use in the same labora- 
 tory are calibrated. That is, if a 50 cc. measuring flask is 
 to be capable of measuring exactly one tenth of the liquid 
 contained in a 500 cc. measuring flask, both must be correct 
 at the same temperature. It is equally desirable that the 
 burettes and pipettes used should accord with the same 
 standard, and the one most commonly adopted is based 
 upon the Mohr liter, 17. 5 C. It is also plain that a lab- 
 oratory for volumetric work should possess as uniform a 
 temperature as possible. 
 
 CALIBRATION OF BURETTES. 
 
 Each student should calibrate at least one burette, as 
 follows : 
 
 Procedure. Clean the burette thoroughly, by pouring 
 into it a warm solution of chromic acid in concentrated 
 
C A LIBRA TION OF B URE TTES. 59 
 
 sulphuric acid. Stopper the burette and bring the acid in 
 contact with its entire length by shaking. Pour the acid 
 back into its receptacle, and wash out the burette thor- 
 oughly with water. Unless the water runs from the bu- 
 rette without leaving drops upon the sides, the process must 
 be repeated. When clean, fill the burette with distilled water, 
 allow it to run out through the stopcock, or rubber tip, until 
 convinced that no air bubbles are inclosed. Fill the burette 
 to the zero mark and draw off the liquid until the meniscus 
 is just below the zero mark. To take the exact reading, 
 wrap around the burette a piece of colored paper, with its 
 straight, smooth edges held evenly together (color turned 
 inside), and held two small divisions below the meniscus. 
 Move the eye so that the edge of the paper at the back of 
 the burette is just hidden by that in front, and note the 
 position of the lowest point of the meniscus of the water. 
 Estimate the tenths of the small divisions, corresponding 
 to hundredths of a cubic centimeter, and record the reading 
 in the notebook. 
 
 Weigh a 50 cc. flat-bottomed flask (of thin glass), which 
 must be dry on the outside, to the nearest centigram. Re- 
 cord the weight in the notebook. Place the flask under-the 
 burette, and draw out into it about 10 cc. of water, removing 
 any drop on the tip by touching it against the inside of the 
 neck of the flask. Do not attempt to stop exactly at the 10 
 cc. mark, but do not vary more than o. I cc. from it. Note 
 thejtime, and at the expiration of three minutes (or longer), 
 take the reading upon the burette accurately, and record it in 
 the notebook. Meanwhile, weigh the flask and water to. 
 centigrams and record its weight. Draw off the liquid from 
 io cc. to about 20 cc. into the same flask without emptying 
 it ; weigh, and at the expiration of three minutes take the 
 reading, and so on throughout the length of the burette. 
 When it is completed, re-fill the burette and check the first 
 calibration. 
 
 The differences in readings represent the apparent vol- 
 ume, the differences in weights, the true volumes. For 
 example, if an apparent volume of 10.05 was found to weigh 
 10.03 grams, it may be assumed with sufficient accuracy that 
 
60 VOL UME TRIG ANAL YSIS. 
 
 the error in that 10 cc. amounts to 0.02 cc., or 0.002 for each 
 cubic centimeter. The records may conveniently be made 
 in the notebook under these headings : 
 
 Readings ; Differences ; Weights ; Differences ; Calcu- 
 lated Corrections. 
 
 Notes. i. The inner surface of the burette must be abso- 
 lutely clean, if the liquid is to run off freely. Chromic acid 
 in sulphuric acid is usually found to be the best cleansing 
 agent, but the mixture must be warm and concentrated. This 
 solution can be prepared by adding to concentrated commer- 
 cial sulphuric acid a few crystals of potassium bichromate, and 
 i cc. of water. Warm the mixture gently and pour off the 
 solution. It is convenient to have such a solution ready at 
 hand, as burettes frequently need cleaning. The rubber tip 
 should be removed before the cleansing agent is added. 
 
 2. It is always necessary to insure the absence of air 
 bubbles in the tips by running the liquid rapidly through 
 them. These bubbles may otherwise escape during titration, 
 and vitiate results. 
 
 3. To obtain an accurate reading, the eye must be on a 
 level with the meniscus. This may be attained by the use of 
 a paper, or by using a float. The latter is useful, provided it 
 moves freely in the burette, but care must be taken that such 
 is the case, otherwise a float is worse than useless. 
 
 4. The eye soon becomes accustomed to estimating the 
 tenths of the divisions. If the paper is held as directed, two 
 divisions below the meniscus, one whole division is visible to 
 correct the judgment. It is not well to attempt to bring the 
 meniscus exactly to a division" mark on the burette. Such 
 readings are usually less accurate than those in which the 
 hundredths are estimated. 
 
 5. It is obvious that it would be useless to weigh the water 
 with an accuracy greater than that of the readings taken on 
 the burette. The latter cannot exceed o.oi cc. in accuracy, 
 which corresponds to o.oi gram. 
 
 The student should clearly understand that all other weigh- 
 ings except those for calibration, should be made accurately to- 
 o.oooi gram. 
 
 6. A small quantity of liquid adheres to the side of even 
 a clean burette. This slowly unites with the main body of 
 
CALIBRATION OF FLASKS, 6l 
 
 liquid, but requires an appreciable time. Three minutes is a 
 sufficient interval, but not too long, and should be Adopted in 
 every instance throughout_the whole volumetric practice, 
 before final readings are recorded. 
 
 7. Should the error discovered in any interval of 10 cc. 
 on the burette exceed o.io cc., it is advisable to weigh smaller 
 portions (even i cc.), to locate the position of the variation of 
 bore in the tube, rather than to distribute the correction uni- 
 formly over the corresponding 10 cc. The latter is the usual 
 course for small corrections, and it is convenient to calculate 
 the correction corresponding to each cubic centimeter and 
 to record it in the form of a table or calibration card, or to 
 plot a curve representing the values. 
 
 8. Burettes may also be calibrated by drawing off the 
 liquid in successive portions through a 5 cc. pipette which has 
 been accurately calibrated, as a substitute for weighing. If 
 many burettes are to be examined this is a more rapid method. 
 
 9. Pipettes are calibrated in the same general way as bu- 
 rettes. Thej^rjiust_b_e_cleaned, and are then filled with water, 
 and the latter is drawn oflTand weighed. A definite interval 
 must be allowed for draining, and a definite practice adopted 
 as regards the removal of the liquid which collects at the end 
 of the tube, if the pipette be designed to deliver a specific 
 volume when emptied. This liquid may, at the end of a ^defi- 
 nite interval, be removed either by touching the side of the 
 vessel or by gently blowing out the last drops. Either prac- 
 tice must be uniformly adhered to. 
 
 CALIBRATION OF FLASKS. 
 
 Procedure. Clean the flask and dry it carefully outside 
 and inside. Tare it accurately, and place on the opposite 
 balance-pan the number of grams corresponding to the vol- 
 ume desired ; pour water into the flask until the weight of 
 the latter counterbalances the weight on the pan. Remove 
 the flask from the balance, stopper it, place it in a bath at 
 the desired temperature, usually 17.5 C, and after an hour, 
 mark on the neck with a diamond, the location of the lowest 
 point of the meniscus. 
 
 Notes. i. The allowable error in counterbalancing 
 the water and weights varies with the volume of the flask. 
 
62 VOL UME TRIG ANAL YSIS. 
 
 It should not exceed one ten-thousandth of the weight of 
 water. 
 
 2. Other methods are used which involve the use of cali- 
 brated apparatus, from which the desired volume of water 
 may be run into the dry flask, and the graduation marked 
 directly upon it. For a description of one of these, the stu- 
 dent is referred to the Am. Chem. J., 16, 479. 
 
 3. Flasks may be graduated either for " contents " or for 
 "delivery." In the former case they contain the specified 
 volume when filled to the graduation ; in the latter case the 
 flask will deliver the specified volume, if allowed to drain for a 
 definite time. By placing two marks upon the flask it may be 
 graduated for both contents and delivery. 
 
 To calibrate a flask for delivery, it should be filled with 
 water, then emptied and allowed to drain for a definite inter- 
 val (three minutes). It is then tared, the requisite weights 
 are placed upon the balance pan, and water added to counter- 
 balance these. It is then placed in a bath at the required 
 temperature and, after an hour, marked. 
 
 Flasks thus calibrated will deliver a definite volume of a 
 solution without being washed out. It is, however, a more 
 general custom to graduate flasks for contents. 
 
 GENERAL DIRECTIONS. 
 
 It is essential to the success of analysis that uniformity of 
 practice shall prevail throughout all volumetric work, with 
 respect to those matters which can influence the accuracy of 
 measurement of liquids. Whatever conditions are imposed, 
 for example, during the calibration of a burette, pipette, or 
 flask, (notably the time allowed for draining), must also pre- 
 vail whenever the flask or burette is used. 
 
 The student should be constantly watchful to insure par- 
 allel conditions during both standardization and analysis, with 
 respect to the final volume of liquid in which a titration 
 takes place. The standard of the solution is only accurate 
 under the conditions which prevailed when it was determined. 
 
 It is plain that the standard solutions must be scrupu- 
 lously protected from concentration or dilution, after their 
 value has been established. Accordingly, great care must 
 be taken to thoroughly rinse out all burettes, flasks, etc., 
 
GENERAL DIRECTIONS. 63 
 
 with the solutions which they are to contain, in order to 
 remove all traces of water, or other liquid which could act 
 as a diluent. It is best to wash out a burette at least three 
 times with small portions of a solution, allowing them to 
 run out through the tip, before assuming that it is in a con- 
 dition to be filled and used. It is, of course, possible to dry 
 the measuring instruments in a hot closet, but this is tedious 
 and unnecessary. 
 
 To the same end, all solutions should be kept stoppered, 
 and away from direct sunlight or heat. The bottles should 
 be shaken before use, to collect any liquid which may have 
 distilled from the solution and condensed on the sides. 
 
 Care should be taken when selecting a spot for volumetric 
 work, that no source of heat is sufficiently near to raise the 
 temperature of the solutions. The temperature should 
 always be as near 17.5 C. as is practicable. 
 
 Much time may be saved by estimating the approximate 
 volume of a standard solution which will be required for a 
 titration (if the data are obtainable), before beginning the 
 operation. It is then possible to run in rapidly approxi- 
 mately the required amount, after which it is only necessary 
 to determine the end-point with accuracy. In such cases, 
 however, the knowledge of the amount probably to be re- 
 quired should never be allowed to influence the judgment 
 regarding the end-point. 
 
64 VOL UME TRIG ANAL YSIS. 
 
 I. SATURATION METHODS. 
 
 ALKALIMETRY AND ACIDIMETRY. 
 
 GENERAL DISCUSSION. 
 
 STANDARD solutions of acid and alkali are required for 
 these processes, together with such indicators as will accu- 
 rately designate the point of saturation. 
 
 Standard Acid Solutions may properly be prepared from 
 either hydrochloric, sulphuric, or oxalic acids. Hydrochloric 
 acid has the advantage of forming soluble compounds 
 with the alkaline earths, but its solutions cannot be boiled 
 without loss of strength ; sulphuric acid solutions may be 
 boiled without loss, but the acid forms insoluble sulphates of 
 three of the alkaline earths ; oxalic acid can be accurately 
 weighed for the preparation of solutions, and its solutions 
 may be boiled without loss, but it also forms insoluble oxal- 
 ates with three of the alkaline earths, and cannot be used 
 with certain of the indicators. 
 
 Standard Alkali Solutions may be prepared from sodium 
 or potassium hydroxide, sodium carbonate, barium hydrox- 
 ide, or ammonia. Of sodium and potassium hydroxide, it 
 may be said that they can be used with all indicators, and 
 their solutions may be boiled, but they absorb carbon dioxide 
 readily, and attack the glass of bottles ; sodium carbonate 
 may be weighed directly, if its purity is assured, but the 
 presence of the carbonic acid of the carbonate is a disad- 
 vantage with many indicators ; barium hydroxide solutions 
 may be prepared which are entirely free from carbon diox- 
 ide, and such solutions immediately show by precipitation 
 any contamination from absorption, but the hydroxide is not 
 freely soluble in water ; ammonia yields a clean solution, and 
 does not absorb carbon dioxide as readily as the caustic alka- 
 lies, but its solutions cannot be boiled, nor can they be used 
 with all indicators. 
 
INDICA TOftS. 
 
 Half-normal () or deci-normal ( T ^) solutions are employed 
 in most analyses (except in the case of the less soluble ba- 
 rium hydroxide). Solutions of the latter strength are con- 
 venient, when small percentages of acid or alkali are to be 
 determined. 
 
 INDICATORS. 
 
 An indicator, to be of service in acidimetric processes, 
 must be a substance of basic or acid character, which, like 
 litmus, will show by a change of color, the presence of the 
 slightest excess of free acid or alkali. The number of or- 
 ganic bodies which have been proposed as indicators is large, 
 but of these a few only have come into general use. The 
 most important among the latter are presented in the table 
 below, with their characteristics : 
 
 
 
 
 . 
 
 .y s 
 
 <J 
 
 i 
 
 u 
 
 
 'i 
 
 i 
 
 1! 
 
 ll 
 
 S 
 
 s 
 
 1 
 
 Indicator. 
 
 c 
 o 
 
 c 
 
 2 M - 
 
 zS 
 
 11 
 
 "5 2 
 
 * 3 
 |1 
 
 
 
 J3 
 
 
 1 
 
 s| 
 
 *" 
 
 (U^fc 
 
 |fl 
 
 | = 
 
 3 
 
 Litmus. 
 
 Red. 
 
 Blue 
 
 Unreliable. 
 
 Reliable 
 
 Reliable 
 
 Reliable. 
 
 Methyl Orange. 
 
 Pink. 
 
 Yellow. 
 
 Reliable. 
 
 Unreliable. 
 
 Reliable. 
 
 Unreliable 
 
 Phenolphthalein 
 
 Colorless. 
 
 Pink | Unreliable. 
 
 Reliable. 
 
 Unreliable. 
 
 Reliable. 
 
 Lactnoid. 
 
 Purple red. 
 
 Blue 
 
 Unreliable. 
 
 Reliable. 
 
 Reliable 
 
 Unreliable. (?) 
 
 Cochineal. 
 
 Purple red. 
 
 Blue. 
 
 Reliable. 
 
 Reliable 
 
 Reliable 
 
 Unreliable. 
 
 Rosolic acid 
 
 Yellow. 
 
 Pink 
 
 Unreliable. 
 
 Reliable. 
 
 Unreliable 
 
 Unreliable 
 
 Alizarine. 
 
 Yellow. 
 
 Red. 
 
 Unreliable. 
 
 Reliable. 
 
 Reliable. 
 
 Reliable. 
 
 1 Reliable with oxalic acid. 
 
 Litmus solution, for use as an indicator, must be specially 
 prepared. For the details of its preparation and preserva- 
 tion, the student is referred to Suttons Volumetric Analysis, 
 under " Indicators." A general discussion of the subject of 
 indicators will also be found there. 
 
 Methyl Orange (also known as Orange No. Ill) is not 
 affected by carbonic acid or sulphuretted hydrogen, in cold 
 solution, and is, therefore, the most convenient indicator for 
 use in the presence of carbonates or sulphides, unless 
 
66 VOLUMETRIC ANALYSIS. 
 
 organic acids are also present. The customary strength for 
 the indicator solution is I gram per liter, which may be dis- 
 solved in a few cubic centimeters of alcohol, and the solution 
 diluted. 
 
 Methyl Orange can be used in the presence of borates. 
 
 Phenolphthalein is of special value for the titration of 
 organic acids, provided ammonia or ammonium salts are not 
 present. In the presence of carbonates it can only be used 
 in hot solution. The indicator solution contains I gram in 
 100 grams of alcohol. 
 
 Lacmoid solutions should contain I gram in 200 cc. of 
 alcohol. It shows a neutral reaction with the salts of some 
 of the heavy metals, thus allowing the titration of free acid 
 in their presence. 
 
 Cochineal solutions are prepared by treating three parts of 
 cochineal, with two hundred parts water and fifty parts alco- 
 hol. This indicator is of special value for use with ammonia. 
 
 Of the indicators mentioned in the table, methyl orange 
 and lacmoid are most sensitive to alkalies, and phenolphtha- 
 le'in is most readily changed by acids. It is possible to 
 obtain from the same solution an acid reaction toward phe- 
 nolphthalein and a neutral or slightly alkaline reaction 
 toward methyl orange. It is obvious, then, that it is desir- 
 able to employ the same indicator both for standardization 
 and analysis. 
 
 Since the indicators must require a certain quantity of 
 acid or alkali in excess, to cause the change of color, it is 
 also plain that only the requisite quantity (usually one or two 
 drops of solution) should be used. 
 
 PREPARATION OF HALF-NORMAL SOLUTIONS OF HYDRO- 
 CHLORIC ACID AND SODIUM HYDROXIDE. 
 
 Procedure. Calculate the number of cubic centimeters 
 of aqueous hydrochloric acid (sp. gr. 1.12 or 1.2) required to 
 furnish 36.456 grams of the gaseous compound. (For this 
 purpose consult the table on p. 119). Measure out a vol- 
 ume of acid about 10 per cent, in excess of the calculated 
 quantity, into a clean 2-liter bottle, and dilute with distilled 
 
PREPARATION OF SOLUTIONS. 67 
 
 water to an approximate volume of 2000 cc. Shake the 
 solution thoroughly for at least a minute, to insure uni- 
 formity. 
 
 Weigh out, upon the laboratory balances, about 46 grams 
 of sodium hydroxide. Dissolve the hydroxide in water, and 
 dilute to 2000 cc. Shake this solution also for a minute. 
 
 Select two clean burettes, and fill them with the solutions, 
 after rinsing them out three times with 10 cc. of the solution, 
 which should be allowed to run out through the tip to insure 
 the displacement of all water from that part of the burette. 
 When the burettes are ready for use, and all air bubbles dis- 
 placed from the tip, note the exact position of the liquid in 
 each, and record the readings in the notebook. Run out 
 from the burette about 40 cc. of the acid into a beaker, and 
 add two drops of a solution of methyl orange ; dilute the 
 acid to about 100 cc., and run out alkali solution from the 
 other burette until the pink has given place to a yellow. 
 Wash down the sides of the beaker with a little distilled 
 water, if the solution has spattered upon them, return the 
 beaker to the acid burette, and again restore the pink ; con- 
 tinue these alternations until the point is accurately fixed at 
 which a single small drop of either solution serves to pro- 
 duce a distinct change of color. It is usually more satisfac- 
 tory to select as an end-point the appearance of the faintest 
 pink which can be recognized. If the titration has occupied 
 more than three minutes, the readings of the burettes may 
 be immediately taken and recorded in the notebook. 
 
 Re-fill the burettes and repeat the titration. Correct the 
 burette readings as indicated by the burette calibrations, and 
 obtain the ratio of the sodium hydroxide solution to that of 
 hydrochloric acid by dividing the number of cubic centime- 
 ters of acid used, by the number of cubic centimeters of 
 alkali required for neutralization. The check results should 
 not vary by more than 0.2 per cent, of the total ratio. 
 
 When this ratio has been fully established, weigh out, 
 from a weighing tube, into No. 4 lipped beakers, two por- 
 tions of about i gram each of pure calcium carbonate, not- 
 ing the weights exactly (to o.oooi gram) in the notebook. 
 Cover the carbonate with 25 cc. of water and add two drops 
 
68 V OL UME TRIG ANAL YSIS. 
 
 of methyl orange solution ; fill the burettes and note initial 
 readings ; run the acid into the beaker, with cautious stir- 
 ring, until the carbonate has dissolved, avoiding loss by 
 effervescence, wash down the sides of the beaker, and then 
 run in alkali until the indicator becomes yellow. Finish the 
 titration as described above. Note the. readings on the bu- 
 rette after the proper interval, and record them in the note- 
 book. From the data then recorded, it is possible to deter- 
 mine the volume of hydrochlor c acid neutralized by the 
 pure calcium carbonate, and hence the weight of gaseous 
 hydrochloric acid in each cubic centimeter. The standardi- 
 zation must be repeated until these values agree within 0.2 
 per cent. 
 
 Compare the value just obtained with the weight of the 
 acid which should be present in i cc. of -^- HC1 and dilute 
 the solution accordingly. (For example : a solution contain- 
 ing .01900 gram HC1 per cubic centimeter should be diluted 
 according to the proportion .01900 : .01822 = x : 1000 ; 
 i. e., each 1000 cc. of that solution should be diluted to 
 1042.3 cc.) Measure off 2 liters accurately in a graduated 
 flask, observing precautions mentioned on page 62, and add 
 the requisite volume of water from a burette. From the 
 known ratio of the two solutions, and the known value of 
 the acid, calculate the requisite dilution for the alkali solu- 
 tion, and add the necessary volume of water to it also. De- 
 termine the ratio between these new solutions after shaking 
 thoroughly, and re-standardize the acid against calcium car- 
 bonate. The values thus found should not differ from the 
 calculated values for half-normal solutions, by more than 0.2 
 per cent, in either case. If a greater variation be found, 
 the dilution and standardization must be repeated, before 
 the solutions are ready for use. 
 
 Notes. i. The solutions are prepared of greater strength 
 than that finally desired, as they are more readily diluted 
 than strengthened. Commercial sodium hydroxide is usually 
 impure, and always contains more or less carbonate ; a fur- 
 ther allowance is therefore made for this factor by placing the 
 weight taken at 46 grams for the 2 liters. If the hydroxide is 
 known to be pure, a lesser amount (say 42 grams) will suffice. 
 
PKEPARA TION OF SOL UTIONS. 69 
 
 2. Too much care cannot be taken to insure perfect uni- 
 formity of solutions before standardization, and thoroughness 
 in this respect will often avoid much waste of time. A solu- 
 tion once thoroughly mixed does not alter. 
 
 3. The liquid is diluted to 100 cc. during standardization 
 to make the volume approximately equal to that which will 
 prevail during analysis. Compare remarks on page 62. 
 
 4. The change from yellow to pink is better defined than 
 the reverse change. The end-point should be chosen exactly 
 at the point of change ; any darker tint is unsatisfactory, 
 since it is impossible to carry shades of color in the memory 
 and to duplicate them from day to day. 
 
 5. A variation of 0.2 per cent, of the total value is not 
 excessive in a beginner's work. It must not be regarded as a 
 fixed standard, however, or as necessarily of general appli- 
 cation. 
 
 6. The calcium carbonate is covered with water to lessen 
 the violence of the action of the acid. It is usually well to 
 add a moderate excess of acid, and stir. If this fails to dis- 
 solve the carbonate, add more, and so on. The excess of 
 acid is then neutralized by the alkali, and this excess may be 
 calculated from the known ratio of the two solutions. This is 
 an indirect process of standardization. 
 
 7. Anhydrous sodium carbonate may be substituted for 
 calcium carbonate in the standardization of the acid solution, 
 if the purity of the carbonate can be assured. It has the ad- 
 vantage of solubility, and is better for use with sulphuric acid 
 since the calcium carbonate may become partially coated with 
 insoluble calcium sulphate, and fail to be acted upon by the 
 acid. 
 
 Instead of standardizing the acid solution as described, it 
 is equally practicable to standardize the alkali solution against 
 purified oxalic acid (C 2 H 2 O 4 .2H 2 O), potassium acid oxalate 
 (KHC 2 O 4 .H 2 O), potassium tetroxalate (KHC 2 O 4 .C 2 H 2 O 4 . 
 2H 2 O), or potassium acid tartrate (KHC 4 H 4 O 6 ). The oxalic 
 acid and the oxalates should be specially prepared to insure 
 purity, the main difficulty lying in the preservation of the 
 water of crystallization. 
 
 It should be noted that the acid oxalate and the acid tar- 
 trate each contain one hydrogen atom replaceable by a base, 
 while the tetroxalate contains three such atoms, and the oxalic 
 
7 o VOL UME TRIG ANA L YSIS. 
 
 acid two. Each of the two salts first named behave as mono- 
 basic acids, and the tetroxalate as a tribasic acid. 
 
 8. The sulphuric acid solution may also be standardized 
 by precipitating the acid as barium sulphate, which is weighed 
 as in gravimetric analysis. Hydrochloric acid may be simi- 
 larly standardized by precipitation and weighing, as silver 
 chloride. 
 
 DETERMINATION OF THE TOTAL ALKALINE STRENGTH OF 
 SODA ASH. 
 
 Procedure. Weigh out, on the laboratory balances, two 
 portions of soda ash of about 5 grams each. Place them on 
 small watch-glasses and dry them at 1 10 C, until the weight 
 is constant within 0.005 grams, weighing at intervals of 
 thirty minutes and cooling in a desiccator. Finally weigh 
 accurately, and transfer the soda ash to a No. 4 lipped 
 beaker ; weigh the watch-glasses, and take the difference as 
 the weight of the sample for analysis. Dissolve the ash in 
 75 cc. of water, warming gently, and filter off the insoluble 
 residue ; wash the filter until the washings are freed from 
 carbonate, cool the filtrate to the temperature of the labora- 
 tory, and transfer it to a 250 cc. measuring flask, washing 
 out the beaker thoroughly. Add distilled water until the 
 lowest point of the meniscus is level with the graduation on 
 the neck of the flask, and remove any drops of water that 
 may be on the neck above the graduation, with a strip of 
 filter paper ; make the solution thoroughly uniform, by pour- 
 ing it out into a dry beaker and back into the flask several 
 times. 
 
 Measure off 50 cc. of this solution in a measuring flask, 
 but first pour into the smaller flask at least two small por- 
 tions of the soda-ash solution, and shake to displace any 
 water. Finally fill the flask to the mark with the solution, 
 and remove any drops on the neck above the graduation. 
 Empty it into a beaker and wash out the small flask, unless 
 it is graduated to deliver 50 cc. (Compare note 3, p. 62.) 
 Dilute the solution in the beaker to 100 cc., add two drops 
 of methyl orange solution, and titrate for the alkali with the 
 
SODA ASH. y r 
 
 half-normal acid, using the half-normal alkali to complete the 
 titration, as described under the preparation of solutions. 
 From the corrected volumes of acid and alkali employed, 
 and the data derived from the standardization, calculate the 
 percentage of alkali present, assuming it all to be present as 
 sodium carbonate. 
 
 It is advisable to measure out a second portion of 50 cc. 
 from the main solution in each case, to confirm the original 
 titration. 
 
 Notes. i. Soda ash is crude sodium carbonate. If made 
 by the ammonia process, it may contain also sodium chloride 
 sulphate, and hydrate ; when made by the Le Blanc process, 
 it may contain sodium sulphide, silicate, and aluminate, and 
 other impurities. Some of these, notably the hydrate, com- 
 bine with acids and contribute to the total alkaline strength, 
 but it is customary to calculate this strength in terms of 
 sodium carbonate ; /. <?., as though no other alkali were 
 present. 
 
 2. In order to secure a sample which shall represent the 
 average value of the ash, it is well to take at least 5 grams. 
 As this is too large a quantity for convenient titration, an ali- 
 quot portion of the solution is measured off, representing one 
 fifth of the entire quantity. 
 
 It is also possible to weigh out exactly 2.6525 grams of the 
 soda ash, dissolve, filter, and titrate the entire solution, when 
 the number of cubic centimeters of half-normal acid used will 
 indicate directly the alkaline strength in terms of sodium car- 
 bonate. The student should verify this statement by calcu- 
 lation. 
 
 3. It is customary to dry the soda ash at 110 C. before 
 analysis. Greater uniformity of results is then attainable. 
 
 Complete expulsion of the moisture would require a tem- 
 perature just below the fusion point of the carbonate. 
 
 4. The residue insoluble in water must be completely 
 washed to remove soluble alkali, and the filtrate must be 
 cooled to a temperature approximating 17.5 C. before dilu- 
 tion to a definite volume, in a measuring flask which is cor- 
 rect at that temperature. 
 
 A 50 cc. pipette may be equally well employed to measure 
 out the aliquot portion-, in place of the 50 cc. flask. 
 
7 2 VOL UME TRIG A NA L YSIS. 
 
 5. The determination of the caustic alkali in the soda ash 
 may be accomplished by precipitating the carbonate with 
 barium chloride, removing it by rapid filtration, and titrating 
 for the alkali in the filtrate. The carbonated alkali is then 
 calculated as the difference between the caustic alkali and the 
 total alkali. 
 
 DETERMINATION OF THE ACID STRENGTH OF OXALIC ACID. 
 
 Procedure. Weigh out two portions of the acid of about 
 I gram each. Dissolve these in 50 cc. of warm water, filter, 
 if the solution is not clear, and wash the filter completely 
 with hot water, until freed from oxalic acid. Add to the fil- 
 trate two drops of phenolphthalein solution, and run in alkali 
 from the burette until the solution is pink ; add acid from 
 the other burette until the pink is just destroyed, and then 
 add 0.5 cc. (not more] in excess. Heat the solution to boil- 
 ing for three minutes. If the pink returns during the boil- 
 ing, discharge it with acid and again add 0.5 cc. in excess 
 and repeat the boiling. If the color does not then reappear, 
 add alkali until it does, and a drop or two of acid in excess 
 and boil again for one minute. If no color reappears during 
 this time, complete the titration in the hot solution, ending 
 with the change from colorless to pink. From the corrected 
 volume of alkali required to react with the oxalic acid, calcu- 
 late the weight of the latter present, in terms of the crystal- 
 lized acid (C 2 H 2 O 4 .2H 2 O), and from this, the percentage 
 purity of the sample. 
 
 Notes. i. It has already been pointed out that it is desir- 
 able to employ the same indicator throughout standardization 
 and analysis statement, which is applicable in this instance. 
 The student is advised, if practicable within the time devoted 
 to the subject, to re-standardize acid and alkali using phe- 
 nolphthalein as the indicator, and concluding each titration 
 by boiling the solution as described above, or, what is per- 
 haps better, to standardize the alkali solution against one of 
 the substances named in note 7, page 69, using phenol- 
 phthalein. 
 
OXALIC ACID. 73 
 
 The differences resulting from the change of indicator are 
 small, and the student may neglect them in this instance, per- 
 forming the titration as outlined above to gain some practice 
 with phenolphthalein ; but it should be remembered that if 
 the highest accuracy is desired, a re-standardization through- 
 out is essential. 
 
 2. All commercial caustic soda contains some carbonate, 
 and as phenolphthalein is acted upon by carbon dioxide, the 
 solution must be boiled to expel the gas. Phenolphthalein 
 does not show an alkaline reaction with acid carbonates ; 
 hence solutions containing carbonates and this indicator be- 
 come colorless when half the carbonate has been acted upon 
 by acid. Upon boiling, the bicarbonate loses carbon dioxide, 
 forming normal carbonate, and the pink returns. This must 
 be again discharged, and the solution boiled, and so on. 
 
 A similar procedure is necessary with all the indicators 
 mentioned, except methyl orange ; the latter does not, how- 
 ever, give reliable results with organic acids, as its own acid 
 is stronger than many of them. 
 
 It is possible to remove the carbonate from the caustic 
 alkali by the cautious addition of barium hydroxide be- 
 fore standardization ; the barium carbonate is removed by 
 filtration. 
 
 3. Hydrochloric acid is volatilized from aqueous solutions, 
 except such as are very dilute. If the directions in the pro- 
 cedure are strictly followed, no loss of acid need be feared, 
 but the amount added in excess must not exceed 0.5 cc. 
 
 4. The end-point should be the faintest visible shade of 
 color, as the same difficulty would exist here as with methyl 
 orange, if an attempt were made to match shades of pink. 
 
I 
 
 74 VOLUMETRIC ANALYSIS. 
 
 II. OXIDATION PROCESSES. 
 
 GENERAL DISCUSSION. 
 
 Under this section may properly be included, beside ox- 
 idation processes, the rather limited number of methods 
 in which standard solutions of reducing agents only are 
 employed, since a corresponding oxidation of the reducing 
 agent must always be a part of the reaction. In general it 
 may be stated that oxidizable substances are determined by 
 direct titration, while oxidizing substances are usually deter- 
 mined by indirect methods. 
 
 Many quantitative determinations are made possible by 
 the application of these volumetric methods involving oxida- 
 tion or reduction, which are not practicable by gravimetric 
 procedures. ' A notable example is that of the determination 
 of iron in the presence of aluminum. ] The mixture of 
 hydroxides thrown down by ammonia may be ignited, 
 weighed, and the iron subsequently determined volumetric- 
 ally, by solution of the precipitate,,, reduction of the iron, 
 and oxidation by potassium permanganate or bichromate. 
 The aluminum is then determined by difference. 
 
 The important oxidizing agents employed for volumetric 
 solutions are potassium bichromate, potassium permanga- 
 nate, potassium ferricyanide, iodine, ferric chloride, and 
 sodium hypochlorite. 
 
 The important reducing agents which are used in the 
 form of standard solutions are ferrous sulphate (or ferrous 
 ammonium sulphate), oxalic acid, sodium thiosulghate, stan- 
 nous chloride, and arsenious acid. Othlff"Teducing agents* 
 as sulphurous acid, sulphuretted hydrogen, and zinc (nascent 
 hydrogen) take part in the processes, but not as standard 
 solutions. 
 
 The most important combinations among the foregoing 
 are the following : Potassium bichromate and ferrous salts ; 
 potassium permanganate and ferrous salts ; potassium per- 
 manganate and oxalic acid ; iodine and sodium thiosulphate ; 
 hypochlorites and arsenious acid. 
 
BICHROMATE PROCESS. 75 
 
 BICHROMATE PROCESS FOR THE DETERMINATION 
 
 OF IRON. 
 
 GENERAL DISCUSSION. 
 
 Ferrous salts may be promptly and completely oxidized to 
 ferric salts, even in cold solution, by the addition of potas- 
 sium bichromate, provided sufficient free acid is present to 
 combine with, and hold in solution, the ferric iron resulting 
 from the oxidation. 
 
 The free acid may be either hydrochloric or sulphuric, 
 but the former is usually preferred, since it is by far the 
 best solvent for iron and its compounds. The reaction in 
 the presence of hydrochloric acid is as follows ; 6 FeCl 2 
 + K 2 Cr 2 7 + 14 HC1 = 6 FeCl 3 + 2 CrCl 3 + 2 KC1 
 + 7 H 2 0. 
 
 The weight of potassium bichromate necessary for a nor- 
 mal solution was shown on page 55 to be 49.08 grams. It is 
 possible to prepare a standard solution of the bichromate by 
 directly weighing the requisite quantity, and dissolving it in 
 a definite quantity of water. The commercial salt, though 
 rarely sufficiently pure for this purpose as it often contains 
 potassium sulphate, may be purified by re-crystallization 
 from hot water, but must then be dried, and finally heated 
 to fusion to expel the last traces of moisture. The fusion 
 temperature must not be exceeded, as the bichromate will 
 lose oxygen if more strongly heated. 
 
 It is, perhaps, a more satisfactory mode of procedure to 
 make up a solution of the commercial salt and determine its 
 strength by comparison with iron, either in the form of iron 
 wire of known purity, or ferrous ammonium sulphate, 
 FeSO 4 . (NH 4 ) 2 SO 4 . 6 H 2 O. A standard wire is now offered 
 in the market which answers the purpose well, and its iro 
 contents may be determined for each lot by a number o' 
 gravimetric determinations. It may be best preserved i 
 jars containing calcium chloride but this must not be al- 
 lowed to come in contact with the wire. It should, how- 
 ever, even then be carefully examined for rust, before use. 
 
*6 VOLUMETRIC ANALYSIS. 
 
 
 
 If ferrous ammonium sulphate is used as the standard, 
 clear crystals only must be selected, and it is perhaps even 
 better to determine by gravimetric methods, once for all, the 
 iron contents of a sample which has been ground and mixed. 
 
 It is well to have on hand a solution of this salt for use in 
 connection with the bichromate. Such a solution is more 
 stable if about 5 cc. of concentrated sulphuric acid per 
 liter, are added. 
 
 It is plain that all of the iron in the solution must be in 
 the ferrous condition before titration. The available agents 
 for the reduction of any ferric iron are stannous chloride, 
 sulphurous acid, sulphuretted hydrogen, and zinc ; of these 
 stannous chloride acts most readily, the completion of the 
 reaction is most easily noted, and the excess of the reagent 
 is most readily removed. The latter object is accomplished 
 by oxidation by means of mercuric chloride added in excess, 
 as the mercury salts have no effect upon ferrous iron or 
 the bichromate. The reactions involved are 2 FeC] 3 
 + SnCl 2 = 2 FeCl 2 + SnCl 4 ; and SnCl 2 + 2 HgCl 2 = 
 SnCl 4 -\- 2 HgCl. The mercurous chloride is precipitated. 
 
 It is essential that the solution should be cold and that 
 the stannous chloride should not be present in great excess, 
 lest a secondary reaction take place, resulting in the reduc- 
 tion of the mercurous chloride to metallic mercury : SnCl 2 
 + 2 HgCl = SnC) 4 + 2 Hg. The occurrence of this 
 secondary reaction is indicated by the darkening of the pre- 
 cipitate, and since potassium bichromate oxidizes this mer- 
 cury slowly, solutions in which it has been precipitated are 
 worthless as iron determinations. 
 
 No indicator has been found which may be used within 
 the solution, on account of the deep green of chromium 
 salts ; the use of potassium ferricyanide outside the solu- 
 tion is therefore necessary to detect the presence of fer- 
 ous iron. A drop of the iron solution and one of the 
 ndicator solution are brought together on a white surface 
 best a porcelain tile and examined for a blue precipi- 
 tate of the ferrous ferricyanide. It is plain that the potas- 
 sium ferricyanide must contain no ferrocyanicle, for which 
 it should be carefully tested. The latter, if present, may 
 
BICHROMATE PROCESS. 
 
 77 
 
 be oxidized by the addition of a little bromine to the solu- 
 tion, after which the ferricyanide must be recrystallized. 
 
 The indicator solution must be very dilute to diminish 
 the interference of its own color ; a crystal the size of the 
 head of a pin in 25 cc. of water is an ample quantity. 
 This solution must be freshly prepared each day, as the 
 dilute solution is not stable. 
 
 No metals may be present in the titrated solution which, 
 like iron, are reduced by stannous chloride and oxidized by 
 potassium bichromate : notably, copper, antimony, and plat- 
 inum. For this reason a platinum crucible must never be 
 allowed to remain in an iron solution, as ferric chloride 
 exerts a slight solvent action upon the platinum. 
 
 The bichromate solution may be placed in burettes with 
 rubber tips without danger of deterioration of the solution. 
 
 STANDARDIZATION OF A POTASSIUM BICHROMATE SOLUTION. 
 
 Procedure. Pulverize about 5 grams of potassium bi- 
 chromate, dissolve it in water, and dilute to approximately 
 1000 cc. 
 
 Pulverize about 40 grams of ferrous ammonium sulphate, 
 dissolve it in water, dilute to about 1000 cc., and add 5 
 cc. of concentrated sulphuric acid. It is not necessary to 
 select clear crystals of the sulphate. 
 
 Shake the solutions until they are uniform, and place 
 them in burettes, with the precautions mentioned on page 
 
 6 7 . 
 
 Prepare a solution of potassium ferricyanide of the 
 strength recommended above, and place single drops of 
 this solution on the surface of a porcelain tile. 
 
 Run out from a burette into a beaker about 40 cc. of the 
 ferrous solution, add 15 cc. of hydrochloric acid (sp. gr. 
 1.12), dilute it to 150 cc., and run in the bichromate solution 
 from another burette. Since both the solutions are approx- 
 imately deci-normal, 35 cc. of the bichromate solution may 
 be added without testing. Test at that point, by removing 
 a very small drop of the iron solution on the end of a stir- 
 ring rod, and mixing it with a drop of indicator on the tile. 
 
7 8 VOLUMETRIC ANALYSIS. 
 
 If a blue precipitate appears at once, 0.5 cc. of the bichro- 
 mate solution may be run out before testing again. The 
 stirring rod which has touched the indicator should be dipped 
 in distilled water, before returning it to the iron solution. 
 As soon as the blue appears to be less intense, add the 
 bichromate solution in small portions, finally a single drop 
 at a time, until the point is reached at which no blue color 
 appears after the lapse of thirty seconds from the time of 
 mixing solution and indicator on the tile, the time being 
 accurately noted. At the close of the titration a large drop 
 of the iron solution should be taken for the test. To deter- 
 mine the end-point beyond any question, as soon as the thirty 
 seconds have elapsed remove another 'drop of the solution 
 of the same size as that last taken, and mix it with the 
 indicator, placing it beside the last previous test. If the 
 last test shows a blue tint in comparison with the previous 
 one, the end-point has not been reached ; if no difference can 
 be noted the reaction is complete. Should the end-point be 
 overstepped, more ferrous ammonium sulphate solution may 
 be added. 
 
 From the corrected volumes of the solutions used, cal- 
 culate the value of the ferrous solution in terms of the ox- 
 idizing solution. 
 
 Weigh out two portions of iron wire, of about 0.24-0.26 
 grams each, examining the wire carefully for rust. It 
 should be handled and wiped with wash-leather, not touched 
 by the fingers, should be weighed on a watch-glass, and be 
 so bent as not to interfere with the movement of the 
 
 *-.: 
 
 balance. 
 
 Dissolve the wire in a covered beaker in 30 cc. of hydro- 
 chloric acid (sp. gr.vi.i2), warming gently; wash off the 
 cover and sides of the beaker, and add stannous chloride 
 solution to the hot liquid, from a dropper, until the solution 
 is colorless, but avoid more than a drop or two in excess. 
 Dilute with 150 cc. of water, and cool completely. When 
 cold, add rapidly about 30 cc. of mercuric chloride solu- 
 tion (50 grams per liter). Allow the solutions to stand 
 three minutes and then titrate without delay, as just 
 described. Calculate the volume of the bichromate solution 
 
BICHROMATE PROCESS. 79 
 
 which would be required if the solution were deci-normal, 
 and add about this quantity. The ferrous ammonium sul- 
 phate solution may be used if the end-point is passed, and 
 much time saved. 
 
 From the corrected volumes of the bichromate solution 
 required to oxidize the iron actually present in the wire, cal- 
 culate the value of each cubic centimeter in terms of iron 
 (Fe), and also the amount of iron in each cubic centimeter 
 of the ferrous ammonium sulphate solution. Record these 
 values in the notebook. 
 
 Repeat the standardization until the results for the value 
 of each cubic centimeter in terms of iron are concordant 
 within O.OQOOI gram. 
 
 Notes. i. Note carefully the statements in the "General 
 Discussion " bearing upon the steps in the standardization. 
 
 2. The hydrochloric acid is added to the ferrous solution 
 to insure the presence of sufficient free acid for the titration. 
 
 3. The time interval for the indicator tests must be care- 
 fully noted. Some time must elapse before the completion of 
 the reaction when the ferrous iron is nearly all oxidized, but if 
 left too long, the combined effect of light and dust causes a 
 reduction and a deposition of a blue precipitate, as irv the 
 process of " blue-printing." Thirty seconds is a necessary 
 and also a sufficient interval. 
 
 4. The accuracy of the work may be much impaired by 
 the removal of unnecessarily large quantities of solution for 
 the tests. At the beginning of the titration, while much fer- 
 rous iron is still present, the end of the stirring rod need only 
 be moist with the solution, but at the close of the titration 
 drops of considerable size may properly be taken for the final 
 tests. The stirring rod should be washed to prevent transfer 
 of indicator to the main solution. 
 
 If the end-point is determined as prescribed, it can be as 
 accurately fixed as that of other methods, and if a ferrous 
 solution is at hand, the titration need consume hardly more 
 time than that of the permanganate process, to be described 
 later on. 
 
 5. The solution should be allowed to stand about three 
 minutes after the addition of mercuric chloride to permit the 
 
go VOLUMETRIC ANALYSIS. 
 
 complete deposition of mercurous chloride. It should then 
 be titrated without delay to avoid re-oxidation of the iron by 
 the oxygen of the air. 
 
 6. The potassium bichromate solution may be diluted to 
 form an exactly deci-normal solution if desired, according to 
 the principles stated on page 68. 
 
 DETERMINATION OF IRON IN LIMONITE. 
 
 Procedure. Grind the mineral to a fine powder, weigh 
 out two portions of about 0.5 gram into No. 7 porcelain 
 crucibles, heat these crucibles to dull redness for ten min- 
 utes, allow them to cool, and place them, with their contents, 
 in 'beakers containing 30 cc. of hydrochloric acid (sp. gr. 
 1.12). Heat at a temperature just below boiling until the 
 undissolved residue is white, or until solvent action has 
 ceased ; if a dark residue remains, collect it on a filter, 
 wash free from hydrochloric acid, and ignite the filter in 
 a platinum crucible. Mix the ash with a small quantity of 
 sodium carbonate and heat to fusion ; cool, and dissolve 
 the fused mass in boiling water in the crucible. Unite 
 solution and precipitate (if any) with the acid extraction, 
 washing out the crucible ; heat the solution to boiling, add 
 stannous chloride solution until it is colorless, avoiding a 
 large excess, cool, and when cold, add 40 cc. of mercuric 
 chloride solution, and proceed with the titration as already 
 described on page 77. 
 
 Calculate the percentage of iron (Fe) in the limonite. 
 
 Notes. i. Limonite is a native, hydrated oxide of iron. 
 It frequently occurs in or near peat beds, and contains more 
 or less organic matter, which, if brought into solution, would 
 be acted upon by the potassium bichromate. This organic 
 matter is destroyed by roasting. Since a high temperature 
 tends to lessen the solubility of ferric oxide, the heat should 
 not be raised above low redness. 
 
 2. A white residue, or one known to be free from iron, 
 may be neglected, and need not be filtered off. 
 
BICHROMATE PROCESS. 81 
 
 3. The quantity of stannous chloride required for the re- 
 duction of the iron in the limonite will be much larger than 
 that added to the solution of iron wire, in which the iron was 
 mainly ferrous. It should, however, be added from a dropper. 
 
 4. The platinum crucible, if used for the carbonate fusion, 
 must not be put into the iron solution. A platinum crucible 
 may also be used for the roasting, if preferred, with the same 
 precaution with respect to the iron solution. 
 
 5. It is sometimes advantageous to dissolve a large por- 
 tion say, 5 grams and to take one tenth of it for titra- 
 tion. The sample will then probably represent more closely 
 the average value of the ore. 
 
82 VOLUMETRIC ANALYSIS, 
 
 DETERMINATION OF CHROMIUM IN CHROME 
 IRON ORE. 
 
 Procedure. Fuse 10 grams of borax to a glass in a large 
 platinum crucible. Grind the chrome iron ore to the finest 
 powder, and weigh into the crucible about 0.5 gram. Heat 
 over a Bunsen burner, and stir with a stout platinum wire 
 until a clear glass is formed ; transfer the crucible to the 
 blast lamp, add 2 grams of sodium carbonate, and heat to 
 quiet fusion, using the highest temperature attainable. 
 
 Mix 1.5 gram of sodium carbonate and 1.5 grams of potas- 
 sium nitrate, and divide the mixture into six portions. Pro- 
 ject these portions into the crucible at suitable intervals, 
 watching carefully after each addition to prevent loss of 
 material, particularly with the last portions. Stir the 
 liquid mass occasionally, and continue the heating until no 
 more gas is evolved. 
 
 Cool the crucible, remove the fused mass as described on 
 page 32, and place both in a casserole ; boil with water until 
 the fused mass is disintegrated, remove the crucible, wash it 
 carefully, and add sulphuric acid to the solution in slight 
 excess. Run in ferrous ammonium sulphate solution from 
 a burette until the ferrous iron is in excess, and titrate for 
 that excess with the potassium bichromate solution. 
 
 From the corrected volumes of the two standard solutions, 
 calculate the amount of iron oxidized by the chromium from 
 the chrome iron ore, and subsequently the weight of chro- 
 mium in solution and the percentage in the ore. 
 
 Notes. i. Chrome iron ore is essentially a ferrous chro- 
 mite, or combination of FeO and Cr 2 O 3 . The borax glass 
 dissolves these oxides, and the nitrate oxidizes them to ferric 
 oxide (Fe 2 O 3 ) and chromic anhydride (CrO 3 ), the latter com- 
 bining with the alkali to form sodium chromate. The excess 
 of nitrate is decomposed, leaving the alkali as oxide, which 
 combines with some of the non-volatile acids present. Af- 
 ter fusion, the chromium is in the same state of oxidation as 
 in the bichromate solution, and reacts in the same way with 
 the ferrous salt. 
 
CHROME IRON ORE. 83 
 
 Each atom of chromium in the ore is capable of oxidizing 
 three atoms of iron : 2 Cr 2 O 3 -\- 3 O 2 = 4 CrO 3 ; 6 FeSO 4 
 + Na 2 Cr 2 O 7 + 7 H 2 SO 4 = 3 Fe 2 (SO 4 ) 3 + Na 2 SO 4 + 
 Cr 2 (S0 4 ) 3 + 7 H 2 0. 
 
 2. After the oxidation of the chromium is approximately 
 complete, the effervescence increases with each addition of 
 the oxidizing mixture, and greater care is required to avoid 
 loss. The determination requires constant attention while 
 the crucible is over the blast lamp. 
 
 The use of a graphite jacket to surround the crucible 
 makes easier the maintenance of a high temperature, but is 
 not indispensable. Occasional stirring prevents the accu- 
 mulation of undecomposed material at the bottom of the 
 crucible. 
 
 3. If a standard solution of a ferrous salt is not at hand, 
 a weight of iron wire, somewhat in excess of that required 
 if the substance were pure chromic oxide (Cr 2 O 3 ), may be 
 weighed out, dissolved in acid, reduced with stannous chlo- 
 ride, and treated as in the standardization of the bichromate 
 solution. The excess of iron is then determined by means 
 of the latter. 
 
8 4 VOLUMETRIC ANALYSIS. 
 
 PERMANGANATE PROCESS FOR THE D^TERMINA- 
 TION OF IRON. 
 
 GENERAL DISCUSSION. 
 
 Potassium permanganate oxidizes ferrous salts, in cold, 
 acid solution, promptly and completely to the ferric con- 
 dition, while in hot, acid solution it also enters into a defi- 
 nite reaction with oxalic acid, by which the latter is oxi r 
 dized to carbon dioxide and water. 
 
 The reactions involved are these : , 
 
 10 Fe6O 4 -r- 2 KMuO 4 + 8 H 2 SO 4 = 5 Fe^SO*), + K 2 SO 4 
 + 2 MnSO 4 + 8 H 2 O. 
 
 5 C 2 H 2 4 (2 H 2 0) + 2 KMn0 4 + 3 H 2 SO 4 = K 2 SO 4 + MnSO 4 
 -f 10 CO 2 + 8 H 2 O -f (10 H 2 O). 
 
 These are the fundamental reactions upon which its exten- 
 sive use depends, but beside iron and oxalic acid, the per- 
 manganate enters into reaction with tin, copper, mercury, 
 and manganese (the latter only in neutral solution), by which 
 these metals are changed from the lower to the higher state 
 of oxidation, and it also reacts with sulphurous acid, sul- 
 phuretted hydrogen, nitrous acid, ferrocyanides, and most 
 soluble organic bodies. It should be noted that it is only 
 with oxalic acid, among organic compounds, that there is 
 a definite reaction suitable for quantitative purposes. 
 
 From the definition of a normal oxidizing solution (page 
 55) the normal solution of potassium permanganate for use 
 in the presence of acid must contain 31.62 grams of the 
 reagent. This is seen from the following considerations : 
 Two molecules of the permanganate yield, as shown in the 
 equations above, one molecule of potassium salt correspond- 
 ing to the oxide K 2 O, and two molecules of manganous salt 
 corresponding to the oxide MnO, leaving five available oxy- 
 gen atoms (2 KMnO 4 = K 2 O. 2 MnO. O 5 ). The five oxygen 
 atoms furnished by the two gram-molecules of the perman- 
 ganate (316.2 grams) are equivalent to 10 grams of hydro- 
 gen. Accordingly, the normal solution must contain one 
 
PERMANGANATE PROCESS. 85 
 
 tenth of two gram-molecules, or one fifth of one gram-mole- 
 cule ; i. e.> 31.62 grams. 
 
 In neutral solution the permanganate is decomposed as 
 indicated by the equation 2 KMnO 4 = K 2 O. 2 MnO 2 . O 3 . 
 The normal solution for such purposes should contain one 
 sixth of two gram-molecules; i. e., 52.7 grams. 
 
 Potassium permanganate is acted upon by hydrochloric 
 acid ; the action is rapid in hot or concentrated solutions 
 but slow in cold, dilute solutions. The use of the perman- 
 ganate in the presence of hydrochloric acid, or its salts, may 
 therefore be attended by the possibility, of error, and it is 
 usually preferable to replace the hydrochloric acid of iron 
 solutions by sulphuric acid, before titration. This may be 
 done by evaporation with an excess of the latter until the 
 heavy, white fumes of sulphuric anhydride appear. 
 
 The greater solubility of iron compounds in 1 hydrochloric 
 acid makes it desirable to titrate, if possible, directly in such 
 solutions, and experiments made with this end in view have 
 shown that in cold, dilute hydrochloric acid solutions, to 
 which considerable quantities of manganous sulphate or 
 chloride, and an excess of phosphoric acid have been added, 
 it is possible, with practice, to obtain satisfactory results ; 
 but the end-point is less permanent than in sulphuric acid 
 solutions. Such a process is described in the J. Am. Chem. 
 Soc. t 17, 405. The reaction between hydrochloric acid and 
 the permanganate is : 
 
 2KMn0 4 +'i6HCl=2 KC1 + 2 MnCl 2 + 5C1 2 + 8 H 2 O. 
 
 Potassium permanganate has an intense coloring power, 
 and, since the solution resulting from the oxidation of the 
 iron and the reduction of the permanganate is colorless, the 
 latter becomes its own indicator. The slightest excess is 
 indicated with great accuracy by the color of the solution, 
 which renders the titration one of the most satisfactory 
 known. 
 
 The commercial salt is rarely sufficiently pure to admit of 
 direct weighing to form a standard solution, but it may be 
 purified by re-crystallization. The more common practice is 
 
86 VOLUMETRIC ANALYSIS. 
 
 to standardize the solution, which may be accomplished by 
 comparison with iron wire, ferrous ammonium sulphate, ox- 
 alic acid, potassium tetroxalate, or potassium acid oxalate. 
 Other substances have been proposed, but the foregoing are 
 those in common use. 
 
 The remarks on page 75 referring to the use of iron wire 
 and ferrous ammonium sulphate apply with equal force here. 
 The pure oxalic acid, or the oxalates, must be freshly pre- 
 pared, and with great care ; they are likely to lose water of 
 crystallization on standing. It must also be borne in mind 
 that the reaction with the oxalates takes place only in hot 
 solution. 
 
 The reducing agents available for the necessary reduction 
 of the iron before titration, are zinc, sulphurous acid, or sul- 
 phuretted hydrogen ; stannous chloride is excluded unless 
 the titration is to be made in the presence of hydrochloric 
 acid. Since the excess of both the gaseous reducing agents 
 can only be expelled by boiling, with consequent uncertainty 
 regarding the re-oxidation of the iron, zinc is the more satis- 
 factory agent ; but for prompt and complete reduction it is 
 essential that the solution should be brought into intimate 
 contact with the zinc. This is brought about by the use of 
 a modified Jones reductor, as shown in the figure, page 87.* 
 
 To prevent needless consumption of the zinc, it is first 
 amalgamated by dissolving 5 grams of mercury in 25 cc. of 
 concentrated nitric acid, diluted with an equal bulk of water, 
 and pouring into this solution (diluted to 250 cc. in a 1000 
 cc. flask), 500 grams of granulated zinc, 20-30 mesh. The 
 whole is shaken thoroughly for two minutes, the solution 
 poured off, and the zinc washed thoroughly. It may then be 
 preserved in bottles. 
 
 The tube A has an inside diameter of 18 mm., and is 300 
 mm. long; the small tube has an inside diameter 6 mm., and 
 extends 100 mm. below the stopcock. At the base of the 
 tube A is coiled a piece of stout platinum wire ; on this is 
 placed a plug of glass wool, about 8 mm. thick, and upon 
 
 *The details of the reductor and preparation of the zinc are taken from 
 Blair's Chemical Analysis of Iron, page 95 et seq. 
 
PERMANGANATE PROCESS. 
 
 this a thin layer of asbestos, such as is used for Gooch 
 filters, i mm. thick. The tube is then filled with the amal- 
 gamated zinc to within 50 mm. of the top, and on the zinc 
 is placed a plug of glass wool. The 60 mm. funnel B is 
 fitted into the tube 
 with a rubber stop- 
 per, and the reduc- 
 tor is connected with 
 a suction bottle, F. 
 The bottle D is a 
 safety bottle to pre- 
 vent contamination 
 of the solution by 
 water from the 
 pump. 
 
 The iron solution 
 during its passage 
 through the reduc- 
 tor comes into in- 
 timate contact with 
 the zinc, and is re- 
 duced by the nascent 
 hydrogen evolved. 
 The column of zinc 
 should never be less 
 than five inches in 
 length. Great care 
 must be used to pre- 
 vent the access of 
 
 air to the reductor after it has been washed out ready for 
 use. If air enters, hydrogen peroxide forms, which reacts 
 with the permanganate, and the results are worthless. 
 
 It is also possible to reduce the iron by treatment with 
 zinc, in a flask from which air is excluded, the zinc being 
 completely dissolved. This method is, however, less con- 
 venient and more tedious than the reductor. 
 
 Potassium permanganate solutions are not usually stable 
 for long periods, and change more rapidly when first pre- 
 pared than after standing some days. This is probably 
 
88 VOLUMETRIC ANALYSIS. 
 
 caused by interaction with the organic matter contained 
 in all distilled water, except that distilled from an alkaline 
 permanganate solution. The solutions should, however, be 
 protected from the light as far as possible, since sunlight 
 induces decomposition, with a deposition of manganese diox- 
 ide, and it has been recently shown* that the decomposition 
 proceeds with considerable rapidity, with \ the evolution of 
 oxygen, after the Jlioxide has begun to form. As commer- 
 cial samples of the, permanganate are likely to be contami- 
 nated by the dioxide, it is advisable to filter solutions through 
 asbestos before standardization. Such solutions are rela- 
 tively stable. 
 
 The permanganate solution cannot be placed in burettes 
 with rubber tips, as a reduction takes place upon contact 
 with the rubber. The solution has so deep a color that 
 the lower line of the meniscus cannot be detected ; readings 
 must therefore be made from the upper edge. 
 
 \ 
 
 STANDARDIZATION OF A POTASSIUM PERMANGANATE 
 SOLUTION. 
 
 Procedure. Dissolve about 3.25 grams of potassium per- 
 manganate crystals in 200 cc. of water, in a beaker, warm- 
 ing to hasten solution. Filter through a layer of asbestos, 
 cool, dilute to about 1000 cc., and mix thoroughly. Fill a 
 glass-stoppered burette with this solution, observing usual 
 precautions, and fill a second burette with the ferrous am- 
 monium sulphate solution prepared for use with the po- 
 tassium bichromate. Run out into a beaker about 40 cc. of 
 the iron solution, add 10 cc. of dilute sulphuric acid (i : 5), 
 and run in the permanganate solution to a slight perma- 
 nent pink. Repeat, until the ratio of the two solutions is 
 fixed. 
 
 Weigh out into beakers two portions of iron wire of about 
 0.25 gram each. Dissolve these in dilute sulphuric acid (5 
 cc. of concentrated acid and 100 cc. of water), warming to 
 promote solution. Meanwhile prepare the reductor for use 
 
 * Morse, Hopkins, and Walker, Am. Chem.J., 18, 401. 
 
PERMANGANATE PROCESS. 89 
 
 as follows : Connect the suction bottle with the vacuum 
 pump, fill the reductor while the stopcock is closed (or 
 nearly so) with warm dilute sulphuric acid (5 cc. of acid in 
 100 cc. water), and then open the stopcock so that the acid 
 runs through slowly. Continue to pour in acid until 200 
 cc. have passed through, then close the cock while a small 
 quantity of liquid is still left in the funnel. Remove the fil- 
 trate, and again pass through 100 QC. of the warm, dilute 
 acid. Test this with the permanganate solution. A single 
 drop should color it permanently ; if it does not, repeat the 
 washing. Be sure that no air enters the reductor. 
 
 Pour the iron solution while hot (but not boiling) through 
 the reductor at a rate not exceeding 50 cc. per minute. 
 Wash out the beaker with dilute sulphuric acid, and fol- 
 low the iron solution, without interruption, with 175 cc. of 
 the warm acid, and finally with 75 cc. of distilled water, 
 leaving the funnel partially filled. Remove the filter bottle, 
 and cool the solution under the water tap. Add 10 cc. of 
 dilute sulphuric acid, and titrate to a faint pink with the 
 permanganate solution directly in the filter bottle. Should 
 the end-point be overstepped, the ferrous ammonium sul- 
 phate solution may be added. From the volume ^of the 
 solution required to oxidize the iron in the wire, calculate 
 the value of each cubic centimeter in terms of metallic iron 
 (Fe). The results should be concordant within o.ooooi gram. 
 
 Notes. i. A careful study of the "General Discussion" 
 should be made in connection with the steps of this and the 
 following procedure. 
 
 2. The funnel of the reductor must never be allowed to 
 empty, and if it is left partially filled, the reductor is ready 
 for subsequent use without the previous washing. A prelim- 
 inary test is always a safeguard against error, however. 
 
 If more than a small drop of permanganate solution is 
 required to color 100 cc. of the dilute acid after the reductor 
 is well washed, an allowance must be made for the iron in 
 the zinc. 
 
 The rate of filtration of the iron solution should not ex- 
 ceed that prescribed, but the rate may be increased some- 
 what when the wash-water is added. It is well to allow the 
 
VOLUMETRIC ANALYSIS 
 
 iron solution to run nearly, but not entirely, out of the funnel 
 before the wash-water is added. If it is necessary to inter- 
 rupt the process, the complete emptying of the funnel can 
 always be avoided by closing the stopcock. 
 
 It must be borne in mind that only the nascent hydrogen 
 is efficient as a reducing agent. That which is visible is 
 molecular hydrogen and without influence upon the ferric iron. 
 
 3. The dilute sulphuric acid for washing must be warmed 
 ready for use before the reduction of the iron begins. 
 
 4. The end-point is more permanent in cold than hot 
 solutions, possibly because of a slight action of the perman- 
 ganate upon the manganous sulphate formed during the titra- 
 tion. If the solution turns brown, it is an evidence of insuf- 
 ficient acid, and more should be immediately added. The 
 results are likely to be less accurate in this case, however, 
 as a consequence of secondary reactions between the fer- 
 rous iron and the manganese dioxide thrown down. 
 
 5. The potassium permanganate may, of course, be diluted 
 and brought to an exactly T ^ solution from the data here 
 obtained. The percentage of iron in the iron wire, as estab- 
 lished by gravimetric methods, must be taken into account 
 in the calculation. 
 
 DETERMINATION OF IRON IN LIMONITE. 
 
 Procedure. Weigh out two portions of the powdered 
 limonite, roast, and bring them into solution as described 
 on page 80, but dissolve finally in casseroles. Add cau- 
 tiously to the solution 5 cc. of concentrated sulphuric acid, 
 and evaporate on the steam bath until the solution is nearly 
 colorless. Cover the casseroles and heat over the flame of 
 the lamp until the heavy white fumes of sulphuric anhy- 
 dride are freely evolved. Cool the casseroles, add 100 cc. 
 of water, and boil until the ferric sulphate is dissolved; 
 pour the warm solution through the reductor, proceed as 
 described under standardization, and titrate with the per- 
 manganate solution in the filter flask, using the ferrous 
 ammonium sulphate solution, if need be. From the volume 
 of permanganate solution used, calculate the equivalent 
 quantity of iron (Fe), and the percentage in the limonite. 
 
PERMANGANATE PROCESS. 
 
 9 1 
 
 Notes. i. The preliminary roasting is probably neces- 
 sary, even though the sulphuric acid subsequently chars the 
 carbonaceous matter. Certain .nitrogenous bodies are not 
 rendered insoluble in the acid, and would be oxidized by 
 the permanganate. 
 
 2. The hydrochloric acid, both free and combined, is dis- 
 placed by the less volatile sulphuric acid at its boiling point. 
 The ferric sulphate separates at this point, since there is no 
 water to hold it in solution, and care is required to prevent 
 bumping. 
 
 3. The ferric sulphate usually has a silky appearance, and 
 is easily distinguished from the flocculent silica which remains 
 undissolved. A small quantity of glass wool may be placed 
 in the neck of the funnel to prevent the passage of this silica 
 into the reductor. 
 
9 2 VOLUMETRIC ANALYSIS. 
 
 DETERMINATION OF THE OXIDIZING POWER OF 
 PYROLUSITE. 
 
 Pyrolusite, when pure, consists of manganese dioxide. 
 Its value, as an oxidizing agent and for the production of 
 chlorine, depends upon the percentage of MnO 2 in the 
 sample. This percentage is determined by an indirect 
 method, in which the manganese dioxide is reduced and 
 dissolved by an excess of ferrous sulphate or oxalic acid, 
 and the unused excess determined by titration with per- 
 manganate. 
 
 Procedure. Grind the mineral in an agate mortar until 
 no grit whatever can be detected when the powder is 
 placed between the teeth. Dry the ground sample on 
 a watch-glass at 110 C. for an hour, transfer it to a 
 stoppered weighing tube, and weigh out two portions of 
 about 0.5 gram into No. 3 beakers. Calculate the weight 
 of oxalic acid (C 2 H 2 O 4 . 2 H 2 O) required to react with the 
 weights of pyrolusite taken for analysis, assuming it to be 
 pure manganese dioxide : MnO 2 -f- C 2 H 2 O 4 (2 H 2 O) + H 2 SO 4 
 = MnSO 4 -f- 2 CO 2 + H 2 O + (2 H 2 O). Weigh out about 
 0.2 gram in excess of this quantity of pure oxalic acid 
 into the corresponding beakers, weighing the acid accu- 
 rately, and recording the weight in the notebook. Cover 
 the beakers, and pour into each 25 cc. of water and 50 cc- 
 of dilute sulphuric acid (i 15); warm the liquid gently, until 
 the evolution of carbon dioxide ceases. If a residue re- 
 mains which is sufficiently colored to obscure the end-reac- 
 tion of the permanganate, it must be removed by nitration. 
 Finally, heat the solution to a temperature just below 
 boiling, and, while hot, titrate for the excess of the oxalic 
 acid with potassium permanganate solution. From the cor- 
 rected volume of the solution required, calculate the amount 
 of oxalic acid undecomposed by the pyrolusite ; subtract 
 this from the total quantity of acid used, and calculate the 
 weight of manganese dioxide which would react with the bal- 
 ance of the acid, and from this the percentage in the sam- 
 ple. Consult Part IV, page 107. 
 
PYROLUSITE. 93 
 
 Notes. i. The success of the analysis is largely depend- 
 ent upon the fineness of the powdered mineral. If properly 
 ground, solution should be complete in fifteen minutes or less. 
 
 2. The ground pyrolusite is somewhat hygroscopic. It 
 should be dried at a low temperature (no ), as a higher heat 
 tends to expel water of constitution from hydrated oxides 
 which may also be present. 
 
 3. A moderate excess of oxalic acid above that required 
 to react with the pyrolusite is necessary to promote solution ; 
 otherwise the residual quantity of oxalic acid would be so 
 small that the last particles of the mineral would scarcely 
 dissolve. It is also desirable that a sufficient excess of the 
 acid should be present to react with a considerable volume 
 of the permanganate solution during the titration. 
 
 4. Care should be taken that the sides of the beaker are 
 not overheated, as oxalic acid would be decomposed by heat 
 alone, if crystallization should occur on the sides of the 
 vessel. Strong sulphuric acid also decomposes the oxalic 
 acid. The dilute acid should, therefore, be prepared outside 
 the beaker. 
 
 5. Ferrous ammonium sulphate or iron wire may be 
 substituted for the oxalic acid. The reaction is then the 
 following: 2 FeSO 4 + MnO 2 + 2 H 2 SO 4 = Fe 2 (SO 4 ) 3 + 
 MnSO 4 -|- 2 H 2 O. The excess of ferrous iron may also 
 be determined by means of potassium bichromate, if desired. 
 
 Great care is required to prevent the oxidation of the iron 
 by the air, if ferrous salts are employed. 
 
 6. Other volumetric processes may be employed for this 
 determination, one of which is outlined in the following reac- 
 tions : MnO 2 + 4HC1 = MnCl 2 + C1 2 + 2 H 2 O ; Cl, 
 + 2 KI = I 2 + 2 KC1 ; I 2 + 2 Na 2 S 2 O 3 = Na 2 S 4 O 6 + 
 2 Nal. The chlorine generated by the pyrolusite is passed 
 into a solution of potassium iodide. The liberated iodjne 
 is then determined by titration with sodium thiosulphate, as 
 described on page 97. This is a direct process, although it 
 involves three steps. 
 
 It is also possible to absorb and weigh the liberated carbon 
 dioxide evolved during the reaction with the oxalic acid, and 
 from this weight to find the percentage of manganese dioxide 
 in the sample. This is a gravimetric process. 
 
94 VOLUMETRIC ANALYSIS. 
 
 IODIMETRY. 
 
 GENERAL DISCUSSION. 
 
 The titration of iodine against sodium thiosulphate, with 
 starch as an indicator, may perhaps be regarded as the 
 most accurate of volumetric processes. It may be used 
 both in acid and in neutral solutions to measure free iodine, 
 and the latter may, in turn, serve as a measure of any 
 substance capable of liberating iodine from potassium 
 iodide under suitable conditions for titration. For exam- 
 ple : the quantity of potassium bromate in a commercial 
 sample of that salt may be determined through the follow- 
 ing reactions : KBrO 3 + 6 KI + 3 H 2 SO 4 = 3 K 2 SO 4 
 + KBr + 3 I 2 + 3 H 2 0, and I 2 + 2 Na^O, = Na 2 S 4 O 6 
 + 2 Nal. 
 
 Another illustration is afforded by the process outlined 
 in note 6, page 93. 
 
 Iodine is an oxidizing agent, and, as such, must conform 
 to the same conditions as other similar bodies, with re- 
 spect to its normal solutions. From the equation SO 2 + I 2 
 + H 2 O = SO 3 + 2 HI, it is plain that 126.85 grams of 
 iodine suffice to liberate the oxygen necessary to oxidize 
 I gram of hydrogen, and that, accordingly, that weight of 
 iodine is requisite for a normal solution. Deci- and centi- 
 normal iodine solutions are commonly used. 
 
 Iodine acts as an oxidizing agent either through the de- 
 composition of water, in the presence of an oxidizable body, 
 as illustrated by the reaction As 2 O 3 + 2 I 2 + 2 H 2 O 
 As 2 O 5 + 4 HI, or by increasing the proportion of the neg- 
 ative constituent of a compound through the direct with- 
 drawal of the positive component, as typified by the 
 equations : 2 Na 2 S 2 O 3 + L> = Na 2 S 4 O 6 + 2 Nal, and H 2 S 
 + I 2 = 2 HI + S. 
 
 The tendency of the iodine to combine with hydrogen is 
 not sufficient to cause it to decompose water, unless some 
 body be present which will readily combine with the oxygen 
 thus set free. 
 
 A complete equipment for iodimetric work requires solu- 
 
IODIMETRY. 95 
 
 tions of iodine, sodium thiosulphate, potassium iodide, and 
 starch. 
 
 Commercial iodine requires re-sublimation before it can 
 be regarded as sufficiently pure to be weighed for a standard 
 solution. It should be sublimed between watch-glasses, 
 after the addition of potassium iodide to unite with any 
 chlorine present in combination with the iodine, and should 
 be subsequently dried over sulphuric acid. It may then be 
 dissolved in a stoppered flask, in a solution of potassium 
 iodide {about 18 grams of the iodide to 12 of the iodine), 
 and diluted to a definite volume. 
 
 Its solutions are decomposed by sunlight, with the forma- 
 tion of hydriodic acid, and a high temperature tends to vol- 
 atilize the iodine. They are not stable for long periods,, 
 and require frequent standardization, against arsenious acid, 
 anhydrous sodium thiosulphate, or standard solutions of the 
 latter. 
 
 Iodine solutions act upon rubber ; hence only burettes, 
 with glass stopcocks should be used. 
 
 Sodium thiosulphate (Na 2 S 2 O 3 . 5 H 2 O) is rarely wholly 
 pure as sold commercially, but may be purified by crystalli- 
 zation, if need be. The carbon dioxide absorbed from the 
 air by distilled water decomposes the salt, with the separa- 
 tion of sulphur ; and if standard solutions are to be pre- 
 pared directly, boiled water, which has been cooled out of 
 contact with the air, must be used. 
 
 Solutions of the thiosulphate must be protected from 
 light and heat, both of which promote decomposition. 
 They may be standardized against pure iodine, or with 
 the intervention of potassium iodide against potassium 
 bromate, potassium iodate, or potassium bichromate. The 
 reactions on page 94 indicate the principle involved. 
 
 It should be noted that chlorine and bromine oxidize the 
 thiosulphate to sulphate, while the iodine leads only to the 
 formation of sodium tetrathionate, Na^Og. 
 
 Commercial potassium iodide generally contains a small 
 quantity of iodate, which, in acid solution, liberates iodine, 
 as indicated by a yellow coloration. The reaction is: KIO 3 
 + 5 KI + 3 H 2 S0 4 = 3 K 2 S0 4 + 3 I, + 3 H 3 O. The 
 
9 6 VOLUMETRIC ANALYSIS. 
 
 ioclate is not necessarily uniformly distributed through the 
 iodide, and, in order that an accurate blank test for iodate 
 may be made, which shall apply to each analysis, it is neces- 
 sary to bring a considerable quantity of the iodide into solu- 
 tion, and to take a measured volume of this solution for 
 each analysis. The strength is adapted to the work in 
 hand. 
 
 The starch solution, for use as an indicator, must be 
 freshly prepared. A soluble starch is now obtainable which 
 serves well, and a solution of 0.5 gram of this starch in 
 25 cc. of boiling water is sufficient. It is ready for use 
 when cold, and from i cc. to 2 cc. suffices. 
 
 If soluble starch is not at hand, potato starch may be 
 used. Mix about I gram with 5 cc. of cold water to a 
 smooth paste, pour 1 50 cc. of boiling water over it, warm for 
 a moment on the hot plate, and put it aside to settle. De- 
 cant the supernatant liquid through a filter and use the clear 
 filtrate. 5 cc. of this solution are needed for a titration. 
 
 The solution of potato starch is less stable than the sol- 
 uble starch. The solid particles of the starch, if not re- 
 moved, become so colored by the iodine that they are not 
 readily decolorized by the thiosulphate. 
 
 The iodo-starch blue is discharged by caustic alkalies, or 
 normal carbonates of the fixed alkalies, but not by the 
 bicarbonates. 
 
 STANDARDIZATION OF IODINE AND SODIUM THIOSULPHATE 
 
 SOLUTIONS. 
 
 Procedure. Weigh out, on the laboratory balances, 13 
 grams of commercial iodine. Place it in a mortar with 18 
 grams of potassium iodide and triturate with small portions 
 of water until all -is dissolved. Dilute the solution to 
 
 IOOO CC.* 
 
 Weigh out 25 grams of sodium thiosulphate, dissolve it 
 in water, and dilute to 1000 cc. 
 
 * It will be found more economical to have a considerable quantity of the 
 solution prepared by a laboratory attendant, and to have all unused solutions 
 returned to the common stock. 
 
IODIMETRY. 
 
 97 
 
 Place these solutions in burettes (the iodine in a glass- 
 stopped burette), observing the usual precautions to prevent 
 dilution. Run out 40 cc. of the thiosulphate solution into 
 a beaker, dilute with 150 cc. of water, add I cc. to 2 cc. 
 of the soluble starch solution, and titrate with the iodine 
 to the appearance of the blue of the iodo-starch. Repeat, 
 until the ratio of the two solutions is established. 
 
 (Method A.) 
 
 Weigh out, into No. 4 beakers, two portions of 0.175 
 0.200 gram each, of pure arsenious acid. Dissolve in 10 cc. 
 of sodium hydroxide solution, with stirring. Dilute the 
 solutions to 150 cc. and add hydrochloric acid until the 
 solution contains a few drops in excess, and finally add a 
 concentrated solution of 5 grams of sodium bicarbonate 
 (HNaCO 3 ). Cover the beakers to avoid loss. Add the 
 starch solution, and titrate with the iodine to the appear- 
 ance of the blue of the iodo-starch, taking care not to pass 
 the end-point. 
 
 From the corrected volume of the iodine solution used to 
 oxidize the arsenious acid, calculate the quantity of iodine 
 in each cubic centimeter, and its relation to the normal. 
 From the ratio between the solutions, calculate similar val- 
 ues for the thiosulphate solution. 
 
 (Method B) 
 
 Weigh out into No. 4 beakers two portions of about 
 0.1500.175 gram of potassium bromate, or potassium 
 iodate. Dissolve these in 59 cc. of water and add a suf- 
 ficient volume of potassium iodide solution to furnish 3 
 grams of the salt. Add to the mixture 10 cc. of dilute 
 sulphuric acid (i 15), allow the solution to stand for three 
 minutes, and dilute to 1500:. ; run in thiosulphate solution 
 from a burette until the color of the iodine is nearly de- 
 stroyed, then add I cc. to 2 cc. of starch solution, titrate 
 to the disappearance of the iodo-starch blue, and finally 
 add iodine solution until the color is just restored. Make 
 a blank test for the amount of thiosulphate solution re- 
 
9 8 VOLUMETRIC ANALYSIS, 
 
 quired to react with the iodine liberated by the iodate in 
 the potassium iodide solution, and deduct" this from the 
 total volume used in the titration. From the data obtained, 
 calculate the weight of thiosulphate in each cubic centimeter 
 of the solution, and its relation to a normal solution, and, 
 subsequently, similar values for the iodine solution. 
 
 Notes. i. The two methods of standardization seem to 
 yield equally satisfactory results, and the student is advised 
 to try both. The arsenious acid and the potassium salts both 
 require careful examination to establish their purity. The 
 former usually requires re-sublimation, and the two latter 
 re-crystallization. 
 
 2. The color of the iodo-starch is somewhat less satis- 
 factory in concentrated solutions of alkali salts, notably the 
 iodides. The dilution prescribed obviates this difficulty. 
 
 3. Arsenious acid dissolves more readily in caustic alkali 
 than in the bicarbonates, but the presence of caustic alkali 
 during the titration is not admissible. It is, therefore, de- 
 stroyed by the addition of acid, and the solution is then 
 made alkaline with the bicarbonate. Normal carbonates of 
 the fixed alkalies cannot be used. 
 
 The reaction during titration is the following : 
 
 Na 3 AsO 3 + I + 2 HNaCO 3 = Na 3 AsO 4 + 2 Nal 
 + 2 CO 2 + H 2 O. 
 
 As the reaction between sodium thiosulphate and iodine 
 is not always free from secondary reactions in the presence of 
 even the weakly alkaline bicarbonate, it is best to avoid the 
 addition of any considerable excess of iodine. Should the 
 end-point be passed by a few drops, the thiosulphate may be 
 used to correct it. 
 
 4. The potassium iodide should be measured from a stock 
 solution for the reasons stated on page 95. It is then pos- 
 sible to make an accurate blank test for the iodate. 
 
 DETERMINATION OF ANTIMONY IN STIBNITE. 
 
 The sample for analysis should be pure, leaving, at most, 
 only a siliceous residue. 
 
IODIMETRY. gg 
 
 Procedure. Weigh out two portions of about 0.35-0.40 
 gram of the mineral (which should be well ground), into two 
 small dry beakers (No. 2). Pour over the stibnite 5 cc. of 
 hydrochloric acid (sp. gr. 1.20) and warm gently, but keep 
 well below the boiling point. When the residue is white, 
 add to each I gram of solid tartaric acid. Dilute the solu- 
 tion very cautiously by adding water in portions of 5 cc.,. 
 stopping as soon as the solution turns red. It is possible 
 that no coloration will appear, in which case cautiously con- 
 tinue the dilution to 125 cc. If a red precipitate or colora- 
 tion does appear, warm the solution until it is colorless and 
 again dilute cautiously. Continue this to a total volume of 
 125 cc., and boil for a minute. 
 
 Meanwhile, dissolve 6 grams of sodium bicarbonate in 
 200 cc. of water, in a No. 6 beaker ; pour the cold acid so- 
 lution of the antimony into this, avoiding loss by efferves- 
 cence. Make sure that the solution contains an excess of 
 the bicarbonate, and then add I cc. to 2 cc. of starch solu- 
 tion and titrate with iodine solution to the appearance of 
 the blue, avoiding an excess. 
 
 From the corrected volume of the iodine solution required 
 to oxidize the antimony, calculate the weight of the latter in 
 the solution and the percentage in the stibnite. 
 
 Notes. i. The success of this determination is largely 
 dependent upon close adherence to the directions as given, 
 particularly with respect to the amounts of reagents and the 
 dilution. 
 
 2. Antimony chloride is volatile with the steam from its 
 concentrated solutions ; hence these solutions must not be 
 boiled until they have been diluted. 
 
 3. The separation of antimony oxy-chloride from solutions 
 of the chloride, on dilution with water, is prevented by the 
 addition of the tartaric acid. 
 
 4. Stibnite is native antimony sulphide, and upon solu- 
 tion in hydrochloric acid sulphuretted hydrogen is liberated, 
 a part of which is absorbed by the acid, unless the heating 
 is long continued. Upon dilution, a point is reached at 
 which the sulphide of antimony, being no longer held in so- 
 lution by the acid, separates. If the dilution is immediately 
 
I00 VOLUMETRIC ANALYSIS. 
 
 stopped and the solution warmed, this sulphide is again 
 brought into solution and at the same time some of the sul- 
 phuretted hydrogen is expelled. This procedure must be 
 continued until the sulphuretted hydrogen is all removed, 
 since it reacts with iodine. (H 2 S -j- I 2 = 2 HI -f- S.) 
 
 If no precipitation of the sulphide occurs, it is an indica- 
 tion that it was all expelled immediately after solution. 
 
 5. If, for any reason, a white precipitate of the oxy- 
 chloride separates during dilution (which should not occur if 
 the directions are followed), it is best to discard the deter- 
 mination and to start anew. 
 
 6. The reaction between the iodine and the antimony is 
 parallel with that between iodine and arsenious acid. 
 
BLEACHING POWDER. IOI 
 
 CHLORIMETRY. 
 
 V 
 
 GENERAL DISCUSSION. 
 
 Under chlorimetry are included those processes by which 
 not only free chlorine, but also bromine, hypochlorous and 
 hypobromous acids are estimated. The reagent employed 
 is arsenious acid, in bicarbonate solution. In this weakly 
 alkaline solution the reaction between chlorine and the 
 arsenious acid is parallel with that of iodine. 
 
 A solution of arsenious acid which has been prepared 
 from the pure acid may be used without standardization, 
 and is stable for long periods, but the commercial acid re- 
 quires re-sublimation to remove arsenic sulphide, which 
 may be present in small quantity. To prepare the solution, 
 dissolve about 5 grams of the powdered acid, accurately 
 weighed, in 10 cc. of a concentrated sodium hydroxide so- 
 lution, dilute the solution to 300 cc., and make it faintly 
 acid with hydrochloric acid. Add 30 grams of sodium 
 bicarbonate, and dilute the. solution to 1000 cc. in a meas- 
 uring flask. If desired, the value of this solution may 
 be checked by titration against the standardized iodine 
 solution. 
 
 The indicator required is made by dipping strips of filter 
 paper in a starch solution, to which i gram of potassium 
 iodide has been added. These strips are allowed to drain 
 and spread upon a watch-glass. When touched by a drop 
 of the solution, the paper turns blue until an excess of the 
 arsenious acid has been added. The paper must be moist 
 when used. 
 
 DETERMINATION OF THE AVAILABLE CHLORINE IN BLEACH- 
 ING POWDER. 
 
 Procedure. Weigh out from a stoppered test-tube into 
 a porcelain mortar, about 3.5 grams of bleaching powder. 
 Keep the mortar away from the door of the balance case, 
 to avoid injury to the balance. Triturate the powder in the 
 mortar with successive portions of water, until it is well 
 ground and transferred to a 500 cc. measuring flask. Fill 
 
102 VOLUMETRIC ANALYSIS. 
 
 the flask to the graduation and shake thoroughly. Meas- 
 ure off 25 cc. of this semi-solution in a measuring flask, 
 or pipette, observing the precautions named on page 70, 
 and the further precaution that the liquid removed shall 
 contain its proportion of suspended matter. 
 
 Empty the flask into a beaker and wash it out. Run 
 in the arsenious acid solution from a burette, until no 
 further reaction takes place with the starch-iodide paper 
 when touched by a drop of the solution of bleaching pow- 
 der. From the volume of solution required to react with 
 the bleaching powder, calculate the percentage of chlorine 
 in the latter, assuming the titration reaction to be that be- 
 tween chlorine and arsenious acid. Note that one twenti- 
 eth of the total weight of bleaching powder enters into the 
 reaction. 
 
 Notes. i. Bleaching powder may be regarded as con- 
 taining both calcium chloride and hypochlorite. Its effi- 
 ciency, when treated with acids, depends upon the quantity 
 of the latter constituent, since the hydrochlorous acid yields 
 as bleaching agents both oxygen and chlorine. It is cus- 
 tomary, however, to express the value of the bleaching agent 
 in terms of available chlorine, as though only that were a 
 factor in its efficiency. The chlorine present as chloride is, 
 of course, not available for bleaching purposes. 
 
 2. Bleaching powder readily loses chlorine on exposure 
 to the air, as a result of the absorption of carbon dioxide. 
 The sample must be carefully protected, but even then it is 
 rarely possible to obtain closely agreeing results from sepa- 
 rate samples. For technical purposes, it is usually sufficient 
 to examine one sample. The student should check his re- 
 sults by titrating two portions from the 500 cc. 
 
 3. The powder must be triturated until it is fine, other- 
 wise the lumps will inclose calcium hypochlorite, which will 
 fail to react with the arsenious acid. The clear supernatant 
 liquid gives percentages which are below, and the sediment 
 percentages which are above the average. The liquid meas- 
 ured off should, therefore, carry with it its proper proportion 
 of the sediment. 
 
 
SULPHOCYANATE PROCESS. 103 
 
 III. PRECIPITATION METHODS. 
 
 SULPHOCYANATE PROCESS FOR THE DETER- 
 MINATION OF SILVER. 
 
 GENERAL DISCUSSION. 
 
 The addition of a solution of potassium or ammonium 
 sulphocyanate to one of silver in nitric acid, causes a depo- 
 sition of silver sulphocyanate, as a white curdy precipitate. 
 If ferric nitrate is also present, the slightest excess of the 
 sulphocyanate, over that required to combine with the sil- 
 ver, is indicated by the deep red which is characteristic of 
 the sulphocyanate test for iron, 
 
 The reactions involved are: AgNO 3 + KSCN = AgSCN 
 + KNO 3 , and 3 KSCN + Fe(NO 3 ) 3 = Fe(SCN) 3 + 
 3 KN0 3 . 
 
 The normal solution of the sulphocyanate should contain 
 a sufficient quantity of the salt to combine with I gram of 
 hydrogen to form sulphocyanic acid ; i. e., a gram-molecule, 
 or 97.23 grams KSCN. The sulphocyanate cannot be accu- 
 rately weighed ; its solutions must, therefore, be standard- 
 ized against silver nitrate, either in the form of a standard 
 solution, or by weighing out small portions. 
 
 The reaction with silver may be carried out in nitric acid 
 solution, and in the presence of copper, if the latter does 
 not exceed 70 per cent. Above that percentage it is neces- 
 sary to add silver, in known quantity, to the solution. 
 
 The liquid must be cold at the time of titration and en- 
 tirely free from nitrous compounds. 
 
 A saturated solution of ferric alum, to which a moderate 
 quantity of nitric acid has been added, serves as an indi- 
 cator. The volume used is 5 cc. and should be the same for 
 each titration. 
 
104 
 
 VOLUMETRIC ANALYSIS. 
 
 STANDARDIZATION OF A POTASSIUM SULPHOCYANATE 
 SOLUTION. 
 
 Procedure. Crush a few crystals of silver nitrate in a 
 mortar, transfer them to a watch-glass, and dry for an hour 
 at 110 C. Protect the nitrate from dust or organic matter. 
 Weigh out two portions of about 0.5 gram each. Dissolve 
 these in 50 cc. of water and add 10 cc. of nitric acid (sp. 
 gr. 1.2), which has been recently boiled, and 5 cc. of the 
 indicator solution. Run in the sulphocyanate solution from 
 a burette, until a faint red tinge can be detected in the solu- 
 tion after vigorous stirring. From the corrected volume 
 used, calculate the value of the solution in terms of metal- 
 lic silver, and its relation to a normal solution. Repeat, 
 until the results are concordant. 
 
 Notes. i. The crystals of silver nitrate sometimes 
 inclose water, which is expelled on drying. If the nitrate has 
 come into contact with organic bodies, it suffers a reduction 
 and blackens during the heating. 
 
 2. It is plain that a standard solution of silver nitrate 
 (made by weighing out the crystals) is convenient or neces- 
 sary, if many titrations of this nature are to be made. In the 
 absence of such a solution, the liability of passing the end- 
 point is lessened by setting aside a small fraction of the silver 
 solution, which can be added at the close of the titration to 
 counteract any accidental excess of sulphocyanate. 
 
 DETERMINATION OF SILVER IN COIN. 
 
 Procedure. Weigh out two portions of the coin, of about 
 0.5 gram each. Dissolve them in 15 cc. of nitric acid (sp. 
 gr. 1.2), and boil until all the nitrous compounds are ex- 
 pelled ; cool the liquid, dilute to 50 cc., add 5 cc. of the in- 
 dicator solution, and titrate with the sulphocyanate to the 
 appearance of the faint red coloration. 
 
 From the corrected volume of the sulphocyanate solution 
 required, calculate the weight of silver present, and the 
 percentage in the coin. 
 
 Note. These solutions, containing the silver precipitate^ 
 as well as those from the standardization, should be placed in 
 the receptacle for " silver residues." 
 
PART IV. 
 
 STOICHIOMETRY. 
 
 The stoichiometrical problems with which the analytical chemist 
 has to deal are not, as a rule, difficult either to solve or to compre- 
 hend. The student will find that a moderate time devoted to the 
 thoughtful study of these problems will do much to prevent em- 
 barrassment in later professional experience, where the ability to 
 make the necessary calculations for the interpretation of analyt- 
 ical data is no less important than the manipulative skill by which 
 the data are obtained. 
 
 Detailed solutions of a few typical problems are given below. 
 The student should study these carefully, and assure himself that 
 they are fully understood. 
 
 i. A "chemical factor" expresses the ratio between a spe- 
 cific quantity of a chemical compound and the equivalent quantity 
 of some other body. For example, if it is wished to determine 
 the weight of sulphur which corresponds to a specific weight of 
 barium sulphate, the latter is multiplied by the factor, or ratio 
 
 represented by the fraction EaSQ , or ^' _ 7 Q = 0.1373. It may 
 
 233-5 32-07 
 also be expressed by the proportion BaSO 4 : S = wt. BaSO 4 
 
 : x, from which it is plain that x = 3 ' 7 . wt. BaSO 4 . 
 
 233-5 
 Again, ff the weight of FeO in Fe 2 O 8 is desired, the factor 
 
 becomes = = 0.9000. Similarly, the factor for 
 
 Fe 2 O 8 160.04 
 
 the conversion of KC1 to K 2 O is ^^ = - : = 0.6320. 
 
 The logarithmic equivalents of these values are called log factors. 
 In the calculation of these factors, the atomic or molecular rela- 
 tions of the two substances must be kept clearly in mind ; thus, it 
 is plainly incorrect to express the ratio of ferrous to ferric oxide by 
 
 FeO 
 
 the fraction ^ p^-, since each molecule of the higher oxide must 
 re 2 u 3 
 
 correspond to two molecules of the lower. Carelessness in this 
 respect is one of the most frequent sources of error. 
 
106 STOICHIOMETRY. 
 
 2. To calculate the volume of a reagent required for a specific 
 operation, it is necessary to know the exact reaction which is to be 
 brought about, and, as with the calculation of factors, to keep in 
 mind the molecular relations between the reagent and the sub- 
 stance reacted upon. For example, to estimate the weight of 
 barium chloride necessary to precipitate the sulphur from o.i gram 
 
 488.70 
 
 of pure pyrite (FeS 2 ), the proportion should stand 2 BaCl 2 . 2 H 2 O : 
 120.16 
 FeS 2 = x : o.i, where x represents the weight of the chloride 
 
 required. Each of the two atoms of sulphur will form a mole- 
 cule of sulphuric acid upon oxidation, which, in turn, will require 
 a molecule of the barium chloride for precipitation. To determine 
 the quantity of the barium chloride required, it is necessary to in- 
 clude in its molecular weight the water of crystallization, since this 
 is inseparable from the chloride when it is weighed. This applies 
 equally to other similar instances. 
 
 If the strength of an acid is expressed in percentage by weight, 
 due regard must be paid to its specific gravity. For example, hy- 
 drochloric acid (sp. gr. 1.12) contains 23.8 per cent. HC1 by 
 weight; i. c., 0.2666 gram. 
 
 3. No rules for universal application to " indirect gravi- 
 metric analyses " can be laid down. A single example will be 
 explained. 
 
 Given a mixture of KC1 -f- NaCl weighing 0.15 gram, which 
 contains 53 per cent, chlorine, to calculate the weight of KC1 and- 
 of NaCl in the mixture. 
 
 The weight of chlorine in the mixture is (0.15 X Q-53) or 0.0795 
 gram. Assuming that this chlorine was all in combination with 
 potassium, the corresponding weight of KC1 would be 0.1672 
 gram (Cl : KC1 ~ 0.0795 : 0-1672). This is an excess of 0.0172 
 gram over the actual weight of the mixture, and it is plain that 
 this difference is occasioned by the replacement of certain of 'the 
 molecules of potassium chloride, weighing 74.56 units, by mole- 
 cules of sodium chloride weighing 58.50 units. To express this, 
 let it be supposed that the mixture is made up of n molecules 
 
 KC1 and n' molecules NaCl ; then it may be said that n KC1 -j- 
 
 58.50 74-56 74-56 
 
 n f NaCl = 0.15 gram, and n KC1 -f- n' KC1 = 0.1672 gram, then 
 
 by subtracting the first equation from the second it is shown 
 
 74.56 58.50 
 
 that ri (KC1 NaCl) = 0.0172 gram. That is, the differ- 
 ence in weight is equal to n' times the difference in the molecu- 
 
.S 1 TO 1C HIO ME TRY. 107 
 
 lar weights of the two chlorides. The actual weight of NaCl 
 present (x) is equal to 5 8. 50;*', or, since ' = ~ - , x = 
 
 / 0.0172 \ 
 58.50^ fi~I JT~ /' This may be expressed in the form 
 
 (74.56 5^.50) : 58.50 = 0.0172 : x, from which x = 0.0626. 
 The weight of NaCl subtracted from that of the mixture gives 
 the weight of KC1. 
 
 The weights of the chlorides may also be calculated algebra- 
 
 35-4S 
 ically by solving the equations x -\- y = 0.15 and > x -\- 
 
 o y = -795 where x is the weight of KC1 and y is the 
 5 8 -5 
 weight of NaCl in the mixture. 
 
 4. It is sometimes desirable to weigh out such a quantity of 
 substance for analysis, that the number of cubic centimeters of 
 standard solution entering into the reaction shall represent directly 
 the percentage of the desired constituent. This may be readily 
 done, by considering the relation of the solution to a normal solu- 
 tion and the atomic or molecular weight of the desired component. 
 For example, suppose it is desired to calculate such a weight for 
 K 2 CO 3 in pearlash, when a half-normal acid solution is used. 
 Since half-normal acid and alkali solutions are equivalent, and 
 since, by definition, the half-normal K 2 CO 3 solution contains 34.55 
 grams per liter, each cubic centimeter of the acid solution must be 
 equivalent to 0.03455 gram K 2 CO 3 . Hence, 100 cc. would neu- 
 tralize 3.455 grams pure K 2 CO 3 , and this becomes the desired 
 weight of the pearlash. Similarly, the required weight of limonite, 
 where the iron (Fe) is to be determined by means of a deci-normal 
 K 2 Cr 2 O 7 solution, is 0.5602 gram. 
 
 5. One of the most frequently recurring cases in volumetric 
 analysis is that in which it is wished to express the value of a spe. 
 cific solution in terms of some substance other than that against 
 which it has been standardized ; as, for instance, the value of a 
 permanganate solution which has been standardized against oxalic 
 acid, in terms of iron. Although such problems apparently vary 
 widely, there are common principles which can be applied to them 
 all. These are stated below, and the student should assure him- 
 self that they are fully understood. 
 
 Suppose, for example, it is desired to find the iron value 
 (Fe) of a permanganate solution, of which i cc. is equivalent to 
 0.0063 gram C 2 H 2 O 4 . 2 H 2 O. 
 
! o8 ? TO I C HI O ME TR Y. 
 
 From a comparison of the reactions on page 84, it is seen that 
 10 molecules of ferrous sulphate and 5 molecules of oxalic acid 
 each react with the same amount (2 molecules) of the perman- 
 ganate. These two quantities being, then, equivalent to the same 
 third quantity, must be equivalent to each other ; in other words, 
 10 molecules of ferrous sulphate and 5 molecules of oxalic acid 
 have the same reducing power. But, as stated above, the value is 
 desired in terms of metallic iron (Fe), not FeSO 4 , but as it is plain 
 that 10 FeSO 4 are equivalent to 10 Fe, it is proper to make the 
 
 proportion 
 
 560.2 630.25 
 
 10 Fe : 5 C 2 H 2 O 4 . 2 H 2 O = x : .006302 
 
 in which x = 0.005602 gram. Here, again, as in example 2, it is 
 necessary to include the water of crystallization in the molecular 
 weight of the oxalic acid, as it is weighed with it. 
 
 The same conclusion is arrived at, if we consider the relation of 
 the solution to the normal. As given, it is deci-normal and must, 
 therefore, be equivalent to a deci-normal solution of iron. From 
 the equations cited, it is seen that 10 FeSO 4 unite with 5 O, there- 
 fore each molecule is equivalent to i hydrogen atom in reducing 
 power. The normal solution must, then, contain i gram-molecule 
 of ferrous sulphate, or 56.02 grams Fe, and each cubic centimeter 
 of the deci-normal solution would contain 0.005602 gram, the 
 value obtained above. 
 
 Again, suppose the value of the same permanganate solution 
 were desired in terms of molybdenum (Mo), the reactions with 
 permanganate being 
 
 5 Moi 2 Oi9 + 17 Mn 2 O 7 60 MoO 3 -f- 34 MnO, and 
 5 C 2 H 2 O 4 . 2 H 2 O -f Mn 2 O 7 2 MnO + ioCO 2 + 15 H 2 CX 
 (Mn 2 O 7 is the anhydride of HMnO 4 .) 
 
 It is plain that in these equations as they stand, the molecular 
 quantities of oxidizing agent are not equal. They can be made 
 so by simply multiplying the second equation by 17, and they then 
 become, 
 
 5 Mo 12 Oi9 -\- 17 Mn 2 O 7 = 34 MnO -|- 60 MoO 3 , and 
 85 C 2 H 2 O 4 . 2 H 2 O + 17 Mn 2 O 7 = 34 MnO + 170 CO 2 + 
 255 H 2 0. 
 
 It is now possible to reason in the same way as before, and to 
 conclude that 85 molecules of the oxalic acid have the same reduc- 
 
S TO 1C If IO ME TRY. 109 
 
 ing power as 5 molecules of the oxide Mo 12 O 19 , or 60 atoms of 
 molybdenum. Accordingly, 
 
 575.88 10714.25 
 
 60 Mo : 85 C 2 H 2 O 4 . 2 H 2 O = x : 0.006302 
 
 in which x = 0.0003387 gram. 
 
 Since 5 Mo 12 O 19 unite with 85 O, a normal solution of the 
 former as a reducing #gent, would contain T ^ of the 5 gram-mole- 
 cules or 3.387 grams Mo, and the deci-normal solution 0.3387 
 grams per liter. This agrees with the values already obtained. 
 
 6. It is sometimes necessary to calculate the value of solutions 
 according to the principles just explained, when several successive 
 reactions are involved. Such problems may be solved by a series 
 of proportions, but it is usually possible, after stating these, to 
 eliminate the common factors and solve but a single one. 
 
 For example, suppose it is desired to express the value of a 
 permanganate solution, of which i cc. 0.008 gram iron (Fe), 
 in terms of calcium oxide (CaO). The reactions involved in 
 the volumetric determination of calcium are the following : CaCl 2 
 -4- (NH 4 ) 2 C 2 O 4 = CaC 2 O 4 + 2 NH 4 C1 ; CaC 2 O 4 + H 2 SO 4 
 + 2 H 2 O = CaSO 4 4- C 2 H 2 O 4 . 2 H 2 O ; 5 C 2 H 2 O 4 . 2 H 2 O + 
 2 KMnO 4 + 3 H 2 SO 4 = K 2 SO 4 + MnSO 4 + 10 CO 2 + 
 18 H 2 O. 
 
 From the considerations stated under 5, the following propor- 
 tions may be made : 
 
 10 Fe : 5 C 2 H 2 O 4 . 2 H 2 O = .008 : x 
 5 C 2 H 2 O 4 . 2 H 2 O : 5 CaC 2 O 4 = x : y 
 5 CaC 2 O 4 : 5 CaO = y : z 
 
 Canceling the common factors, there remains simply 
 
 560.2 280.4 
 
 10 Fe : 5 CaO = .008 : z 
 
 Similarly, from the reactions given in note 6, page 93, the equiv- 
 alent of the iodine liberated may be calculated in terms of MnO 2 
 as follows : Supposing the weight of iodine to be 0.5 gram, then 
 
 2 I : 2 KI = 0.5 : x 
 2 KI : 2 Cl = x : y 
 2 Cl : 2 HC1 = y : z 
 2 HC1 : MnO 2 = z : w 
 
 Canceling the common factors, there remains 
 2 I : MnO 2 = 0.5 : w 
 
no S TOICHIOME TR Y. 
 
 To solve such problems as 5 and 6, it is necessary to know the 
 reactions involved, and the way in which the various components 
 break up ; then to compare the reactions and to search for those 
 molecular quantities of the compounds in question, which are 
 equivalent in their action upon a common agent. Having found 
 
 these, as shown above, express the molecular ratio between them 
 
 253.7 86.99 
 in the form of a proportion; as, for example, 2 1 : MnO = 0.5 : w. 
 
 Expressed in the form w = - - 0.5, it is plain that this ratio is 
 
 OO' / 
 
 in no way different in principle from the chemical factor men- 
 tioned in paragraph i ; indeed, it is the factor for the conversion 
 of iodine to manganese dioxide. 
 
 PROBLEMS. 
 
 (The reactions necessary for the solution of these problems are 
 either stated with the problem, or may be found in the earlier 
 text. The atomic weights used are those given in the table on 
 page 117.) 
 
 GRAVIMETRIC ANALYSIS. 
 
 1. Calculate the chemical factors for (a) (NH 4 ) 2 O from 
 2 (NH 4 )C1. PtCl 4 ; (b) for K in 2 KC1. PtCl 4 ; (c) for P in 
 Mg 2 P 2 O 7 ; (d) for Fe 2 O 3 from Fe 3 O 4 . 
 
 Answers : (a) 0.1175, (b) 0.1611, (c) 0.2787, (d) i.o^. 
 
 2. If 0.5 gram of platinum remains after the ignition of the 
 precipitate of the double salt, 2 NH 4 C1. PtCl 4 , derived from 
 
 1 gram of an ammonium compound, calculate the percentage of 
 NH 3 in the latter. 2 NH 4 C1. PtCl 4 = 2 NH 3 + 2 HC1 + 
 
 2 C1 2 + Pt. Answer: 8.76 %. 
 
 3. What weight of Mn 3 O 4 corresponds to i gram of Mn 2 P 2 O 7 ? 
 
 Answer : 0.5375 gram. 
 
 4. How many cubic centimeters of aqueous ammonia (sp. gr. 
 0.96) containing 9. 90, -per cent. NH 3 by weight, will be required to 
 precipitate the iron as Fe(OH) 3 from i gram of (NH 4 ) 2 SO 4 . 
 FeSO 4 . 6 H 2 O ? Answer: 1.37 cc. 
 
 5. How many cubic centimeters of HNO 3 (sp. gr. 1.135) con- 
 taining 20 per cent. HNO 3 by weight, are required to oxidize the 
 iron in i gram of FeSO 4 . (NH 4 ) 2 SO 4 . 6 H 2 O, in the presence of 
 sulphuric acid? 6 FeSO 4 + 2 HNO 3 + 3 H 2 SO 4 = 
 
 3 Fe 2 (SO 4 ) 3 -f 2 NO + 4 H 2 O. Answer: 0.24 cc. 
 
PROBLEMS. ! j j 
 
 6. The ignited precipitate of Fe 2 O 3 -f- A1 2 O 3 from 1.5 grams 
 of a silicate weighs 0.4069 gram ; this mixture loses 0.0200 gram 
 when ignited in hydrogen. What is the percentage of Fe 2 O 3 . 
 and A1 2 O 3 in the sample ? Fe 2 O 3 + 3 H 2 = 2 Fe -f- 3 H 2 O. 
 
 Answer: 22.68 % A1 2 O 3 ; 4.44 % Fe 2 O 3 . 
 
 7. How many cubic centimeters of " magnesia mixture " (64 
 grams MgCl 2 per liter) will be required to precipitate the arsenic 
 from 0.2 gram As 2 S 3 , after oxidation to arsenic acid? H 3 AsO 4 -j- 
 MgCl 2 + 3 NH 4 OH = MgNH 4 AsO 4 + 2 NH 4 C1 + 3 H 2 O. 
 
 Answer : 2.42 cc. 
 
 8. How many cubic centimeters of an ammonium oxalate so- 
 lution [(NH 4 ) 2 C 2 O 4 . H 2 O] (40 grams per liter), are required to- 
 precipitate the calcium as oxalate from i gram of apatite 
 (Ca 3 (PO 4 ) 2 . CaCl 2 ) ? How many cubic centimeters of " magnesia 
 mixture " (containing 64 grams MgCl 2 per liter) are necessary 
 to combine with the phosphoric acid in the same weight of 
 apatite ? Answer : 33.73 cc. and 7.06 cc. 
 
 9. If a calcium oxalate precipitate (which is contaminated by 
 silica) from 0.83 gram of dolomite be ignited under such condi- 
 tions that the decomposition products may be passed through 
 Ba(OH) 2 solution, and the resulting precipitate of barium 
 carbonate be found, on drying, to weigh 0.9500 gram, what is 
 the percentage of CaO in the sample? Answer: 32.51 J . 
 
 10. How many cubic centimeters of a potassium tetroxalate 
 solution (KHC 2 O 4 . C 2 H 2 O 4 . 2 H 2 O), containing 50 grams per 
 liter, would be required to precipitate the calcium from i gram 
 of a sample of dolomite yielding 2 % Fe 2 O 3 , 10 % MgO, and 
 45 % CO 2 , assuming the iron, magnesium, and calcium to be 
 present wholly as carbonates, the iron as ferrous carbonate ? 
 
 Answer : 19.05 cc. 
 
 11. How many cubic centimeters of sulphuric acid (sp. gr. 
 1.75), containing 81 per cent. H 2 SO 4 by weight, are necessary to 
 replace the nitric acid in the nitrates formed from 5 grams of a 
 brass containing 65 % Cu, 34.5 % Zn and 0.5 / Pb ? 
 
 Answer: 5.37 cc. 
 
 12. If 5.23 grams of brass yield 0.0345 gram PbSO 4 , and sub- 
 sequently 0.0031 gram PbO 2 on electrolysis of the filtrate, what is 
 the percentage of Pb in the brass? Answer: 0.5 %. 
 
 13. If in the analysis of a brass containing 65 / copper, an 
 error is made in weighing a 5 -gram portion, by which o.ooi gram 
 
! T 2 S TOICHIOME TR Y. 
 
 too much is weighed out, what would be the percentage of copper, 
 as determined ? If the same error is made in weighing 0.2 gram 
 of apatite containing 40 % P2O 5 , what will be the apparent per- 
 centage ? What will be the percentage error in each case ? 
 
 Answers : 65.01 % Cu ; 40.2 % P 2 O 5 ; 0.02 % and 0.5 %. 
 
 14. If the dry cupric sulphide from 0.82 gram of brass loses 
 0.1345 gram on ignition in hydrogen, what is the percentage of 
 copper in the brass ? 2 CuS == Cu 2 S + S. Answer . ^^ %> 
 
 15. If 1.5 grams of glass yield 0.38 gram KC1 -f- NaCl, from 
 which 0.646 gram 2 KC1. PtCl 4 is obtained, what is the percentage 
 of Na,0 in the glass ? ^^ . 6.43 %. 
 
 1 6. A mixture of BaO and CaO weighing 0.2438 gram yields 
 0.4876 grams of mixed sulphates. What is the weight of each 
 oxide in the original mixture ? 
 
 Answer: 0.1288 gram CaO ; 0.1150 gram BaO. 
 
 17. Calculate the percentage of pure Na 2 CO 3 in an impure 
 sample, from the following data : Crucible -f- SiO 2 = 20.0697 
 grams; crucible -+- SiO 2 + Na 2 CO 3 (impure) = 20.3264 grams; 
 crucible -|- SiO 2 (excess) -f- Na 2 SiO 3 (after fusion) = 20.2239 
 grams. Assume the reaction to be Na 2 CO 3 + SiO 2 = Na 2 SiO 3 
 -f- CO 2 . Answer: 96.25 %. 
 
 1 8. A sample of pyrite weighing 0.5 gram yields 1.6 grams 
 BaSO 4 . Calculate the percentage FeS 2 in the sample. 
 
 Answer: 82.35 %. 
 
 VOLUMETRIC ANALYSIS. 
 
 1. How much crude cream of tartar should be taken for an 
 analysis in order that the number of cubic centimeters of NaOH 
 solution required to react with it, shall represent directly the per- 
 centage of KHC 4 H 4 O 6 ? How much oxalic acid in order that 
 each cubic centimeter of -^ KMnO 4 may represent i % C 2 H 2 O 4 . 
 2 H 2 O ? KHC 4 H 4 O 6 + NaOH = KNaC 4 H 4 O 6 + H 2 O. 
 
 Answer: 0.409 gram KHC 4 H 4 O 6 ; 0.6302 gram C 2 H 2 O 4 . 2 H 2 O. 
 
 2. What weight of potassium ferrocyanide, K 4 Fe(CN) 6 . 3 H 2 O, 
 should a normal solution contain, for use as a reducing agent? 
 10 K 4 Fe(CN) 6 . (3 H 2 O) + 2 KMnO 4 + 8 H 2 SO 4 = 
 10 K 3 Fe(CN) 6 + 6 K 2 SO 4 + 2 MnSO 4 + 8 H 2 O + (30 H 2 O). 
 
PROBLEMS. n 3 
 
 3. Calculate the percentage of carbon dioxide (CO 2 ) in a 
 sample of calcium carbonate from the following data : 
 
 Total volume HC1 = 35 cc. ; total volume T N ^ NaOH = 15 cc. ; 
 weight carbonate i.oo gram. Answer : 35.20 / . 
 
 4. Calculate the weight of KHC 2 O 4 . C 2 H 2 O 4 . (2 H 2 O) neces- 
 sary for a liter of normal solution, (V) as a standard acid solution 
 (compare note 7, on page 69), (b) as a reducing agent. KHC 2 O 4 . 
 C 2 H 2 O 4 . (2 H 2 O) + 2 MnO 2 + 3 H 2 SO 4 = 2 MnSO 4 + 
 KHSO 4 + 4 CO 2 + 4 H 2 O + (2 H 2 O). 
 
 Answer : (a) 84.72 ; (fr) 63.54 grams. 
 
 5. Given the following data, calculate the percentage purity of 
 the oxalic acid : 
 
 Standardization: Weight CaCO 3 1.050 gram; HC1 solution 
 used 45 cc. ; NaOH solution used = 4.8 cc. ; i cc. NaOH 
 solution 1.042 cc. HC1 solution. 
 
 Analysis: Weight oxalic acid = 1.500 gram; NaOH solution 
 used = 42.5 cc. ; HC1 solution used = 0.5 cc. 
 
 Answer: 96.52 / . 
 
 6. Given the following data, calculate the percentage purity of 
 the cream of tartar (KHC 4 H 4 O 6 ) : 
 
 Weight of substance = 2.500 grams ; NaOH solution used = 
 25.51 cc. ; H 2 SO 4 solution used 0.5 cc. ; i cc. H 2 SO 4 solu- 
 tion = 1.02 cc. NaOH solution; i cc. NaOH 4 solution^ ^0.0255 
 gram CaCO 3 . Answer : 95.90 %. 
 
 7. Solutions of alkali carbonates with phenolphthalein become 
 colorless as soon as the carbonate has changed to bicarbonate. 
 Calculate the percentage NaOH in a sample of soda ash from the 
 following data, assuming the hydrate to be neutralized before the 
 carbonate is attacked : Weight of soda ash = i gram ; HC1 
 solution is . The solution becomes colorless when 25 cc. HC1 
 have been added, but requires 40 cc. for complete neutraliza- 
 tion, after boiling out the carbon dioxide. Na 2 CO 3 -f- HC1 = 
 HNaCOs + NaCl ; NaHCO 3 + HC1 = NaCl + CO 2 + H 2 O. 
 
 Answer: 20.02 / . 
 
 8. If 10 cc. of a sulphuric acid solution yield 0.1220 gram 
 BaSO 4 , how much must the solution be diluted for an exactly ^ 
 solution? Answer: 1000 cc. to 1044 cc. 
 
 9. If i cc. of a potassium bichromate solution will oxidize 0.0066 
 gram iron, to what volume must 100 cc. of the solution be diluted 
 to make a T $ 7 solution ? Answer: 100 cc. to 1178 cc. 
 
! j 4 STOICHIOME TR Y. 
 
 10. Calculate the percentage of iron (Fe) in a sample of limon- 
 ite from the following data : 
 
 Weight of limonite = 0.55 gram ; K 2 Cr 2 O 7 solution used = 
 51.1 cc. ; i cc. K 2 Cr 2 O 7 solution = .0058 gram Fe ; FeSO 4 solu- 
 tion used = 5 cc. ; 5 cc. of FeSO 4 solution contains 0.008 gram 
 FeO. Answer: 52.74 / . 
 
 11. A sample of iron wire is dissolved, out of contact with air, 
 in 30 cc. HC1, of which i cc. = 0.95 cc. J HC1. The iron re- 
 quires 40 cc. yjj K 2 Cr 2 O 7 for oxidation. What excess of HC1 was 
 used? Answer: 13.16 cc. 
 
 12. How much stannous chloride (SnCl 2 ) by weight will it 
 require to reduce the iron from 0.5 gram magnetite (FeO. Fe 2 O 3 ), 
 dissolved out of contact with air ? Answer : 0.4093 gram. 
 
 13. How many cubic centimeters of HC1 (sp. gr. 1.12) are 
 required to dissolve 0.55 gram limonite (2 Fe 2 O 3 . 3 H 2 O), assum- 
 ing the only impurity to be 1.5 per cent, quartz? 
 
 Answer : 2.37 cc. 
 
 14. If 0.75 gram of a silicate yields 0.4 gram Fe 2 O 3 -f- A1 2 O 3 , 
 and the iron present requires 20 cc. K 2 Cr 2 O 7 solution (i cc. = 
 0.0784 gram FeSO 4 (NH 4 ) 2 SO 4 . 6 H 2 O), calculate the percentage 
 FeO and A1 2 O 3 in the sample. 
 
 Answer: 38.37 % FeO; 10.72 % A1 2 O 3 . 
 
 15. What weight of iron wire containing 99.85 / Fe will react 
 with the chromium from 0.5 gram chromite (FeO. Cr 2 O 3 )? 
 
 Answer: 0.7504 gram. 
 
 1 6. If i cc. of a potassium permanganate solution will oxidize 
 0.0085 g ram Fe, calculate the value of the same solution in terms 
 of (a) KHC 2 O 4 .C 2 H 2 O 4 . 2 H 2 O ; (V) KNO 2 ; (c) Mn ; (d) 
 K 4 Fe(CN) 6 . 3 H 2 O. 
 
 10 KHC 2 O 4 . C 2 H 2 O 4 . (2 H 2 O) + 8 KMnO 4 + 17 H 2 SO 4 = 
 
 9 K 2 SO 4 + 8 MnSO 4 + 40 CO 2 + 32 H 2 O + (20 H 2 O); 
 
 10 KNO 2 + 4 KMnO 4 + n H 2 SO 4 = 7 K 2 SO 4 + 4 MnSO 4 
 + 10 HNO 3 + 6 H 2 O; 3 MnO + Mn 2 O 7 = 5 MnO 2 , and 
 2 KMnO 4 = K 2 O. Mn 2 O 7 ; compare also problem 2. 
 
 Answer: (a) 0.009640 gram; (b) 0.006463 gram; (c) 0.002502 
 gram; (d) 0.06414 gram. 
 
 17. Calculate the value of a permanganate solution, of which 
 i cc. = 0.008 gram Fe, in terms of MoO 3 . Mn 2 O 7 + 10 FeO 
 = 5 Fe 2 O 3 -\- 2 MnO ; 7 Mn 2 O 7 -f- Mo 24 O 37 = 24 MoO 3 -f- 
 14 MnO. Answer: 0.007051 gram. 
 
PROBLEMS. uij 
 
 1 8. Given the following data, calculate the percentage of iron 
 in the limonite : 
 
 Weight of limonite = 0.55 gram ; KMnO 4 solution used 
 30 cc. ; i cc. KMnO 4 solution = 0.0084 gram C 2 H 2 O 4 . 2 H 2 O. 
 
 Answer: 40.74 %, 
 
 19. The calcium oxalate precipitate from 0.5 gram marble r 
 when treated with sulphuric acid, liberates sufficient oxalic acid 
 to reduce 43 cc. of permanganate solution (i cc. = 0.01150 gram 
 Fe). Calculate the percentage of .calcium (Ca) in the marble. 
 
 Answer: 35.38 %, 
 
 20. If i cc. KMnO 4 solution will oxidize 0.008 gram iron (Fe) r 
 calculate the equivalent of the same solution in terms of hydrogen 
 peroxide (H 2 O 2 ), and also the volume of oxygen which will be 
 evolved by each cubic centimeter of the permanganate solution 
 during the reaction, assuming that i cc. of oxygen weighs 0.00143 
 gram under the existing conditions. 5 H 2 O 2 -|- 2 KMnO 4 -|- 
 3 H 2 SO 4 = K 2 SO 4 . -f- 2 MnSO 4 -\- 5 O 2 + 5 H 2 O. 
 
 Answer: 0.002431 gram; 1.6 cc, 
 
 21. Given the following data, calculate the percentage of MnO 2 
 in the pyrolusite : 
 
 Weight of pyrolusite = 0.48 gram ; weight FeSO 4 . (NH 4 ) 2 SO 4 . 
 6 H 2 O = 4.3501 grams; K 2 Cr 2 O 7 solution used = 10 cc. ; i cc. 
 
 K 2 Cr 2 O 7 solution = 0.005 gram Fe. 
 
 Answer: 92.45 %. 
 
 22. Given the following data, calculate the percentage of 
 MnO 2 in the pyrolusite : 
 
 Weight pyrolusite = 0.48 gram ; weight iodine liberated from 
 KI = 1.296 grams. 
 
 For reactions, see note 6, page 93. Answer: 92.62 %. 
 
 23. If i cc. iodine solution is equivalent in oxidizing power to 
 0.00149 gram KBrO 3 , to what volume must 100 cc. be diluted to 
 
 make a ^ solution ? 
 
 Answer: 107 cc. 
 
 24. Calculate the percentage purity of the sample of potas- 
 sium bichromate from the following data : 
 
 Weight of sample = 0.1237 gram ; Na 2 S 2 O 3 solution used = 
 25 cc. ; i cc. Na 2 S 2 O 3 solution = 1.004 cc. iodine solution ; i cc. 
 iodine solution = 0.004975 gram As 2 O 3 . 
 
 K 2 Cr 2 7 + 6 KI + 7 H 2 SO 4 = 4 K 2 SO 4 + Cr 2 (SO 4 ) 3 + 
 3 ^2 ~h 7 H 2 O. Answer: 100%. 
 
! ! 6 -S- TOICHIOME TR Y. 
 
 25. Calculate the percentage purity of a sample of potassium 
 iodate (KIO 3 ) from the following data : 
 
 Weight of sample = 0.25 gram ; Na 2 S 2 O 3 solution used = 
 50 cc. ; i cc. Na 2 S 2 O 3 solution = 0.015 gram I. Answer : 84.34 / . 
 
 26. If i cc. of an iodine solution has the same oxidizing power 
 as 0.0034 gram KIO 3 , calculate its value in terms of antimony 
 (Sb). Answer : 0.005742 gram. 
 
 27. What is the relation of each of the following solutions to 
 a normal solution of the reagent ? 
 
 Na 2 S 2 O 3 . 5 H 2 O : i cc. = 0.001783 gram KIO 3 . 
 
 KMnO 4 (acid solution) : i cc. = 0.006303 gram C 2 H 2 O 4 . 2 H 2 O. 
 
 As 2 O 3 (as a reducing agent) : i cc. = 0.01772 gram Cl. 
 
 As 2 O 3 (as an acid) : i cc. = 0.01061 gram Na 2 CO 3 . 
 
 NaOH : i cc. = 0.1694 gram KHC 2 O 4 . C 2 H 2 O 4 . 2 H 2 O. 
 
n8 
 
 ATOMIC WEIGHTS. 
 
 TABLE OF ATOMIC WEIGHTS.* 
 O = 16.00. 
 
 Aluminum . . 
 
 Al 
 
 27.11 
 
 Mercury . . . 
 
 Hg 
 
 200.0 
 
 Antimony . . 
 
 Sb 
 
 120.43 
 
 Molybdenum 
 
 Mo 
 
 95-9 8 
 
 Argon .... 
 
 A 
 
 ? 
 
 Neodymium . . 
 
 Nd 
 
 140.5 
 
 Arsenic . . . 
 
 As 
 
 75-9 
 
 Nickel .... 
 
 Ni 
 
 58.69 
 
 Barium . . . 
 
 Ba 
 
 137-43 
 
 Nitrogen . . . 
 
 N 
 
 14.04 
 
 Bismuth . . . 
 
 Bi 
 
 208.11 
 
 Osmium . . 
 
 Os 
 
 190.99 
 
 Boron .... 
 
 B 
 
 10.95 
 
 Oxygen . . 
 
 O 
 
 16.0 
 
 Bromine . . . 
 
 Br 
 
 79-95 
 
 Palladium . . 
 
 Pd 
 
 106.36 
 
 Cadmium . . 
 
 Cd 
 
 111.93 
 
 Phosphorus . . 
 
 P 
 
 31.02 
 
 Caesium . . . 
 
 Cs 
 
 132.89 
 
 Platinum . . . 
 
 Pt 
 
 194.89 
 
 Calcium . . 
 
 Ca 
 
 40.08 
 
 Potassium . . 
 
 K 
 
 39^ 
 
 Carbon . . . 
 
 C 
 
 12.01 
 
 Praseodymium . 
 
 Pr 
 
 M3-5 
 
 Cerium . . 
 
 Ce 
 
 140.2 
 
 Rhodium . . . 
 
 Rh 
 
 103. or 
 
 Chlorine . . . 
 
 Cl 
 
 35-45 
 
 Rubidium . . 
 
 Rb 
 
 85-43- 
 
 Chromium . . 
 
 Cr 
 
 52.14 
 
 Ruthenium . 
 
 Ru 
 
 101.68- 
 
 Cobalt . . . 
 
 Co 
 
 58.93 
 
 Samarium . . 
 
 Sm 
 
 150.0 
 
 Columbium . . 
 
 Cb 
 
 94.0 
 
 Scandium . . 
 
 Sc 
 
 44.0 
 
 Copper . . . 
 
 Cu 
 
 63.60 
 
 Selenium . . . 
 
 Se 
 
 79.0 
 
 Erbium . . . 
 
 Er 
 
 166.3 
 
 Silicon . . . 
 
 Si 
 
 28.40 
 
 Fluorine . . 
 
 Fl 
 
 19.03 
 
 Silver .... 
 
 Ag 
 
 107.92 
 
 Gadolinium . . 
 
 Gd 
 
 156.1 
 
 Sodium . . . 
 
 Na 
 
 2 3-5 
 
 Gallium . . . 
 
 Ga 
 
 69.0 
 
 Strontium . . 
 
 Sr 
 
 87.61 
 
 Germanium . . 
 
 Ge 
 
 7 2 -3 
 
 Sulphur . . 
 
 S 
 
 32.07 
 
 Glucinum . . 
 
 Gl 
 
 9.08 
 
 Tantalum . . . 
 
 Ta 
 
 182.6 
 
 Gold .... 
 
 Au 
 
 197.24 
 
 Tellurium . . . 
 
 Te 
 
 127.0 
 
 Helium . . . 
 
 He 
 
 ? 
 
 Thallium . ... 
 
 Te 
 
 204.15 
 
 Hydrogen . . 
 
 H 
 
 1-0075 
 
 Thorium . . . 
 
 Th 
 
 232.63 
 
 Indium . 
 
 In 
 
 1 1^.7 
 
 Tin 
 
 Sn 
 
 I IQ.OC 
 
 Iodine .... 
 
 I 
 
 O / 
 126.85 
 
 Titanium . . . 
 
 Ti 
 
 7 O 
 48.15 
 
 Iridium . . . 
 
 Ir 
 
 193.12 
 
 Tungsten . . . 
 
 W 
 
 184.84 
 
 Iron .... 
 
 Fe 
 
 56.02 
 
 Uranium . . . 
 
 U 
 
 2 39-59 
 
 Lanthanum . . 
 
 La 
 
 138.6 
 
 Vanadium . . 
 
 V 
 
 51.38 
 
 Lead .... 
 
 Pb 
 
 206.92 
 
 Ytterbium . . 
 
 Yb 
 
 173.0 
 
 Lithium . . . 
 
 Li 
 
 7-03 
 
 Yttrium . . . 
 
 Y 
 
 88.95 
 
 Magnesium . . 
 
 Mg 
 
 24.29 
 
 Zinc .... 
 
 Zn 
 
 65.41 
 
 Manganese . . 
 
 Mn 
 
 54-99 
 
 Zirconium . . 
 
 Zr 
 
 90.6 
 
 * F. W. Clarke, /. Am. Ghent. Soc. t 18, 213. 
 
REAGENTS. 119 
 
 STRENGTH OF REAGENTS.* 
 
 GRAMS PER LITER. 
 
 Ammonium Molybdate t (of MoO 3 ) 68 grams. 
 
 Ammonium Oxalate, (NH 4 ) 2 C 2 O 4 . 2 H 2 O .... 40 grams. 
 
 Barium Chloride, BaCl 2 . 2 H 2 O 20 grams. 
 
 Magnesium Ammonium Chloride (of MgCl 2 ) ... 64 grams. 
 
 Mercuric Chloride, HgCl 2 50 grams. 
 
 Potassium Hydroxide, KOH (sp. gr. 1.27) .... 480 grams. 
 
 Potassium Sulphocyanate, KSCN 5 grams. 
 
 Silver Nitrate, AgNO 3 . . . . '. ' 4 25 grams. 
 
 Sodium Hydroxide, NaOH 100 grams. 
 
 Sodium Carbonate, Na 2 CO 3 150 grams. 
 
 Sodium Phosphate, HNa 2 PO 4 . 12 H 2 O 100 grams.- 
 
 Stannous chloride, SnCl 2 , made by saturating hydrochloric acid 
 with tin, diluting with an equal volume of water, and adding 
 a slight excess of acid from time to time. A strip of metallic 
 tin is kept in the bottle. 
 
 Aqueous ammonia, sp. gr. 0.96 contains 9.90% NH 3 by weight, 
 at 15 C.t 
 
 Aqueous ammonia, sp. gr. 0.90 contains 28.30% NH 8 by weight, 
 at 15 C4 
 
 Ammonia (0.96) may be prepared by diluting four volumes of ammonia 
 (0.90) with seven volumes of water. 
 
 Hydrochloric acid, sp. gr. 1.12, contains 23.8% HC1 by weight, 
 at 15 C. 
 
 Hydrochloric acid, sp. gr. 1.20, contains 39.1% HCl by weight, 
 at 15 C. 
 
 Hydrochloric acid (1.12) may be prepared by diluting five volumes of 
 hydrochloric acid (1.20) with four volumes of water. 
 
 Nitric acid, sp. gr. 1.20, contains 32.4% HNO 3 by weight, at 
 
 15 c-ll 
 
 Nitric acid, sp. gr. 1.42, contains 69.8% HNO 3 by weight, at 
 15 C.|| 
 
 Nitric acid (1.20) may be prepared by diluting two volumes of nitric 
 acid (1.42) with three volumes of water. 
 
 *The concentrations given in this table are those upon which the proce- 
 dures in the foregoing pages are based. It is obvious, however, that an exact 
 adherence to these quantities is not essential. & 
 
 t This solution is prepared according to the formula of Blair and Whitfield, 
 J. Am. Client. Soc., 17, 760. 
 
 J Lunge and Wiernik, Ztschr. angew. C/iem, 1889, 183. 
 
 Lunge and Marschlewski, Ztschr. angew. Chem, 1891, 133. 
 
 || Kolb. Dingl. pol.J., 182, 233. 
 
LOGARITHMS OF NUMBERS. 
 
 Natural 
 
 numbers. 
 
 O 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 PROPORTIONAL PARTS. 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 IO 
 
 oooo 
 
 0043 
 
 0086 
 
 0128 
 
 0170 
 
 02120253 
 
 0294 
 
 0334 
 
 0374 
 
 4 
 
 8 
 
 I 2 
 
 17 
 
 21 
 
 25 
 
 29 
 
 33 
 
 37 
 
 II 
 
 0414 
 
 0453 
 
 0492 
 
 053' 
 
 0569 
 
 0607 0645 
 
 0682 
 
 07190755 
 
 4 
 
 8 
 
 ii 
 
 *s 
 
 T 9 
 
 23 
 
 26 
 
 3 
 
 34 
 
 12 
 
 0792 
 
 0828 
 
 0864 
 
 0899 
 
 0934 
 
 0969 1004 
 
 I0 3P 
 
 1072] 1 106 
 
 3 
 
 7 
 
 10 
 
 1 4 
 
 i? 
 
 21 
 
 24 
 
 28 
 
 3i 
 
 I 3 
 
 "39 
 
 "73 
 
 1206 
 
 1239 
 
 1271 
 
 !33 X 335 
 
 1367 
 
 J 399 r 43 
 
 3 
 
 6 
 
 10 
 
 J 3 
 
 1 6 
 
 IC_) 
 
 23 
 
 26 29 
 
 14 
 
 1461 
 
 1492 
 
 1523 
 
 1553 
 
 1584 
 
 1614 
 
 1644 
 
 1673 
 
 1703 
 
 1732 
 
 3 
 
 6 
 
 9 
 
 12 
 
 *S 
 
 18 
 
 21 
 
 2 4 
 
 27 
 
 '5 
 
 1761 
 
 1790 
 
 18x8 
 
 i8 47 
 
 1875 
 
 1903 
 
 1931 
 
 1959 
 
 1987 
 
 2014 
 
 3 
 
 6 
 
 8 
 
 II 
 
 M 
 
 1 7 
 
 20 
 
 22 
 
 25 
 
 16 
 
 2041 
 
 2068 
 
 2095 
 
 2122 
 
 2148 
 
 2175 2201 
 
 2227 
 
 2253 
 
 2279 
 
 3 
 
 5 
 
 8 
 
 II 
 
 ij 
 
 16 
 
 18 
 
 21 24 
 
 7 
 
 2304 
 
 2330 
 
 2355 
 
 2380 
 
 2405 
 
 2430 
 
 2455 
 
 2480 
 
 2504 
 
 2529 
 
 2 
 
 5 
 
 7 
 
 10 
 
 12 
 
 15 
 
 17 
 
 20 
 
 22 
 
 18 
 
 2553 
 
 2577 
 
 2601 
 
 2625 
 
 2648 
 
 2672 
 
 2695 
 
 2718 
 
 2742 
 
 2765 
 
 2 
 
 5 
 
 7 
 
 9 
 
 12 
 
 M 
 
 16 
 
 19 
 
 21 
 
 !9 
 
 2788 
 
 2810 
 
 2833 
 
 2856 
 
 2878 
 
 2900 
 
 2923 
 
 2945 
 
 2967 
 
 2989 
 
 2 
 
 4 
 
 7 
 
 9 
 
 II 
 
 13 
 
 16 
 
 18 
 
 20 
 
 20 
 
 3010 
 
 3032 
 
 3054 
 
 3075 
 
 3096 
 
 3 Il8 
 
 3 T 39 
 
 3160 
 
 3181 
 
 3201 
 
 2 
 
 4 
 
 6 
 
 8 
 
 I I 
 
 r o 
 
 IS 
 
 J 7 
 
 19 
 
 21 
 
 3222 
 
 3243 
 
 3263 
 
 3284 
 
 3304 
 
 3324 
 
 3345 
 
 3365 
 
 3385 
 
 3404 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 22 
 
 3424 
 
 3444 
 
 3464 
 
 3483 
 
 3502 
 
 3522 
 
 354i 
 
 356o 
 
 3579 
 
 3598 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 T 5 
 
 17 
 
 2 3 
 
 3617 
 
 3636 
 
 3 6 55 
 
 3671 
 
 3692 
 
 37" 
 
 3729 
 
 3747 
 
 3766 
 
 3784 
 
 2 
 
 4 
 
 6 
 
 7 
 
 9 
 
 II 
 
 !j 
 
 IS 
 
 17 
 
 24 
 
 3802 
 
 3820 
 
 3838 
 
 3856 
 
 3874 
 
 3892 
 
 3909 
 
 3927 
 
 3945 
 
 3962 
 
 2 
 
 4 
 
 5 
 
 7 
 
 9 
 
 II 
 
 12 
 
 M 
 
 16 
 
 25 
 
 3979 
 
 3997 
 
 4014 
 
 403 1 
 
 4048 
 
 4065 
 
 4082 
 
 4099 
 
 4116 
 
 4133 
 
 2 
 
 3 
 
 5 
 
 7 
 
 9 
 
 10 
 
 12 
 
 14 
 
 J 5 
 
 26 
 
 415 
 
 4166 
 
 4183 
 
 42OO 
 
 4216 
 
 4232 
 
 4249 
 
 4265 
 
 4281 
 
 4298 
 
 2 
 
 3 
 
 5 
 
 7 
 
 8 
 
 10 
 
 II 
 
 J 3 
 
 '5 
 
 27 
 
 43*4 
 
 433 
 
 4346 
 
 4362 
 
 4378 
 
 4393 
 
 4409 
 
 4425 
 
 4440 
 
 4456 
 
 2 
 
 3 
 
 5 
 
 6 
 
 8 
 
 9 
 
 II 
 
 *3 
 
 14 
 
 28 
 
 4472 
 
 4487 
 
 4502 
 
 45'8 
 
 4533 
 
 4548 
 
 4564 
 
 4579 
 
 4594 
 
 4609 
 
 2 
 
 3 
 
 5 
 
 6 
 
 8 
 
 9 
 
 II 
 
 12 
 
 14 
 
 2 9 
 
 4624 
 
 4639 
 
 4654 
 
 4669 
 
 4683 
 
 4698 
 
 4713 
 
 4728 
 
 4742 
 
 4757 
 
 I 
 
 3 
 
 4 
 
 6 
 
 7 
 
 9 
 
 IO 
 
 12 
 
 13 
 
 30 
 
 477 1 
 
 4786 
 
 4800 
 
 4814 
 
 4829 
 
 4843 
 
 4857 
 
 4871 
 
 4886 
 
 4900 
 
 I 
 
 3 
 
 4 
 
 6 
 
 7 
 
 9 
 
 IO 
 
 II 
 
 1 3 
 
 31 
 
 4914 
 
 4928 
 
 4942 
 
 4955 
 
 4969 
 
 4983 
 
 4997 
 
 5011 
 
 5024 5038 
 
 I 
 
 3 
 
 4 
 
 6 
 
 7 
 
 8 
 
 10 
 
 II 
 
 12 
 
 3 2 
 
 505 1 565 
 
 5079 
 
 5092 
 
 5 I0 5 
 
 5"9 
 
 5132 
 
 SMS 
 
 5^95^2 
 
 I 
 
 3 
 
 4 
 
 5 
 
 Z 
 
 8 
 
 9 
 
 I I 
 
 12 
 
 33 
 
 5185 
 
 5198' 
 
 5211 
 
 5224 
 
 5237 
 
 5250 
 
 5263 
 
 5276 
 
 5289 5302 
 
 I 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 9 
 
 10 
 
 12 
 
 34 
 
 53i5 
 
 5328 
 
 5340 
 
 5353 
 
 5366 
 
 5378 
 
 5391 
 
 5403 
 
 5416 
 
 5428 
 
 I 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 9 
 
 IO 
 
 II 
 
 35 
 
 544 1 
 
 5453 
 
 5465 
 
 5478 
 
 5490 
 
 552 
 
 5514 
 
 5527 
 
 5539 
 
 555i 
 
 I 
 
 2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 9 
 
 10 
 
 II 
 
 36 
 
 5563 
 
 5575 
 
 5587 
 
 5599 
 
 5611 
 
 5623 
 
 5635 
 
 5647 
 
 5658 
 
 5670 
 
 I 
 
 2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 10 
 
 II 
 
 37 
 
 5682 
 
 5 6 94 
 
 5705 
 
 57i7 
 
 5729 
 
 5740 
 
 5752 
 
 5763 
 
 5775 
 
 5786 
 
 
 2 
 
 3 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 38 
 
 5798 
 
 5809 
 
 5821 
 
 5832 
 
 5843 
 
 5855 
 
 5866 
 
 5877 
 
 5888 
 
 5899 
 
 
 2 
 
 3 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 39 
 
 59" 
 
 5922 
 
 5933 
 
 5944 
 
 5955 
 
 5966 
 
 5977 
 
 5988 
 
 5999 
 
 6010 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 
 
 9 
 
 IO 
 
 40 
 
 6021 
 
 6031 
 
 6042 
 
 6053 
 
 6064 
 
 6075 
 
 6085 
 
 6096 
 
 6107 
 
 6117 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 S 
 
 9 
 
 10 
 
 4i 
 
 6128 
 
 6138 
 
 6149 
 
 6160 
 
 6170 
 
 6180 
 
 6191 
 
 6201 
 
 6212 
 
 6222 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 42 
 
 6232 
 
 6243 
 
 6253 
 
 6263 
 
 6274 
 
 6284 
 
 6294(6304 
 
 6314 
 
 6325 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 43 
 
 6 335 
 
 6345 
 
 6355 
 
 6365 
 
 6375 
 
 6385 
 
 6395 
 
 6405 
 
 6415 
 
 6425 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 44 
 
 6435 
 
 6444 
 
 6454 
 
 6464 
 
 647.4 
 
 6484 
 
 6493 
 
 6503 
 
 6513 
 
 6522 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 45 
 
 6 53 2 
 
 6542 
 
 6551 
 
 656! 
 
 6571 
 
 6580 
 
 6590 
 
 6599 
 
 6609 
 
 6618 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 .7 
 
 8 
 
 9 
 
 46 
 
 6628 
 
 6637 
 
 6646 
 
 6656 
 
 6665 
 
 6675 
 
 6684 
 
 6693 
 
 6702 
 
 6712 
 
 
 1 
 
 3 
 
 4 
 
 "5 
 
 6 
 
 7 
 
 7 
 
 8 
 
 47 
 
 6721 
 
 6730 
 
 6739 
 
 6749 
 
 6758 
 
 6767 
 
 6776 
 
 6785 
 
 6794 
 
 6803 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 7 
 
 8 
 
 48 
 
 6812 
 
 6821 
 
 6830 
 
 6839 
 
 6848 
 
 6857 
 
 6866 
 
 6875 
 
 6884 
 
 6393 
 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 49 
 
 6902 
 
 6911 
 
 6920 
 
 6928 
 
 6937 
 
 6946 
 
 6955 
 
 6964 
 
 6972 
 
 698! 
 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 5 
 
 6990 
 
 6998 
 
 7007 
 
 7016 
 
 7024 
 
 7033 
 
 7042 
 
 7050 
 
 7059 
 
 7067 
 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 5 1 
 
 7076 
 
 7084 
 
 70937101 
 
 7110 
 
 7118 
 
 71267135 
 
 7 : 43 
 
 7152 
 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 5 2 
 53 
 
 7160 
 7243 
 
 7168 
 7251 
 
 717717185 
 7259 7267 
 
 7i93 
 7275 
 
 7202 
 7284 
 
 7210 7218 
 7292 7300 
 
 7226 
 7308 
 
 7235 
 73 l6 
 
 
 2 
 2 
 
 2 
 2 
 
 3 
 3 
 
 4 
 4 
 
 5 
 5 
 
 6 
 6 
 
 7 
 
 6 
 
 7 
 7 
 
 54 
 
 7324 
 
 7332 
 
 7340 7348 
 
 7356 
 
 7364 
 
 7372 
 
 73So 
 
 7388 
 
 7396 
 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 6 
 
 7 
 
LOGARITHMS OF NUMBERS. 
 
 Natural 
 numbers. 
 
 O 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 PROPORTIONAL PARTS. 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 55 
 
 7404 
 
 7412 
 
 7419 
 
 7427 
 
 7435 
 
 7443 
 
 745 1 
 
 7459 
 
 7466 
 
 7474 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 7 
 
 56 
 
 7482 
 
 7490 
 
 7497 
 
 7505 
 
 7513 
 
 7520 
 
 7528 
 
 753 6 
 
 7543 
 
 755i 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 7 
 
 57 
 
 7559 
 
 7566 
 
 75747582 
 
 7589 
 
 7597 
 
 7604 
 
 7612 
 
 7619 
 
 7627 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 7 
 
 58 
 
 7634 
 
 7642 
 
 7649 7657 
 
 7664 
 
 7672 
 
 76797686 
 
 7694 
 
 7701 
 
 I 
 
 I 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 59 
 
 7709 
 
 7716 
 
 7723 
 
 773 1 
 
 7738 
 
 7745 
 
 7752 
 
 7760 
 
 7767 
 
 7774 
 
 I 
 
 I 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 60 
 
 7782 
 
 7789 
 
 7796 
 
 7803 
 
 7810 
 
 7818 
 
 7825 
 
 7832 
 
 7839 
 
 7846 
 
 I 
 
 I 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 6 
 
 61 
 
 7853 
 
 7860 
 
 7868 
 
 7875 
 
 7882 
 
 7889 
 
 7896 
 
 7903 
 
 7910 
 
 7917 
 
 I 
 
 I 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 6 
 
 62 
 
 7924 
 
 793 1 
 
 7938 
 
 7945 
 
 795 2 
 
 7959 7966 
 
 7973 
 
 7980 
 
 7987 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 6 
 
 63 
 
 7993 
 
 8000 
 
 8007 
 
 8014 
 
 8021 
 
 8028 
 
 8035 
 
 8041 
 
 8048 
 
 8055 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 64 
 
 8062 
 
 8069 
 
 8075 
 
 8082 
 
 8089 
 
 8096 
 
 8102 
 
 8109 
 
 8116 
 
 8122 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 65 
 
 8129 
 
 8136 
 
 8142 
 
 8149 
 
 8156 
 
 8162 
 
 8169 
 
 8176 
 
 8182 
 
 8189 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5. 
 
 5 
 
 6 
 
 66 
 
 8i95 
 
 8202 
 
 8209 
 
 8215 
 
 8222 
 
 8228 
 
 8235 
 
 8241 
 
 8248 
 
 8254 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 67 
 
 8261 
 
 8267 
 
 8274 
 
 8280 
 
 8287 
 
 8293 
 
 8299 
 
 83068312 
 
 8319 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 68 
 
 8325 
 
 833i 
 
 8338 
 
 8344 
 
 835i 
 
 8357 
 
 8363 
 
 8370 
 
 8376 
 
 8382 
 
 I 
 
 I 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 "69 
 
 8388 
 
 8395 
 
 8401 
 
 8407 
 
 8414 
 
 8420 
 
 8426 
 
 8432 
 
 8439 
 
 8445 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 70 
 
 8451 
 
 8457 
 
 8463 
 
 8470 
 
 8476 
 
 8482 
 
 8488 
 
 8494 
 
 8500 
 
 8506 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7i 
 
 8513 
 
 8519 
 
 8525 
 
 853i 
 
 8537 
 
 8543 
 
 8549 
 
 8555 
 
 8561 
 
 8567- 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 5 
 
 72 
 
 8573 
 
 8579 
 
 8585 
 
 8 59 T 
 
 8597 
 
 8603 
 
 8609 
 
 8615 
 
 8621 
 
 8627 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 5 
 
 73 
 
 8633 
 
 8639 
 
 8645 
 
 8651 
 
 8657 
 
 8663 
 
 8669 
 
 8675 
 
 8681 
 
 8686 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 5 
 
 74 
 
 8692 
 
 8698 
 
 8704 
 
 8710 
 
 8716 
 
 8722 
 
 8727 
 
 8733 
 
 8739 
 
 8745 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 5 
 
 75 
 
 8751 
 
 8756 
 
 8762 
 
 8768 
 
 8774 
 
 8779 
 
 8.785 
 
 8791 
 
 8797 
 
 8802 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 5 
 
 76 
 
 8808 
 
 8814 
 
 8820 
 
 8825 
 
 8831 
 
 8837 
 
 8842 
 
 8848 
 
 8854 
 
 8859 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 5 
 
 77 
 
 8865 
 
 8871 
 
 8876 
 
 8882 
 
 8887, 
 
 8893 
 
 8899 
 
 8904 
 
 8910 
 
 8915 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 78 
 
 8921 
 
 8927 
 
 8932 
 
 8938 
 
 8943 
 
 8949 
 
 8954 
 
 8960 
 
 8965 
 
 8971 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 79 
 
 8976 
 
 8982 
 
 8987 
 
 8993 
 
 8998 
 
 9004 
 
 9009 
 
 9015 
 
 9020 
 
 9026 
 
 r 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 80 
 
 9031 
 
 9036 
 
 9042 
 
 9047 
 
 9053 
 
 9058 
 
 9063 
 
 9069 
 
 9074 
 
 9079 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 81 
 
 90859090 
 
 9096 
 
 9101 
 
 9106 
 
 9112 
 
 9117 
 
 9122 
 
 9128 
 
 9133 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 82 
 
 9 I 3 8 9 I 43 
 
 9149 
 
 9 J 54 
 
 9159 
 
 9^5 
 
 9170 
 
 9175 
 
 9180 
 
 9186 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 83 
 
 9191 
 
 9196 
 
 9201 
 
 9206 
 
 9212 
 
 9217 
 
 9222 
 
 9227 
 
 9232 
 
 9238 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 84 
 
 9243 
 
 9248 
 
 9253 
 
 9258 
 
 9263 
 
 9269 
 
 9274 
 
 9279 
 
 9284 
 
 9289 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 85 
 
 9294 
 
 9299 
 
 9304 
 
 9309 
 
 9315 
 
 9320 
 
 9325 
 
 9330 
 
 9335 
 
 9340 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 86 
 
 9345 
 
 9350 
 
 9355 
 
 9360 
 
 93 6 5 
 
 9370 
 
 9375 
 
 9380 
 
 9385 
 
 939 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 5 
 
 87 
 
 9395 
 
 9400 
 
 9405 
 
 9410 
 
 9415 
 
 9420 
 
 9425 
 
 943 
 
 9435 
 
 9440 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 88 
 
 9445 
 
 945 
 
 9455 
 
 9460 
 
 9465 
 
 9469 
 
 9474 
 
 9479 
 
 9484 
 
 9489 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 89 
 
 9494 
 
 9499 
 
 9504 
 
 959 
 
 9513 
 
 9518 
 
 9523 
 
 9528 
 
 9533 
 
 9538 
 
 O 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 90 
 
 9542 
 
 9547 
 
 9552 
 
 9557 
 
 9562 
 
 9566 
 
 957i 
 
 9576 
 
 958i 
 
 9586 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 91 
 
 959 
 
 9595 
 
 9600 
 
 9605 
 
 9609 
 
 9614 
 
 9619 
 
 9624 
 
 9628 
 
 9633 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 92 
 
 9638 
 
 96439647 
 
 9652 
 
 9657 
 
 9661 
 
 9666 
 
 9671 
 
 9675 
 
 9680 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 93 
 
 9685 
 
 9689 
 
 9694 
 
 9699 
 
 9703 
 
 97089713 
 
 9717 
 
 9722 
 
 9727 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 94 
 
 9731 
 
 97 3 6 
 
 974i 
 
 9745 
 
 975 
 
 9754 
 
 9759 
 
 9763 
 
 9768 
 
 9773 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 95 
 
 9777 
 
 9782 
 
 9786 
 
 9791 
 
 9795 
 
 9800 
 
 9805 
 
 9809 
 
 9814 
 
 9818 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 96 
 
 9823 
 
 9827 
 
 9832 
 
 9836 
 
 9841 
 
 9845 9850 
 
 9854 
 
 9859 
 
 9863 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 97 
 
 9868 
 
 9872 
 
 9877 
 
 9881 
 
 9886 
 
 9890 9894 
 
 9899 
 
 9903 
 
 9908 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 -4 
 
 98 
 
 9912 
 
 9917 
 
 9921 
 
 9926 
 
 993 
 
 9934 9939 
 
 9943 
 
 9948 
 
 9952 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 99 
 
 9956 
 
 9961 
 
 9965 
 
 9969 
 
 9974 
 
 9978 9983 
 
 9987 
 
 999 i 
 
 9996 
 
 
 
 I 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 3 
 
 4 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
ANTILOGARITHMS. 
 
 ^ 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 PROPORTIONAL PARTS. 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 .00 
 
 1000 
 
 1002 
 
 1005 
 
 1007 
 
 1009 
 
 1012 
 
 1014 
 
 1016 
 
 1019 
 
 IO2I 
 
 O 
 
 o 
 
 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 .01 
 
 1023 
 
 1026 
 
 1028 
 
 1030 
 
 1033 
 
 1035 
 
 1038 
 
 1040 
 
 1042 
 
 1045 
 
 O 
 
 
 
 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 .02 
 
 1047 
 
 1050 
 
 1052 
 
 1054 
 
 1057 
 
 1059 
 
 1062 
 
 1064 
 
 1067 
 
 1069 
 
 o 
 
 o 
 
 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 03 
 
 1072 
 
 1074 
 
 1076 
 
 1079 
 
 1081 
 
 1084 
 
 1086 
 
 1089 
 
 1091 
 
 1094 
 
 
 
 
 
 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 .04 
 
 1096 
 
 1099 
 
 IIO2 
 
 1104 
 
 1107 
 
 IIO9 
 
 11.12 
 
 1114 
 
 1117 
 
 III9 
 
 
 
 I 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 O C 
 
 1122 
 
 II2S 
 
 1127 
 
 1130 
 
 1132 
 
 "35 
 
 1138 
 
 1140 
 
 "43 
 
 1146 
 
 o 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 .06 
 
 1148 
 
 "5 1 
 
 "53 
 
 1156 
 
 "59 
 
 1161 
 
 1164 
 
 1167 
 
 1169 
 
 "72 
 
 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 .07 
 
 "75 
 
 1178 
 
 1180 
 
 "83 
 
 1186 
 
 1189 
 
 II9I 
 
 "94 
 
 "97 
 
 "99 
 
 o 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 .08 
 
 1 202 
 
 1205 
 
 1208 
 
 I2II 
 
 1213 
 
 1216 
 
 1219 
 
 1222 
 
 1225 
 
 1227 
 
 o 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 3 
 
 .09 
 
 1230 
 
 1233 
 
 1236 
 
 1239 
 
 1242 
 
 1245 
 
 1247 
 
 I25O 
 
 I2 53 
 
 1256 
 
 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 3 
 
 .10 
 
 1259 
 
 1262 
 
 1265 
 
 1268 
 
 1271 
 
 1274 
 
 1276 
 
 1279 
 
 1282 
 
 1285 
 
 o 
 
 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 3 
 
 .11 
 
 1288 
 
 1291 
 
 1294 
 
 1297 
 
 1300 
 
 1303 
 
 1306 
 
 1309 
 
 1312 
 
 1315 
 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 3 
 
 .12 
 
 1318 
 
 1321 
 
 1324 
 
 1327 
 
 1330 
 
 1334 
 
 1337 
 
 1340 
 
 1343 
 
 1346 
 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 3 
 
 13 
 
 1349 
 
 1352 
 
 1355 
 
 1358, 
 
 1361 
 
 '365 
 
 1368 
 
 1371 
 
 1374 
 
 '377 
 
 o 
 
 
 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
 .14 
 
 1380 
 
 1384 
 
 1387 
 
 1390 
 
 *393 
 
 1396 
 
 1400 
 
 1403 
 
 1406 
 
 1409 
 
 o 
 
 
 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
 .15 
 
 1413 
 
 1416 
 
 1419 
 
 I 4 22 
 
 1426 
 
 1429 
 
 1432 
 
 M35 
 
 M39 
 
 1442 
 
 o 
 
 
 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
 .l6 
 
 1445 
 
 1449 
 
 1452 
 
 H55 
 
 H59 
 
 1462 
 
 I 4 66 
 
 1469 
 
 1472 
 
 1476 
 
 o 
 
 
 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
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 1807 
 
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 1816 
 
 
 
 
 
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 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
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 1820 
 
 1824 
 
 1828 
 
 1832 1837 
 
 1841 
 
 1845 
 
 1849 
 
 1854 
 
 1858 
 
 
 
 
 
 2 
 
 2 
 
 3 
 
 3 
 
 3 
 
 4 
 
 27 
 
 1862 
 
 1866 
 
 1871 
 
 [875:1879 
 
 1884 
 
 1888 
 
 1892 
 
 1897 
 
 1901 
 
 o 
 
 
 
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 2 
 
 3 
 
 3 
 
 3 
 
 4 
 
 .28 
 
 1905 
 
 1910 
 
 1914 
 
 1919 1923 
 
 1928 
 
 1932 
 
 1936 
 
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 3 
 
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 4 
 
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 195 
 
 J 954 
 
 1959 
 
 1963 
 
 1968 
 
 1972 
 
 1977 
 
 1982 
 
 1986 
 
 1991 
 
 
 
 
 
 2 
 
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 3 
 
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 2004 
 
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 3 
 
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 2 
 
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 3 
 
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ANTILOGARITHMS. 
 
 4 
 , J 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 PROPORTIONAL PARTS. 
 
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 2 
 
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 4 
 
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 6 
 
 7 
 
 8 
 
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 7 
 
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 4 
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 4 
 
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 7 
 
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 3 
 
 5 
 
 6 
 
 8 
 
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 12 
 
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 6730 
 
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 3 
 
 5 
 
 6 
 
 8 
 
 9 
 
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 12 
 
 14 
 
 83 
 
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 2 
 
 3 
 
 5 
 
 6 
 
 8 
 
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 13 
 
 
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 6918 
 
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 6966 
 
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 7031 
 
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 3 
 
 5 
 
 6 
 
 8 
 
 10 
 
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 15 
 
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 7079 
 
 7096 
 
 7112 
 
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 7211 
 
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 3 
 
 5 
 
 7 
 
 8 
 
 10 
 
 12 
 
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 7244 
 
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 7278 
 
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 7328 
 
 7345 
 
 7362 
 
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 2 
 
 3 
 
 5 
 
 7 
 
 8 
 
 10 
 
 12 
 
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 15 
 
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 7413 
 
 7430 
 
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 7464 
 
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 755i 
 
 7568 
 
 2 
 
 3 
 
 5 
 
 7 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
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 7586 
 
 7603 
 
 7621 
 
 7638 
 
 7656 
 
 7674 
 
 7691 
 
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 7727 
 
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 4 
 
 5 
 
 7 
 
 9 
 
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 12 
 
 14 
 
 16 
 
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 7762 
 
 7780 
 
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 7870 
 
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 2 
 
 4 
 
 5 
 
 7 
 
 9 
 
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 14 
 
 16 
 
 .90 
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 7943 
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 7962 
 8147 
 
 7980 
 8166 
 
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 8185 
 
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 8035 
 8222 
 
 8054 
 8241 
 
 8072 
 8260 
 
 8091 
 8279 
 
 8110 
 8299 
 
 2 
 
 2 
 
 4 
 4 
 
 6 
 
 6 
 
 { 
 
 9 
 9 
 
 1 1 
 1 1 
 
 roro 
 
 15 
 
 17 
 17 
 
 .92 
 93 
 94 
 
 8318 
 8511 
 8710 
 
 8337 
 8531 
 8730 
 
 8356 
 8551 
 
 8750 
 
 8375 
 8570 
 8770 
 
 8395 
 8590 
 8790 
 
 8610 
 8810 
 
 8433 
 8630 
 8831 
 
 8453 
 8650 
 8851 
 
 8472 
 8670 
 8872 
 
 8492 
 8690 
 8892 
 
 2 
 
 2 
 2 
 
 4 
 4 
 
 4 
 
 6 
 6 
 6 
 
 8 
 8 
 8 
 
 10 
 10 
 10 
 
 12 
 12 
 12 
 
 M 
 
 M 
 
 II 
 
 16 
 
 17 
 18 
 18 
 
 95 
 
 
 8933 
 
 8954 
 
 8974 
 
 8995 
 
 9016 
 
 9036 
 
 9057 
 
 9078 
 
 9099 
 
 2 
 
 4 
 
 6 
 
 8 
 
 IO 
 
 12 
 
 15 
 
 17 
 
 19 
 
 .96 
 
 97 
 
 9120 9141 
 93339354 
 
 9162 
 9376 
 
 9183 
 
 9397 
 
 9204 
 9419 
 
 9226 
 9441 
 
 9 2 47 
 9462 
 
 9268 
 9484 
 
 92909311 
 
 9506 9528 
 
 2 
 
 2 
 
 4 
 4 
 
 6 
 
 7 
 
 8 
 9 
 
 II 
 II 
 
 13 
 
 15 
 J 5 
 
 17 
 17 
 
 19 
 
 20 
 
 .98 
 99 
 
 9550 
 9772 
 
 9572 
 9795 
 
 9594 
 
 9616 
 9840 
 
 9638 
 9863 
 
 9661 
 9886 
 
 9908 
 
 9705 
 
 9727 
 9954 
 
 975 
 9977 
 
 2 
 2 
 
 4 
 
 5 
 
 7 
 7 
 
 9 
 9 
 
 II 
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 14 
 
 r 6 
 16 
 
 1 8 
 18 
 
 20 
 2O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
INDEX. 
 
 Acidimetry 64 
 
 Acid solutions, normal . . . . 55 
 standard ... 64 
 
 Accuracy demanded 20 
 
 Alkalimetry 64 
 
 Alkali solutions, normal . . . 55 
 
 standard ... 64 
 
 Ammonium nitrate, acid ... 36 
 
 Antimony, determination of . . 98 
 
 Apatite, analysis of 36 
 
 Asbestos filters .... 14, 27, 28 
 Atomic weights, table of . . .118 
 
 Balances, use and care of . . . 16 
 
 Bichromate process for iron . . 75 
 
 Brass, analysis of 46 
 
 Burette, description of .... 56 
 
 calibration of .... 58 
 
 cleaning of 60 
 
 reading of . . . . 59, 60 
 
 Calcium, determination of . . . 41 
 
 Calibration, definition of . . . 57 
 
 of burettes .... 58 
 
 of flasks . . . . 61 
 
 Chlorimetry 101 
 
 Chlorine, gravimetric determina- 
 tion 21, 27 
 
 Chlorine, volumetric determina- 
 tion 101 
 
 Chrome iron ore, analysis of . .82 
 
 Colloidal precipitates .... 12 
 
 Copper, determination of ... 48 
 
 Crucibles, use of 9 
 
 Crystalline precipitates . . . . 12 
 
 Desiccators .... 
 Direct methods . . 
 Dolomite, analysis of 
 
 Economy of time . . 
 End-point, definition of 
 Evaporation of liquids 
 
 9 
 54 
 
 19 
 53 
 10 
 
 Ferrous-ammonium sulphate, an- 
 alysis of 29 
 
 Filters, how fitted 
 Filtration . . . . 
 Flasks, calibration of 
 
 graduated 
 Funnels . 
 
 . ... , . 13 
 
 . . . . 6i 
 
 " < 57 
 
 .... 13 
 
 Gelatinous precipitates .... 15 
 
 General directions 8 
 
 General directions for volumetric 
 
 analysis 62 
 
 Gooch filter 14, 27, 28 
 
 Gravimetric analysis 21 
 
 definition of, 7 
 
 Hardened filters 14 
 
 Ignition of precipitates . ... 15 
 Indicators, definition of . . 
 for acidimetry . 
 Indirect methods .... 
 Integrity demanded . . . 
 
 53 
 65 
 
 54 
 
 20 
 
 lodimetry 94 
 
 Iron, gravimetric determination of, 29 
 volumetric determination of, 80,90 
 
 Lead, determination of . . . .46 
 Limonite, determination of iron 
 
 in, 80, 90 
 
 Liquids, evaporation of . . . 10 
 Logarithms 120 
 
 Magnesium, determination of . 43 
 Mohr liter 58 
 
 Neatness . . . . . . 
 
 Normal solutions . . . . 
 
 advantages of . . 
 
 preparation of . . 
 
 Oxalic acid, strength of . . 
 
 Oxidation processes . . . 
 Oxidizing solutions, normal 
 
 8 
 54 
 56 
 66 
 
 . 72 
 53.74 
 55 
 
 Permanganate process for iron . 84 
 Phosphoric anhydride, determina- 
 tion of 36 
 
 Pipette, description of .... 57 
 
INDEX. 
 
 I2 5 
 
 Platinum crucibles, care of . . 10 
 
 Precipitates, colloidal .... 12 
 
 crystalline .... 12 
 
 separation from filter, 24 
 
 Precipitation 12 
 
 Precipitation methods . . 53, 103 
 
 Problems no 
 
 Pyrolusite, oxidizing power of . 92 
 
 Reagents 
 
 Reducing solution, normal . 
 Reductor, Jones .... 
 
 II 
 
 55 
 86 
 
 Saturation methods . . . . 53, 64 
 
 Silver, determination of ... 104 
 
 Soda ash, alkaline strength of . 70 
 
 Sodium chloride, analysis of . . 22 
 
 preparation of, 21 
 
 Solubility, quantitative .... 7 
 
 Standardization, definition of . . 54 
 
 Standard solutions . . . . 53, 54 
 
 Stibnite, analysis of 98 
 
 Stirring rods 13 
 
 Stoichiometry 105 
 
 Strength of reagents 119 
 
 Suction, use of 14 
 
 Sulphocyanite process for silver . 103 
 
 Testing of washings 15 
 
 Titration, definition of .... 53 
 
 Vacuum pump, use of .... 14 
 
 Volumetric analysis 53 
 
 definition of . 8 
 
 Wash-bottles 9 
 
 Washed filters 13 
 
 Washing of precipitates ... 14 
 
 Washings, testing of 15 
 
 Zinc, determination of .... 51 
 

** "XiJjOvV 
 
 o\/cr,^ iw *i.oo ON rut ^. F OURTH 
 
 1 SEVPMT,, DA ^ 
 

 UDl 
 
 UNIVERSITY OF CALIFORNIA LIBRARY