•■ 
 
 ?%3 
 
 9fe 
 
 flfc 
 
 wm 
 
 m 
 
 mm 
 
 '<^.^ 
 
(ffcrneU Itniocrattg ffiibrarg 
 
 Stljaca, Ntm $otk 
 
 THE GIFT OF 
 
 Cavnapie. Inst it a, "Wo vi, 
 
Cornell University Library 
 QD 464.B7S64 
 
 The atomic weights of boron and fluorine 
 
 3 1924 012 376 285 
 
Cornell University 
 Library 
 
 The original of this book is in 
 the Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924012376285 
 
THE ATOMIC WEIGHTS OF 
 BORON AND FLUORINE 
 
 BY 
 EDGAR F. SMITH and WALTER K. Van HAAGEN 
 
 PUBLISHED BY 
 
 The Carnegie Institution of Washington 
 
 Washington, 1918 
 
THE ATOMIC WEIGHTS OF 
 BORON AND FLUORINE 
 
 BY 
 EDGAR F. SMITH and WALTER K. Van HAAGEN 
 
 PUBLISHED BY 
 
 The Carnegie Institution of Washington 
 
 Washington, 1918 
 
CARNEGIE INSTITUTION OF WASHINGTON 
 Publication No. 267 
 
 PRESS OF J. B. LIPPINCOTT COMPANY 
 PHILADELPHIA 
 
INTRODUCTION. 
 
 When the present work was undertaken the writers contem- 
 plated the use of anhydrous borax as the initial material in deter- 
 mining the atomic weight of certain elements, e.g., fluorine. After 
 numerous trials, a method was worked out which admitted of the 
 complete conversion of sodium tetraborate into sodium fluoride, 
 and the preliminary experiments made with this method gave a 
 value for fluorine which was practically identical with the present 
 international figure (19.0) . However, as soon as the same method 
 was applied to borax, the purity and the anhydrous condition of 
 which were above suspicion, the atomic weight of fluorine (on 
 the assumption that B = 11.0) became too high. 
 
 Although it was realized from the beginning that it would be 
 desirable to redetermine the atomic weight of boron before the 
 latter could properly be used in fixing other atomic weights, it 
 was not anticipated — in view of the most reliable previous work 
 upon this constant — that it would differ much from the accepted 
 value (11.0). 
 
 A closer study of the literature bearing upon this subject soon 
 revealed that the inconsistencies and uncertainties in previous 
 determinations are much greater than might reasonably be 
 expected of a rather common, non-metallic, uniformly trivalent * 
 element of low atomic weight; and thus it has come to pass that 
 the major part of the present investigation is devoted to the 
 determination of the atomic weight of boron. The work outlined 
 in the following pages deals with the preparation of pure sub- 
 stances and the conversion, either directly or indirectly, of anhy- 
 drous sodium tetraborate into the chloride, fluoride, sulphate, 
 nitrate, and carbonate of sodium. The atomic weight of boron 
 was thus based upon the rather well-known atomic weights of 
 sodium, chlorine, sulphur, nitrogen, and carbon, and (with slight 
 variations) led to the value 10.900 for boron. 
 
 Incidentally the work also seemed to furnish sufficient data 
 for a recalculation of the atomic weight of fluorine. The value 
 
 1 Trivalent at least with respect to oxygen and the halogens. On the valence of boron 
 see A. Stock, E. Kuss, and O. Priess, Ber. 47, 3115-49 (1914). 
 
IV INTRODUCTION. 
 
 found for boron was used in deriving the atomic weight of this 
 element, although some calculations were referred directly to 
 sodium sulphate, and one was based on a cross-ratio between 
 sodium fluoride and sodium chloride. All methods, rather con- 
 sistently, gave the average value 19.005 for fluorine. 
 
 Chapter III consists of a constructive, critical discussion of 
 previous determinations based upon the analysis of borax. 
 
CONTENTS. 
 
 Paqb 
 
 Introduction iii 
 
 Chapter I. General Part. 
 
 Principle of the method 1 
 
 Distilled water 3 
 
 Boric acid 5 
 
 Sodium carbonate 5 
 
 Borax 7 
 
 Methyl alcohol 9 
 
 Formic and hydrofluoric acids. (Other reagents) 11 
 
 The apparatus 12 
 
 The dehydration of borax 15 
 
 Concerning the complete dehydration of borax 20 
 
 Balance and weighing; constants used 23 
 
 Chapter II. 
 
 A. The atomic weight of boron 26 
 
 Preliminary experiments 26 
 
 Final determinations 27 
 
 Experiment IV. Na 2 B,0 7 : 2NaCl : Na 2 S0 4 27 
 
 Experiments V, IX, X, XI. Na 2 B.0 7 : 2NaF : Na 2 SO< 31 
 
 Experiment VI. Na 2 B 4 7 : Na 2 S0 4 36 
 
 Experiment VII. Na 2 B 4 0, : 2NaNO, 37 
 
 Experiment VIII. Na 2 B 4 7 : Na 2 CO a 38 
 
 Tabulation 41 
 
 The atomic weight of boron referred to "borax glass" 42 
 
 B. The atomic weight of fluorine 44 
 
 Chapter III. 
 
 Review of previous determinations of the atomic weight of boron 48 
 
 General considerations 48 
 
 A. The determination of water in crystallized borax 51 
 
 B. The analysis of anhydrous borax (the distillation method) 53 
 
 C. The titration of borax 58 
 
 Summary 63 
 
 v 
 
CHAPTER I. GENERAL PART. 
 PRINCIPLE OF THE METHOD. 
 
 According to Rosenbladt, 1 the characteristic green color 
 imparted to an ordinary alcohol flame by boric acid was known 
 to Geoffroy in 1732. In course of time it was found that this 
 test became more delicate when methyl alcohol was used. In 
 1887 Gooch 2 and Rosenbladt, 3 both working independently, 
 successfully adapted this qualitative test to the estimation of 
 boric acid, which until then had presented great difficulties to the 
 analyst. 4 In order to estimate boron in a soluble borate, for 
 example, it was merely necessary to liberate the boric acid by the 
 addition of a stronger acid, and then expel the former as its methyl 
 ester, by repeated evaporations with methyl alcohol, after which 
 the ester was hydrolyzed and the boric acid thus fixed, by a 
 suitable absorbent or "retainer." This general method for the 
 elimination of boric acid from borax, with certain modifications, 
 was also pursued in the present work; the methyl borate, 
 however, was allowed to escape, since the weights of the anhy- 
 drous borax and the residual sodium salt served to establish the 
 desired ratios. 
 
 This volatilization method was first used in atomic weight 
 determinations by Ramsay and Aston, 6 who distilled borax with 
 hydrochloric acid and methyl alcohol and weighed the residual 
 sodium chloride. 
 
 Rosenbladt expelled the boric acid in the presence of sulphuric 
 acid. Gooch, according to his original communication, found it 
 difficult to choose between acetic and nitric acids. As the esteri- 
 fication of boric acid is counteracted by water, it is readily seen 
 that the latter should be absent, or nearly so, unless a vast excess 
 of methyl alcohol be used. For such reasons the use of acetic 
 
 1 Z. anorg. Chem. 26, 18 (1887). 
 
 »Chem. N. 55, 7 (1887). 
 
 8 Loc. cit. 
 
 4 More recent modifications in the estimation of boric acid, and additional references, 
 
 may be found in a paper by Wherry and Chapin, J. Am. Chem. Soc, 30, 1687 
 
 (1908). 
 s J. Chem. Soc. 63, 211 (1893). 
 
 1 
 
I THE ATOMIC WEIGHTS OF 
 
 acid seems inadvisable, since sodium acetate is not readily dehy- 
 drated. This objection does not apply to the other acids men- 
 tioned, i.e., to hydrochloric, sulphuric, and nitric acids. All of 
 these have been used in the present work. In addition carbonic 
 acid, or rather its anhydride, has been employed in converting 
 borax into sodium carbonate. 
 
 The action of hydrofluoric acid seems to be not strictly analo- 
 gous to that of the acids just mentioned. Although sodium 
 fluoride and boric acid are undoubtedly formed at first, a number 
 of secondary reactions may take place between these primary 
 products and the excess of hydrofluoric acid, leading chiefly to the 
 formation of borofluoric acid and, possibly, of sodium boro- 
 fluoride. 6 It is true that the mixture thus obtained will give up 
 considerable portions of boric acid when evaporated with methyl 
 alcohol, but the quantitative elimination of boric acid by this 
 means, with reasonable quantities of methyl alcohol, seemed very 
 doubtful. Again, sodium borofluoride, upon ignition, will give 
 up boron trifluoride and leave sodium fluoride. However, at 
 the temperature required to effect this decomposition, appreci- 
 able quantities of the sodium salt itself may be volatilized. At 
 any rate, the conclusion was soon reached that the elimination of 
 boric acid as methyl borate in the presence of an alkali fluoride 
 and hydrofluoric acid could not be rendered sufficiently accurate 
 for an atomic weight determination, even if it should be possible 
 to expel boric acid completely by this method. 
 
 Therefore, if the distillation method were to be applied to 
 borax with a view of obtaining sodium fluoride as an end-product, 
 the problem clearly resolved itself into this : An acid had to be 
 found which would react "normally" with borax and its sodium 
 salt would have to be readily transposed to the fluoride by means 
 of hydrofluoric acid. Formic acid was found to be such an acid. 
 It gave results that left little to be desired. 
 
 Besides purity of materials, the essential prerequisites in 
 deriving an acceptable atomic weight ratio are definite and 
 weighable substances constituting the ratio sought and complete- 
 ness of the reaction correlating the two terms of that ratio. That 
 
 6 See also Abegg, Fox, and Herz on possible reactions between boric acid, potassium 
 fluoride, and hydrofluoric acid. Z. anorg. Chem. 35, 129 (1903). 
 
BOEON AND FLUORINE. 3 
 
 borax, a well-crystallized salt of moderate solubility, represents 
 a definite atomic aggregate seems reasonably certain. That 
 anhydrous borax, although obtained with some difficulty, is no 
 less definite, is practically non-hygroscopic, and may be weighed 
 with ease, will be shown in the sequel. The other salts, namely, 
 the chloride, fluoride, sulphate, nitrate, and carbonate of sodium, 
 have all met with more or less application in atomic weight work. 
 Of these the sulphate was found to be the most stable at the 
 fusion temperature and left practically nothing to be desired 
 when fused in a jacketed vessel. The fluoride, in spite of its high 
 melting-point (at 980°), was somewhat volatile; but when heated 
 in the bulb (soon to be described) could be fused to constant 
 weight with comparative ease. Other precautions observed in 
 the heating of these salts will be given in their appropriate places. 
 The completeness of the reaction, i.e., the complete expulsion 
 of boric acid, was tested for, in two cases by means of the flame 
 spectrum; in others, with turmeric paper — by both methods with 
 negative results. Indirectly the completeness of the reaction may 
 be inferred from the following considerations: If a number of 
 samples of borax had been converted, by identical operations, 
 into only one kind of salt, e.g., sodium chloride, mere concordance in 
 the results would not necessarily prove that the elimination of boric 
 acid had been complete; under such conditions constant errors 
 are not unknown to have made their appearance. In the present 
 instance, however, borax was converted into a number of different 
 salts, involving avariety of operations and great diversity in condi- 
 tions. A fair concordance obtained by the latter method would 
 indicate that the elimination of boric acid must have been complete. 
 
 DISTILLED WATER. 
 
 Ordinary distilled water was redistilled with a little potassium 
 permanganate made alkaline with potassium hydroxide. The 
 first third of the distillate was rejected. The portion collected 
 was redistilled with a little potassium bisulphate. The product 
 was then redistilled twice. A block-tin condenser was used. The 
 water was stored in well-seasoned flasks of resistance glass, pro- 
 vided with caps fitted on the outside of the neck to prevent con- 
 tact of the water with ground surfaces. 
 
 The seal between the distilling flask and the metal condenser 
 
THE ATOMIC WEIGHTS OF 
 
 Fiq. 1. 
 
 was effected by a modification of the well-known funnel-top seal 
 
 suggested by T. W. Richards. The device is shown in figure 1. 
 
 The auxiliary glass bulb (a) is easily made from a round-bottomed 
 
 flask of suitable dimensions ; with 
 accurately blown ware an excellent 
 seal may thus be obtained without 
 grinding. The opening at (c) should, 
 of course, be in proper alignment 
 with the constriction at (6), which 
 serves as a seat for the condenser. 
 The neck of the bulb has two side- 
 vents (dd) and is loosely packed with 
 glass wool, held in position by a 
 clamp of platinum wire. Glass wool 
 was used because even in careful 
 boiling a very slight spray of the solu- 
 tion itself may reach this part of the 
 apparatus. 
 The water obtained in the preceding way was used in the 
 
 recrystallizations. In the quantitative determinations small 
 
 quantities of water were to be evaporated 
 
 to dryness, and it was prepared by distil- 
 ling once more from an all-platinum still; 
 
 it was freshly prepared for each deter- 
 mination and stored in a platinum 
 
 vessel. The "head" of the platinum 
 
 still used is indicated in figure 2. The 
 
 stirrup-shaped "spray-guard" (e) was 
 
 inserted into the ground-in neck of the 
 
 condenser and held in position by the 
 
 pins (/). This still was also used for the 
 
 distillation of hydrofluoric acid. In an 
 
 apparatus of moderate dimensions, and 
 
 particularly when the liquid is to be 
 
 distilled with other dissolved or suspended substances, traces 
 
 of such matter may reach the dome of the condenser, in spite 
 
 of all precautions in heating. It is under such conditions that 
 
 the "spray-guard" just mentioned is of value. 
 
 Fiq. 2. 
 
BORON AND FLUORINE. 5 
 
 BORIC ACID. 
 
 Several courses were open for the preparation of borax. It is 
 doubtful whether the impurities (such as silica, lime, organic mat- 
 ter, etc.) in commercial borax can easily be removed by recrystal- 
 lization. Hence for the purposes of this investigation the synthe- 
 sis of the salt from its acid and basic components in purest form, 
 though laborious, was preferred. The further purification of the 
 product could easily be completed by recrystallization. 
 
 Pure boric acid was prepared as follows: A good "C. P." 
 grade was crystallized three times from water, the crystals being 
 drained and washed centrifugally each time. The product was 
 then dehydrated and fused to a clear glass in platinum. Approx- 
 imately 500 grams of this anhydrous acid were covered with 
 2 liters of redistilled and almost anhydrous methyl alcohol, which 
 contained only a trace of acetone. The mixture was boiled under 
 a reflux condenser in an all-glass apparatus until solution was 
 complete. In this reaction part of the boric acid forms the methyl 
 ester, whereas the remainder probably does not react at all, or 
 serves as a dehydrating agent and separates out on cooling in 
 crystalline crusts on the sides of the flask. The clear liquid, con- 
 taining the methyl borate, was decanted and distilled from an 
 apparatus constructed entirely of glass. Evidently the ester was 
 partly hydrolyzed during this process, for a considerable portion 
 of boric acid remained in the flask. 
 
 The clear, colorless distillate, containing the methyl borate, 
 was mixed with an equal volume of boiling water, agitated from 
 time to time, and allowed to stand, when crystals of boric acid 
 separated out on cooling. The product was drained and washed 
 centrifugally and crystallized once from water. As was expected, 
 the method gave a poor yield in the end, but the boric acid thus 
 obtained was of great purity. 
 
 SODIUM CARBONATE. 
 
 A very pure commercial grade of sodium carbonate was fused 
 in a platinum dish in portions of 100 grams each with a small 
 quantity of pure, precipitated calcium carbonate. 7 After dis- 
 integration of the melt in water the cold liquid was decanted and 
 
 7 Smith and Exner, Proo. Am. Philos. Soc. 43, No. 176, p. 134 (1904). 
 
6 
 
 THE ATOMIC WEIGHTS OF 
 
 filtered. "Quantitative" paper and a platinum funnel were used. 
 The paper had been specially washed with hydrochloric and 
 hydrofluoric acids, followed by large quantities of water; finally 
 it was treated with a hot solution of sodium carbonate before the 
 main solution was filtered. 
 
 Traces of calcium carbonate which may contaminate the 
 filtrate were effectively removed by a subsequent operation, con- 
 sisting in the exposure of the solution of the sodium carbonate 
 (contained in a large platinum-lined dish) to an atmosphere of 
 
 Fig. 3. 
 
 carbon dioxide for many days. The resulting sodium bicarbonate 
 was then drained and washed centrifugally and the precipitation 
 as bicarbonate repeated three times. Needless to say, platinum 
 utensils were used throughout. Finally the salt was gently ignited 
 to the normal carbonate. Spectroscopic tests showed the prepa- 
 ration to be free from calcium. 
 
 Figure 3, in vertical projection, shows the apparatus used in 
 precipitating the bicarbonate. The arrangement was found quite 
 convenient for conducting the precipitation under pressure and 
 practically without interruption. The air in the upper reservoir 
 
BORON AND FLUORINE. 7 
 
 of the Kipp generator is compressed by means of the stout rubber 
 bulb (a) and the stop-cock (6) closed. The empty bottle (c) 
 merely serves as a reservoir for the compressed air and communi- 
 cates with the mercury manometer (d), which also serves as a 
 safety valve. The bell-jar (e) is ground upon a glass plate and 
 covers the platinum dish (/) containing the sodium carbonate 
 solution. After the bell-jar has been filled with carbon dioxide 
 through the delivery tube (g) (which does not come in contact 
 with the solution) cylinder (h) may be filled with water to the 
 desired height. In the present instance an additional pressure of 
 only about 30 cm. of water was applied. This pressure, of course, 
 does not hasten the absorption of the gas very markedly, but as 
 the reaction was quite slow a slight acceleration was not unwel- 
 come. Even under the pressure applied, the upper reservoir 
 of the generator had to be wired to its base and the bell- 
 jar securely clamped to the plate. As practically no carbon 
 dioxide is wasted, the apparatus (when properly adjusted) will 
 run for days and requires little attention; it is advisable, of 
 course, to restore the original pressure occasionally by means 
 of the rubber bulb. 
 
 The carbon dioxide was generated by the action of pure 
 hydrochloric acid on white marble. The gas passed through two 
 large towers; the first contained beads coated with moist sodium 
 bicarbonate, the other was similarly charged with moist silver 
 carbonate. Finally, before reaching the bell-jar, it was conducted 
 through two wash-bottles containing solutions of sodium bicar- 
 bonate. The contents of the platinum dish remained entirely 
 free from chloride. 
 
 BORAX. 
 
 Crystallized boric acid and sodium carbonate, prepared as 
 indicated in the preceding sections, were next brought together 
 by introducing small portions of the acid in solid form into a 
 boiling solution of the carbonate contained in a platinum dish, 
 until the boric acid was slightly in excess of the theoretical require- 
 ment for the formation of the tetraborate. Boiling of the clear 
 solution was continued until no more carbon dioxide was evolved. 
 The crystal meal, which separated out on cooling and stirring, 
 was drained on the platinum cones of a hand centrifugal and 
 
8 THE ATOMIC WEIGHTS OP 
 
 washed with a small quantity of cold water, previously boiled. 
 The product was recrystallized twice from water free from carbon 
 dioxide and drained and washed as before. In these recrystal- 
 lizations the solution was "inoculated" with a trace of the 
 decahydrate (prepared for the purpose) as soon as the temperature 
 of the solution had fallen a little below 55°, which approximately 
 marks the transition point between the penta- and decahydrates. 
 The preparation thus obtained was used in some of the preliminary 
 determinations. 
 
 There seemed to be a remote possibility that this borax was 
 not entirely free from unknown organic derivatives which might 
 have accompanied the boric acid because of its preparation from 
 the methyl ester. While no evidence to this effect could be ob- 
 tained, it seemed best to dehydrate the borax and fuse it to a 
 clear glass before the final recrystallizations. Pure borax from 
 another source had been fused for hours in the platinum dish 
 before it was used for the fusion of the borax in question. 
 Even at the risk of making a rather superfluous statement, 
 mention must be made of the extreme brilliancy of the "borax 
 glass" thus obtained and the total absence of the slightest 
 color from the melt, even when examined "end-on" and in thick 
 layers. 
 
 The "borax glass" was dissolved in water, free from carbon 
 dioxide, and recrystallized four times in the manner and with the 
 precautions already indicated. The product was dried and partly 
 dehydrated over solid potassium hydroxide. The salt, even before 
 the final recrystallizations, contained no perceptible traces of 
 carbonate, for a powdered sample moistened with water and 
 dilute hydrochloric acid remained free from bubbles, even when 
 examined under the magnifying glass. Under the microscope the 
 crystals presented an entirely uniform and homogeneous appear- 
 ance. In some instances the mother liquors were allowed to 
 evaporate to dryness over caustic potash, when nothing but borax 
 (free from carbonate) was obtained. The crystals obtained by 
 spontaneous evaporation of such solutions were remarkably stable 
 and showed no sign of efflorescence, even when exposed for weeks 
 to ordinary atmospheric conditions. 
 
 Reliable tests indicating the presence, in borax, of traces of 
 other borates (either more basic or more acid in character) are 
 
BORON AND FLUORINE. 9 
 
 lacking. However, such borates are prepared only with difficulty 
 and as, in the present instance, the proportion of the components 
 and the conditions of formation were those corresponding to the 
 tetraborate with 10 molecules of water, it may safely be assumed 
 that the preparation was "pure" also from this point of view. 
 The final product was used in the experiments recorded in table 1. 
 
 METHYL ALCOHOL. 
 
 The methyl alcohol used in the quantitative elimination of 
 boric acid from borax should, of course, be anhydrous, or very 
 nearly so. It should also be as pure as possible, for it seems that 
 the smaller the amount of the usual impurities in the alcohol, 
 the more readily will methyl borate be formed with a mini- 
 mum expenditure of the reagent. The methyl alcohol for 
 the final determinations, therefore, was prepared by the saponi- 
 fication of methyl oxalate which admittedly yields a very pure 
 product. 
 
 The methyl oxalate was made from dehydrated oxalic acid 
 and a good grade of almost anhydrous commercial methyl alcohol. 
 The mixture was heated in the water-bath for several hours under 
 a reflux condenser. It was then distilled from an all-glass appa- 
 ratus and the distillate collected as soon as it began to solidify 
 in the receiver. The product was drained and washed centrifu- 
 gally. Almost 2 kilograms of methyl oxalate were obtained in 
 this manner. It was melted on the water-bath and, after the 
 addition of some water, saponified by introducing small quanti- 
 ties of caustic soda solution through the upright condenser 
 until an excess of the alkali had been added. The resulting 
 mixture was boiled for several hours under the reflux condenser 
 and finally distilled. 
 
 In testing the purity of the resulting aqueous methyl alcohol, 
 it was found that a neutral solution of silver nitrate produced a 
 slight white precipitate. The latter dissolved readily in dilute 
 nitric acid and did not consist of silver carbonate. The addition 
 of silver nitrate to extremely dilute solutions of ammonium 
 hydroxide and other soluble hydroxides gave similar precipitates, 
 which turned brown on boiling. The test seemed to indicate, 
 therefore, that the methyl alcohol was contaminated with a trace 
 of some volatile base, such as ammonia, and that the precipitate 
 
10 THE ATOMIC WEIGHTS OF 
 
 consisted of silver hydroxide. 8 That traces of sodium hydroxide 
 should have been carried into the receiver seemed unlikely, for 
 special precautions were observed in the distillation. Ammonia, 
 however, might have been introduced from the caustic soda, which 
 may contain (and was found to contain) traces of this substance. 
 The silver nitrate test seemed extremely delicate. It will be 
 recalled that Nessler's test can not be applied in the presence of 
 alcohol, and indicators (with the possible exception of methyl 
 orange) did not show any perceptible alkalinity of the alcohol. 
 
 The trace of free ammonia, though probably unobjectionable 
 in the present case, was removed in the following manner: An 
 aliquot portion of the methyl alcohol was diluted with more water 
 and mixed with a few drops of very dilute hydrochloric acid until 
 methyl orange, the indicator, showed a slight acidity. The main 
 portion of the alcohol was then mixed with the required amount 
 of the same acid and distilled; a considerable portion, however, 
 was allowed to remain behind and was rejected. The distillate 
 was boiled for a long time, under a reflux condenser, with sodium 
 hydroxide prepared from sodium and, after distillation, gave no 
 test with silver nitrate. The process was then repeated twice. 
 Finally the alcohol (distilled again from pure sodium hydroxide) 
 was fractionated with a Hempel column, boiled with lime for 
 several days, and distilled. The resulting product still contained 
 almost 1 per cent, of water, as indicated by the hydrometer. As 
 the residues, to be treated with the alcohol in the quantitative 
 determinations, were never absolutely anhydrous, it did not seem 
 worth while to remove the last fraction of water from the alcohol 
 by other means. 
 
 8 Silver hydroxide is usually referred to as a hypothetical compound which exists 
 only in solution. According to some qualitative tests, white silver hydroxide 
 may be observed for an instant when the solutions of the soluble hydroxides are 
 very dilute. It seems uncertain whether the existence of this compound has 
 merely been inferred from the properties of the corresponding copper derivative 
 or whether it has actually been identified. 
 J. D. Bruce (Chem. N. 50, 208 (1884)), on mixing a dilute solution of silver nitrate 
 in 90 per cent, alcohol with an equivalent amount of caustic potash in alcohol 
 at — 40" F., obtained a white precipitate, but did not succeed in separating the 
 compound unchanged. A number of papers on the properties and solubility of 
 "silver hydroxide" have been published, but it seems that such investigations 
 invariably apply to "moist silver oxide" as the initial substance. See, for 
 example, Carnelly and Walker, J. Chem. Soc. 53, 59 (1888); Bottger, Z. phys. 
 Chem. 46, 521 (1903); Whitby, Z. anorg. Chem. 67, 107; A. A. Noyes and Kohr 
 J. Am. Chem. Soc. 24, 1141 (1902). 
 
BORON AND FLUORINE. 11 
 
 The methyl alcohol was then twice redistilled from an all-glass 
 still (used only for this purpose) and was stored in a capped flask 
 of resistance glass. It was redistilled for each individual determi- 
 nation recorded in table 1. A portion of 100 c.c. when evaporated 
 in platinum left no weighable residue. 
 
 FORMIC AND HYDROFLUORIC ACIDS. (OTHER 
 REAGENTS.) 
 
 An excellent "C. P." grade of formic acid was diluted some- 
 what with water and distilled after the addition of a small quan- 
 tity of barium hydroxide. The product was redistilled with silver 
 carbonate. 
 
 Formic acid, when distilled through glass, invariably left a 
 slight white residue upon evaporation to dryness. Even after 
 distillation from a platinum retort, a slight brownish residue 
 remained. The platinum condenser used for this purpose gave 
 excellent service in the distillation of hydrofluoric acid; formic 
 acid, however, seemed to dissolve traces of some unknown material 
 from the condenser, even after the latter had again been cleaned 
 in a variety of ways and after the acid had been redistilled several 
 times. Whether this contamination originated from impurities in 
 the platinum itself, or in the gold solder in the seams of the con- 
 denser, seemed uncertain. At any rate, as soon as the condenser in 
 question had been replaced by a seamless one of pure platinum, the 
 distillate of formic acid left no residue upon evaporation. 
 
 After the preliminary distillations from glass the formic acid 
 was concentrated by fractionation and finally distilled from the 
 platinum apparatus just mentioned. The acid was freshly dis- 
 tilled for each determination and was stored in a platinum vessel. 
 
 Hydrofluoric acid was purified as follows: The commercial 
 acid was treated with potassium fluoride until the filtrate gave 
 no further turbidity with pure potassium carbonate. 9 A consider- 
 able excess of potassium fluoride was then added, the clear liquid 
 decanted after standing for some time, and distilled from a lead 
 still. The product was redistilled with a little potassium per- 
 manganate and the first third of the distillate rejected. After 
 the addition of sodium phosphate the distillate was rectified 
 
 ' As the potassium fluoride contained some silica it could not be used in this test. 
 2 
 
12 THE ATOMIC WEIGHTS OF 
 
 again from a lead still provided with a platinum condenser. The 
 hydrofluoric acid thus obtained was redistilled four times from 
 an all-platinum still, that is to say, twice with a little pure silver 
 carbonate, and finally twice alone. The product left no residue 
 upon evaporation and was free from perceptible traces of silica, 
 lead, iron, chlorine, and organic matter — the chief impurities to 
 be met with in this acid. 
 
 The purification of other reagents, besides those already 
 described, will be given as such reagents may be called for in the 
 prosecution of this study. 
 
 THE APPARATUS. 
 
 For reasons which will become apparent in due time, the final 
 conversions of borax into other salts had to be carried out in a 
 flask or long-necked bulb through which a current of air was 
 passed. Platinum proved to be the only material suitable for 
 this purpose. The platinum bulb applicable to all essential 
 exigencies of the problem, without being too cumbersome or too 
 complicated, is shown in figure 4; the sketch is largely self- 
 explanatory. 
 
 The bulb proper was 4 cm. in diameter and had a capacity of 
 about 30 c.c. The neck was 1.5 cm. wide and the volume of the 
 entire flask approximately 40 c.c. The inner tube, which served 
 to send a current of air through the bulb, was fused near its 
 upper end into a cup-shaped stopper ground into the neck of the 
 flask and, furthermore, was provided with two annular, perforated 
 platinum disks (as indicated in the sketch) which were 4.5 cm. 
 apart and all but touched the walls of the neck. These disks 
 served a threefold purpose. In the first place they acted as guides 
 for the inner tube and thus prevented undue strain upon the 
 ground-in stopper and insured its proper insertion. This function 
 of the disks must not be scorned, for a ground-in, rather shallow 
 platinum stopper of this description — although the neck be 
 reinforced, as in the present case — is easily rendered useless and 
 becomes a constant source of annoyance unless the two ground 
 surfaces be in proper alignment just before closing. With the 
 present device the stopper easily slid into its seat when the appa- 
 ratus was removed from its supports. In the second place these 
 perforated disks acted as effective "spray-guards" in preventing 
 
BORON AND FLUORINE. 
 
 13 
 
 mechanical loss. It is scarcely necessary to add that evaporation 
 of solutions was always carried out at a temperature much below 
 the respective boiling-points. Nevertheless, traces of dissolved 
 air, upon being expelled on warming, may cause serious loss, 
 which will be en- 
 tirely prevented by 
 these plates. Finally 
 these perforated 
 disks serve to pre- 
 vent a flame at the 
 mouth of the bulb 
 from "striking 
 back." As will be 
 explained later, the 
 alcoholic vapors ex- 
 pelled in the volatil- 
 ization of boric acid 
 were ignited from 
 time to time. 
 
 The method of 
 supporting the bulb 
 during the experi- 
 ment is indicated in 
 the sketch. Two 
 stout lugs, diamet- 
 rically opposite and 
 fused to the upper 
 part of the neck, 
 rested on the prongs 
 of a fork made of 
 heavy platinum 
 wire. The advan- 
 tages of this device 
 
 over any other method of support are too obvious to be detailed. 
 The flange of the cup-shaped stopper, carrying the inner tube, 
 rested on a similar fork. The forks were independent of each 
 other, but they were permanently set into appropriate clamps 
 which could be adjusted in the usual manner. 
 
 The elbow (abc) served to connect the inner tube to the con- 
 
 Fig. 4. 
 
14 THE ATOMIC WEIGHTS OF 
 
 stricted end of the platinum combustion tube and gave rise to 
 two ground joints at (a) and (c). In the final determinations 
 this combustion tube had no particular significance. Originally 
 it was intended to vaporize the methyl alcohol from boats placed 
 in the combustion tube and to conduct the vapor through the 
 bulb. However, as this method seemed to offer no particular 
 advantages and was not easily controlled, all liquid reagents (such 
 as water, acids, methyl alcohol) were introduced through the 
 tubulature shown at (6) by means of a small platinum funnel. 
 
 In general the ground joint at (a) was disturbed as little as 
 possible during a determination. When operations had to be 
 interrupted the apparatus was disconnected at (c) and the bulb 
 together with the elbow piece put on a suitable rack in a desic- 
 cator. Before each weighing, however, the elbow was removed ; 
 the bulb could then be closed completely by the hollow platinum 
 stopper (d). The entire apparatus weighed about 56 grams. 
 
 It may not be amiss to add, concerning the ground platinum 
 stoppers and connections, that manufacturers often use pumice 
 and oil for grinding such parts, and a platinum surface so treated, 
 of course, requires careful cleaning. In the present instance all 
 platinum parts having ground surfaces were immersed for some 
 time in molten sodium carbonate and then in molten potassium 
 bisulphate; but after this treatment the joints were found to 
 "stick" and were as useless as before. To remedy this defect 
 the stoppers and joints were carefully reground with a mixture 
 of pure, very finely powdered oxalic acid and glycerol. This 
 required considerable time, as the oxalic acid acts only as a very 
 mild abrasive. The parts thus prepared were then thoroughly 
 cleaned and ignited and finished with a little glycerol alone. Any 
 particles of oxalic acid which might have become embedded in 
 the platinum were easily decomposed upon ignition. The con- 
 nections obtained in this way proved very satisfactory. A proper 
 functioning of the joint at (a) was imperative, because it marked 
 the juncture between the container to be weighed and the rest of 
 the apparatus. A number of "make-and-break" operations at 
 this joint did not perceptibly affect the weight of the former. 
 
 The bulb was not allowed to come in contact with a direct 
 gas flame, but was heated in an air-bath formed by a large platinum 
 crucible. For the lower temperatures the crucible was set into a 
 
BORON AND FLUORINE. 15 
 
 plate of asbestos board (not shown in the sketch) covered with 
 sheet nickel. Noxious vapors could be removed by a small hood 
 placed over the part of the apparatus which projected above the 
 asbestos board. This hood consisted of two well-fitting, over- 
 lapping cylindrical shells of sheet copper which, when in position, 
 formed a complete cylinder. The latter was capped by a platinum 
 funnel, the stem of which could be connected to an exhaust. A 
 vertical slot, in the side of the cylinder, served for the introduc- 
 tion of a thermometer, or pyrometer, to roughly measure the 
 temperature within the air-bath. In the stronger ignitions, such 
 as were necessary in fusing the salts, the asbestos board was dis- 
 pensed with; but the bulb was protected by a crucible, which in 
 this case rested on a triangle and could be covered with a platinum 
 lid consisting of two overlapping sections. In this manner the 
 heat was concentrated on the bulb proper without overheating 
 the neck. 
 
 The current of air which passed through the apparatus during 
 an experiment was produced by a water blast. Before reaching 
 the pump the air was drawn through a solution of caustic soda. 
 It was then conducted through a solution of potassium perman- 
 ganate containing potassium hydroxide, and next through moist 
 soda-lime, fused caustic potash, concentrated sulphuric acid, and 
 finally, before reaching the platinum combustion tube, through a 
 tower filled with freshly fused caustic potash. The train was 
 constructed entirely of glass. The plug of the combustion tube 
 was provided with a platinum inlet tube which was joined to the 
 glass train by means of a "glass spring," the free end of which 
 was ground into the metal tube. 
 
 THE DEHYDRATION OF BORAX. 
 
 For obvious reasons it seemed desirable to refer the analyses 
 of borax to the anhydrous salt. It was found, however, that the 
 complete expulsion of water from borax is no simple matter. The 
 observations of Dobrovolsky in 1869, concerning the dehydration 
 of this salt, seem to have attracted no attention until they were 
 mentioned by Brauner in 1906. 10 According to Dobrovolsky only 
 small quantities (0.1 to 0.3 gram) of borax can be dehydrated 
 completely, whereas larger quantities retain water. 
 
 J "In Abegg's Handbuch d. anorg. Chem., Vol. Ill, part 1, p. 6. 
 
16 THE ATOMIC WEIGHTS OF 
 
 The dehydration of this salt was studied more fully by Hoskyns 
 Abrahall, u in 1889. He found that when borax was heated to 
 between 250° and 300° for 20 hours, under reduced pressure, 
 about 0.5 per cent, of water still remained, but that "practically 
 the whole of the water that could be expelled at this temperature 
 came off in the first 3 or 4 hours." 12 It is interesting to note that 
 this chemist condensed all the water given up by a sample of 
 crystallized borax heated to 265° in a vacuum. This water "did 
 not act on turmeric paper and left no appreciable residue when 
 left to evaporate in the cold over sulphuric acid." The crucible 
 containing the borax was then heated over a direct flame, first 
 over a Bunsen burner and finally over the blast-lamp, and in 
 two instances in a small Fletcher furnace capable of melting cast 
 iron. However, Abrahall's experiments show that, depending 
 upon the mode of heating, appreciable and varying quantities 
 of borax were volatilized; hence he concluded that the dehydration 
 of borax was untrustworthy for the derivation of an atomic ratio. 
 (See also quotation on p. 52). 
 
 A number of experiments relative to the volatility of borax, 
 upon fusion, were carried out by Waldbott u for practical and 
 general analytical purposes. He discovered, for example, that 
 a portion of borax glass, weighing about a gram, lost 14 per cent, 
 when heated over the blast-lamp for 3 hours and that a quantity 
 of fused borax (cir. 12.0 grams), kept in a kiln at about 1400° 
 for 60 hours, lost almost 50 per cent, of its original weight. Inci- 
 dentally, it may be mentioned that, from several analyses of the 
 residues, Waldbott drew the conclusion that no segregation takes 
 place during fusion, but that the salt is volatilized as such, i.e., 
 as Na 2 B 4 7 . This flatly contradicts Leonard," who states that 
 "the residue contains rather less soda than that required for the 
 formula Na2B 4 7 , and that the residue is not constant." 
 
 Waldbott's observations in this particular are probably more 
 
 11 J. Chem. Soc, 61, 650 (1892). The paper was edited and published by Ewan and 
 Hartog. 
 
 12 More recently, J. Hoffman (D.Chem. Ind. 39, 411-412 (1917), has studied the pro- 
 gressive dehydration of borax at various temperatures (from below 100° to 318°) 
 and finds that the final molecule of water is exceedingly tenacious, according to 
 an abstract published in the J. Chem. Soc. 112, II, 206. 
 
 » J. Am. Chem. Soc, 16, 410-418 (1894). 
 
 " Chem. N. 77, 104 (1898). 
 
BORON AND FLUORINE. 17 
 
 reliable than those of Leonard, who gives no experimental data 
 besides stating that his conclusions were based upon the titration 
 of borax before and after fusion in a crucible for several hours, 
 and that the residue required less standard acid for exact neutrali- 
 zation than did the original borax glass. Such a titration does 
 not necessarily prove that the portion volatilized had a composi- 
 tion different from that of borax, for, during a protracted ignition 
 over a gas flame, the contents of the crucible might have absorbed 
 appreciable quantities of sulphur dioxide and, as a result, required 
 less acid for neutralization. Waldbott analyzed the residual borax 
 by expelling the boron with ammonium fluoride and weighing the 
 alkali as sodium sulphate. 
 
 Although any possible absorption of sulphur from the flame 
 was also overlooked by Waldbott, it is easily seen that such an 
 error would have had less effect upon his analyses than upon the 
 titrations made by Leonard. However this may be, it is certain, 
 and not at all surprising, that borax can not be kept fused for any 
 considerable time without loss. Our best criterion of complete 
 dehydration is constancy of weight after several ignitions. Obvi- 
 ously this criterion could not be applied to borax which was 
 being fused in an open vessel, such as a crucible or dish — the only 
 vessels used in this particular instance in the past. The final 
 dehydration of borax, therefore, was carried out in the apparatus 
 already described, (p. 12). Completely dehydrated borax could 
 be kept fused in this vessel for hours without any loss of the salt 
 itself. A receptacle of this description was also well adapted to 
 the subsequent volatilization of boric acid. 
 
 The general plan pursued in the dehydration of borax may 
 now be given. The pure decahydrate, immediately after centri- 
 fugal draining, was placed in a desiccator containing caustic 
 potash. The latter served the double purpose of protecting the 
 salt from the carbon dioxide of the air and of removing part of 
 the water of crystallization. In some instances it was found that 
 the borax, consisting of a fine crystal meal, had been converted 
 into the pentahydrate by this treatment. The latter salt is better 
 suited for the subsequent expulsion of water, as it does not dissolve 
 in its water of hydration and does not intumesce to such a marked 
 degree as the deca-salt. This salt was placed in a rather capacious 
 (150 c.c.) platinum crucible with a perforated lid, through which 
 
18 THE ATOMIC WEIGHTS OF 
 
 a platinum tube was inserted, thus making the device resemble a 
 Rose crucible. It was set into a plate of asbestos board covered 
 with sheet nickel and was heated by means of a ring-burner which 
 supplied the heat mainly to the sides of the vessel. In this manner 
 the crucible and contents were kept at a gentle heat for several 
 hours, while a steady stream of dry air free from carbon dioxide 
 was passed through the apparatus. Finally the heat was increased 
 sufficiently to melt the porous, silky mass to a clear glass. The 
 residue was then again fused completely over a direct flame and 
 allowed to flow toward the edge of the crucible. The mass thus 
 collected on the side cracked sufficiently of its own accord on 
 cooling, and a convenient sample could easily be removed for 
 further treatment. The exclusion of carbon dioxide in the dehy- 
 dration and fusion of this salt is probably not essential, because 
 any absorption of this gas would be counteracted by the boric 
 acid under these conditions. Nevertheless it seemed best to 
 exclude this gas as much as possible. 
 
 This clear, flawless mass, often called "borax glass," is gen- 
 erally assumed to be anhydrous sodium tetraborate. A portion 
 of such borax glass, however, weighing 1.22243 grams, was 
 transferred to the platinum bulb already described and was kept 
 fused for about 15 minutes; it then weighed 1.22191 grams. This 
 process of re-fusing and re-weighing was repeated a few times 
 until the weight finally became constant at 1.22106 grams, show- 
 ing that the borax glass had given up fully 0.1 per cent, of volatile 
 matter. As will be seen, this loss usually amounted to about 
 0.2 per cent. At least an hour of actual fusion was required for 
 a 1-gram sample to reach constant weight. 
 
 The question naturally arose whether this decrease in weight 
 was to be attributed to the loss of water. It certainly was not 
 due to the volatilization of borax or some other compound of 
 sodium, for during the entire fusion a sodium flame could not 
 be obtained at the mouth of the bulb — a most delicate test which, 
 by actual experiment, was found to show unweighable amounts 
 of borax, unless the lower part of the bulb was heated almost to 
 a white heat and the air current accelerated considerably. 16 
 
 "This "flame test" was applied as follows: From time to time a small, pointed 
 Bunsen flame was played across the mouth of the platinum bulb. The gas was 
 filtered through cotton wool before reaching the burner, which was constructed 
 
BORON AND FLUORINE. 19 
 
 It seemed entirely possible that this final loss was due to the 
 volatilization of boric acid. It is true, Abrahall had shown that 
 up to 265° no volatilization of this component took place during 
 the expulsion of water of crystallization. This observation, how- 
 ever, gave no clue as to what might take place at or above the 
 fusion temperature. As any possible trace of boric acid could not 
 conveniently be tested for directly, under the conditions, the entire 
 question was disposed of by the following simple experiment. 
 
 A sample of "borax glass," weighing 1 gram, was fused in the 
 platinum flask in a stream of dry air until its weight was constant. 
 A small quantity of pure water was then added and the contents 
 digested at a gentle heat for many hours. The water was finally 
 evaporated very slowly and the residue again fused to constant 
 weight. The latter was 0.026 milligram in excess of the final weight 
 recorded just before the evaporation with water. In other words, 
 the two final weighings before and after the treatment with water 
 were identical, for the apparent difference found did not exceed 
 the experimental error in weighing. It should be added that the 
 second dehydration of the borax required fully as much time and 
 effort as the first. This experiment seemed to justify the conclu- 
 sion that, by the method indicated, borax can be completely 
 dehydrated without any loss of the salt itself, that no boric acid 
 is volatilized with the water, and that the final loss sustained by 
 borax glass upon fusion is due entirely to the removal of the last 
 traces of water. 
 
 In some experiments it was found that the borax had actually 
 begun to vaporize within the bulb, for a distinct film of fused 
 borax was noticeable on the end of the inner platinum tube; how- 
 ever, as the long neck of the bulb remained comparatively cool, 
 no weighable quantities of the salt had left the apparatus. This 
 water, it should be added, was not hygroscopic water, which 
 might have been taken up just before the substance was trans- 
 ferred to the bulb, but represented the last portion of the original 
 water of crystallization. Pure borax glass was found to be prac- 
 
 of narrow-bore nickeled brass tubing and was kept scrupulously clean. Such a 
 flame was also used occasionally to ignite the vapors escaping from the bulb in 
 the final treatment of the residues with methyl alcohol. Crude as it may seem, 
 this method of testing proved quite satisfactory and, as carried out, precluded 
 the possibility of contaminating the contents of the bulb. 
 
20 THE ATOMIC WEIGHTS OF 
 
 tically non-hygroscopic under ordinary conditions. Beads of this 
 substance were exposed to the air for months without losing their 
 luster, and a sample fused in a crucible and spread around the 
 sides gained only 0.006 per cent, when exposed for 3 hours; even 
 after 20 hours it had gained only 0.014 per cent. 
 
 The final dehydration of borax by fusion to constant weight 
 is of the greatest importance in the present work. It accounts 
 very largely, if not entirely, for the new value found for the 
 atomic weight of boron, for it will be shown that if the analyses 
 in the present investigation had been referred to the roughly 
 dehydrated "borax glass," the apparent atomic weight of boron 
 would have been practically 11.0 (see p. 43). The method of 
 dehydration noted above was strictly adhered to in each case and 
 constitutes one of the most important steps in the analysis. In 
 this manner pure anhydrous sodium pyroborate was probably 
 obtained for the first time without the loss of some of the salt 
 itself by volatilization. It is of interest to observe that the com- 
 pletely dehydrated product could be kept fused in the bulb for 
 hours without appreciable change in weight, even when a slow 
 current of air passed through the apparatus. It would seem that 
 anhydrous borax is one of the most stable alkali salts under these 
 conditions. 
 
 CONCERNING THE COMPLETE DEHYDRATION OF BORAX. 
 
 That borax, even in a state of fusion, should retain appreciable 
 quantities of water is noteworthy and suggestions as to the reason 
 for this peculiar behavior may properly be offered at this time. 
 Substances which part with the last portions of water only upon 
 prolonged ignition and at elevated temperatures are, of course, 
 well known, and the difficulties involved in the complete dehydra- 
 tion of certain minerals, of silica and alumina (to mention only 
 a few), are known to every analyst. Such substances as these, 
 however, are "infusible"; hence, the difficulty just referred to is 
 not entirely unexpected. 
 
 Salts, on the other hand, may, as a rule, be considered com- 
 pletely dehydrated as soon as a state of fusion has been reached. 
 Not so with borax. Here the analyst is confronted by the peculiar 
 fact that about 99.8 per cent, of the water of hydration can be 
 driven off with ease, whereas 0.2 per cent, or less is removed 
 
BORON AND FLUORINE. 21 
 
 only with great difficulty, although the salt is kept in a complete 
 state of fusion and although anhydrous borax is not particularly 
 hygroscopic. The rather artificial distinction between "water of 
 crystallization" and "water of constitution" can be of little 
 assistance in this case and amounts to begging the question. It 
 would lead to the rather extravagant conclusion that only about 
 ■j^t, or even less, of the water originally present was "water of 
 constitution." The experimental fact may be explained, it is 
 thought, in a much simpler and more reasonable manner. 
 
 Practically nothing is known concerning the state or form in 
 which water, or the elements of water, exist in hydrated salts, 
 and it matters little in this discussion. Certain it is that such 
 water of crystallization escapes as vapor when the salt is heated, 
 and that in many instances when the loss of water begins at a 
 rather low temperature this water must pass through the liquid 
 state before escaping as steam. At some stage, then, during the 
 dehydration of borax there must be minute particles or globules 
 of water momentarily in contact with sodium borate, which would 
 mean, of course, so many droplets of dissolved borax in contact 
 with the solid. Now these droplets, or this "mist" of borax solu- 
 tion, distributed through the porous mass of partly dehydrated 
 borax, must have the properties of an ordinary borax solution; 
 hydrolysis, for example, must take place as usual. It is well 
 known that there are good reasons for assuming that borax in 
 water solution is extensively hydrolyzed, that is to say, that this 
 solution is the scene of such reactions as the following : 
 
 Na 2 B 4 7 +H 2 ^2NaB0 2 +2HB0 2 
 Na 2 B 4 7 +3H 2 0^:2NaOH +4HB0 2 
 
 Such or similar reactions would naturally take place in the 
 "mist" referred to above; and it is true that hydrolysis gradually 
 decreases and finally disappears as we evaporate the solvent; in 
 the present case the metaborate or the hydroxide of sodium com- 
 bine again with the boric acid to form the original sodium borate. 
 Bearing in mind, however, that the complete combination of 
 sodium hydroxide and the very weak boric acid takes place quite 
 slowly, it is not unreasonable to suppose that in the evaporation 
 of the droplets of borax solution the expulsion of the water may 
 be comparatively rapid on account of the minute quantities 
 
22 THE ATOMIC WEIGHTS OF 
 
 involved, whereas the recombination of the base and the acid is 
 relatively slow. In other words, the re-formation of borax, under 
 such conditions, may lag behind, as it can not keep pace with the 
 evaporation of the solvent. . Thus it would seem quite conceivable 
 that the original globules of borax solution, upon evaporation, 
 would leave minute residues containing some uncombined sodium 
 metaborate (or hydroxide) and boric acid. The latter combine 
 very slowly, on account of the weak nature of the acid, and the 
 union is complete only after prolonged fusion. 
 
 According to this view the last traces of water expelled from 
 fused borax are not merely the last portions of the water of crystal- 
 lization proper, but are rather to be looked upon as water of 
 neutralization, resulting from the recombination of sodium meta- 
 borate (or hydroxide) with boric acid, both of which were pro- 
 duced by a transient hydrolysis during the earlier stages in the 
 dehydration; and this view explains why the last traces of water 
 should be removed with greater difficulty than the bulk. Hence, 
 the final loss of water in the dehydration of borax may, in all 
 probability, be due to the completion of such reactions as the 
 following : 
 
 2 NaB0 2 +2HB0 2 = Na s B 4 07+H 2 
 2 NaOH +4HB0 2 = Na 2 B 4 0,-|-3H 2 
 
 The preceding remarks seem to justify the general conclusion 
 that many other salts which are extensively hydrolyzed in water 
 solution should also show an anomalous behavior when deprived 
 of the last trace of their "water of crystallization." Such, indeed, 
 appears to be the case. Every chemist is familiar with the diffi- 
 culties encountered in drying sodium carbonate without decom- 
 posing some of the carbonate itself. Undoubtedly the anhydrous 
 substance itself begins to dissociate in this case and thereby suffers 
 a loss of carbon dioxide; moisture, however, seems to aggravate 
 this loss and to cause some carbon dioxide to be given off at a 
 lower temperature. Again, in the work upon the atomic weight 
 of columbium, 18 it was found quite difficult to dehydrate sodium 
 metacolumbate (Na 2 Cb 2 06.7H 2 0) completely. This salt, which 
 is also strongly hydrolyzed by water, had to be ignited for 10 
 hours or more before constant weight was reached. As this salt is 
 
 — ... - ■ v 
 
 '•J. Am. Chem. Soc. 37, 1793 (1915). 
 
BORON AND FLUORINE. 23 
 
 infusible, any columbic acid (a very weak acid) and sodium 
 hydroxide produced by a transient hydrolysis might find it par- 
 ticularly difficult to recombine and form the original columbate 
 and water. Hence, the prolonged ignition. 
 
 In the special case of borax the last portion of water may also 
 be assumed to be held in a somewhat different manner, which 
 would not require the supposition of any hydrolytic action. 
 Borax, in a state of fusion, is often said to dissociate into sodium 
 metaborate and boric anhydride: 
 
 Na 2 B 4 7 ^:2NaB0 2 +B 2 O s 
 
 This dissociation may conceivably commence before the water 
 has been driven out completely. The hygroscopic boric anhydride 
 would naturally combine with any water still present and thus 
 retard the final dehydration. 
 
 This question of the complete dehydration of borax has been 
 discussed at some length here because previous investigators have 
 made extensive use of fused borax in atomic weight work without 
 fully realizing the difficulties presented by the dehydration of 
 this salt. The question, therefore, is all-important. The results 
 obtained in the present investigation, as previously indicated, 
 hinge upon this very point. 
 
 BALANCE AND WEIGHING; CONSTANTS USED. 
 
 All weighings were made on a Troemner balance No. 10, which 
 was kept in a double case and was easily sensitive to 0.02 mg. 
 The weights were carefully calibrated by the substitution method. 
 
 Weighings were made by comparing the platinum bulb con- 
 taining the substance, by substitution, with a counterpoise con- 
 sisting of a stoppered platinum bottle which had approximately 
 the same weight and surface as the former. Weights from a 
 second set served as a tare on the other balance pan. The counter- 
 poise was also ignited (protected from the free flame, of course) 
 before each weighing; both objects, having nearly the same initial 
 temperature, were then allowed to cool, side by side, in a large 
 desiccator placed near the balance case for at least 4 to 5 hours. 
 The stoppers were inserted just before weighing was begun. When 
 the bulb had reached constant weight, which usually required 
 about an hour, it was substituted by the counterpoise, which had 
 
24 THE ATOMIC WEIGHTS OF 
 
 been exposed to the same conditions for the same length of time. 
 The difference between the objects was thus determined. 
 
 The densities used in the reductions to vacuum for the various 
 substances involved are given below. They refer to the fused salts. 
 
 Density. Density. 
 
 Na*B 4 7 2.357 Na,CO, 2.533 19 
 
 NaCl 2.161 » NaF 2.804 
 
 NaaSO, 2.698 18 Brass 8.40 
 
 NaNO, 2.255 
 
 The density of sodium borate (which had been fused in a 
 double platinum crucible for several hours) was determined in 
 toluene. It was found that 3.8607 grams of the salt displaced 
 1.4103 grams of toluene at 25°. The density of the toluene at the 
 same temperature was 0.8610, referred to water at 4°. From 
 these data 2.357 20 is deduced as the density of fused borax. 
 
 The density of fused sodium nitrate was determined in a 
 similar way. It was found that 8.2077 grams of this salt displaced 
 3.1344 grams of toluene at 25°. This yields 2.255 for the density 
 of fused sodium nitrate. 
 
 For fused sodium fluoride, 5.1199 grams displaced 1.5739 
 grams of toluene at 25°; 6.6544 grams displaced 2.0414 grams of 
 toluene. Hence, the density of the salt was found to be 2.801 
 and 2.807, respectively. The average, 2.804, was taken as the 
 density of fused sodium fluoride. The weights given in these 
 determinations refer to the vacuum standard. 
 
 The antecedent atomic weights used in calculating the atomic 
 weights of boron and fluorine are the following: 
 
 O =16.000 S =32.069 
 
 Na =22.997 N = 14.010 
 
 CI =35.457 C= 12.005 2l 
 
 17 Baxter and Wallace, J. Am. Chem. Soc. 38, 261 (1916). 
 
 " Richards and Hoover, Ibid. 37, 111 (1915). 
 
 » Ibid., p. 105. 
 
 20 For present purposes this agrees well with the value 2.367 found by Filhol (Ann. 
 chim. phys. (3) 21, 415 (1847)). Ramsay and Aston (J. Chem. Soc. 63, 210 
 (1893)), found 2.29; this seems to indicate that the sodium borate was not 
 entirely free from water. 
 
 sl This value has been questioned by E. Moles (J. chim. phys. IS, 51 (1917)). It is 
 the value obtained by Richards and Hoover, J. Am. Chem. Soc. 37, 106 (1915). 
 As other determinations on record also point to a somewhat higher value than 
 12.00, it seemed safe enough to use the value given above. 
 
BORON AND FLUORINE. 25 
 
 The third decimals in the above values are uncertain. How- 
 ever, as the atomic weights of boron and fluorine were to be 
 calculated to three decimals, and since these two values are 
 roughly of the order of magnitude of the antecedents, it seemed 
 reasonable to assume the latter also to the third decimals. The 
 above fundamental values were decided upon before the final 
 calculations were made. Whether another set of values would 
 have led to a more concordant series of results for boron is of 
 little consequence in the present case. If the methods applied 
 in this investigation were to furnish a severe check upon the 
 fundamental atomic weights used, a much larger number of 
 individual determinations would have been necessary (see table 1, 
 p. 42). For the determination of the atomic weights of boron 
 and fluorine, however, the number of experiments seems adequate. 
 
CHAPTER II. 
 
 A. THE ATOMIC WEIGHT OF BORON. 
 PRELIMINARY EXPERIMENTS. 
 
 In the preliminary experiments one sample of commercial, 
 thrice recrystallized borax was converted into sodium fluoride by 
 a method to be outlined in the following paragraphs, while 
 another sample was changed to sodium chloride by an analogous 
 method. These conversions were made in a platinum crucible of 
 35 c.c. capacity and showed that the method, carried out in this 
 manner, will yield excellent results for ordinary analytical pur- 
 poses. However, in these instances, ordinary "borax glass" was 
 used, borax which had not been fused to constant weight. There 
 were, of course, other quite obvious reasons why the final deter- 
 minations could not be conducted in a crucible — such as the 
 volatility of the halides of sodium (particularly that of the 
 fluoride) and the impracticability of properly applying the "flame 
 test" * for boric acid. 
 
 Three conversions of borax were then effected in the platinum 
 bulb described in Chapter I. In these analyses a special prepara- 
 tion of borax was used (see p. 8); the samples thus analyzed, 
 however, were not considered to be of the degree of purity desired, 
 as they had been removed before the borax was fused and re- 
 crystallized for the final work. These experiments were merely 
 intended to thoroughly test the apparatus and to give practice in 
 the various manipulations involved. It may be added, however, 
 that these three preliminary experiments (in which the borax was 
 dehydrated completely) also supported the low value for boron 
 finally derived. Nevertheless the results, for the reasons just 
 stated, have not been included in table 1. The final experiments 
 to be recorded in the following pages, therefore, begin with 
 experiment iv, i.e., the first experiment in which the final and 
 best preparation of borax was used. 
 
 In the following description of the individual analyses the 
 number of the experiment refers to the corresponding number in 
 
 1 See note on page 18. 
 26 
 
THE ATOMIC WEIGHTS OF BORON AND FLUORINE. 27 
 
 table 1, which gives the results in the order in which they were 
 obtained; none have been omitted. In this account, however, 
 the experiments, involving identical operations, have been 
 described collectively. 
 
 In some instances the weight of the original "borax glass" 
 was also determined and may be found in the table. Unfortun- 
 ately, this preliminary weight was not taken in every case, for 
 the exact amount of the residual water, at first, seemed of little 
 importance, the chief object being to remove the water completely 
 and to make truly anhydrous borax the initial substance. Later 
 it was realized that very important conclusions were to be drawn 
 from the quantity of such residual water; its significance is evident 
 from table 2 and will be discussed in due time. 
 
 FINAL DETERMINATIONS. 
 
 Experiment IV: The Ratios Between Sodium Tetraborate, Sodium Chloride, 
 
 and Sodium Sulphate. 
 
 The distillation of anhydrous borax with hydrochloric acid 
 and methyl alcohol had been utilized by Ramsay and Aston in 
 deriving the ratio of sodium borate to sodium chloride. The 
 results obtained by them will be discussed in Chapter III. In 
 the present case it seemed well to determine the ratio Na 2 B 4 7 : 
 2NaCl by a method strictly analogous to that leading to the ratio 
 Na 2 B.i07 : 2NaF, for in addition to the direct ratios the relation 
 NaCl : NaF, by cross-reference, was to be used. As previously 
 indicated in Chapter I, the conversion of borax into sodium 
 fluoride was most easily effected indirectly through the formate, 
 a method which will be described more fully in the next experi- 
 ment. Hence, the conversion of borax into sodium chloride also 
 was to include the use of formic acid. 
 
 As the general procedure in the final dehydration of borax 
 was the same in all determinations, it will be outlined before the 
 experiment proper is described. 
 
 The empty bulb (protected from the direct flame) was strongly 
 ignited for at least 30 minutes while a current of dry air passed 
 through the apparatus. It was weighed and ignited again until 
 two consecutive weighings did not differ more than 0.02 milligram, 
 approximately. With the empty bulb such an agreement could 
 usually be obtained after two ignitions. The jacketing of the 
 3 
 
28 THE ATOMIC WEIGHTS OF 
 
 bulb during such an ignition is, of course, highly important. 
 The term "constant" weight, as used in the sequel, should be 
 taken to imply a variation of not more than 0.03 milligram, unless 
 otherwise stated. A much closer agreement was often observed, 
 but in view of the experimental error in weighing such instances 
 must have been largely accidental. 
 
 A sample of "borax glass" 2 was now transferred to the bulb 
 and kept fused in a current of dry air, free from carbon dioxide, 
 until its weight was constant. Needless to say, the inner platinum 
 tube, after the introduction of borax, was not again removed 
 until the entire experiment had been completed. It was found 
 that one gram of vitreous borax must be kept fused in this manner 
 for about an hour before it is worth while to take its weight. It 
 was then re-fused for a period of from 20 to 40 minutes, depending 
 on the size of the sample. In experiment xi, for instance, the 
 vitreous borax (after the preliminary weighing) was kept fused 
 for fully 90 minutes before reweighing. It still contained 0.1 
 milligram of water; for, after another fusion lasting 40 minutes, 
 the weight decreased by this amount. Another fusion, again of 
 40 minutes' duration, produced no further change in weight. 
 The flame of a large grid-burner served as a source of heat; the 
 time given refers to actual fusion. It should be added that the 
 final weight of the fused borax could in every case be fixed with 
 great precision. Numerous weighings and refusions showed that 
 the weight remained quite constant after the water had once 
 been expelled. 
 
 The anhydrous borax thus obtained was digested, at a gentle 
 heat and for many hours, with a few cubic centimeters of purest 
 water. The quantity of water, as a rule, was sufficient to com- 
 pletely dissolve the borax at 70°. Solution could be facilitated 
 by gentle agitation, as the bulb at this stage of the analysis was 
 not connected with the combustion tube. A slight excess of 
 formic acid (see p. 11) was then added and the mixture very 
 slowly evaporated to dryness in a current of air. As the contents 
 of the bulb were concealed from view and the progress of the 
 reaction could not be directly observed, ample time had to be 
 allowed. The dry residue was next digested with a few cubic 
 
 ' The preliminary dehydration of borax has been described in Chapter I. 
 
BORON AND FLUORINE. 29 
 
 centimeters of methyl alcohol (see p. 9) and the methyl borate 
 gradually expelled in a current of air. Air proved entirely satis- 
 factory for this purpose and showed no tendency to form explosive 
 mixtures. At first the air-bath (i.e., the outer platinum crucible) 
 was kept at a temperature of about 50°, which was raised very 
 slowly. Finally, when no more alcoholic vapors were given off, 
 the temperature was gradually increased to about 110°, or even 
 a little higher. 
 
 After cooling, the evaporation was repeated several times with 
 fresh portions of methyl alcohol. In each evaporation 5 to 8 c.c. 
 of the alcohol were used and a drop of formic acid was added to 
 the last portions. The best indication as to the progress of this 
 volatilization of the boric acid could be obtained by igniting the 
 vapors, from time to time, at the mouth of the bulb (see note 
 on p. 18). The flame was easily extinguished again by interrupt- 
 ing the air current for a moment. As long as any considerable 
 amount of methyl borate was present in the vapors, the flame 
 showed the familiar green coloration. It is evident that the 
 delicacy of this color reaction depends not only on the amount of 
 boric acid present, but also on the relative amount of alcohol 
 used. However, it was found that the presence of about 0.1 per 
 cent, of boric acid could be detected in sodium formate by this 
 flame test when only small quantities (2 to 3 c.c.) of methyl 
 alcohol were used. 
 
 When the flame test no longer indicated the presence of boric 
 acid, the contents of the bulb were digested with a few cubic 
 centimeters of water and again evaporated to dryness. The 
 treatment with alcohol was then repeated. The vapors, when 
 ignited, again showed a very faint green at first. Two more 
 evaporations with 2 c.c. of water, followed by treatment with 
 several portions of about 3 c.c. of methyl alcohol, were carried 
 out. Five small portions of alcohol were used in the final evapo- 
 rations. The total quantity of methyl alcohol used in this 
 determination was not noted; however, it did not exceed 40 grams. 
 In some of the later experiments the exact total was recorded. 
 
 That the residue (sodium formate) after such treatment con- 
 tained no perceptible traces of boric acid was proved as follows 
 (see also p. 3) : Another sample of borax had been converted 
 into sodium formate by the method just outlined. The residue 
 
30 THE ATOMIC WEIGHTS OP 
 
 gave no test for boric acid with turmeric paper. A second portion 
 of sodium formate (containing approximately 0.02 per cent, of 
 boric acid) did respond to this test. After two evaporations with 
 methyl alcohol, however, the turmeric test gave a negative result. 
 As formic acid seemed to interfere with the turmeric reaction, 
 the residues were changed to sodium chloride by evaporation 
 with hydrochloric acid before testing for boric acid. Slight traces 
 of the latter were probably lost in this way; if so, the value of the 
 test was not greatly affected thereby. 
 
 To return to the description of the main experiment. Before 
 the final evaporation with the alcohol the outside of the bulb 
 was rinsed with a little methyl alcohol and water to remove 
 possible traces of boric acid resulting from a slight decomposition 
 of the methyl ester. The residual sodium formate, which un- 
 doubtedly was free from boric acid, was dissolved in a small 
 quantity of water mixed with an excess of pure hydrochloric 
 acid and evaporated to dryness. The formate was thus completely 
 transposed to the chloride. In order to make doubly sure, how- 
 ever, the sodium chloride obtained was gradually heated to about 
 200° and, when cool, again moistened with a few drops of hydro- 
 chloric acid and evaporated. It was then dried very slowly in a 
 current of air and finally fused. During the actual fusion the 
 air current was all but stopped and gradually increased again 
 during the slow cooling. The salt was then weighed. A second 
 fusion, conducted as the first, produced no appreciable change in 
 weight. 
 
 The hydrochloric acid used in this transposition was obtained 
 by allowing pure concentrated sulphuric acid to drop into strong 
 hydrochloric acid (method of Hare) free from arsenic and other 
 appreciable impurities. The hydrogen chloride gas thus released 
 was washed with concentrated hydrochloric acid and allowed to 
 fill a closed vessel containing a quartz dish with pure water. A 
 solution of hydrogen chloride was thus obtained by direct contact 
 of its components, without the use of a delivery tube. The 
 apparatus was constructed entirely of glass and the quartz dish 
 had previously been subjected to a prolonged action of hydro- 
 chloric acid. 
 
 After the sodium chloride had come to constant weight it 
 was evaporated with a moderate excess of pure sulphuric acid. 
 
BORON AND FLUORINE. 31 
 
 In order to insure a complete interaction the residue, after the 
 expulsion of the hydrogen chloride, was dissolved in a little water 
 and concentrated by evaporation. Finally the temperature was 
 gradually raised to expel the excess of the acid. The last traces 
 of sulphuric acid were removed by keeping the sodium sulphate 
 in a state of fusion for some time. The evaporations were acceler- 
 ated by a current of air. When the sodium sulphate had been 
 kept fused for about 30 minutes the bulb was lowered so as to 
 bring the lower (curved) end of the inner tube within the neck 
 of the bulb. This part of the inner tube could thus be raised to a 
 much higher temperature and the complete removal of the acid 
 and decomposition of possible traces of bisulphate be made certain. 
 These operations were then repeated. It was found that after 
 the free sulphuric acid had once been expelled in this manner, 
 the weight of the normal salt remained remarkably constant, 
 even after prolonged fusion in the jacketed bulb, with a current 
 of air passing through the latter. 
 
 After the completion of the experiment the sodium sulphate 
 was dissolved in a little water. The solution was neutral to 
 methyl orange; the addition of a trace of dilute hydrochloric acid 
 produced a pink tint. In converting the sodium chloride into 
 the sulphate an excess of sulphuric acid was not to be avoided 
 and the complete removal of this excess proved rather laborious. 
 Nevertheless the results and the test show that the method was 
 entirely reliable. 
 
 The sulphuric acid used in this experiment, and in those to 
 follow, was prepared by distilling an excellent "C. P." grade from 
 a long-necked Jena retort. Only the middle portion of the dis- 
 tillate was collected and redistilled as before. The acid was 
 diluted and used as indicated. 
 
 Experiments V, IX, X, XI : The Ratios Between Sodium Tetraborate, Sodium 
 Fluoride, and Sodium Sulphate. 
 
 The method finally adopted to convert borax into sodium 
 fluoride has been indicated in Chapter I. That the direct con- 
 version of the borate into the corresponding fluoride by means 
 of hydrofluoric acid and methyl alcohol was most unpromising 
 has also been emphasized. There was still another method which 
 seemed to be entitled to a fair trial. This consisted in igniting 
 a mixture of powdered borax and ammonium fluoride, whereby 
 
32 THE ATOMIC WEIGHTS OP 
 
 volatile ammonium borofluoride (NH4BF4) and sodium fluoride 
 are produced. Reischle 3 recommended this procedure for the in- 
 direct determination of boric acid in borax, the only difference 
 being that he prefers to finish with sulphuric acid and to weigh 
 the resulting sodium sulphate. 
 
 The determination, according to Reischle, is carried out as 
 follows: Powdered borax (the decahydrate) is mixed with six 
 times its weight of resublimed ammonium fluoride and gently 
 heated. The major portion of the boron is thus expelled as 
 ammonium borofluoride. After cooling, the residue is evaporated 
 with sulphuric acid, which, as the author states, removes the last 
 traces of boron fluoride and ammonium borofluoride. According 
 to Reischle this method is superior to all others, including Gooch's 
 distillation method. By the latter method Reischle found from 
 90.8 to 101.0 per cent, of the boric acid present. Without dis- 
 cussing the pros and cons, it seems entirely proper to say that these 
 poor results are not entirely chargeable to the Gooch method. 
 i4| The ammonium fluoride method has also been adopted, and 
 found satisfactory, by Waldbott 4 in the analysis of borax. The 
 method may be of great value for ordinary analytical purposes; 
 for the derivation of a ratio it was soon discovered to be of little 
 promise. 
 
 In the present instance the initial substance, the substance 
 which had to be weighed, was fused borax. In order to produce 
 a thorough mixture with the reagent the anhydrous borax was 
 dissolved in water and evaporated with an excess of ammonium 
 fluoride, which was added either in solid form to the concentrated 
 borax solution or in the form of a solution obtained by combining 
 pure hydrofluoric acid with redistilled ammonia. It was found 
 that the resulting mixture is evaporated to dryness with great 
 difficulty, for even when the apparatus was heated in an oven the 
 formation of crusts retarded the evaporation to an annoying degree. 
 Several such treatments would have been required to make sure of 
 the complete removal of the boron with the production of pure 
 sodium fluoride, the weight of which was to be determined before 
 it was converted into the sulphate. In the final ignition, further- 
 more, appreciable quantities of sodium fluoride were volatilized, a 
 loss which is probably aggravated by the repeated sublimation 
 
 1 Z. anorg. Chem. 4, 111-116 (1893). 'J. Am. Chem. Soc, 16, 410-418 (1894). 
 
BORON AND FLUORINE. 33 
 
 of rather large quantities of ammonium salts. The method 
 therefore was not suited to an atomic weight determination. 
 
 The principle of the method finally adopted for the conversion 
 of sodium borate into sodium fluoride has been used in experiment 
 iv, where it was applied in the corresponding conversion, involving 
 sodium chloride as an end-product. The method depends on the 
 facts (1) that formic acid reacts "normally" with a solution of 
 borax, that is to say, it liberates boric acid with the production 
 of sodium formate without any disturbing secondary reactions; 
 (2) that sodium formate is easily transposed to a halide by 
 evaporation with a haloid acid. 
 
 It may not be amiss to add a few more words as to the appli- 
 cability of formic acid in this reaction. In the mere expulsion of 
 boric acid by the volatilization method, irrespective of the com- 
 position of the residual sodium salt, acids other than formic may, 
 of course, be used to advantage. In the present case, however, 
 the remaining sodium salt was to be the fluoride, and here formic 
 acid served admirably, if only as a "go-between." In view of the 
 fact that the direct use of hydrofluoric acid presented many 
 difficulties (see p. 2) it would perhaps be difficult to find another 
 acid more suitable than formic as an auxiliary reagent in the con- 
 version of borax into sodium fluoride. 
 
 The chief advantages of formic acid for this purpose seem to 
 be the following: The sodium salt of this acid is most easily 
 dehydrated, and therefore, in the present instance, the only water 
 present in the dry residue (consisting of sodium formate and boric 
 acid) is in combination with the latter, probably forming meta- 
 boric acid. A minimum of free or loosely combined water, of 
 course, is favorable to the formation of the boric ester when the 
 mass is treated with methyl alcohol. It has already been men- 
 tioned that acetic acid, for example, would not answer as well 
 because its sodium salt is dehydrated with difficulty and at a 
 much higher temperature. In the second place, sodium formate 
 is exceedingly soluble in water and also soluble in methyl alcohol. 
 Consequently, only small quantities of water need be used when 
 the residue is dissolved and evaporated in order to expose fresh 
 surfaces before another treatment with the alcohol. The solu- 
 bility of the formate in the alcohol also facilitates the interaction 
 of the substances in question. 
 
34 THE ATOMIC WEIGHTS OF 
 
 Possibly the only drawback involved in the use of formic 
 acid, at this stage of the reaction, is its volatility — a property, 
 however, which it shares with a number of other available acids 
 and which is of the greatest importance in the final transposition 
 of the formate to the fluoride. The volatility of formic acid, it 
 is true, favors a slight reversion of the original reaction between 
 this acid and borax; that is to say, sodium formate and boric acid, 
 in very concentrated solution or in the dry state, tend to react 
 again (when heated) with the re-formation of some sodium borate. 
 The extent of this reversion, however, is not alarming under the 
 conditions and is easily counteracted by the addition of a drop 
 or two of strong formic acid to the alcohol in the subsequent 
 evaporations, particularly to the last portions of alcohol used. 
 This mode of procedure insures the complete decomposition of 
 the last traces of borax and was adhered to throughout the work. 
 
 The complete removal of the boric acid was carried out exactly 
 as indicated in the description of experiment iv and need not be 
 repeated. It may be of interest to indicate the quantities of 
 methyl alcohol used in some of these experiments. In experiment 
 ix 82 grams of methyl alcohol were used. This represents the 
 total and includes the final portions which were practically super- 
 fluous. The total quantities of methyl alcohol used in experiments 
 x and xi were 61 and 85 grams, respectively. Considering the 
 quantities of boric acid that had to be expelled these amounts 
 of methyl alcohol actually used seem rather moderate. 
 
 The sodium formate was now ready to be converted into the 
 fluoride. It was therefore dissolved in a small quantity of water, 
 an excess of pure hydrofluoric acid (see p. 11) added, and the 
 mixture slowly evaporated to dryness in a current of air. The 
 residue thus obtained was finally heated to about 200°, allowed 
 to cool, and again moistened with a little strong hydrofluoric 
 acid. After the expulsion of the latter it was quite safe to assume 
 that the residue consisted of pure sodium fluoride. In the pre- 
 liminary experiments it was found that, for most purposes, a 
 single evaporation of the dry, porous formate with an excess of 
 strong hydrofluoric acid is quite sufficient, for subsequent treat- 
 ments with the haloid acid produced no appreciable change in 
 weight. 
 
 To be doubly sure of the complete conversion of the formate, 
 
BORON AND FLUORINE. 35 
 
 proceed as follows: After the first evaporation with hydrofluoric 
 acid ignite the residue gently; any possible residual particles of 
 sodium formate are hereby decomposed and changed to the 
 carbonate, which is then easily decomposed by a second evapora- 
 tion with hydrofluoric acid. A decided excess of hydrofluoric 
 acid is desirable in this transposition in order to produce the acid 
 sodium salt, which is much more soluble than the normal salt. 
 The acid salt crystallizes without water and is easily dried. 
 Upon further ignition hydrogen fluoride is expelled, which, on 
 account of its eagerness to combine with water, carries with it 
 the last traces of the latter. The drying of sodium fluoride 
 presents no particular difficulties, although it became necessary 
 to fuse the salt before the final weighing, for the normal salt 
 produced by the decomposition of the acid salt is a very porous 
 mass which was found to take up traces of moisture. 
 
 In the fusion of sodium fluoride several precautions had to be 
 observed because this salt, in spite of its high melting-point 
 (cir. 980°), is rather volatile and its fusion in a crucible, even for 
 ordinary quantitative purposes, must be carried out with care. 5 
 Even in the present case, where the salt was contained in a long- 
 necked bulb, an appreciable loss of sodium was observed when 
 the salt was fused in a current of air. During the fusion, there- 
 fore, the air current was interrupted. When the mass had cooled 
 somewhat, dry air was again allowed to pass through the bulb 
 while the upper part of the apparatus was ignited. The entire 
 process was then repeated. In this manner it was possible to 
 dry and fuse the salt without loss and to re-fuse it without appre- 
 ciable change in weight. The rather close concordance in the 
 values obtained for the atomic weight of fluorine (table 3) is 
 probably due, in no small measure, to the precautions observed 
 in the fusion of the sodium fluoride. 
 
 The fused sodium fluoride was changed to the sulphate in a 
 manner quite similar to the corresponding treatment of sodium 
 chloride in experiment iv, the only difference being that in the 
 present case the reaction proceeded more slowly. Owing to the 
 fused condition of the sodium fluoride, traces of the latter may 
 escape transposition even if the sulphuric acid be in excess and 
 
 6 Some quantitative experiments on the volatility of sodium fluoride, when heated 
 in a crucible, are due to Waldbott, J. Am. Chem. Soc, 16, 418 (1894). 
 
36 THE ATOMIC WEIGHTS OF 
 
 even after the expulsion of this excess. It was imperative, there- 
 fore, to allow ample time for this interaction; after the first 
 expulsion of the bulk of the hydrogen fluoride it was best to 
 digest the residue with dilute sulphuric acid for some time before 
 the final evaporation. This mode of procedure is particularly 
 advisable when larger quantities of fused sodium fluoride are to be 
 transposed. Finally the sodium sulphate was fused and weighed 
 as described before. In the evaporation of sodium fluoride with 
 sulphuric acid in experiment ix an accident occurred and the 
 weight of the sodium sulphate, therefore, could not be recorded. 
 The solution of the residual sodium sulphate in water was 
 neutral in reaction. In two experiments the solution was acidified 
 with hydrochloric acid and tested with hydrogen sulphide; no 
 precipitation of platinum sulphide was observed. 
 
 Experiment VI: The Ratio of Sodium Tetraborate to Sodium Sulphate. 
 
 In this experiment anhydrous borax was changed directly to 
 the sulphate without the intervention of either formic or a haloid 
 acid. The general procedure calls for little additional description. 
 The "borax glass" was fused to constant weight. After solution 
 in water a moderate excess of pure dilute sulphuric acid was 
 added, the mixture digested for some time, and gradually con- 
 centrated at a gentle heat in a current of air until, finally, a tem- 
 perature of about 140° had been reached; this temperature was 
 maintained for 2 hours. The expulsion of boric acid proceeds 
 quite readily in the presence of sulphuric acid. Even after the 
 first evaporation with water following the first distillations with 
 methyl alcohol, the green flame of the boric ester could no longer 
 be obtained, which indicates that the residual quantity of any 
 boric acid must have been quite small. Nevertheless, two more 
 treatments with water, alternating with repeated evaporations 
 with alcohol, were resorted to. The reasons for the ease with 
 which boric acid is thus expelled in the presence of sulphuric 
 acid is to be sought, no doubt, in the peculiar properties of the 
 latter acid; its dehydrating action is favorable to the formation of 
 the boric ester and its "strength" and high boiling-point prevent 
 even the slightest reversion of the reaction under the conditions. 
 
 The result obtained from this experiment is of interest. In 
 the first place, the presence of silica in the borax would have 
 made itself felt in this analysis. It is a common impurity in 
 
BORON AND FLUORINE. 37 
 
 commercial borax, in which it probably exists as a boro-silicate. 
 If an appreciable quantity of it had been present in the borax 
 used a the analyses involving the use of hydrofluoric acid would 
 have yielded a low weight for the end-product and, hence, a high 
 atomic weight for boron; whereas the analyses not involving the 
 use of hydrofluoric acid would have led to an end-product too 
 high in weight and, hence, to a low atomic weight for boron. A 
 glance at table 1 (p. 42) will show that both categories of analysis 
 gave fairly concordant values. The difference between the results 
 obtained in the present experiment (vi) and experiment xi, for 
 example, is practically negligible, although it is only the latter 
 determination which involves the use of hydrofluoric acid. 
 
 Furthermore, it may be gathered from this experiment (vi) 
 that no appreciable quantities of sodium fluoride were lost in the 
 other experiments, when this salt was fused, for the sulphate 
 obtained directly leads to a result in fair agreement with those 
 in which the sulphate had been obtained by the transposition of 
 the fused fluoride. In general, therefore, the result of experiment 
 vi seems to form a rather severe check upon the analyses which 
 included the formate and fluoride of sodium as intermediate 
 products. 
 
 Experiment VII: The Ratio op Sodium Tetraborate to Sodium Nitrate. 
 
 The procedure followed in this experiment was analogous to 
 the scheme outlined in the other determinations. The borax, 
 fused to constant weight, was dissolved in a little water and the 
 boric acid set free by the addition of an excess of pure nitric acid. 
 The mixture was evaporated to dryness and subjected to a number 
 of distillations with methyl alcohol until free from boric acid. 
 The residue was redissolved in water, evaporated to dryness, and 
 again treated with several portions of methyl alcohol. This series 
 of operations was repeated once more; occasionally a drop of 
 nitric acid was added to the alcohol. A grand total of 56 grams 
 of methyl alcohol was used in this experiment. 
 
 After the evaporation of the last portion of alcohol the residue, 
 
 * In the present instance it is only from the sodium carbonate used that any silica 
 might have been introduced into the borax. However, the method used for the 
 purification of the sodium carbonate has been found to remove 6ilica quite 
 effectively. 
 
38 THE ATOMIC WEIGHTS OF 
 
 consisting of sodium nitrate, was dried in a current of air (the 
 temperature finally reached was about 200°) and weighed. This 
 gave the weight of the unfused salt, after which the sodium 
 nitrate was dissolved in a little water containing a few drops of 
 nitric acid, again evaporated and dried, and finally fused for a 
 moment at a temperature only slightly above the fusion point 
 of this salt (cir. 315°). The weight of the product (the fused salt) 
 was determined again and found to be 0.1 mg. lower than the 
 first weight, that of the unfused salt. The mean of these two 
 weighings was assumed to be the true weight and was used in 
 the computation. The difference (0.1 mg.) between these weigh- 
 ings is considerably greater than permissible in the range of 
 "constant" weight for the other salts. However, the difference 
 did not seem excessive in the case of sodium nitrate, which can 
 not be kept fused for any length of time without decomposition. 
 The weight of the unfused salt, resulting after the evaporation of 
 the alcohol, was probably somewhat too high on account of a 
 trace of moisture; the weight of the salt fused after evaporation 
 with dilute nitric acid was a trifle too low, presumably, as a result 
 of a slight decomposition. Hence, "splitting the difference" 
 seemed permissible in this case. It may be added that the water 
 solution of the final product was neutral in reaction. 
 
 The nitric acid used in this experiment was prepared as 
 follows: A good grade of sodium nitrate was recrystallized a 
 few times until it was free from chlorides. This salt was then 
 distilled with pure, concentrated sulphuric acid from a long- 
 necked retort; the first third of the distillate being rejected. 
 The middle fraction was redistilled with pure barium nitrate and 
 again rectified. Finally the acid was redistilled, just before use, 
 from a quartz distilling bulb. 
 
 Experiment VIII: The Ratio of Sodium Tetraborate to Sodium Carbonate. 
 
 This interesting ratio may be arrived at in various ways. 
 Before giving the method finally adopted we may indicate at 
 least two other attempts which seemed to bid fair to lead to the 
 ratio desired. 
 
 First it would have been possible to expel the boric acid in 
 the presence of formic acid and to change the resulting formate, 
 by strong ignition, to the carbonate, which is the final product 
 
BORON AND FLUORINE. 39 
 
 of this decomposition by heat. Of course there were some mis- 
 givings as to the propriety (in atomic weight work) of the last 
 step in this method; nevertheless it was given a trial. It was 
 possible to prevent the ignition of the hydrogen and carbon 
 monoxide produced in this decomposition and to obtain colorless 
 sodium carbonate as an end-product. However, at the same time 
 it was noticed that this decomposition was accompanied invari- 
 ably by a slight mechanical loss, even when the reaction was 
 conducted very slowly and with the greatest care, in the long- 
 necked platinum bulb and in an atmosphere of carbon dioxide. 
 At certain stages in this decomposition, evidently a very fine 
 dust or "mist" of the sodium salt itself was formed, traces of 
 which escaped from the bulb and thus caused the loss referred to. 
 Such phenomena are not particularly surprising in reactions of 
 this sort — that is to say, in decompositions by heat which involve 
 a rather violent rearrangement within the molecule. Similar 
 difficulties have been met with in the ignition of other substances, 
 such as the chlorates. It is therefore evident that the quanti- 
 tative conversion of sodium formate into the carbonate by 
 ignition was practically out of the question, unless perhaps the 
 entire apparatus had been subjected to a radical modification. 
 
 Another possibility which suggested itself was the following: 
 The saponification of a suitable ester of carbonic acid, say methyl 
 carbonate, by borax, with the simultaneous production of sodium 
 carbonate and the methyl ester of boric acid. Methyl carbonate 
 was prepared by allowing an ethereal solution of methyl iodide 
 to react, at a gentle heat, with dry silver carbonate in a flask 
 provided with a reflux condenser. The first distillate was frac- 
 tioned a few times, and the fraction finally collected boiled at 
 90.5°. The yield was poor, but the quantity obtained (about 5 
 grams) was sufficient for a trial. A sample of fused borax was 
 then dissolved in water, evaporated to dryness, and evaporated 
 a number of times with a solution of methyl carbonate in methyl 
 alcohol, while a current of ah, free from carbon dioxide, was 
 passed through the apparatus. The residue was finally tested for 
 combined carbonic acid, but only a bare trace could be detected. 
 The original borax was entirely free from carbonates; the trace 
 just mentioned had probably been introduced by a little carbon 
 dioxide in the water used in the first evaporation. The methyl 
 
40 THE ATOMIC WEIGHTS OF 
 
 carbonate distilled off unchanged and it was quite evident that 
 no reaction had taken place between this ester and the borax. 
 The method finally adopted is based on the following reaction : 
 
 Na 2 B 4 7 +CO,+6H 2 ^± NaaC0 3 +4H 3 B0 3 
 
 If a water solution of borax be treated with carbon dioxide an 
 equilibrium will be reached corresponding to the above relation. 
 It should be possible, therefore, to so influence this reaction as to 
 lead to a complete conversion of borax into carbonate by a con- 
 tinued removal of the boric acid; which, of course, may be done 
 by means of methyl alcohol if the amount of water present be 
 relatively small. In fact, according to L. C. Jones, 7 the reaction 
 can easily be influenced in this sense. This investigator did not 
 contemplate its application for quantitative purposes and no 
 quantitative data based thereon have been discovered. However, 
 the reaction proceeded more readily than anticipated and its 
 pronounced reversibility caused no particular difficulties. 
 
 The mode of conducting the experiment was as follows: After 
 the complete dehydration and weighing of the borax it was 
 dissolved in a little water and evaporated to dryness in a stream 
 of carbon dioxide. The residue, which probably contained a 
 considerable portion of the sodium as carbonate, was evaporated 
 many times with small portions of methyl alcohol, exactly as 
 indicated in the other experiments, the only difference being that 
 a steady stream of carbon dioxide, instead of air, was allowed to 
 pass through the apparatus. When the green flame of the boric 
 ester could no longer be detected at the mouth of the bulb the 
 residue was dissolved in water and the distillations with small 
 portions of the alcohol were resumed. The entire cycle of oper- 
 ations was then repeated twice. A grand total of 84 grams of 
 methyl alcohol was used in the determination. Finally, after 
 long-continued drying at a moderate heat, the sodium carbonate 
 was heated to fusion in the atmosphere of carbon dioxide which 
 was gradually replaced by dry air as the substance cooled. This 
 method of fusing sodium carbonate in carbon dioxide had been 
 successfully applied by others 8 and was also found satisfactory in 
 
 » Am. Jour. Sci., V, 442. 
 
 • Sackur, Ber. 43, 449 (1910); and T. W. Richards and C. R. Hoover, J. Am. Chem. 
 Soc, 37, 95 (1915). 
 
BORON AND FLUORINE. 41 
 
 the present case. A second fusion, under similar conditions, 
 produced practically no change in weight. 
 
 The carbon dioxide used in this experiment, generated from 
 pure dilute hydrochloric acid and white marble, was passed 
 through a large tower containing beads, coated with moist sodium 
 bicarbonate; through a second tower charged with moist silver 
 carbonate; through a wash-bottle containing a solution of sodium 
 bicarbonate and four similar bottles charged with glass beads 
 and concentrated sulphuric acid, after which, before reaching the 
 platinum combustion tube, it passed through a column of freshly 
 fused granulated potassium carbonate. 
 
 TABULATION. 
 
 The results obtained in the experiments outlined in the pre- 
 ceding pages may now be presented in table 1 . The constants used 
 in the calculations have been given (p. 24). If it is remembered 
 that the results are based on a variety of methods and are referred 
 to five different antecedent atomic weights (of Na, CI, S, C, N) the 
 agreement between the individual determinations is satisfactory. 
 
 The objection may be raised, not entirely without justifica- 
 tion, that each type of analysis should be represented by a larger 
 number of individual determinations. That this would have 
 been highly desirable is not to be denied. While it is true that 
 any single determination in table 1 leading to B = 10.900 might 
 be of small value, it will be admitted that, in the aggregate, these 
 eight results, by virtue of their agreement, can not be without 
 significance. Furthermore, it may not be irrelevant to add that 
 each analysis, although the solitary representative of its type, 
 was carried out with considerable care and involved no small 
 expenditure of time and labor. These eight results, therefore, 
 obtained by a number of different methods involving a great 
 variety of conditions are of greater value than an equal number 
 of determinations based on a single reaction and involving only 
 one set of conditions. The latter plan is less likely to lay bare 
 any constant error in the method than is the former. 
 
 In brief, the borax (there is reason to believe) was of the 
 utmost purity and the general plan of analysis reduced the prob- 
 ability of introducing constant errors to a minimum; hence the 
 final value derived for boron is probably quite near the truth. 
 
42 
 
 THE ATOMIC WEIGHTS OF 
 
 That this new value (10.900) really does not seriously conflict 
 with most previous determinations of this constant and in fact 
 is actually supported by a number of them will be shown in 
 Chapter III. 
 
 Table 1. 
 
 
 
 
 
 
 After 
 
 
 Salt 
 
 
 
 a 
 
 
 
 Weight 
 
 
 
 re- 
 
 
 in 
 
 
 
 
 
 u 
 
 
 Weight 
 
 of 
 
 
 
 moval 
 
 Weight 
 
 pre- 
 
 Weight 
 
 of 
 Na 2 S0 4 
 (grams 
 
 
 £1 
 
 
 of 
 
 anhy- 
 
 Acid 
 
 ~ 
 
 of 
 
 of 
 
 ced- 
 
 
 <+4 
 O 
 
 -+-i 
 
 "borax 
 
 drous 
 
 used to 
 
 -c 
 
 boric 
 
 salt ob- 
 
 ing 
 
 Ratio 
 
 -*> 
 
 
 glass" 
 
 Na 2 B 4 - 
 
 liberate 
 
 o 
 
 acid 
 
 tained 
 
 col- 
 
 used: 
 
 bj) 
 
 .1 
 
 (grams 
 
 7 
 
 boric 
 
 "3 
 
 resi- 
 
 (grams 
 
 umn 
 
 Na 2 B 4 7 : 
 
 '3 
 
 a 
 
 
 hi 
 
 in 
 vacuo). 
 
 (grams 
 in 
 
 acid. 
 
 Si 
 
 dues 
 evap- 
 
 in 
 
 vacuo) . 
 
 evap- 
 orated 
 
 in 
 
 vacuo). 
 
 
 H 
 
 
 vacuo) . 
 
 
 a 
 
 orated 
 
 
 with: 
 
 
 
 
 
 
 
 
 with: 
 
 
 
 
 
 +3 
 < 
 
 
 
 
 
 
 NaCl 
 
 
 
 (l)2NaCl 
 
 10.896 
 
 IVj 
 
 [0.90027] 
 
 0.89853 
 
 HCOOH 
 
 o 
 
 HC1 
 
 0.52112 
 
 H 2 S0 4 
 
 0.63313 
 
 (2)Na 2 S0 4 
 
 10.905 
 
 VI 
 
 t 
 
 0.69695 
 
 HCOOH 
 
 o3 
 i- 
 O 
 
 ft 
 C3 
 
 *T3 
 
 HF 
 
 NaF 
 0.29042 
 
 Na 2 S0 4 
 
 H 2 S0 4 
 
 0.49113 
 
 Na 2 S0 4 
 
 10.901 
 
 1 
 
 CD 
 
 1.59374 
 
 H 2 S0 4 
 
 03 
 0J 
 
 H 2 S0 4 
 
 1.12315 
 
 NaN0 3 
 
 
 
 Na 2 S0 4 
 
 10.898 
 
 VII I 
 
 13 
 o 
 
 1 
 
 1.86458 
 
 HNOa 
 
 
 HNO s 
 
 1.57250 
 NasCOs 
 
 
 
 2NaN0 3 
 
 10.900 
 
 VIII f 
 
 1.97702 
 
 C0 2 
 
 
 C0 2 
 
 1.03946 
 
 — 
 
 — 
 
 Na 2 C0 3 
 
 10.903 
 
 
 
 
 
 P. 
 
 
 NaF 
 
 
 
 
 
 IX I 
 
 [1.99615] 
 
 1.99197 
 
 HCOOH 
 
 '3 
 03 
 
 HF 
 
 0.83003 
 
 NaF 
 
 
 
 
 " 
 
 x ! 
 
 [1.60535] 
 
 1.60201 
 
 HCOOH 
 
 o 
 
 HF 
 
 0.66757 
 
 NaF 
 
 H 2 S0 4 
 
 1.12889 
 
 Na 2 SO, 
 
 10.902 
 
 XII 
 
 [2.65241] 
 
 2.64768 
 
 HCOOH 
 
 
 HF 
 
 1.10329 
 
 H 2 S0 4 
 
 1.86597 
 
 Na 2 S0 4 
 
 10.896 
 
 
 Average 
 
 10.900 
 
 Note: The braces are to indicate that the four samples of "borax glass," although 
 taken from the same original preparation of borax, represent three different lots 
 that had been dehydrated independently. 
 
 THE ATOMIC WEIGHT OF BORON REFERRED TO " BORAX GLASS." 
 
 Table 2 has been compiled from data recorded in table 1. 
 It shows how, and to what extent, an incomplete dehydration of 
 borax (yielding "borax glass") would have affected the atomic 
 weight of boron. It also shows that a tolerably concordant series 
 of results would have been reached if ordinary "borax glass" had 
 been used as the initial substance, as the average indicates that 
 
BORON AND FLUORINE. 
 
 43 
 
 the final value (though obviously incorrect) would have been in 
 excellent agreement with the present value (11.0). 
 
 It should be borne in mind that the samples of "borax glass" 
 represented in this table had not been dehydrated in one lot; 
 they were taken from three different lots which had been dehy- 
 drated separately. Unfortunately the weight of the "borax 
 glass" was not determined in experiments v, vi, vn, and viii, as 
 the true significance of the residual water was not fully realized 
 at first. However, we have little reason to doubt that these 
 samples of borax glass would have shown approximately the same 
 
 Table 2. 1 
 
 
 Weight of 
 "borax 
 glass" 
 (grams 
 
 in vacuo). 
 
 Residual 
 
 water, 
 
 per cent. 
 
 Weight of salt 
 
 obtained 
 
 (grams in vacuo). 
 
 Ratio used, 
 borax 
 glass : 
 
 Apparent atomic 
 weight of boron. 
 
 -*3 
 
 a 
 a. 
 
 (a) 
 From 
 borax 
 contain- 
 ing per- 
 centage 
 of water 
 observed. 
 
 (b) 
 
 If ''borax 
 glass" 
 
 had con- 
 tained 
 0.3 per 
 
 cent, of 
 water. 
 
 IV 
 
 0.90027 
 
 0.193 
 
 NaCl: 
 0.52112 
 
 Na 2 SO,: 
 0.63313 
 
 2NaC] 4 
 Na 2 SO 
 
 10.993 
 11.003 
 
 11.047 
 11.057 
 
 IX 
 
 1.99615 
 
 0.209 
 
 NaF: 
 0.83003 
 
 
 2NaF 
 (F=19.005) 
 
 11.007 
 
 11.053 
 
 X 
 
 1.60535 
 
 0.208 
 
 
 Na 2 SO«: 
 1.12889 
 
 Na 2 SO« 
 
 11.007 
 
 11.054 
 
 XI 
 
 2.65241 
 
 0.178 
 
 
 Na 2 S0 4 : 
 1.86597 
 
 Na 2 SO« 
 
 10.986 
 
 11.048 
 
 
 Average 
 
 10.999 
 
 11.052 
 
 1 Experimental data taken from table 1 
 
 percentage of moisture (cir. 0.2 per cent.) as the other portions. 
 As the braces in table 1 indicate, it was (strictly speaking) only 
 in experiments vi and vn that the residual water was not deter- 
 mined at all. The percentage of water in the borax of experiment 
 xi is somewhat lower than that in the preceding sample, probably 
 because (before it was transferred to the bulb) it had been re-fused 
 in the crucible in which the preliminary dehydration of the crystals 
 had been carried out. 
 
 The full significance of table 2, particularly of the last column, 
 may be gathered from the discussion of Ramsay and Aston' a 
 determinations in Chapter III (p. 57). 
 
 4 
 
44 
 
 THE ATOMIC WEIGHTS OF 
 
 Naj SO ( 
 
 Naj SO4 
 
 ntoS 
 
 Ha. 2 SO« 
 
 Ha.,00, 
 
 Ki.BO^ 
 
 B. THE ATOMIC WEIGHT OF FLUORINE. 
 
 The various salts derived from borax in the determinations 
 recorded in table 1 may be grouped around the central substance, 
 borax, in such a manner as to bring out their relation, not only 
 to borax itself, but also to one another. This arrangement is 
 shown in the following diagram (figure 5) : 
 
 This diagram 
 shows at a glance that 
 the results might be 
 correlated in a great 
 variety of ways. It is 
 easily seen that any 
 two salts on different 
 lines, radiating from 
 borax and represent- 
 ing independent de- 
 terminations, might 
 be compared, indi- 
 rectly, if their quan- 
 tities were computed 
 with reference to a 
 fixed quantity, say 100 grams, of borax; the "cross-ratios" thus 
 obtained might serve for checking purposes or for the calculation of 
 the atomic weights of other elements besides boron. However, the 
 experimental data did not seem to warrant the calculation of more 
 than one additional atomic weight, namely that of fluorine. Of the 
 possible cross-ratios only one, NaCl : NaF (indicated by a dotted 
 line in the diagram), has been used. Eight values for fluorine 
 have been calculated from the data recorded in table 1 and are 
 given in table 3, together with the ratios used. In four of these 
 the new value for boron (10.900) has been included for reference. 
 Three values are based on the atomic weights of sodium and 
 sulphur; one value, as already mentioned, has been computed 
 from a cross-ratio. The agreement between the individual values 
 is excellent and is largely due to the following factors: complete 
 dehydration of the borax, complete elimination of boric acid, 
 and avoidance of loss in the ignition of sodium fluoride. 
 
 In this connection it may not be amiss to add a few words 
 concerning the value of cross-ratios in atomic weight determina- 
 
 Fig. 5. 
 
BORON AND FLUORINE. 
 
 45 
 
 tions. Comparisons by cross-reference have been advocated and 
 frequently been utilized by F. W. Clarke 9 and have often fur- 
 nished valuable data and checks upon experimental work. As a 
 rule, however, the original experimenter scarcely ever determines 
 a cross-ratio for its own sake. In most cases two compounds 
 may be brought into direct relation without the intervention of a 
 third. In some instances, however, such direct comparisons are 
 most unpromising, if not impossible, for practical reasons. For 
 such reasons, an indirect ratio, or cross-ratio, may be preferable 
 to a direct ratio. 
 
 Table 3. 1 
 
 From 
 Exp. No. 
 
 Ratio used. 
 
 Atomic 
 weight of 
 fluorine. 
 
 IV and V 
 
 V 
 
 V 
 IX 
 
 X 
 
 X 
 XI 
 XI 
 
 NaCl : NaF (cross-ratio) 
 2NaF : NazB^O, 
 2NaF : N&SO, 
 2NaF : Na^O? 
 2NaF : Na 2 B 4 7 
 2NaF : Na 2 S0 4 
 2NaF : Na 2 B 4 7 
 2NaF : Na 2 S0 4 
 
 19.002 
 19.005 
 19.006 
 19.004 
 19.006 
 19.008 
 19.005 
 19.002 
 
 
 Average 
 
 19.005 
 
 1 Experimental data recorded in table 1 (p. 42.) 
 
 In the determination of the atomic weight of fluorine, for 
 example, it would seem very desirable to establish its ratio to 
 another halogen. However, since the chemistry of the halides 
 holds forth no very promising means of comparing the fluoride 
 of a given element directly with another halide of the same ele- 
 ment, practically no efforts have been made in this direction. 
 True enough, the analyses of silver fluoride by Berzelius 10 and 
 possibly those by Fremy n would fall within the category; the 
 properties of silver fluoride, however, are such as to deprive these 
 analyses of any practical value in the fixing of the atomic weight 
 
 "A Recalculation of the Atomic Weights, 3d ed. (1910). 
 
 10 Afhandlingar i Fys. Kemi Miner. 4, 243, 455 (1815). The original paper we have 
 
 not seen. The reference is that given by Brauner (in Abegg's "Handbuch"). 
 The data are also given in Christensen's paper on the atomic weight of fluorine 
 (Jour. prak. Chem. (2) 35, 541-559 (1887). 
 
 11 Ann. chim. phys. (3) 47, 1 (1856). 
 
46 THE ATOMIC WEIGHTS OF 
 
 of fluorine. The work of McAdam and Smith, 12 who converted 
 sodium fluoride into sodium chloride, is the only modern deter- 
 mination on record which seeks to establish such a direct ratio 
 between these two halides by chemical means. Unfortunately, 
 their work was interrupted prematurely and the experience of 
 those authors shows that the reaction in question did not proceed 
 smoothly. 
 
 It would seem that the ratio of fluorine to another halogen, 
 say chlorine, may be established much more readily by an indirect 
 comparison — that is to say, by converting a sample of a suitable 
 compound to the chloride, and another sample of the same prep- 
 aration to the fluoride by an independent analysis. The ratio 
 between the two halides could then be easily calculated. In the 
 present work borax has been used as such an intermediate sub- 
 stance for the indirect comparison of sodium chloride and sodium 
 fluoride. Originally it was intended to repeat the conversion of 
 borax into sodium chloride with larger quantities of material, for 
 in experiment iv the quantities involved are rather small, but 
 this plan was abandoned in favor of the conversion of borax into 
 the other salts. At any rate, even the single conversion to the 
 chloride aids in exhibiting the applicability of the indirect method 
 in this particular case. 
 
 Such a comparison, by cross-reference, has certain general 
 advantages over a direct comparison. In the determination of an 
 atomic weight, from a direct ratio, the initial substance must 
 not only be pure in the ordinary sense, but its composition must 
 exactly correspond to the formula assumed. In an indirect com- 
 parison, the initial substance must also be free from impurities, 
 it is true, but the exact proportion of the elements within the 
 compound is immaterial. In the present case the borax should 
 consist of a union of pure Na 2 and pure B 2 3 ; the exact ratio 
 in which these two oxides are combined is of no consequence so 
 long as we draw upon the same homogeneous preparation for 
 analysis. Obviously the atomic weight of boron need not be 
 known in this case. 
 
 The new value for fluorine (19.005) is considerably lower than 
 that calculated by Clarke (19.041) 13 and also lower than that 
 
 " J. Am. Chem. Soc. 34, 592 (1912). 
 18 Op cit., p. 408 (1910). 
 
BORON AND FLUORINE. 47 
 
 preferred by Brauner (19.02). 14 Jacquerod and Tourpaian 15 
 derived the atomic weight of fluorine from the weight of a normal 
 liter of silicon tetrafluoride and found F = 19.09. Even if the 
 method adopted by these investigators should be flawless it must 
 not be forgotten that the figure for fluorine depends on the atomic 
 weight of silicon, which was assumed to be 28.3. Any possible 
 error in the latter value, it is true, would scarcely be sufficient 
 to account for the high value for fluorine. It is safe to say, how- 
 ever, that the atomic weight of silicon is still too uncertain to 
 serve for reference in fixing other atomic weights. 
 
 The paper by McAdam and Smith has already been mentioned. 
 These authors converted weighed quantities of sodium fluoride 
 into sodium chloride by means of hydrochloric acid gas, and from 
 two analyses they derived two values for fluorine: 19.0176 and 
 19.0133 (with Na =23.00 and CI = 35.46). It may be gathered 
 from their paper that the second conversion was possibly not quite 
 complete. However, as the difference between these two values 
 is very small it is permissible to take the average, or 19.015. 
 This result is based on weighings in air. If the mean quantities 
 involved be reduced to the vacuum standard and the atomic 
 weight of fluorine be recalculated with the antecedents used in 
 the present paper, F will be 19.009. This value agrees quite 
 well with the value just found (19.005), particularly when it is 
 realized that the method applied by McAdam and Smith would 
 have a tendency to lead to a high value for fluorine. The sodium 
 fluoride (produced by heating the acid salt) had to be used in a 
 porous state and would have had a tendency to retain, or take 
 up, a trace of water. (This was actually found not to be the 
 case, however). The weight of the resulting sodium chloride, on 
 the other hand, would have been too low if the conversion had 
 not been quite complete. Either, or both, of these errors — if at 
 all operative to a measurable degree — would have increased the 
 value of the ratio NaF : NaCl, and hence the atomic weight of 
 fluorine. For such reasons the agreement between McAdam and 
 Smith's value (19.009) and that obtained in the present investi- 
 gation (19.005) is all the more striking. 
 
 14 In Abegg-Auerbach's Handbuch d. anorg. Chem., Vol. IV, part 2, p. 12 (1913). 
 
 15 J. chim. phys. 11, 269-74 (1913). 
 
CHAPTER III 
 
 REVIEW OF PREVIOUS DETERMINATIONS OF THE 
 ATOMIC WEIGHT OF BORON. 
 
 GENERAL CONSIDERATIONS. 
 
 At this point it will be quite proper to consider the work of 
 other chemists upon the atomic weight of boron and, if possible, 
 point out the most probable errors which may have affected that 
 work. It is not thought that the observations, and value for 
 boron as given in this communication, are in any sense final, but 
 great confidence is placed in them; and since this new figure for 
 the atomic weight of boron is practically 1 per cent, lower than 
 the constant now in use, this investigation would, indeed, be 
 incomplete without a careful survey of previous determinations. 
 
 It is to previous analyses of borax that attention must be 
 directed, for this compound of boron has been used extensively. 
 It may be assumed that the preparations of borax used in such 
 work in the past were of reasonable purity, the latter implying 
 not merely the absence of appreciable traces of foreign matter, 
 but also the proper proportion of the constituents of the salt 
 itself. While, in some cases, exception to this assumption might 
 be taken by the severe critic, it must be noted that many investi- 
 gators do not describe the preparation of the borax used by them 
 in sufficient detail to admit of a profitable criticism of the method 
 of preparation. 
 
 In passing, it may be remarked that the analyses of boron 
 compounds, other than borax, have not added materially to the 
 existing knowledge of the atomic weight in question. Abrahall l 
 determined the ratio BBr 3 : 3Ag, which (according to Clarke) 
 leads to the value 10.819 for boron. The boron used in this prep- 
 aration of boron tribromide had been obtained by the method of 
 Wohler and Deville and must have been rather impure. Gautier * 
 analyzed the sulphide, carbide, chloride, and bromide of boron 
 and obtained values the average of which is quite close to the 
 
 'Journ. Chem. Soc, 61, 650 (1892). 'Ann. chim. phys. (7) 18, 352 (1899). 
 
 48 
 
THE ATOMIC WEIGHTS OP BORON AND FLUORINE. 
 
 49 
 
 number now in use, 11.0. It will be admitted, however, that the 
 selection of the first two compounds (the sulphide and carbide) 
 and the methods of analysis seem unfortunate for the purpose 
 in view. Furthermore, Gautier himself admits 3 that the carbide 
 was not pure. 
 
 The boron was prepared by Moissan's method and the sul- 
 phide, chloride, and bromide obtained from it were probably 
 reasonably pure. Unfortunately, however, the methods of analy- 
 sis are inadequate. The bromide of boron, for example, was 
 analyzed as follows: The compound (on the average 3.5625 g. 
 were used) was decomposed by water and the solution diluted 
 to 1 liter. Portions of 50 c.c. each were withdrawn and the hydro- 
 bromic acid determined as silver bromide. The average quantity 
 of boron tribromide actually analyzed, therefore, was only 0.1781 
 g.; the average amount of silver bromide actually determined 
 weighed only 0.4002 g., not 20 times this amount. These figures 
 (with Br = 79.92) wouldlead to 10.97 for the atomic weight of boron. 
 This value, however, is rendered extremely uncertain by the 
 volumetric operations and the author admits 4 that a variation of 
 from0.6 to 0.7mg. ("atthemost ") in the weight of the silver bromide 
 was considered satisfactory. A variation of + 0.3 mg., would 
 have caused the atomic weight of boron to vary from 10.78 
 to 11.16, whereas Gautier's own results vary only from 10.981 
 
 3 Thecarbideof boron was heated in chlorine 
 which removed the boron as BCU. The 
 residual carbon was burned in oxygen 
 and weighed as carbon dioxide. The 
 accompanying two experiments are 
 given by Gautier (loc. cit., p. 371). The 
 author then continues as follows: "Le 
 poids du carbone et celui de l'acide 
 carbonique ne presentent pas une concordance absolue. Cela tient a la pr&ence , 
 dans le borure, d'une trfes petite quantity de mature 6trangere; le poids de 
 borure a &t6 diniinue' de cette quantity pour le calcul." (I) 
 
 The carbon corresponding to 0.3359 gram of CO2 is only 0.0916 gram. The total 
 amount of carbon actually found was 0.0941 g., or 0.0025 g. in excess of the 
 theory. In other words, after removal of the boron as BC1 3 , the total carbon 
 left behind in two experiments contained 0.0025 g. (=2.66 percent.) of an 
 unknown impurity which was subtracted from the original weight of the boron 
 carbide ! 
 
 •"Pour determiner la quantity d'acide bromhydrique contenu dans les solutions 
 obtenues, nous avons fait chaque fois deux determinations simultanees sur jV du 
 volume total, soit sur 50 c.c, et nous n'avons consider^ l'experience comme 
 valable que lorsque le poids de bromure d'argent obtenu pour chacune d'elles 
 ne diffe>ait que de A a ^ de milligramme au plus." (Loc. cit., p. 377.) 
 
 (1) 
 
 (2) 
 
 B„C 
 
 C 
 
 CO, 
 
 0.2686 
 0.3268 
 
 0.0429 
 0.0512 
 
 0.1515 
 0.1844 
 
 0.5954 
 
 0.0941 
 
 0.3359 
 
50 
 
 THE ATOMIC WEIGHTS OF 
 
 to 11.043. Hence it must be inferred that the author rejected 
 a number of analyses. The chloride was analyzed in a similar 
 way. 
 
 These remarks suffice to indicate that the binary compounds 
 of boron have not yet been analyzed with sufficient accuracy for 
 atomic weight purposes. To this end a reinvestigation of the 
 halides of boron would seem desirable and in such an investigation 
 the more recent work of A. Stock et al. 6 might prove of great 
 value, according to whom certain substituted hydrides of boron 
 (e.g., B 2 H B Br) must be regarded as analogues of the corresponding 
 derivatives of carbon and hence seem to involve quadrivalent 
 boron. On the other hand, boron appears to be strictly trivalent 
 
 Table 4. — The atomic weight of boron derived from previous analyses of borax. 
 
 (a) Determination of water in crystallized borax: 
 
 Berzelius * 
 
 Laurent 2 
 
 Dobrovolsky 3 
 
 Abrahall 4 
 
 Ramsay and Aston 6 
 
 Armitage 8 
 
 (6) The analysis of anhydrous borax (distillation 
 method) : 
 Ramsay and Aston: 6 
 
 Na 2 B 4 7 : 2NaCl 
 
 Na 2 B 4 7 : 2NaCl : 2AgCl « 
 
 (c) The titration of borax: 
 Rimbach : 7 
 
 Na 2 B 4 O 7 .10H 2 O : 2HC1 
 
 Armitage: 8 
 
 Na 2 B 4 7 : S0 4 
 
 Year. 
 
 1822\ 
 1849/ 
 
 1869 
 
 1892 
 1893 
 1898 
 
 1893 
 1893 
 
 1893 
 1898 
 
 Atomic weight of 
 boron as recalcu- 
 lated by — 
 
 Clarke. 
 
 11.019 
 
 (10.855 
 
 111.532 
 
 10.702 
 
 10.942 
 
 10.983 
 
 10.957 
 11.054 
 
 10.970 
 10.943 
 
 Brauner. 
 
 08 
 85 
 
 (11.. 
 \10.; 
 
 }l0.87 
 
 10.70 
 10.94 
 10.99 
 
 10.97 
 11.05 
 
 11.01 « 
 10.94 
 
 i Pogg. Ann. 2, 129, 8, 19. 
 
 > Compt. rend. 29, 6. 
 
 ' Quoted by Brauner in Abe gg'a " Handbuch, 
 
 etc.," Vol. Ill, 1, p. 6 (1906). 
 •Jour. Chem. Soo. 61, 650-666 (1892), 
 
 (edited by Ewan and Hartog.) 
 
 'Ibid. 63, 211-217 (1893). 
 
 • Chem. N. 77, 78 (1898) ; see also Brauner, 
 
 op. cit., p. 8, 9. 
 'Ber. 26, 164-171 (1893). 
 8 See note on p. 59 
 
 c A. Stock and O. Priess, Ber. 47, 3109-13 (1914), and a number of other papers; see 
 also reference on p. iii. 
 
BORON AND FLUOR JNE 51 
 
 with reference to oxygen and the halogens. The tribromide, for 
 example, was found to be incapable of combining with more 
 bromine either at room temperature or at — 80°. 
 
 It may be added, however, that the ratios BX 3 : 3AgX and 
 BX 3 : 3Ag (X= halogen) are not particularly advantageous, for 
 practical reasons. As already indicated by the editors of Abra- 
 hall's paper, an experimental error in the ratio BBr 3 : 3Ag would 
 be magnified 23 times in the atomic weight of boron. 
 
 In considering former analyses of borax itself, they may con- 
 veniently be discussed under three heads, as indicated in table 4. 
 The last two columns give the atomic weight of boron as recal- 
 culated by Clarke and by Brauner, respectively. 
 
 A. The Determination of Water in Crystallized Borax. 
 
 It is generally conceded that the determination of water of 
 crystallization in a salt is liable to lead to a doubtful atomic 
 weight, since the water-content may vary with atmospheric con- 
 ditions and since the salt may occlude traces of mother liquor. 
 These objections, no doubt, also apply to crystallized borax; at 
 the same time the dehydration of this salt seems to present even 
 more serious difficulties which were overlooked or, at any rate, 
 not fully appreciated by previous investigators; namely, the 
 volatility of the borate itself and the retention of water by the 
 end-product. The former was noticed, although underrated, 
 by Abrahall and by Armitage; the latter, i.e., the retention of 
 water, it would seem, was first suspected, but not remedied, by 
 Dobrovolsky. 
 
 These difficulties, particularly the retention of water, have 
 been dwelt upon in the experimental part of the present work, 
 but on account of their importance will bear repetition. It is 
 evident from the earlier discussion of this question that borax 
 can not be dehydrated quantitatively by ignition in an open 
 vessel, such as a dish or a crucible, for the experimenter then 
 faces the dilemma of either not removing the water completely 
 or, if successful in this, of volatilizing some of the borax itself. 
 In this connection Abrahall's own words may be of interest. 
 He says: 
 
 "The determination of the atomic weight of boron by this method 
 necessitates the determination of the precise range of temperature 
 
52 THE ATOMIC WEIGHTS OF 
 
 within which all the water of crystallization of borax can be driven off, 
 while none of the anhydrous substance is volatilized. That this is no 
 easy matter, the above experiments (Abrahall's) clearly show." 6 
 
 It seems necessary to go a step further than Abrahall and say 
 that such a range of temperature does not exist. For, in order 
 to expel the last traces of water from borax the latter must be 
 kept in a state of fusion for a long time at a temperature at which 
 the salt itself begins to volatilize. It is evident, therefore, that 
 the complete and quantitative dehydration of this salt can be 
 effected only in an apparatus similar to that described in the 
 earlier part of this paper. 
 
 Now, at a temperature near the fusion point of borax the 
 water retained, in general, will exceed the loss due to volatilization 
 of sodium borate. It is not surprising, therefore, that in most 
 determinations recorded under (a) (p. 51), the percentage of 
 the water found should be too low and the atomic weight of boron 
 too high. The low results are undoubtedly due to the loss of 
 borax itself (by strong ignition), which would increase the appar- 
 ent percentage of water. In fact, Abrahall himself suspected this 
 to be a source of error in some of bis determinations. 
 
 While there can be little doubt that all determinations of water 
 in borax were influenced by these factors, the determinations made 
 by Armitage are open to a further objection. This chemist 
 effected the "air-drying" of borax by washing the crystals with 
 alcohol and ether, and finally exposing them for 6 hours in a 
 vacuum. That this method of drying should leave the 10 mole- 
 cules of water of crystallization untouched is, indeed, doubtful; 
 hence it is not surprising that the percentage of water found by 
 Armitage is one of the lowest on record. 
 
 There appears, therefore, to be no escape from the conclusion 
 that all previous determinations of water in crystallized borax, 
 without exception, lead to untrustworthy values for the atomic 
 weight of boron, largely as a result of the retention of water by 
 the fused salt and the volatilization of the borate itself. These 
 two errors may conceivably balance each other at some stage in 
 the process of dehydration. This state of affairs was probably 
 approached in Laurent's experiments and in some of those carried 
 out by Dobrovolsky. 
 
 8 Loc. cit., p. 655. 
 
BOEON AND FLUORINE. 53 
 
 B. The Analysis op Anhydrous Borax (the Distillation Method). 
 
 The foregoing remarks apply with equal force to the "anhy- 
 drous" borax used by Ramsay and Aston. 7 In their determina- 
 tion of water in crystallized borax the error caused by residual 
 water is less apparent, since some borax was also volatilized. In 
 the conversion of their "anhydrous" borax into sodium chloride 
 this error becomes more noticeable and leads to a grave incon- 
 sistency which, as may be gathered from their paper, was a puzzle 
 to the authors themselves. The authors of the present investiga- 
 tion believe that this inconsistency can now be easily explained; 
 and as such considerations will go far to support the new value 
 for boron derived by them, the following remarks may not be 
 irrelevant, and will be found to add to, rather than detract from, 
 the value of Ramsay and Aston's paper. 
 
 For the sake of uniformity the analyses of the authors just 
 mentioned have been recalculated from the mean ratios given by 
 F. W. Clarke, with the atomic weights used in the present investi- 
 gation. Silver has been assumed to be 107.880. Since 100 parts 
 of anhydrous borax gave 57.933 parts of sodium chloride the 
 atomic weight of boron may be computed from the following 
 expression, in which (M = 4B+157.994) stands for the molecular 
 weight of borax : 
 
 M = 116.908X100, orB = 10 . 951 (I) 
 
 57.933 
 
 The sodium chloride obtained in the last five determinations 
 was dissolved in water and precipitated as silver chloride, and 
 since 100 parts of silver chloride corresponded to 70.546 parts of 
 
 7 Ramsay and Aston's work on the possible volatility of borax and constancy of 
 weight upon fusion is given in the following quotation (loc. cit. p. 211) : 
 
 "Two observations were made of the action on borax of prolonged heating over a 
 Bunsen burner, but the weight remained unaltered. 
 
 (1) " Weight of crucible and borax fused over a Bunsen burner ; 6.4980 
 
 "Weight of crucible and borax fused over a Bunsen burner and heated to bright red- 
 ness for half an hour 6.4980 
 
 (2) "Weight of crucible and fused borax 10.0247 
 
 "Weight of crucible and fused borax heated to bright redness for half an hour 10.0247" 
 
 In view of the more detailed work of Abrahall, Waldbott, and others, including the 
 present writers, the data just quoted are not convincing. It should also be 
 noted that in the actual determinations a blast-lamp was used, not merely a 
 Bunsen burner. Again, it must be inferred from the text that the weights are 
 given in grams. That the combined weight of the platinum crucible and borax 
 should have been only from 6.5 to 10.0 grams seems to indicate that a typo- 
 graphical error, or some other inaccuracy, has crept into these data. 
 
54 THE ATOMIC WEIGHTS OF 
 
 borax the atomic weight of boron may be calculated from the 
 expression : 
 
 M= 286.674X70.546, orB = nQ61 . . . (n) 
 100 
 
 These two results differ by 0.11, or fully 1 per cent., an error 
 which can not be accounted for entirely by the solubility of silver 
 chloride or the non-observance of the modern precautions in this 
 precipitation. 8 Nor can it be due to residual boric acid in the 
 sodium chloride, for the method pursued by those authors does 
 not differ radically from that used in the present communication 
 and, as carried out by them, may safely be assumed to lead to a 
 quantitative elimination of the boric acid. 9 In fact, such errors 
 as these, although probably not entirely absent, may be disre- 
 garded for the present. It is the gross errors, errors of the first 
 magnitude, which should be ferreted out first. For similar reasons 
 the etching of the glass vessel (mentioned by Ramsay and Aston), 
 though by no means negligible, need not be considered. It is 
 safe to assume that the silver chloride (which was collected in a 
 Gooch crucible and finally dried at 200°) was determined with a 
 tolerable degree of accuracy. If this be granted we shall be 
 enabled to dispel the mystery surrounding the above inconsistent 
 values. 
 
 It has been observed that fused borax, as prepared by Ramsay 
 and Aston, invariably retains water. They had what, for the sake 
 of convenience, has in this paper been termed "borax glass," i.e., 
 vitreous borax, insufficiently fluxed for the complete removal of 
 water. This point should be stated with emphasis. The sodium 
 
 8 The present writers do not underrate the importance, in such work, of the solubility 
 of silver chloride. However, it is highly probable that Ramsay and Aston worked 
 with too concentrated solutions, and under such conditions silver chloride invari- 
 ably occludes appreciable quantities of other salts (see Richards and Wells, 
 Carnegie Inst. Washington, Pub. No. 28, p. 31 et seq.) . In other words, these two 
 errors would have balanced each other, to some extent at least. In view of the 
 much more serious and obvious errors, soon to be discussed, it seems permissible 
 to assume that the solubility of silver chloride in Ramsay and Aston's work is 
 relatively unimportant. 
 
 'According to our interpretation, Ramsay and Aston do not "admit" (see Brauner's 
 criticism in Abegg's Handbuch III (1), p. 7 (1906)), that the conversion of borax 
 into sodium chloride was incomplete, but merely consider it as a contingency, 
 as "not improbable," in their own words, solely in an attempt to account for 
 the discrepancy between the two results derived from the ratios NajB^O? : 2NaCl 
 and Na a B«OT : 2AgCl, respectively. 
 
BORON AND FLUORINE. 55 
 
 chloride obtained was finally dried at about 350° in a current of 
 air and, therefore, must also have retained some moisture, for 
 sodium chloride, as obtained under the conditions of the experi- 
 ment must be fused for the complete expulsion of the last traces 
 of water. 10 It is practically certain, therefore, that these two 
 sources of error were operative; doubt can be entertained only 
 concerning their magnitude. Fortunately the determination of 
 the latter is not entirely beyond our reach. 
 
 Again, the residual water in fused borax, as prepared by Ram- 
 say and Aston, is fairly constant and amounts to about 0.2 per 
 cent. It is highly probable that the percentage of water in the 
 "borax glass" used by those investigators was even greater, for 
 the low density of their vitreous borax (2.29, as against the more 
 probable value 2.357; see p. 24) is probably not without sig- 
 nificance and may be taken to show that their "borax glass" was 
 not entirely free from flaws which, in this' case, are not only due 
 to air, but to a mixture of the latter with steam. It may be quite 
 reasonably assumed that this borax glass contained approximately 
 0.3 per cent, of water. It now remains to be seen whether we can 
 also arrive at some legitimate estimate concerning the amount 
 of moisture in the sodium chloride. This, the writers hope, can 
 also be done, with a fair degree of certainty, without drawing 
 upon the imagination. 
 
 From Ramsay and Aston's work the ratio AgCl : NaCl may 
 be computed. The same ratio has been determined, much more 
 accurately, by Richards and Wells. The two ratios, as given by 
 Clarke, are as follows: 
 
 = 40.867 (Ramsay and Aston) 
 
 AgCl 
 100 NaCl 
 AgCl 
 
 = 40.7797 (Richards and Wells) 
 
 10 Sodium chloride is particularly prone to retain traces of water or mother liquor 
 when crystallized from water solution. It seems safe to say that sodium chloride, 
 prepared in this manner, that does not slightly decrepitate just before fusion 
 is yet to be made. In their work upon the atomic weight of columbium (J. Am. 
 Chem. Soc. 37, 1783 (1915)) the writers found that sodium chloride dried at about 
 400° was not free from water. In some cases it retained over 0.1 percent, of 
 moisture which was not given off until the salt was fused. (This statement, 
 although not recorded in the paper just mentioned, is borne out by original 
 notes.) 
 
56 THE ATOMIC WEIGHTS OP 
 
 As already intimated, this difference is probably very largely 
 due to moisture in the sodium salt. If the discrepancy be entirely 
 due to this cause the amount of moisture may be computed from 
 the ratios. It will be found that the moisture in Ramsay and 
 Aston's sodium chloride may have amounted to 0.214 per cent. 
 One will not go far wrong, therefore, by assuming that the 
 sodium chloride contained approximately 0.2 per cent, of water. 
 This amount may seem high, but is not beyond the range of 
 possibility. 11 
 
 On now applying these corrections, approximations though 
 they be, to expressions (I) and (II) there would result: 
 
 M = 116.908X(100-0.3 P er C ent.) orB = 10 . 901 . . . . (Ia) 
 
 57.933-0.2 per cent. 
 M = 286.674 X (70.546-0.3 per cent.) mB = 
 100 
 
 These corrections, far from arbitrary, not only harmonize the 
 inconsistent results obtained by Ramsay and Aston, but lead to 
 values which corroborate the figure found in the present investiga- 
 tion (10.900). The agreement thus established is striking. 
 
 The argument may be supported in still another maimer, as 
 follows: If Ramsay and Aston's weight of their "anhydrous" 
 borax be allowed to stand as recorded by them and the hypo- 
 thetical correction (—0,2 per cent. H 2 0) be applied only to their 
 sodium chloride there would follow : 
 
 M 116-908X100 orB = 11 , Q52 . . (lB) 
 
 57.933-0.2 percent. 
 
 It has been shown (see p. 43) that if such insufficiently dried 
 borax and a water-free end-product had been used in the calcula- 
 tions the result for boron would have been 10.999. In this case 
 the "borax glass" would have contained approximately 0.2 per 
 cent, of water. In the last column in table 2 it has also been shown 
 that if our own borax glass, other things being equal, had con- 
 tained as much as 0.3 per cent, of moisture (the amount probably 
 
 11 See preceding note. In the present case part of this moisture may have been held 
 in combination with the trace of silica resulting from the etching of the glass 
 vessel, for drying at 350° would not have been sufficient to completely dehy- 
 drate silicic acid. 
 
BORON AND FLUORINE. 57 
 
 contained in Ramsay and Aston's material) the atomic weight 
 of boron would have become 11.052. This figure is identical with 
 the value just derived above (Ib), upon the same assumption, 
 from Ramsay and Aston's work. It is, furthermore, of the 
 same order of magnitude as that calculated in expression 
 (II), which gave B = 11.061 and, according to argument, also 
 involved borax containing 0.3 per cent, of water and a water- 
 free end-product (in this case silver chloride). True, these 
 values of 11.05, or thereabouts, are incorrect. Nevertheless 
 their concordance with each other appears to furnish additional, 
 though indirect, proof of the essential correctness of our original 
 assumptions. 
 
 This completes the argument concerning Ramsay and Aston's 
 work. The reasoning seems conclusive and completely deprives 
 Ramsay and Aston's results of incongruities which would scarcely 
 yield as plausibly to any other theories or assumptions. True 
 enough, the quantities of moisture called for by our explanation 
 seem unusually large, not to say excessive. These quantities, 
 however, have been shown not to exceed reasonable limits in this 
 particular case. That the worker in atomic weights must ever 
 be on guard against traces of water in the substances which go 
 to make up the ratio sought has been pointed out repeatedly, and 
 with emphasis, by T. W. Richards. The present case seems to 
 be an unusually forceful illustration of this contention. The 
 percentages of moisture involved in this instance are not merely 
 traces, but quantities which should not be neglected in a careful 
 every-day analysis. We should probably search the entire field 
 of atomic weight determinations in vain for another case so 
 obstinate in this respect and so disastrous in its effect as that 
 presented by borax. 
 
 These remarks, of course, are not meant to suggest that the 
 corrections for moisture should be applied to Ramsay and Aston's 
 results for practical ends; they are too hypothetical for a rigid 
 computative revision. However, the corrections are far from 
 arbitrary and, if applied only for the sake of argument, not only 
 dispose of a grave and puzzling inconsistency, but also lead to 
 values practically identical with the one found in the present 
 investigation. Such considerations seem to offer an acceptable 
 excuse for the digression. 
 
58 THE ATOMIC WEIGHTS OF 
 
 C. The Titration of Borax. 
 
 Rimbach dissolved known quantities of crystallized borax in 
 water and titrated the solution, using a weight-burette, with 
 dilute hydrochloric acid which had been standardized by pre- 
 cipitation with silver nitrate. The percentage of actual hydrogen 
 chloride was computed from the total silver chloride obtained 
 in three independent determinations. Methyl orange, said to be 
 indifferent to boric acid, was used as an indicator. With the 
 atomic weights which (in 1893) seemed most reliable to him, 
 Rimbach himself derived the value 10.945 for the atomic weight 
 of boron. Subsequent recalculations of his analyses point to a 
 much higher figure, that is to say, to the value now in use, 11.0. 
 It was not until the present investigation had practically been 
 completed that it was thought desirable to recalculate Rimbach's 
 analyses with the atomic weights used in the derivation of our 
 own value for boron. The figure thus found was 10.917. 12 That, 
 for present purposes, Rimbach should be credited with the latter 
 value is permissible. It thus appeared, quite unexpectedly, that 
 this recalculated value (10.917) agreed more closely with our own 
 (10.900) than any other previous determination. 
 
 Although Rimbach's value, as recalculated by the writers, is 
 probably nearer the true atomic weight of boron than that found 
 by any of his predecessors in this field, the methods pursued by 
 him are open to a number of objections. We shall not dwell 
 upon those of a more general character : That a titration method, 
 in general, is inferior to a purely gravimetric method; that the 
 use of a hydrated salt is not advisable; or that the hydrochloric 
 acid might have been standardized, preferably, by a method 
 involving the use of the indicator to be used in the final titrations. 
 The chief errors which may have crept into Rimbach's work are 
 of a more serious nature and deserve attention here. 
 
 In order to free borax from adherent moisture, Rimbach 
 exposed the finely powdered decahydrate to the air, merely pro- 
 
 12 Rimbach, using the older atomic weights, finds his hydrochloric acid to contain 
 1.84983 per cent, of actual hydrogen chloride. This percentage has been retained 
 inadvertently it would seem, both by Clarke and by Brauner. The present 
 writers, using the newer atomic weights, obtained 1.85095 for the percentage 
 strength of Rimbach's acid. With this figurej and from the mean quantities 
 involved in the final titrations, the atomic weight of boron was computed and 
 found to be 10.917. The calculation was based on the atomic weights used 
 in the present work and, in addition, on H = 1.0076 and Ag = 107.880. 
 
BOBON AND FLUORINE. 59 
 
 tecting it from dust. The salt, stirred frequently, was thus 
 exposed for 12 days, by the end of which period the weight had 
 become practically constant. It was then assumed to have the 
 theoretical composition of the decahydrate. 
 
 When carbon dioxide is passed through a solution of borax a 
 partial decomposition into sodium carbonate and boric acid takes 
 place; a solution thus treated will finally effervesce upon the 
 addition of an acid. It is only reasonable to suppose, therefore, 
 that the moist borax crystals would also absorb some carbon 
 dioxide from the air. Such an absorption might take place, of 
 course, simultaneously with the evaporation of moisture, so that 
 the net result might still be a decrease in weight. In fact, it was 
 found that a sample of moist, powdered borax, entirely free from 
 carbonate, after being exposed to the laboratory air for several 
 weeks, gave a very slight effervescence with dilute hydrochloric 
 acid. The reaction was slight, but unmistakable. This action 
 of carbon dioxide on the moist crystals probably becomes inap- 
 preciable as soon as the borax is "air-dry." To what extent 
 carbon dioxide may have affected Rimbach's salt it is impossible 
 to say. The effect may have been negligible. Nevertheless the 
 fact remains that no steps were taken to eliminate this source of 
 error, however slight it may have been. The question is of much 
 interest for another reason. As borax, contaminated with traces 
 of carbonate, is said to effloresce more readily than the pure salt, any 
 absorption of carbon dioxide even might have been accompanied 
 by a slight loss of water of crystallization itself. 
 
 While the influence of the factors just discussed is rather 
 uncertain, an error which may have affected the final titration 
 is much more tangible and must not be dismissed without com- 
 ment. In the titration of borax it is assumed that the boric acid 
 resulting from the reaction has no effect upon methyl orange. 
 This assumption, the writers believe, is not strictly correct, for 
 according to their experiments solutions of pure boric acid, par- 
 ticularly when fairly concentrated, are distinctly acid toward this 
 indicator, and it is only in every-day analytical work that this 
 factor may safely be neglected; not so, it would seem, in an 
 analysis of precision. Rimbach, it is true, did not neglect to 
 carefully consider this very point. He found, from a series of 
 experiments, that a solution containing 9 grams of pure ortho- 
 5 
 
60 THE ATOMIC WEIGHTS OF 
 
 boric acid and 5 grams of pure, neutral sodium chloride, and an 
 equal volume of pure water — both liquids containing the same 
 amount of the indicator — required practically equal amounts of 
 dilute hydrochloric acid for the production of the same tint. He 
 naturally concluded from these results that boric acid was neutral 
 to the indicator. It should be remembered, however, that Rim- 
 bach's hydrochloric acid was approximately half-normal; for he 
 distinctly states that this acid was used in these tests. Now, an 
 acid of this concentration is not sufficiently dilute to detect, with 
 certainty, any slight difference in reaction between the two solu- 
 tions, that is to say, between the boric acid solution and the 
 "blank." This may be gathered from the following simple 
 experiment: 
 
 A beaker contained a solution of 9.7 grams of pure H 3 B0 3 in 
 450 cubic centimeters of distilled water. This approaches the 
 quantity and concentration of the boric acid produced in the 
 titration of about 15 grams of crystallized borax, the largest 
 single portion used by Rimbach. A similar beaker contained the 
 same volume of distilled water which came from the same source 
 and the same container as that used in the first beaker. Ten 
 cubic centimeters 13 of a methyl-orange solution, containing 0.010 
 gram of the dye per liter, were added to the contents of each beaker. 
 The tints produced in the two vessels, when viewed separately, 
 indicated neutrality or, possibly, a slight alkalinity in each case. 
 When the boric acid solution and the blank were placed side by 
 side, however, a distinct difference was noticeable: The boric 
 acid solution was slightly acid with reference to the blank. In 
 fact, this difference could easily be measured. The water con- 
 taining only the indicator required the addition of 0.5 c.c. of £ 
 hydrochloric acid solution. It will be observed that this hydro- 
 chloric acid is much more dilute than that used by Rimbach in 
 a similar test. A second experiment involving the same quanti- 
 ties gave like results. Finally 5 grams of pure sodium chloride 
 were dissolved in the solution containing the boric acid; a change 
 in color was not to be observed, which shows that the sodium 
 chloride, produced in the titration of borax, does not perceptibly 
 
 13 Contrary to what might be expected, this amount gives only a faint color under the 
 conditions and probably represents a practicable minimum. The indicator was 
 prepared and used as directed by Rimbach. 
 
BORON AND FLUORINE. 61 
 
 affect the end-point. Furthermore, these experiments prove that 
 boric acid does influence the end-point, inasmuch as the latter is 
 reached prematurely, that is to say, before it would be reached if 
 no boric acid were present. 
 
 In order to fix the end-point with precision Rimbach, in the 
 final titrations, proceeded as follows: Standard hydrochloric 
 acid (about f) was added to the borax solution until a faint 
 acidity was indicated. A more dilute acid (about g-) was then 
 added to a blank until the tint was exactly equal to that of the 
 former solution. The more dilute acid thus required — expressed 
 in terms of the original standard — was subtracted from the acid 
 added to the borax solution and the difference was taken to 
 represent the hydrochloric acid actually needed to react with the 
 borax. It is evident that this mode of procedure did not correct 
 for any possible acidity of the boric acid itself; and if our observa- 
 tions in regard to the acidity of this acid be correct, it is also 
 certain that the approach of the end-point was thus hastened 
 somewhat and that, therefore, the amount of hydrochloric acid 
 recorded was slightly insufficient. 
 
 Obviously we are now in a position to apply a correction to 
 Rimbach's results. But as the concentration of the borax solu- 
 tions used by him and, hence, that of the boric acid solution 
 formed, can only be reproduced approximately, such a correction 
 for the acidity of boric acid can not be rigidly applied. Further- 
 more, the standard of the acid used by the writers to measure this 
 acidity was not determined with the idea of actually revising 
 Rimbach's results on this basis. Nevertheless it may be of interest 
 to see how and to what extent such a correction would have influ- 
 enced Rimbach's value for boron. If, from the above data, we 
 calculate the value of this correction for the mean quantity of 
 borax titrated by Rimbach, the atomic weight of boron would be 
 lowered from 10.917 to 10.887. It is thus seen that a slight inac- 
 curacy in the method, an inaccuracy which would not be notice- 
 able in ordinary analytical work, 14 would affect the atomic weight 
 of boron to the extent of nearly 0.3 per cent, of its approximate 
 value ! 
 
 " In the titration of 1 gram of crystallized borax this error due to the acidity of boric 
 acid would be equivalent to less than 0.02 c.c. of -jg hydrochloric acid, an entirely 
 negligible amount. 
 
62 THE ATOMIC WEIGHTS OF 
 
 To summarize regarding Rimbach's determination : The main 
 factors to be considered in his work are the following : Absorption 
 of carbon dioxide by the borax; improper water-content of the 
 salt; and a slight acidity of boric acid toward the indicator. As 
 no definite conclusions can be reached as to the extent, if any, 
 of the first two factors, it is not possible to say whether Rimbach's 
 result may be high or low. Any errors due to the standardization 
 of the hydrochloric acid, by means of silver chloride, are probably 
 of a different order and of smaller significance than those just 
 mentioned. At any rate, it is interesting that Rimbach's result 
 (10.917, as recalculated by the writers) agrees tolerably well with 
 the value (10.900) found in the present investigation. 
 
 The above test for the slight acidity of boric acid toward 
 methyl orange would, of course, be utterly useless if the boric 
 acid were contaminated by traces of other acids, such as sulphuric 
 acid. Unfortunately the acid prepared from methyl borate had 
 all been used in the preparation of borax; hence, for the above 
 tests the boric acid was prepared as follows : A good commercial 
 grade of boric acid (which did contain a bare trace of sulphuric 
 acid) was twice recrystallized from water. It was then fused in a 
 platinum dish and recrystallized once more from pure water. The 
 product was again dissolved in boiling water and, after complete 
 solution, a few cubic centimeters of redistilled ammonium hydrox- 
 ide were added. The mother liquor from the crystals of boric 
 acid separating out from this solution was strongly alkaline to 
 methyl orange, due to the formation of some ammonium borate. 
 The boric acid thus obtained was recrystallized four times from 
 water. Centrifugal draining and washing were resorted to 
 throughout. The final product, in concentrated solution, was 
 again distinctly acid to methyl orange. It seems unlikely that 
 this acidity was due to anything but the boric acid itself. This 
 preparation was used in the quantitative tests. 
 
 An exhaustive study of the accurate titration of borax was 
 not considered to be within the scope of the present paper. 15 
 
 The two titrations of borax carried out by Armitage do not 
 require a lengthy discussion. This investigator modified Rim- 
 bach's method by substituting fused borax (supposedly anhy- 
 
 16 It may be added that according to Joly (Compt. rend. 100, 103, 1885) solutions of 
 boric acid, dilute or concentrated, are neutral to methyl orange. 
 
BORON AND FLUORINE. 63 
 
 drous) for the decahydrate and by using dilute sulphuric acid 
 instead of hydrochloric acid in the titration. His determinations, 
 which were probably largely preliminary in character, have been 
 published only in abstract. The experimental data on the titra- 
 tion of borax — privately communicated to Brauner 16 upon the 
 latter's request — are not sufficient for a complete recalculation. 
 In the abstract read before the Chemical Society it is stated : 
 
 "A given weight of fused borax was dissolved in water and titrated 
 with dilute sulphuric acid, the strength of which had been determined 
 (I) by titration with solution of pure soda of known strength, (II) as 
 barium sulphate. The value 10.928 was obtained for the atomic weight 
 of boron as a mean of two experiments performed by this method." 17 
 
 The quantities of SO4, given by Brauner, equivalent to the 
 portions of borax used are probably the values calculated by Armi- 
 tage himself. The experimental data upon which these calcula- 
 tions were based (weight of BaSCh, etc.) have not been published. 
 
 SUMMARY. 
 
 The results and conclusions arrived at in the preceding investi- 
 gation may be summarized as follows : 
 
 (1) Anhydrous sodium tetraborate, by treatment with appro- 
 priate acids and by repeated evaporation with methyl 
 alcohol, was converted, both directly and indirectly, into 
 the chloride, fluoride, sulphate, nitrate, and carbonate of 
 sodium. 
 
 (2) The borax used for this purpose was prepared by synthesis 
 from pure sodium carbonate and boric acid. The latter 
 had been obtained by the saponification of distilled methyl 
 borate. JUgj 
 
 (3) The complete dehydration of borax was found to be quite 
 difficult and could be effected only by prolonged fusion. 
 "Borax glass," as obtained ordinarily, was found to hold 
 about 0.2 per cent, of water. The complete removal of 
 the latter, without loss of borax by volatilization, was 
 probably effected for the first time and, of course, was of 
 the utmost importance in an investigation of this kind. 
 The difficulty encountered in the complete dehydration 
 
 " Op. cit., p. 9. " Chem. N. 77, 78 (1898). 
 
64 THE ATOMIC WEIGHTS OF 
 
 of borax has been discussed in detail and — rightly or 
 wrongly — has been attributed to a transient hydrolysis in 
 the earlier stages of the dehydration. 
 
 (4) The removal of boric acid by the method indicated under 
 
 (1) proved to be complete and left little to be desired. The 
 methyl alcohol used for this purpose was prepared by the 
 saponification of distilled methyl oxalate. The essential 
 factors in the volatilization of boric acid seem to be the 
 following: 
 (a) Both the residue treated and the pure methyl alcohol 
 used should be as free from water as possible, if the elimin- 
 ation of the boric acid is to be effected with a minimum of 
 alcohol. 
 (6) Frequent evaporations to dryness with small quantities 
 of methyl alcohol, particularly toward the end of the pro- 
 cess, are preferable to fewer evaporations with larger 
 quantities, 
 (c) Two or three consecutive evaporations with methyl 
 alcohol should, preferably, be followed by solution of the 
 residue in water and evaporation to dryness. Toward the 
 end of the process these evaporations, with alcohol and 
 water, may be alternated to advantage. 
 Incidentally, it is safe to assert that, if these precautions be 
 observed in the estimation of boric acid in a soluble borate by 
 the Gooch-Rosenbladt method, any lack of success is to be 
 attributed to the "retainer" used for fixing the boric acid — in 
 short, to what is taking place in the receiver, not to incomplete 
 volatilization of the boric acid. 
 
 (5) The direct conversion of borax into sodium fluoride (i.e., 
 in the presence of hydrofluoric acid) was found to be 
 impracticable and was brought about indirectly through 
 the formate; the latter, after removal of the boric acid, 
 being easily transposed by hydrofluoric acid. The advan- 
 tages of formic acid for this particular purpose have been 
 given. 
 
 (6) The atomic weight of boron was not derived from a series 
 of identical conversions of borax into some fixed salt, but 
 was based on the equivalent quantities of a number of 
 different sodium salts, such as the chloride, sulphate, 
 
BORON AND FLUORINE. 65 
 
 nitrate, and carbonate. The value of such a method is 
 obvious. The atomic weight of boron thus found was 
 10.900, referred to the oxygen standard. 
 
 (7) These data, which included the ratio between sodium tetra- 
 borate and sodium fluoride, were also used for a recalcula- 
 tion of the atomic weight of fluorine which was thus found 
 to be 19.005. 
 
 (8) The new value for boron (10.900) is practically a whole per 
 cent, lowerthanthe one at present in use (11.0). It seemed 
 desirable, therefore, to search for the chief cause, or causes, 
 of this discrepancy. As the writers are not aware of any 
 serious flaws in their own determinations, it became im- 
 perative to subject the work of others to a somewhat 
 critical study. A number of palpable errors in such work 
 have been pointed out, chief among which is the retention 
 of water by "borax glass." In the light of this criticism 
 of previous determinations it would seem that the various 
 sources of error had conspired, as it were, in favor of the 
 higher value (11.0) for boron. The evidence, both direct 
 and inferential, collected in Chapter III in support of the 
 lower figure (10.900) seems little short of conclusive. 
 
 (9) It is of particular interest to note that if the present 
 writers had used incompletely dehydrated borax — as was 
 done in the past — the atomic weight of boron would have 
 been 11.0. This result, though incorrect, is of value in 
 clinching the argument in favor of the new value (10.900). 
 
 (10) It should be borne in mind that the present work, including 
 the discussion of previous determinations, was confined to 
 borax. It has been hinted, however, that the analyses of 
 other compounds of boron, recorded in the literature, also 
 lead to rather uncertain values for boron. A careful 
 analysis of such compounds, particularly of the halides, 
 would be of interest and furnish a valuable check upon the 
 value derived in the present study.