LIBRARY 
 
 UNIVERSITY OF CALIFORNIA. 
 
 RECEIVED BY EXCHANGE 
 
 Class 
 
Dissociation as Measured by the Freezing 
 Point Lowering and by Conductiv- 
 ity Bearing on the Hydrate Theory . 
 The Composition of the Hy- 
 drates Formed by a Number 
 of Electrolytes. 
 
 DISSERTATION 
 
 SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF 
 
 THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY 
 
 WITH THE REQUIREMENTS FOR THE DEGREE 
 
 OF DOCTOR OF PHILOSOPHY 
 
 BY 
 
 JAMES NEWTON PEARCE. 
 BALTIMORE 
 
 June, 1907 
 
 EASTON, PA. : 
 ESCHENBACH PRINTING COMPANY. 
 
 1907. 
 
Dissociation as Measured by the Freezing 
 Point Lowering and by Conductiv- 
 ity Bearing on the HydrateTheory * 
 The Composition of the Hy- 
 drates Formed by a Number 
 of Electrolytes. 
 
 DISSERTATION 
 
 SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF 
 
 THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY 
 
 WITH THE REQUIREMENTS FOR THE DEGREE 
 
 OF DOCTOR OF PHILOSOPHY 
 
 BY 
 
 JAMES NEWTON PEARCE. 
 
 BALTIMORE 
 
 June, 1907 
 
 OF THE 
 
 ( UNIVERSITY I 
 
 OF 
 
 
 EASTON, PA. : 
 
 ESCHENBACH PRINTING COMPANY. 
 1907. 
 

CONTENTS. 
 
 Acknowledgment 4 
 
 Historical 5 
 
 Five Lines of Evidence for the Existence of Hydrates in Aqueous 
 
 Solutions 6 
 
 Conductivity 18 
 
 Object of this Investigation 21 
 
 Experimental 21 
 
 Conductivity 23 
 
 Specific Gravity 23 
 
 Volumetric Apparatus 24 
 
 Solutions 24 
 
 Water 24 
 
 Calculations for the Composition of Hydrates 24 
 
 Calcium Chloride 26 
 
 Strontium Chloride 30 
 
 Magnesium Chloride 32 
 
 Barium Chloride 34 
 
 Calcium Nitrate 36 
 
 Strontium Nitrate 38 
 
 Magnesium Nitrate 40 
 
 Barium Nitrate 41 
 
 Barium Bromide 43 
 
 Barium Iodide 44 
 
 Cobalt Chloride 44 
 
 Cobalt Nitrate 47 
 
 Copper Chloride 50 
 
 Copper Nitrate 52 
 
 Nickel Nitrate 53 
 
 Aluminium Chloride 58 
 
 Sodium Bromide 60 
 
 . Hydrochloric Acid 63 
 
 Nitric Acid 65 
 
 Sulphuric Acid 66 
 
 Discussion 68 
 
 Summary 75 
 
 Biography 78 
 
 186986 
 
ACKNOWLEDGMENT. 
 
 The author wishes to take this opportunity to express his 
 gratitude to President Remsen, Professor Morse, Professor 
 Jones, Dr. Acree, Dr. Tingle and Dr. Frazer for the valuable 
 instruction and advice received in both lecture room and 
 laboratory. 
 
 Special thanks are due Professor Jones, at whose sugges- 
 tion and under whose guidance this investigation was car- 
 ried out. 
 
 The author would also express his appreciation of the in- 
 struction received from Professor Ames and Professor Bliss 
 in the Department of Physics. 
 
V OF THE 
 
 UNIVERSITY 
 
 OF 
 
 Dissociation as Measured by the Freezing 
 
 Point Lowering and by Conductivity 
 
 Bearing on the Hydrate Theory* The 
 
 Composition of the Hydrates 
 
 Formed by a Number of 
 
 Electrolytes* 
 
 HISTORICAL. 
 
 The work of Arrhenius, 1 Raoult, 2 Loomis, 3 Barnes, 4 and 
 of Jones and his co-workers 5 upon the lowering of the freez- 
 ing point of concentrated aqueous solutions of electrolytes 
 show clearly that, starting with the most dilute solutions, 
 the molecular lowering decreases, passes through a minimum 
 and then increases with increasing concentration. 
 
 Conductivity measurements made by Jones and Knight, 8 
 and Jones and Chambers, 7 over the range of concentrations 
 used in the above freezing point work showed no evidence 
 of a minimum when the data were plotted in curves. Again, 
 if we assume the dissociation as measured by the conductiv- 
 ity method to be correct as represented by a = , and from 
 
 /* 
 
 it calculate the theoretical molecular lowerings in each case, 
 we find that these molecular lowerings decrease regularly, 
 and, when plotted, show no evidence of a minimum. 
 
 It was from the work of Jones and Chambers that the first 
 tentative suggestion was offered as to the cause of this phe- 
 nomenon. Using their own words, it is this: " In concentra- 
 ted solutions the salts must take up a part of the water, form- 
 ing complex compounds with it, and thus removing it from 
 
 1 Ztschr. phys. Chem., 2, 496. 
 
 2 Ibid., 2, 488. 
 
 3 Wied. Ann., 60, 253 (1897); Ibid., 57, 503. 
 
 4 Trans. Roy. Soc. of Canada, Vol. VI., Sec. III., 37. 
 
 5 Ztschr. phys. Chem., 12, 642. Am. Chem. Jour., 22, 5 (1899). Ibid., 22, 110 
 (1899). Ibid., 23, 89 (1900). Ibid., 23, 512 (1900). Ibid., 27, 433 (1902). Ztschr. 
 phys. Chem., 46, 244. Ibid., 49, 385 (1904). Am. Chem. Journ., 31, 303 (1904). 
 
 .Ibid., 32, 308 (1904). Ibid., 33, 534 (1904). Memoir Carnegie Inst., Washington, 
 No. 60. 
 
 e Am. Chem. Jour., 22, 110 (1899). 
 7 /&*., 23, 89 (1900). 
 
the field of action as far as the freezing point lowering is con- 
 cerned. This molecular complex, which is probably very 
 unstable, acts as one molecule in lowering the freezing point 
 of the remaining solvent. Thus the total amount of water 
 present acting as solvent is equal to the total amount of water 
 present diminished by that combined with the salt-molecules. 
 By assuming that a molecule of the salt is in combination 
 with a large number of molecules of water, it is possible to ex- 
 plain all of the freezing point results obtained. 
 
 "The conductivity results must, however, be taken into ac- 
 count. These show, unmistakably, a marked degree of dis- 
 sociation even in the most concentrated solutions employed. 
 There must be, therefore, a certain number of molecules 
 broken down into ions, either by the water acting as a solvent 
 or by the water in combination with the salt, just as salts are 
 probably dissociated in their water of crystallization." 
 
 They also showed that in the concentrated solutions the 
 molecular lowering is often much greater than the theoret- 
 ical lowering, if all of the molecules were completely dissocia- 
 ted into ions. It is only on the assumption set forth by Jones 
 and Chambers that this phenomenon can be explained. 
 
 Thinking that the hygroscopic property of certain sub- 
 stances might throw some light upon the point in question, 
 Chambers and Frazer, 1 at the suggestion of Jones, took up the 
 study of the freezing point lowerings produced by copper 
 sulphate, phosphoric acid, hydrochloric acid, sodium acetate, 
 cadmium iodide, zinc chloride, and strontium iodide, com- 
 pounds with very great affinity for water. In all cases well 
 defined minima were obtained, and from these minima the 
 freezing point lowerings increased with increasing concen- 
 tration, this substantiating the view put forth by Jones and 
 Chambers. 
 Evidence for the Existence of Hydrates in Aqueous Solutions 
 
 i. Relation between the Water of Crystallization and the 
 Temperature at which the Salts Crystallize. If the assump- 
 tion is true, that we are actually dealing with hydrates, un- 
 
 1 Am. Chem. Jour., 23, 512 (1900). 
 
stable complex molecules of solvent and dissolved substance, 
 then we should expect that the complexity of these hydrates 
 would vary with the temperature, and with the existing con- 
 ditions. That such is the case is proved by the fact that 
 almost all of the water except that which is held as water 
 of crystallization may be removed from solutions of salts 
 at the boiling point of these solutions. Furthermore, the 
 same results are obtained by spontaneous evaporation of 
 the solvent from the solutions under reduced pressure at 
 ordinary temperatures. What is still more striking, as we 
 shall see in a subsequent discussion in this paper, is that these 
 same molecular complexes may be broken down to some ex- 
 tent even in solution by the addition of a strong " dehydrating" 
 agent. It is not to be assumed, however, that the resulting 
 hydrate formed in the above three cases is the same. The 
 very large number of cryoscopic measurements, which have 
 been made in this laboratory, gives conclusive evidence that 
 salts which crystallize with water of crystallization do com- 
 bine with a much larger quantity of water when in solution 
 at ordinary temperature. 
 
 If, then, the amount of water with which a salt can crys- 
 tallize from a solution is a function of the temperature, we 
 should expect this amount of water to be larger, the lower 
 the water at which the crystals are formed. 
 
 We also have a class of substances which, under ordinary 
 conditions, crystallize from solution without water of crys- 
 tallization, e. g., the chlorides of potassium and ammonium, 
 and the nitrates of potassium, ammonium, sodium, and bar- 
 ium. 
 
 This is no doubt due, in some measure, to the temperature 
 at which these substances have been allowed to crystallize. 
 It is well known that conditions can be secured under which 
 some of these substances separate from solution with small 
 amounts of water of crystallization. It is still more proba- 
 ble, as we shall see later, that even the so-called anhydrous 
 salts have considerable hydrating power in dilute solution. 
 
 2. Relation between the Water of Crystallization and the 
 
8 
 
 Lowering of the Freezing Point. An extensive investigation 
 of the freezing point lowerings produced by aqueous solu- 
 tions of electrolytes carried out by Jones and Getman, 1 and by 
 Jones and Bassett, 2 has established the fact that there exists 
 between the lowering of the freezing point arid the water of 
 crystallization this general relation; namely, that the magni- 
 tude of the freezing point lowering of a solution of any given 
 electrolyte is directly dependent upon the number of mole- 
 cules of water with which that salt crystallizes from solu- 
 tion. 
 
 A brief summary of this work, to which reference must be 
 made to the curves in the original article, will bring out more 
 clearly this relation. 
 
 If we consider the chlorides of the alkali group, all of which 
 are binary salts, we find that the anhydrous salts, sodium 
 chloride, potassium chloride, and ammonium chloride, give 
 approximately the same depression of the freezing point with 
 increasing concentration. Lithium chloride, with two mole- 
 cules of water of crystallization, gives a considerably greater 
 depression for the same concentrations. 
 
 The ternary chloride of calcium, strontium, magnesium, 
 each of which crystallizes with six molecules of water, give 
 depressions of the same order of magnitude, yet considerably 
 greater than those of the alkali group. Barium chloride, 
 with two molecules of water of crystallization, gives depres- 
 sions lower than those produced by the other members of the 
 alkali-earth group, yet greater than those produced by lith- 
 ium with the same number of molecules of water of crystalli- 
 zation. 
 
 This is to be accounted for by the fact that lithium chlor- 
 ide is a binary electrolyte, yielding two ions while baruim 
 chloride is a ternary electrolyte yielding three ions. Again 
 we find that the chlorides of iron, aluminium, and chromium, 
 which separate from solution with six molecules of water, 
 give much greater depressions of the freezing point than do 
 
 1 Memoir Carnegie Inst. , Washington , No. 60. Ztschr| phys. Chem., 46, 244 
 (1903); 49, 385 (1904). 
 
 2 Am. Chem., Jour., 33, 534 (1905); 34, 290 (1905). 
 
the chlorides of magnesium, calcium, and strontium. This 
 is just what we should expect when we consider that the mem- 
 bers of the iron group form quarternary salts while those of 
 the alkali-earth group form ternary salts. 
 
 Similar relations are found to exist between the bromides, 
 iodides, and nitrates of these metals. 
 
 If, however, we compare the molecular depressions produced 
 the bromides and iodides of potassium, sodium and lithium, 
 we find that in each case the sodium salts with two molecules 
 of water give greater depressions than do the potassium salts 
 crystallizing without water, yet smaller depressions than do 
 the corresponding lithium salts crystallizing with three mole- 
 cules of water. 
 
 Barium bromide, with two molecules of water of crystalli- 
 zation, shows a greater depression than does lithium bromide 
 with three molecules, just as we should expect; it also gives a 
 smaller lowering than do the bromides of calcium, strontium, 
 and magnesium, each of which has six molecules of water of 
 crystallization. 
 
 The nitrates of sodium, potassium, and ammonium, which 
 crystallize without water, give the smallest lowerings of the 
 freezing point, while lithium nitrate, with two molecules, 
 comes next in the order of magnitude. About midway be- 
 tween lithium nitrate and those salts which crystallize with 
 six molecules of water, lie the values for calcium nitrate, which 
 has but four molecules of water. 
 
 The nitrates of aluminium, chromium, and iron crystal- 
 lizing with eight and nine molecules, respectively, give the 
 greatest lowerings of any salts so far studied. Comparing 
 the chlorides, bromides, iodides, and nitrates of the alkali 
 group which crystallize without water, we find that they all 
 show a molecular lowering of the same order of magnitude 
 for the dilute solutions, and this increases very slightly, if 
 at all. 
 
 Lithium chloride and lithium nitrate, each crystallizing with 
 two molecules, give approximately the same molecular lower- 
 ings. The same relation holds for lithium bromide and lith- 
 
IO 
 
 him iodide, which crystallizes with three molecules. Further, 
 the molecular lowerings produced by the nitrate and chloride 
 are less than those produced by the bromide and iodide of 
 lithium. 
 
 Owing to the slight solubility of barium chloride, com- 
 parisons between it and the bromide andiodide can be made 
 only in dilute solutions. At these concentrations all three 
 salts give molecular lowerings of approximately the same 
 order of magnitude. In the more concentrated solutions 
 the iodide gives a greater lowering than the bromide. 
 
 The chlorides, bromides, and iodides of the alkali-earths, 
 which crystallize with six molecules of water, give lowerings 
 of the freezing point which are of approximately the same 
 order of magnitude. As in the case of the alkali metals, the 
 bromides give somewhat greater lowerings than the chlor- 
 ides, and the iodides still greater lowerings than the bromides. 
 
 The nitrates produce about the same lowerings as the cor- 
 responding chlorides which crystallize with the same number 
 of molecules of water, and, therefore, somewhat less than 
 the corresponding bromides and iodides. 
 
 In other words, if we consider in any one group those salts 
 which separate from solution with the same number of mole- 
 cules of water, we find that they produce molecular lowerings 
 of approximately the same order of magnitude. If, on the 
 other hand, the salts in the same group combine with vary- 
 ing amounts of water of crystallization, those salts having 
 the greater combining power will produce the greater molecu- 
 lar lowerings, and -vice versa. 
 
 Again, since the hydrating power is a function of the water 
 of crystallization, the greater .the number of molecules of 
 water with which a salt crystallizes from solution, the greater 
 will be the amount of water removed from the field of action 
 as solvent, and, hence, the greater will be the abnormality in 
 the freezing point lowering, due to this increase in concentra- 
 tion. 
 
 These facts give conclusive evidence of the truth of the 
 theory advanced by Jones and Chambers 1 to account for the 
 
 1 Am. Chem. Jour., 23, 89 (1900). 
 
II 
 
 great abnormalities "that in solution the dissolved substance 
 is combined with a part of the solvent, the amount of the 
 solvent held in combination by the dissolved substance being 
 a function of the concentration of the solution." 
 
 j. Relation between the Minima in the Molecular Lower- 
 ing of the Freezing Point and the Molecular Elevation of the 
 Boiling Point. A short series of boiling point measurements 
 was carried out in this laboratory by Jones and Getman. 1 
 They worked with aqueous solutions of potassium, sodium, 
 lithium and barium chloride, potassium and sodium carbon- 
 ates, and sodium sulphate. 
 
 In all cases slight but well-defined minima were obtained. 
 These occur at somewhat greater concentrations than do the 
 minima in the freezing point lowerings for the same electro- 
 lytes. That this is so is not surprising, since I have already 
 pointed out that the complexity of the hydrates is decreased 
 by increase in temperature. Hence, the amount of water re- 
 moved from the field of solvent is less than at the freezing 
 temperature. Therefore, a greater concentration is required 
 in order that the effect due to hydration may counterbalance 
 the effect due to decrease in dissociation. 
 
 4. The Bearing of Hydrates on the Temperature Coefficient 
 of Conductivity of Aqueous Solutions. The conductivity of 
 a solution is, according to Ostwald, represented thus: fi v = 
 a(c + a) when c and a represent the velocities of the cation 
 and anion respectively, and a. the dissociation at the given 
 volume. Increase in conductivity may be brought about in 
 two ways, either by increase in dissociation or by increasing 
 the velocities of the ions. 
 
 It is a well-known fact that increase of temperature greatly 
 increases the conductivity. Is this due to an increase in the 
 velocity of the ions, or to an increase in dissociation? In an 
 extended study of the temperature coefficients of conduc 
 tivity in aqueous solutions, and on the effect of temperature 
 on dissociation, it was found by Jones and West 2 that the 
 
 1 Ztschr. phys. Chem., 46, 244 (1903). Memoir Carnegie Inst., Washington, No 
 60, p. 12. 
 
 1 Am. Chem. Jour., 34, 357 (1905) 
 
12 
 
 dissociation of electrolytes decreases slightly with rise in 
 temperature between o and 35. Noyes and Coolidge, 1 
 working at high temperature, have found that the dissocia- 
 tion decreases rapidly with rise in temperature. This is just 
 what we should expect from our knowledge of the fact that 
 the dissociating power of the solvent is a function of its own 
 association. Since the association of the solvent decreases 
 with increase in temperature, so should the dissociation of 
 the electrolyte decrease, as has been found to be the case. 
 
 Since, then, we cannot attribute the increase in conduc- 
 tivity with rise in temperature to an increase in the dissocia- 
 tion of the electrolyte, we must conclude that the increase 
 in conductivity with rise in temperature is due to an increase 
 in the velocity of the ions. 
 
 The velocity of the ions depends first upon the driving power 
 or kinetic energy, (2) upon the mass of the ion, and (3) upon 
 the viscosity of the medium. It is a well-known fact that 
 ions of small atomic masses move much more rapidly than 
 those of higher atomic mass. Also, that increase in tempera- 
 ture of a given medium increases the kinetic energy of all 
 particles in that medium. Increase in temperature also de- 
 creases the viscosity of the medium, thereby decreasing the 
 "internal friction" of the ions. 
 
 All of these factors would increase the velocity with which 
 the ions move, and, consequently, increase the conductivity 
 as the temperature is raised. 
 
 Jones 2 has advanced another idea to account for the in- 
 crease in conductivity with increase in temperature. "The 
 mass of the ion decreases with rise in temperature. This 
 does not refer to the charged atom or group of atoms which 
 we usually term the ion, but to this charged nucleus plus a 
 larger or smaller number of molecules which are attached to 
 it, and which the ion must drag along with it through the 
 remainder of the solvent. 
 
 "That the ions are hydrated seems to have been shown al- 
 most beyond question by Jones and his co-workers. That 
 these hydrates are relatively unstable has also been demon- 
 
 1 Ztschr. phys. Chem., 46, 323 (1903). 
 
 2 Memoir, Carnegie Inst., Washington, No. 60, p. 157. 
 
13 
 
 strated; therefore, the higher the temperature, the less com- 
 plex the hydrate existing in solution. The less the number 
 of molecules of the solvent combined with the ion, the smaller 
 the mass of the ion, and the less its resistance when moving 
 through the solvent; consequently, the ion will move faster 
 at the higher temperature. 
 
 "If this factor of diminishing complexity of the hydrate formed 
 by the ion with rise in temperature, plays a prominent r61e 
 in determining the large temperature coefficient of conduc- 
 tivity, then we should expect to find those ions with the largest 
 hydrating power having the largest temperature coefficients 
 of conductivity. The more complex the hydrate, i. e., the 
 greater the number of molecules of water combined with an 
 ion, the greater the change in the complexity of the hydrate 
 with rise in temperature." 
 
 Reference to the experimental data obtained by Jones 
 and West 1 shows how well this idea is substantiated by the 
 facts. To show this we give the following table. In the 
 first column are given those salts which crystallize from solu- 
 tion with no water of crystallization and which, therefore, 
 have but slight hydrating power in solution. In the second 
 column are placed those salts which crystallize with large 
 amounts of water, and which, consequently, have great hydra- 
 ting power. 
 
 Substances with slight hydrating power. Substances with large hydrating power. 
 Temp, coefficients in Temp, coefficients in 
 
 conductivity units. conductivity units. 
 
 Z/ = 2. V= 1024. 
 
 NH 4 C1 2.07 2.94 
 
 NH 4 Br 2.16 2.86 
 
 KC1 2.13 2.84 
 
 KBr 2.18 2.91 
 
 KI 2.09 2.91 
 
 KNO 3 1.86 2.71 
 
 
 Z>= 2. 
 
 v = 1024. 
 
 CaCl 2 
 
 3-n 
 
 5.61 
 
 CaBr 2 
 
 3.01 
 
 5-20 
 
 SrBr 2 
 
 2-93 
 
 5.27 
 
 BaCl 2 
 
 2.86 
 
 5.30 
 
 MgCl 2 
 
 2-55 
 
 4-59 
 
 MnCl 2 
 
 2-37 
 
 4.86 
 
 Mn(N0 3 ) 2 
 
 2.24 
 
 4. 16 
 
 CoCl 2 
 
 2-54 
 
 4-95 
 
 Co(N0 3 ) 2 
 
 2.48 
 
 4.67 
 
 NiCl 2 
 
 2.63 
 
 5-04 
 
 Ni(N0 3 ) 2 
 
 2-51 
 
 4.58 
 
 CuCl 2 
 
 2.15 
 
 5-04 
 
 Cu(N0 3 ) 2 
 
 2.38 
 
 4.88 
 
 i Am. Chem. Jour., 34, 357 (1905). 
 
14 
 
 From the points brought out in (i) we can assume, approxi- 
 mately, that the hydrating power of salts in solution is propor- 
 tional to their water of crystallization. If this assumption is 
 correct, we should expect to find that salts, having the same 
 amounts of water of crystallization, i. e., the same hydrating 
 power, will have the same temperature coefficients of con- 
 ductivity, and such we find to be the case. Further, the values 
 of the temperature coefficients for a given concentration in either 
 column are the same order of magnitude, those in the second 
 column, in each case, being higher than the corresponding 
 values in the first column, as we should expect from the greater 
 hydrating power of the former. It will be seen that the tem- 
 perature coefficients for v = 1024 are higher in every case 
 than for v = 2, for each individual salt. The greater the dilu- 
 tion, the greater the complexity of the hydrate formed and 
 the greater will be the change in the composition of the hydrate 
 with change of temperature. Consequently, the tempera- 
 ture coefficient of conductivity is greater the more dilute the 
 solution. Again, the differences in value between the tem- 
 perature coefficients for v = 2 and v = 1024 is very much 
 smaller in case of salts belonging to the first column than the 
 corresponding differences for the salts of the second. In other 
 words, the temperature coefficients of conductivity increase 
 more rapidly with dilution for salts of greater hydrating power. 
 
 5. The Absorption Spectra of Certain Colored Salts in Aqueous 
 Solution as Affected by the Presence of Certain Other Salts with 
 Large Hydrating Power. It has long been known that aqueous 
 solutions of copper and cobalt halide salts, when treated with 
 hydrochloric acid gas, calcium chloride, zinc chloride, alu- 
 minium chloride, and other strong dehydrating agents, un- 
 dergo a change in color. Thus, when an aqueous solution 
 of cobalt chloride is treated with a little solid calcium chlor- 
 ide or a concentrated solution of this salt, the initial purple- 
 red color is changed to blue. Likewise, the green concentra- 
 ted solution of cupric chloride, when diluted, becomes blue, 
 and when the resulting solution is evaporated or treated 
 with a dehydrating agent the original green color returns. 
 
15 
 
 This change in color takes place regardless of the kind of sub- 
 stance used as a dehydrating agent. One particularly striking 
 fact is this: the quantities of the dehydrating agents required 
 to produce the same change in color are almost universely 
 proportional to the number of molecules of water with which 
 each salt crystallizes from solution. 
 
 A similar color change is met with if we heat to a high tem- 
 perature solutions of colored electrolytes in sealed tubes. 
 This phenomenon falls directly in line with the theory which 
 has been advocated by Jones, that for each concentration of 
 a solution of an electrolyte we have a definite molecular com- 
 plex for a definite temperature, which breaks down with in- 
 creasing temperature. 
 
 Many views have been put forth to explain these color changes. 
 Jones and Uhler 1 undertook a spectrographic study of the ab- 
 sorption spectra of solutions of colored electrolytes. 
 
 The phenomenon of absorption is one of resonance. The 
 waves have definite periods and definite amplitudes. If, 
 now, these waves meet some medium containing particles 
 which vibrate with the same or nearly equal periods, the energy 
 of the wave is given up in setting the particle into vibration 
 and the light is absorbed, as we say. We have the natural 
 law that "that energy of vibration of a given period will be 
 absorbed to the greatest extent by a system whose natural 
 period of vibration is most nearly equal to its own." If the 
 period of the vibration of the light wave differs appreciably 
 from that of the system of particles, we shall have much less 
 absorption. 
 
 If the mass of the vibrating particles, the hydrate, is in- 
 creased by the addition of more water, while the energy of 
 vibration remains the same, the period of vibration will be 
 damped, and when tested, spectroscopically, the absorption 
 bands will be found to grow smaller and smaller as the com- 
 plexity of the hydrate increases. 
 
 If, on the other hand, we decrease the mass of the hydrate 
 while the energy of vibration remains constant, the electrons 
 
 1 Am. Chem. Jour., 37, 126 (1907). Memoir, Carnegie Inst., Washington, No- 
 60. 
 
16 
 
 in the hydrated molecule will vibrate in resonance with a larger 
 number of ether waves, and the result will be that we will 
 have a broadening of the absorption bands. 
 
 They first studied the absorption spectra of a series of aque- 
 ous solutions of cobalt chloride, copper chloride, and copper 
 bromide. 
 
 They found that, with increase in concentration of the cobalt 
 salt alone, the absorption bands widen out rapidly. This 
 is just what we should expect from the results of the freezing 
 point work. It has been found from this work that the hydra- 
 tion per molecule decreases with increase in concentration. 
 In the dilute solutions we have the largest hydrates. These 
 have small amplitudes and long periods, hence they will re- 
 spond to fewer light waves. The result then should be a 
 narrowing of the absorption bands, and such is found to be 
 the case. On adding more of the salt it removes some of the 
 water of the solution from the field of solvent, thus render- 
 ing the large hydrates which previously existed unstable un- 
 der the new conditions. As a result, the former large hydrates 
 break down into simpler forms, which will vibrate in reso- 
 nance with a larger number of waves. The result is a widen- 
 ing of the absorption bands. 
 
 Jones and Uhler next added strong hydrating agents, such 
 as calcium chloride and aluminium chloride, to other series 
 of similar solutions of the same salts. On the basis of our 
 theory the dehydrating agent will remove some of the water 
 from the field as solvent, thereby producing the same effect 
 as increasing the concentration of the colored salt alone. 
 
 A study of the spectrograms shows this to be the fact. 
 Also keeping the concentration of the colored salt constant, 
 as the concentration of the dehydrating agent is increased, 
 the absorption bands broaden with marked regularity. 
 
 Spectrograms were made of these colored salts in solutions 
 of ethyl and methyl alcohol, and acetone, also in binary mix- 
 tures of solvents in which water was the second solvent. 
 
 From the work of Jones and Getman 1 and Jones and Mac- 
 
 1 Am. Chem. Jour., 31, 339 (1904). 
 
17 
 
 Master 1 it was shown that these solvents do not possess any 
 very great power to combine with salts in solution. This 
 being the case, if we should take a solution of copper chloride 
 in ethyl alcohol, the dissolved substance, forming no com- 
 plex with the solvent, would be free to vibrate in resonance 
 with a large number of wave lengths, and would, therefore, 
 increase the width of the absorption bands. The spectro- 
 grams show wider bands than for aqueous solutions. As 
 water was added in varying quantities the absorption bands 
 became narrower, showing the damping effect due to increas- 
 ing hydration. 
 
 Here, again, the facts most beautifully confirm the theory. 
 
 Before leaving this chapter we will sum up our evidence 
 for the existence of hydrates in solutions of electrolytes. 
 
 1. In the case of all electrolytes there exists between the 
 water of crystallization and the temperature at which the 
 crystals are formed a definite relation which, under the same 
 conditions, is constant for a given salt. With increasing dilu- 
 tion the molecules and ions of an electrolyte are able to take 
 up a part of the solvent, forming unstable molecular com- 
 plexes or hydrates. 
 
 For equivalent concentrations the complexity of the hy- 
 drates formed by different salts stands in close relation to the 
 amounts of water with which those salts crystallize from solu- 
 tion. 
 
 2. The abnormality in the freezing point lowerings pro- 
 duced by solutions of electrolytes is a function of the water 
 of crystallization of these electrolytes. Those salts which 
 have a greater number of molecules of water of crystalliza- 
 tion always produce the greater lowering of the freezing point. 
 The same relation has been found to hold for the molecular 
 rise of the boiling point. 
 
 3. The minima in the boiling point and freezing point 
 curves occur at those concentrations at which the effect of 
 hydration just balances that produced by a decrease in the 
 dissociation of the electrolyte. Owing to the instability of 
 the hydrates formed with rise in temperature, the minima 
 
 1 Am. Chem. J., 35, 316 (1906). 
 
i8 
 
 for the boiling point curves occur at greater concentrations 
 than those for the freezing point curves. 
 
 4. The temperature coefficients of conductivity increase 
 with increasing dilution. For salts which crystallize with 
 the same amounts of water the temperature coefficients are 
 of the same order of magnitude. Comparing salts which 
 crystallize with different amounts of water, that one will 
 have the largest temperature coefficient of conductivity which 
 has the greatest power to combine with the solvent. In 
 other words, the greater the power to bring water out of solu- 
 tion, as water of crystallization, the more complex will be 
 the hydrate formed. The more complex the hydrate, the 
 greater will be the temperature coefficient of conductivity. 
 
 5. The absorption bands produced by aqueous solutions 
 of colored electrolytes widen with increase in concentration. 
 The same effect is produced when an indifferent substance 
 of strong dehydrating power is added. Similarly, increasing 
 dilution, with its accompanying increasing hydration, decreases 
 the width of the absorption bands. 
 
 Conductivity. 
 
 The conductivity of a solution of an electrolyte is a func- 
 tion of several conditions: the nature of the electrolyte 
 and the degree of its dissociation; the speed of its component 
 ions; and the viscosity of the solvent. The degree of disso- 
 ciation, in turn, depends upon the concentration of the elec- 
 trolyte and the nature of the solvent. 
 
 As was pointed out by Dutoit and Aston, that" solvent 
 whose molecules are associated to the greatest extent has 
 the greatest dissociating power. 
 
 Weak acids, weak bases, and salts of weak acids and bases 
 show constantly increasing dissociation with increasing dilu- 
 tion, but, within the limits of accuracy of our present methods, 
 no maximum of conductivity is directly obtainable. On 
 the other hand, strong electrolytes show rapidly increasing 
 dissociation with slight increase in dilution a maximum con- 
 ductivity being reached at moderate dilution. 
 
 It is stated by Ostwald 1 that the anions of the halogen acids 
 
 Lehrbuch, 2. 679. 
 
19 
 move more rapidly than do those of the oxyhalogen acids, 
 
 e. g., C1O 3 , BrO 3 , IO 3 ; that C1O 4 has a greater migration veloc- 
 ity than IO 4 . In general, the more complex the ion, the slower 
 its migration velocity. Especially is this the case with the 
 anions of organic acids. With isomeric anions, however, 
 the velocities are approximately equal. With increasing 
 increments of CH 2 the velocity decreases regularly. The same 
 may be said with regard to the organic cations. 
 
 It has been proved by Jones and Getman and by Loomis 1 
 that organic acids are not hydrated. It is clear that increase 
 in ionic volume is accompanied by decrease in ionic speed, 
 doubtless due to increase in friction between ion and solvent. 
 
 With this idea in mind, and with the evidence from the 
 freezing point measurements that the ions form more and 
 more complex hydrates with increasing dilution, we are forced 
 to believe that the conductivities of solutions of strong elec- 
 trolytes are less than they would be, theoretically, if there 
 were no hydration, by an amount which is a function of the 
 volume of the ionic complex. 
 
 Vollmer 2 determined the values of A^ for solutions of potas- 
 sium acetate, sodium acetate, potassium iodide, lithium 
 iodide, lithium chloride, and silver nitrate, in water and alco- 
 
 hol. He found the relation ^ - - = K = 0.33 to hold 
 
 in every case. 
 
 Kawalki 3 found the same relation to exist between the 
 speeds of diffusion of the same electrolytes in water and alco- 
 hol. It is of especial interest to note that the value which 
 
 he obtained for his constant =: - = K' = 0.33 is the same 
 
 D water 
 
 as that found by Vollmer for conductivity. From their 
 results we obtain the relation, 
 
 A/ oo : *oo :: D' : D. 
 That this relation will hold, in case there is hydration or alco- 
 
 1 Wied. Ann., 60, 523 (1897). 
 
 2 Ibid., 52, 328 (1894). 
 8 Ibid., 52, 300 (1894). 
 
20 
 
 holation, is highly probable t since the resistance offered to 
 the ionic complex will be the same in each case. 
 
 As stated by Jahn, 1 "recent measurements have made it 
 probable that the mobility of the ions is not independent of 
 their concentration, that they have greater mobility in more 
 concentrated than in more dilute solutions." Reference to 
 the work of Jones and Bassett 2 shows that this is just what 
 we should expect. They found, by freezing point measure- 
 ments, that the hydration per gram molecule of the electro- 
 lyte decreases, with increasing concentration, to a certain 
 concentration corresponding to the minimum in the molecular 
 lowering of the freezing point, and then decreases very slowly 
 with increasing concentration. In the more concentrated 
 solutions, then, we have smaller changes in hydration; there- 
 fore, smaller changes in the ionic volumes; hence, we should 
 have smaller changes in the mobility of the ions. 
 
 That the conductivity depends, in no small degree, upon 
 the viscosity of the solution has been known for a long time, 
 yet the simultaneous action of the two conditions, dissocia- 
 tion and viscosity, renders it impossible to separate their 
 effects. No simple relation exists other than that the conduc- 
 tivity decreases with increase in viscosity. 
 
 G. Wiedemann 3 first called attention to the fact that the 
 friction which the ions produce in their motion changes in the 
 sense that the fluidity changes. Accordingly, the mobility 
 of the ions should be a function of the fluidity of the solution. 
 
 That the conductivity does not depend exclusively upon 
 the fluidity can be seen in the following case: A i per cent 
 (by volume) solution of cane sugar and a 2.2 per cent solu- 
 tion of methyl alcohol have the same internal friction, mz. y 
 1.046, but the conductivity of potassium chloride in a i per 
 cent sugar solution is decreased 3 per cent, while in 2.2 per 
 cent methyl alcohol it is decreased 3.85 per cent. 
 
 Pissarjewski and Lemcke 4 made the simple assumption 
 that the conductivity is directly proportional to the disso- 
 
 1 Grundriss der Electrochemie, p. 143. 
 * Am. Chem. J., 33, 534 (1905). 
 . Pogg. Ann., 99, 228 (1856). 
 
 Z. physik. Chem., 52, 479 (1905). 
 
21 
 
 elation, and inversely proportional to the viscosity, e. g.,. 
 fi = K . At maximum disociation K = Moo ^oo There- 
 fore, the dissociation is a' = v and not a 
 
 Moo ^oo Moo 
 
 In thfe dilutions which they used the K, calculated 
 
 from a = , varies, while K, calculated from a = 1LJL. 
 Moo Moo ^oo 
 
 is a constant. 
 
 The Object of This Investigation. 
 
 It was my plan in this work to study the relation between 
 the dissociation as measured by the freezing point and con- 
 ductivity methods; to determine to just what extent the con- 
 ductivity of a solution is influenced by the hydration of the 
 ions; and to study the effect of hydration upon the relative 
 velocities of different ions. 
 
 Moreover, it was desired to test the reliability of the conduc- 
 tivity method as a means of measuring the dissociation of 
 strong electrolytes. 
 
 In order to do this, it was found necessary to redetermine 
 as accurately as possible the freezing point lowerings pro- 
 duced by various solutions of a large number of salts. 
 
 The object of the conductivity measurements was to deter- 
 mine the dissociation of the solution in question, as accurately 
 as possible, in order that the theoretical lowering produced 
 by the substance, if there was no hydration, might be calcu- 
 lated. 
 
 The freezing point measurements give us, on the other hand, 
 an exact proportion between the number of dissolved parti- 
 cles, molecules, ions, or the hydrates of these, and the num- 
 ber of molecules of the solvent acting as such. 
 
 EXPERIMENTAL. 
 
 Freezing Point Apparatus. For all concentrations from 
 the most dilute up to those which could not be frozen by 
 mixtures of salt and ice, a bath of rather large dimensions 
 was used. The outer cylindrical vessel was made of heavy 
 
22 
 
 galvanized iron diameter 31 cm., depth 26 cm. and cov- 
 ered on the outside by a heavy coat of felt to prevent radia- 
 tion. Within this was a much smaller vessel of the same 
 material with a tightly fitting cover. Soldered around the 
 large hole in the center of the cover is a conical- shaped collar, 
 which holds firmly the cork through which the thermometer 
 is inserted. By this means the thermometer always reaches 
 to the same depth in the solution. A second smaller hole 
 in the side is provided for the passage of the stirrer. To the 
 bottom and on the outside was soldered a short bolt, which, 
 in turn, was screwed into a nut soldered to the center of the 
 outer vessel. In this way firm support was given the inner 
 vessel and danger of floating was avoided. The freezing 
 tube proper was a large glass tube length 17 cm., diameter 
 5.5 cm., and of 250 cc. capacity. It was supported within the 
 smaller vessel at the bottom by a cork, and at the top by a 
 cork ring which rested upon an iron ledge soldered to the 
 inside of the small vessel. These dimensions allowed for an 
 air space of about 2 cm. all around. 
 
 The stirrer consisted of a gold-plated brass disc with one 
 large hole in the center to permit the passage of the ther- 
 mometer, and around this smaller holes about 0.7 cm. in diam- 
 eter. 
 
 Near the top of the large outer cylinder was soldered a small 
 tube which served to keep the water in the bath at constant 
 level. 
 
 By means of a bath of these dimensions the temperature 
 of the freezing mixture could be kept constant for five or six 
 hours. No attempt was made to control exactly the tem- 
 perature of the bath, but experience taught us that only those 
 freezing mixtures which required from forty seconds to one 
 minute to cool the solution o.i could be depended upon for 
 reliable results. 
 
 For solutions requiring freezing mixtures of calcium chloride, 
 the ordinary cryoscopic apparatus consisting of a battery 
 jar, two test tubes were used. 
 
 For this work 4 thermometers of the Beckmann type were 
 
23 
 
 employed, whose temperature ranges were i.i, 5.6, i2.2 > , 
 and 25. These were graduated into o.oo2, o.oi, o.o2, 
 and o.O5, respectively (whole scale). By means of a high- 
 power lens it was easy to read to a tenth of the above grad- 
 uations. 
 
 Conductivity. 
 
 Apparatus. The conductivity measurements were made 
 by means of the well-known Kohlrausch method, using the 
 Wheatstone bridge, induction coil, and telephone receiver. 
 The wire was calibrated according to the method of Strouhal 
 and Barus. 1 The resistance coils were made by Leeds, of 
 Philadelphia, and had been carefully calibrated. 
 
 Conductivity cells of two types were used. For the more 
 dilute solutions cells of the type devised by Jones and Bing- 
 ham 2 were employed. For the more concentrated solutions 
 U-shaped cells, similar to those used by Jones and Getman, 3 
 were found to be very convenient. 
 
 All conductivity measurements were made at o. For 
 this purpose a small pail was filled with finely crushed ice, 
 moistened with distilled water, and the cells packed into the 
 ice as tightly as possible. The small pail was then placed 
 in a spacious pan and the space between the pail and the pan 
 filled with finely crushed ice. 
 
 Specific Gravity. 
 
 Since the solutions were made up at 20, we thought 
 it best to determine their specific gravities at the same 
 temperature. The 20 bath was a large galvanized iron tub. 
 By means of a very small flame below and a stirrer within, 
 driven by a hot-air motor, the temperature could easily be 
 kept to within o.i of the desired temperature. Through- 
 out this work six pycnometers of the Ostwald type were em- 
 ployed. They were carefully calibrated with pure redis- 
 tilled water. 
 
 1 Wied. Ann., 10, 326 (1880). 
 Am. Chem. J., 34, 481 (1905). 
 Z. physik. Chem., 46, 244 (1903). 
 
2 4 
 
 Volumetric Apparatus. 
 
 The flasks and burettes used in this work were carefully 
 calibrated at 20 by the method of Morse and Blalock. 1 
 
 Solutions. 
 
 Kahlbaum's "chemically pure" materials were used in every 
 case and were further purified whenever it was thought desirable 
 to do so. The method of preparing the solutions varied 
 according to the solute employed. In general, a solution of 
 slightly greater concentration than 2 normal was first made, and 
 from this, by successive dilutions, the lesser concentrations 
 were obtained. Whenever possible, the mother solution was 
 made up by direct weighing; when the nature of the solute 
 did not permit it to be weighed, the mother solution was di- 
 luted to convenient strength, and portions of the dilute solu- 
 tion were standardized either by gravimetric or volumetric 
 methods. 
 
 Water. 
 
 The water which was used in all the solutions was puri- 
 fied according to the method of Jones and Mackay. 2 Ordi- 
 nary distilled water was twice redistilled from an acidified 
 solution of potassium dichromate, and the steam from the 
 second distillation passed through a boiling solution of barium 
 hydroxide. It had, at o, a conductivity of about 1.2 X lo"" 6 
 to 1.7 X io-7. 
 
 Calculation of the Composition of the Hydrates. 
 
 The method of calculating the amount of water combined 
 with the dissolved substance is essentially the same as that 
 used by Jones and Bassett. 3 We have given the observed 
 molecular lowering of the freezing point, the specific gravity 
 of the solutions, and the dissociation. The observed molecu- 
 lar lowering is corrected for the difference between 1000 grams 
 and the amount of water actually present in one liter of the 
 
 1 Am. Chem. J,, 16, 479 (1894). 
 
 2 Ibid., 19, 83 (1897). 
 
 Ibid., 33, 843 (1905); 34, 298 (1905). 
 
25 
 
 solution. This gives the true molecular lowering which would 
 be produced by the substance at the dilution in question if 
 there were 1000 grams of water present. 
 
 From the dissociation we calculate the true molecular low- 
 ering which would be produced by the dissolved substancs 
 if there were no hydration ; and if there is no hydration these 
 two values for the molecular lowering should be equal. 
 
 The calculated lowering, divided by the observed lowering 
 and multiplied by 1000, gives the amount of water present 
 playing the r6le of solvent, if the quantity of the substance 
 present is dissolved in 1000 grams of water. 
 
 The difference between this amount of water and 1000 
 grams gives the amount of water which is combined with the 
 dissolved substance in the solution in question. 
 
 Knowing the number of grams of water which are in com- 
 bination with the dissolved substance, the number of gram 
 molecules of water combined with the substance is obtained 
 by dividing this number by 18. If we divide this value by 
 the concentration in terms of normal, we obtain the number 
 of molecules of water which are in combination with one mole- 
 cule of the dissolved substance when the amount of sub- 
 stance present in one liter of the solution is dissolved in 1000 
 grams of water. 
 
 In the various tables of data the symbols have the following 
 significance : 
 
 In the tables of freezing point measurements ra is the con- 
 centration in terms of gram molecules per liter ; A, the ob- 
 served lowering of the freezing point, corrected for the sepa- 
 ration of ice; A/w, the molecular lowering of the freezing 
 point. 
 
 In the conductivity tables, V denotes the volume of the solu- 
 tion in liters which contains one gram molecular weight of 
 the electrolyte; y. is the conductivity corrected for water; a 
 is the approximate dissociation. 
 
 In the specific gravity tables, m is the concentration; W solt 
 the weight of one liter of the solution ; W salt is the weight of the 
 salt contained in one liter of the solution ; and W HzO is the weight 
 
26 
 
 of water contained in one liter of the solution. The percent- 
 age correction is the correction which must be applied to the 
 freezing point lowering in order to refer it to 1000 grams of 
 the solvent instead of the amount of water that is actually 
 present in one liter of the solution in question. 
 
 In the hydrate tables, m is the concentration in gram mole- 
 cules per liter; a, the approximate dissociation as measured 
 by the conductivity method; L, the theoretical molecular 
 lowering of the freezing point referred to 1000 grams of sol- 
 vent; A/m, the observed molecular lowering; L', the corrected 
 molecular lowering ; M, the number of gram molecules of water 
 in combination with the solute; and H, the number of gram 
 molecules of water combined with one molecule of the salt 
 at the concentration in question. 
 
 Calcium Chloride. 
 
 The data for calcium chloride are given in Tables I. to IV. 
 
 The value of /IQO is surprisingly low, when compared with 
 that obtained by West 1 and by Bassett. 2 It is, however, very 
 nearly equal to that obtained by Jones and Stine. 3 
 
 A study of Table IV. leads us to the following conclusions: 
 The theoretical molecular lowerings, as given in column L, de- 
 crease regularly with increase in concentration, while the cor- 
 rected observed molecular lowerings, as seen in column L', 
 decrease rapidly, reach a minimum at o.i normal, and then 
 increase with increase in concentration. 
 
 It is very probable that the value of L' for o.oi normal is 
 too (large, but owing to the inaccuracy of the method for 
 such dilutions, this is unavoidable. 
 
 It will be seen from column M that the amount of water 
 which has entered into combination with the dissolved salt 
 also passes through a minimum between 0.075 normal and o.io 
 normal the same concentration which gives the minimum 
 molecular lowering of the freezing point. A similar minimum 
 
 1 Am. Chem. J,, 34, 393 (1905). 
 
 2 Ibid., 33, 547 (1905). 
 
 3 The article of Jones and Stine will be published in the American Chemica 
 Journal in the near future. 
 
27 
 
 was noted by Jones and Bassett 1 for concentrations ranging 
 from 0.102 normal to 0.153 normal. It has been assumed 
 hitherto, by Jones and his coworkers, that the minimum in 
 the freezing point lowering always occurs in that concentra- 
 ti n where the effect due to decrease in dissociation is just 
 counterbalanced by the effect due to hydration. The values 
 of L' and M also show that the abnormality of the freezing 
 point lowering is greatly augmented by the relatively great 
 hydrating power of the ions, since it is the ions with which 
 we are chiefly concerned in the dilute solutions. A glance 
 at column H shows us at once the great hydrating power of 
 the ions in dilute solution. The values of H decrease regu- 
 larly with increase in concentration to o.io normal. From 
 that concentration on, the decrease in hydration is very slight 
 as the concentration increases. In these concentrations the 
 combined effect upon the freezing point lowering, due both 
 to the dissociation and to the hydration of the ions, is small, 
 compared with the effect due to the undissociated molecules. 
 
 If we refer to the literature 2 bearing upon the relation be- 
 tween the water of crystallization of a salt and the tempera- 
 ture at which it crystallizes, we see that, over a definite range 
 of temperature, the amount of water of crystallization is con- 
 stant. If, then, we eliminate the hydration due to the ions, 
 we should expect to find the number of molecules of water 
 combined with one molecule of the salt to be a constant for 
 a definite range of temperature. This is clearly shown by 
 the values of H for the more concentrated solutions. 
 
 The values of M are plotted in the curve (Fig. II.) against 
 the concentrations as abscissas. The curve shows, at a glance, 
 that the amount of water held in combination, from the dilu- 
 tion at which the minimum occurs, is a linear function of the 
 concentration. 
 
 The values of H are plotted in the curve (Fig. I.) against 
 the concentrations as abscissas. An explanation regarding 
 
 1 Am. Chem, J , 33, 548 (1905). 
 
 2 Bassett: Ibid., 34, 294 (1905). 
 
28 
 
 6.1 6-2$ 6.5 
 
 OJS ' 1. 
 
 Concentration. 
 Fig. I. 
 
 1.5 
 
 these hydrate curves is necessary at this point. With one 
 or two exceptions, it was found impossible to plot on the paper 
 the values of H for the more dilute solutions. 
 
 These curves show the rapid decrease in hydration until 
 the minimum is reached, and then a very slight decrease with 
 increasing concentration. 
 
2 9 
 
 20 
 
 U 5.25 0.5 
 
 D.75 1. 
 
 Concentration. 
 Fig. II. 
 
 L5 
 
 Table I. Freezing Point Measurements. 
 
 A. 
 
 A/w. 
 
 0.025 
 
 v vJ7tJ 
 
 0.1318 
 
 o 7tj^ 
 5.2720 
 
 2 . 8344 
 
 91.72 
 
 0.05 
 
 0.2511 
 
 5.0220 
 
 2.7OOO 
 
 85.00 
 
 0.075 
 
 0.3651 
 
 4.8690 
 
 2.6177 
 
 80.88 
 
 0. 10 
 
 0.48515 
 
 4-8515 
 
 2.6083 
 
 80.41 
 
 0.25 
 
 1-2335 
 
 4-9340 
 
 2.6526 
 
 
 0.50 
 
 2.6270 
 
 5.2540 
 
 2.8247 
 
 
 0.75 
 
 4.1955 
 
 5 5940 
 
 3.0075 
 
 
 I.OO 
 
 6 . 1040 
 
 6.1040 
 
 3.2817 
 
 
 Table II. Conductivity Measurements. 
 
 V. 
 
 100 
 
 40 
 
 20 
 
 13-34 
 10 
 
 334 
 
 I .00 
 
 = 123.46. 
 
 Ill .23 
 104.66 
 
 100. OI 
 
 95-02 
 92.23 
 87.19 
 
 80.73 
 74.69 
 
 70.98 
 
 a. 
 
 89.67 
 
 84.37 
 80.62 
 76.60 
 
 74-35 
 70.62 
 
 65-39 
 60.49 
 
 57-49 
 
Table III. Specific Gravity 
 
 Measurements. 
 
 m. Sp. gr. 
 
 Wsol. 
 
 fl 
 
 
 WH..O. 
 
 Per cent of 
 correction. 
 
 
 
 .01 
 
 .000982 
 
 1000.982 
 
 i 
 
 .109 
 
 999.873 
 
 0.012 
 
 
 
 .025 
 
 .002539 
 
 1002 . 539 
 
 2 
 
 .772 
 
 999-767 
 
 0.023 
 
 
 
 05 
 
 . 004874 
 
 1004.874 
 
 5 
 
 545 
 
 999.329 
 
 0.067 
 
 
 
 075 
 
 .006814 
 
 1006.814 
 
 8 
 
 .317 
 
 998.497 
 
 0.150 
 
 
 
 .10 
 
 .008971 
 
 1008.971 
 
 n 
 
 .090 
 
 997.881 
 
 O.2II 
 
 
 
 25 
 
 .02267 
 
 1022.67 
 
 27 
 
 .725 
 
 994-954 
 
 0.504 
 
 
 
 50 
 
 [.04451 
 
 1044.51 
 
 55 
 
 .450 
 
 989.06 
 
 1.094 
 
 
 
 .75 1.06641 
 
 1066.41 
 
 83 
 
 .175 
 
 983.23 
 
 1.676 
 
 I 
 
 .00 1.08744 
 
 1087.44 
 
 i 10 . 900 
 
 976.54 
 
 2-345 
 
 Table IV .Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 A/i. 
 
 L'. 
 
 M. 
 
 H. 
 
 0.025 
 
 84.37 
 
 4.9885 
 
 5.2720 
 
 5-2708 
 
 2.869 
 
 114.7 
 
 0.05 
 
 80.62 
 
 4-7590 
 
 5.0220 
 
 5-0187 
 
 2.874 
 
 57-4 
 
 0.075 
 
 76.60 
 
 4.7095 
 
 4 . 8690 
 
 4.8617 
 
 1.742 
 
 23-2 
 
 O.IO 
 
 74-35 
 
 4.6258 
 
 4-8515 
 
 4.8414 
 
 2-474 
 
 24-7 
 
 0.25 
 
 70.62 
 
 4.487 
 
 4-934 
 
 4.910 
 
 4.785 
 
 19.1 
 
 0-5 
 
 65-39 
 
 4-293 
 
 5-254 
 
 5-197 
 
 9.663 
 
 19.3 
 
 0-75 
 
 60.49 
 
 4. no 
 
 5-594 
 
 5-501 
 
 14.048 
 
 18.7 
 
 I.OO 
 
 57-49 
 
 3.998 
 
 6.104 
 
 5-962 
 
 18.30 
 
 18.3 
 
 Strontium Chloride. 
 
 The concentrated mother solution was diluted to convenient 
 strength and equal portions were taken for standardization. 
 The strontium was precipitated and weighed as strontium 
 carbonate. 
 
 The conductivity measurements for this salt gave me, at 
 maximum dissociation, /*oo = 128.57. The corresponding 
 value obtained by Jones and Stine 1 was /too = 128.44. 
 
 The minimum in the freezing point lowerings (column L') 
 is found at 0.25 normal, whereas the minimum in the total 
 combined water occurs at a somewhat greater dilution (0.05 
 normal). The values of H become approximately constant 
 at 0.25 normal, the minimum point in the freezing point 
 lowering. 
 
 The values of m and H for calcium and strontium chlorides 
 Tables IV. and VIII., show numbers of approximately the 
 same order of magnitude. For curves, see Figs. I. and II. 
 
 1 Loc. tit. 
 
Table V. Freezing Point Measurements. 
 
 m. 
 
 o.oi 
 0.02937 
 0.03987 
 0.5011 
 0.7077 
 
 O. 10 
 
 0.25 
 0.50 
 0.75 
 
 1. 00 
 
 0.05273 
 0.1550 
 0.2026 
 0.2476 
 
 0.3472 
 
 o . 48904 
 
 1-1957 
 2.5339 
 4.0989 
 5.9211 
 
 2730 
 2800 
 
 5 
 5 
 5-0752 
 
 4-9349 
 4 . 9060 
 4.8904 
 4.7830 
 5-0678 
 5-4652 
 5.9211 
 
 ^. 
 
 2-8351 
 2.8386 
 2.7382 
 2.6531 
 2.6376 
 2.6292 
 2.5715 
 2-7354 
 2.9385 
 3.1833 
 
 91.87 
 
 91.93 
 86.91 
 
 82.65 
 81.88 
 81.46 
 78.57 
 
 Table VI. Conductivity Measurements. 
 
 ^00 = 
 
 128.57 (Stine 128.4). 
 
 
 V. 
 
 HV. 
 
 a. 
 
 IIOO 
 
 128.57 
 
 
 SSO 
 
 \J / 
 
 127.99 
 
 
 \j \J 
 
 100 
 
 115.64 
 
 89.37 
 
 34-04 
 
 106. 10 
 
 82.56 
 
 25.08 
 
 103.26 
 
 80.32 
 
 19.93 
 
 101 .04 
 
 78.08 
 
 14.03 
 
 98.06 
 
 76.27 
 
 10 
 
 95.98 
 
 74.17 
 
 4 
 
 88.07 
 
 68.59 
 
 2 
 
 82.18 
 
 63.96 
 
 1-333 
 
 74-86 
 
 58.30 
 
 1.0 
 
 71.23 
 
 55-47 
 
 Table VII. Specific Gravity Measurements. 
 
 
 m. Sp. gr. 
 
 Wsol. 
 
 Wsalt. Wl 
 
 . _ Per cent of 
 *** correction. 
 
 
 
 .01 
 
 .0012284 
 
 1001 
 
 2284 
 
 I 
 
 585 
 
 999- 
 
 7034 
 
 
 
 .029 
 
 
 
 02937 
 
 .0038396 
 
 1003 
 
 8396 
 
 4 
 
 6559 
 
 999- 
 
 2837 
 
 
 
 .071 
 
 
 
 .03987 
 
 .0053832 
 
 1005 
 
 3832 
 
 6 
 
 3197 
 
 999- 
 
 0635 
 
 
 
 .093 
 
 
 
 .05017 
 
 .007028 
 
 1007 
 
 028 
 
 7 
 
 .952 
 
 999. 
 
 078 
 
 
 
 .092 
 
 
 
 .07077 
 
 .00956 
 
 1009 
 
 516 
 
 ii 
 
 .217 
 
 998. 
 
 299 
 
 
 
 .170 
 
 
 
 . IO 
 
 .013205 
 
 1013 
 
 215 
 
 15 
 
 85 
 
 997- 
 
 930 
 
 
 
 .207 
 
 
 
 .25 
 
 034433 
 
 1034 
 
 433 
 
 38 
 
 .625 
 
 994- 
 
 808 
 
 
 
 .519 
 
 
 
 .5 
 
 .068379 
 
 1068 
 
 379 
 
 79 
 
 250 
 
 989- 
 
 129 
 
 I 
 
 .087 
 
 
 
 .75 .5 
 
 . 101760 
 
 IIOI 
 
 1 60 
 
 118 
 
 .875 
 
 982. 
 
 88 5 
 
 I 
 
 .711 
 
 I 
 
 .00 ] 
 
 .135423 
 
 1135 
 
 423 
 
 158 
 
 50 
 
 976. 
 
 923 
 
 2 
 
 '308 
 
32 
 
 Table VIII. Hydrates, 
 a. L. A/w. L> '. M. H. 
 
 0.01 
 
 89. 
 
 37 
 
 5 
 
 .1845 
 
 5 
 
 -2733 
 
 5 
 
 .2718 
 
 
 . . . . 
 
 
 
 0.02937 
 
 82. 
 
 56 
 
 4 
 
 .9312 
 
 5 
 
 .2800 
 
 5 
 
 2763 
 
 3 
 
 634 
 
 123.6 
 
 0.03987 
 
 80. 
 
 32 
 
 4 
 
 .8479 
 
 5 
 
 -0752 
 
 5 
 
 .0705 
 
 2 
 
 -439 
 
 61.2 
 
 0.05017 
 
 78. 
 
 08 
 
 4 
 
 .7645 
 
 4 
 
 9349 
 
 4 
 
 .9304 
 
 I 
 
 .871 
 
 37-2 
 
 0.07077 
 
 76. 
 
 27 
 
 4 
 
 .6982 
 
 4 
 
 .9060 
 
 4 
 
 8977 
 
 2 
 
 274 
 
 32-13 
 
 O. IO 
 
 74. 
 
 17 
 
 4 
 
 .6191 
 
 4 
 
 .8904 
 
 4 
 
 .8803 
 
 2 
 
 973 
 
 29-73 
 
 0.25 
 
 68. 
 
 59 
 
 4 
 
 .4115 
 
 4 
 
 .7830 
 
 4 
 
 .7582 
 
 4 
 
 047 
 
 16.18 
 
 0.50 
 
 63. 
 
 96 
 
 4 
 
 2393 
 
 5 
 
 .0678 
 
 5 
 
 .0127 
 
 8 
 
 .572 
 
 17.14 
 
 0.75 
 
 58. 
 
 30 
 
 4 
 
 .0287 
 
 5 
 
 .4652 
 
 5 
 
 -37I8 
 
 13 
 
 .890 
 
 18.52 
 
 I.OO 
 
 55- 
 
 47 
 
 3 
 
 9234 
 
 5 
 
 .9211 
 
 5 
 
 7844 
 
 17 
 
 .873 
 
 17.87 
 
 As in the case of calcium chloride, the values of the theo- 
 retical lowerings (L) are less than the observed lowerings (L ; ) 
 in every instance. 
 
 Magnesium Chloride. 
 
 The value of /*oo for magnesium chloride was found to be 
 123.95. The values of U show a minimum at 0.25 normal, 
 while the values of H begin to be constant at 0.5 normal. 
 Magnesium chloride differs from the other chlorides thus far 
 discussed in that its values for M show no minimum, but in- 
 crease regularly with increasing concentration. 
 
 It should be noticed also that magnesium chloride has greater 
 power to combine with water than any of the halides of the 
 calcium group. Especially is this the case in the dilute solu- 
 tions, where the ions predominate. That this is not due to 
 hydrolysis and the liberation of the free mineral acid is evi- 
 dent from the fact that the molecular lowering of the freezing 
 point in the dilute solutions is in every case considerably 
 higher than the calculated lowering. As we shall see later, 
 in our study of the acids just the reverse was found to be 
 the case. The curves for this salt are found in Figs. I. and II 
 
33 
 
 Table IX. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 0.004928 
 
 0.02741 
 
 0.007317 
 
 0.04072 
 
 O.OI 
 
 0.05472 
 
 0.05108 
 
 0.2678 
 
 0.07171 
 
 0.3687 
 
 0.09986 
 
 0.5133 
 
 0.25 
 
 1.2352 
 
 0.50 
 
 2 . 6768 
 
 0.75 
 
 4.4328 
 
 0.9415 
 
 6.O6I9 
 
 A/w. 
 5.5630 
 
 5.4720 
 
 5.2443 
 5.1421 
 
 1330 
 9408 
 3536 
 9104 
 
 6.4885 
 
 2.9909 
 2.9916 
 2 . 9420 
 2.8195 
 2.7651 
 2.7596 
 2.6563 
 2.8783 
 3.1776 
 3.4615 
 
 99-54 
 
 97.10 
 
 90.75 
 88.25 
 87.68 
 82.81 
 
 Table X. Conductivity Measurements. 
 
 V. 
 
 402.25 
 202 . 92 
 136.67 
 
 100. 
 
 32.21 
 19.57 
 13.94 
 
 10. O 
 
 4.0 
 
 2.0 
 
 1-333 
 1.062 
 
 o = 123.95, 
 
 V-v. 
 
 120.15 
 II6.67 
 113.86 
 
 112.68 
 
 103.08 
 
 98.88 
 
 95.36 
 91.25 
 80.22 
 72.07 
 64.69 
 60.31 
 
 a. 
 96.94 
 
 94-13 
 91.86 
 90.90 
 83-16 
 79-78 
 76.93 
 73-61 
 64.72 
 59-50 
 53.63 
 48.66 
 
 Table XI. Specific Gravity Measurements. 
 
 m. Sp. gr. 
 
 Wsol. 
 
 Wsalt. 
 
 !//. _ Per cent of 
 WH^O. correction. 
 
 
 
 .00493 1.000344 
 
 1000 
 
 344 
 
 O. 
 
 4695 
 
 999.875 
 
 
 
 .OI2 
 
 
 
 .007327 1.000524 
 
 IOOO 
 
 524 
 
 O. 
 
 6970 
 
 999.827 
 
 
 
 .017 
 
 
 
 .01 1.000842 
 
 IOOO 
 
 .842 
 
 0. 
 
 9526 
 
 999.889 
 
 O 
 
 .012 
 
 
 
 .03104 1.002756 
 
 IOO2 
 
 756 
 
 2. 
 
 9568 
 
 999.799 
 
 O 
 
 .O2O 
 
 
 
 .05108 ] 
 
 .004224 
 
 1004 
 
 .224 
 
 4. 
 
 9168 
 
 999.307 
 
 
 
 .069 
 
 O 
 
 .07171 
 
 . 006036 
 
 IOO6 
 
 .036 
 
 6. 
 
 8316 
 
 999-204 
 
 
 
 .079 
 
 
 
 .100 
 
 008505 
 
 1008 
 
 505 
 
 9- 
 
 5260 
 
 998.979 
 
 O 
 
 .102 
 
 O 
 
 .25 
 
 .020966 
 
 I02O 
 
 .966 
 
 23- 
 
 8150 
 
 997.151 
 
 
 
 .28 4 
 
 
 
 .50 
 
 .038496 
 
 1038 
 
 .496 
 
 47- 
 
 630 
 
 990.866 
 
 O 
 
 .9IO 
 
 
 
 75 
 
 .056905 
 
 1056 
 
 .905 
 
 7i. 
 
 445 
 
 985.460 
 
 I 
 
 450 
 
 
 
 .9415 & 
 
 .069617 
 
 IO69 
 
 .617 
 
 89. 
 
 689 
 
 979-930 
 
 2 
 
 .007 
 
34 
 Table XIL Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 A/fii. 
 
 L'. 
 
 M. 
 
 H. 
 
 O.OI 
 
 90.90 
 
 5.2415 
 
 5.4720 
 
 5.47H 
 
 2-334 
 
 233.4 
 
 0.03104 
 
 83-16 
 
 4.9535 
 
 5.3581 
 
 5.3570 
 
 4-I85 
 
 134.82 
 
 0.05108 
 
 79.78 
 
 4.8278 
 
 5 . 2443 
 
 5.2407 
 
 4-377 
 
 85.69 
 
 0.07171 
 
 76.93 
 
 4.7218 
 
 5.1421 
 
 5-1381 
 
 4-501 
 
 62.76 
 
 O.IO 
 
 73.61 
 
 4.5982 
 
 5.I330 
 
 5.1278 
 
 5.737 
 
 57-37 
 
 0.25 
 
 64.72 
 
 4-1675 
 
 4 . 9408 
 
 4.9268 
 
 8.562 
 
 34.24 
 
 0.50 
 
 59-50 
 
 4-0734 
 
 5.3536 
 
 5.3049 
 
 12.898 
 
 25.79 
 
 0.75 
 
 53.63 
 
 3.8550 
 
 5-9104 
 
 5-8247 
 
 18.787 
 
 25.05 
 
 0.9415 
 
 48.66 
 
 3.670I 
 
 6.4385 
 
 6.3098 
 
 23.242 
 
 24.68 
 
 Barium Chloride. 
 
 A nearly saturated solution of this salt was first made. 
 This was diluted to convenient concentration, and equal por- 
 tions were precipitated and weighed as barium sulphate. 
 Owing to the slight solubility of this salt, we did not attempt 
 to work with concentrations greater than 0.4 normal. 
 
 Conductivity measurements gave us the value P& 132.07. 
 
 Table XIII. Freezing Point Measurements. 
 
 m. 
 
 O.OI 
 
 0.025 
 
 0.05 
 
 0.075 
 
 O.IO 
 
 0.25 
 
 0.40 
 
 A. 
 
 0.5463 
 
 L3398 
 
 0.24770 
 
 0.36128 
 
 0.4792 
 
 I . 1669 
 
 1.902 
 
 A/w. 
 5.4630 
 5.3592 
 4.9551 
 4.8171 
 
 4.7925 
 4.6677 
 
 4-7370 
 
 2.9370 
 2.8813 
 2.6639 
 2 . 5898 
 2.5766 
 2 5095 
 2-5575 
 
 96.85 
 94.06 
 
 83.19 
 79-49 
 78.83 
 
 75-47 
 
 Table XIV. Conductivity Measurements. 
 
 /*oo = 132.07. 
 
 V. *,. a. 
 
 100 120.01 90.87 
 
 40 HI.I5 84.16 
 
 20 105.78 80.09 
 
 13.33 100.69 76.24 
 
 10 99.92 75.65 
 
 4 92.18 69.79 
 
 2.5 86.31 65.35 
 
35 
 
 Table XV. Specific Gravity Measurements 
 
 tn. 
 
 Sp. gr. 
 
 Wsol. 
 
 Wsalt. 
 
 WH&. 
 
 Per cent of 
 correction. 
 
 O.OI 
 
 .001878 
 
 1001.87 
 
 2.083 
 
 999 795 
 
 O.O2I 
 
 0.025 
 
 00475 
 
 1004.75 
 
 5.207 
 
 999-545 
 
 0.045 
 
 0.05 
 
 .00929 
 
 1009 . 29 
 
 10.415 
 
 998.879 
 
 O. 112 
 
 0.75 
 
 01369 
 
 1013.69 
 
 15.622 
 
 998.074 
 
 0.197 
 
 O. IO 
 
 .01766 
 
 1017.66 
 
 20.830 
 
 996.83 
 
 0.3l6 
 
 0.25 
 
 .0456 
 
 1045.61 
 
 52.075 
 
 993-542 
 
 0.645 
 
 0.40 
 
 .0726 
 
 1072.65 
 
 83.32 
 
 989.335 
 
 I .066 
 
 Table XV I. Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 k 
 
 \/nt. 
 
 
 L'. 
 
 
 JJf. 
 
 H. 
 
 0.025 
 
 84. 
 
 16 
 
 4- 
 
 9907 
 
 5- 
 
 3592 
 
 5- 
 
 3568 
 
 3-796 
 
 I5I.8 
 
 0.05 
 
 80. 
 
 09 
 
 4- 
 
 8393 
 
 A 
 
 9551 
 
 4- 
 
 9496 
 
 i. 
 
 238 
 
 24.7 
 
 0.075 
 
 7 6. 
 
 24 
 
 4- 
 
 6961 
 
 4 
 
 ,8171 
 
 4- 
 
 8080 
 
 i. 
 
 293 
 
 17.2 
 
 O.IO 
 
 75- 
 
 65 
 
 4- 
 
 6742 
 
 4 
 
 7925 
 
 4- 
 
 7772 
 
 I. 
 
 197 
 
 H-9 
 
 0.25 
 
 6 9 . 
 
 79 
 
 4- 
 
 4562 
 
 4 
 
 6677 
 
 4- 
 
 6374 
 
 2. 
 
 172 
 
 8.69 
 
 0.40 
 
 65- 
 
 35 
 
 4- 
 
 2910 
 
 4, 
 
 7570 
 
 4- 
 
 7061 
 
 4- 
 
 900 
 
 12.25 
 
 What has been said regarding the chlorides of calcium, 
 strontium, and magnesium applies equally well to barium 
 chloride. The low value of H for 0.25 normal is doubtless 
 due to experimental error. 
 
 It is interesting to note that while the molecules of barium 
 chloride have a much smaller hydrating power than the other 
 chlorides of the alkaline earth metals, as we should expect 
 from the fact that it crystallizes with but two molecules of 
 water, the ions which predominate in the dilute solutions 
 have a relatively high hydrating power. 
 
 Another point is to be noted, one to which reference 
 will be made later in this paper. A glance at the curves rep- 
 resenting the values of M and H for the three salts calcium, 
 strontium, and magnesium chlorides will show that in each 
 case the curves for calcium chloride lie above those for stron- 
 tium chloride, while the two curves for magnesium chloride lie 
 above those for calcium chloride. This order is just the re- 
 verse of that for the atomic volumes of the three metals. Al- 
 though barium chloride crystallizes with but two molecules 
 of water, the atomic volume of barium is still larger than 
 that of strontium. This may account for the relatively high 
 hydrating power of the ions of barium salts. 
 
36 
 
 The curves for the values of M and H are given in Figs. 
 II. and I., respectively. 
 
 Calcium Nitrate. 
 
 The mother solution was diluted and 50 cc. portions were 
 taken for standardization. The calcium was precipitated 
 by means of ammonium oxalate and weighed as calcium 
 oxide. The data are given in Tables XVII. to XX. ; the curves 
 are plotted in Figs. III. and IV. 
 
 70 
 
 41 1.25 
 
 1 S 
 
 Concentration. 
 Fig. III. 
 
37 
 
 Table XVII. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/m. 
 
 i. 
 
 a. 
 
 OOI2 ^ 
 
 0.072 
 
 c . 7560 
 
 
 
 *-' A ^ O 
 
 0.025 
 
 0.1303 
 
 O / O*"" 
 
 5.2120 
 
 2 . 802 I 
 
 90.10 
 
 0.05 
 
 o . 2405 
 
 4.8090 
 
 2.5855 
 
 79.27 
 
 0.125 
 
 0.5752 
 
 4.6019 
 
 2.4736 
 
 73.68 
 
 0.25 
 
 I . 1424 
 
 4.5695 
 
 2.4567 
 
 72.83 
 
 0.5 
 
 2.2860 
 
 4.5720 
 
 2.4580 
 
 
 0.75 
 
 3.484 
 
 4.645 
 
 2-4974 
 
 
 I.O 
 
 4.766 
 
 4.766 
 
 2.5623 
 
 
 1-5 
 
 7.616 
 
 5.077 
 
 2.7299 
 
 
 V. 
 
 Table XVIII. Conductivity Measurements. 
 /KOO o = 126.69. 
 
 Hv. a 
 
 0.8o 
 0.40 
 O.2O 
 
 8.0 
 o 
 o 
 
 333 
 o 
 
 0.6667 
 
 108.60 
 
 IO2 . 78 
 96.28 
 85.72 
 77.64 
 66-54 
 58.32 
 51.30 
 40.24 
 
 85.72 
 8I.I3 
 76.0O 
 67.66 
 61.28 
 52.52 
 46.03 
 
 40.49 
 31-75 
 
38 
 Table XIX. Specific Gravity Measurements. 
 
 
 m. 
 
 
 Sp. gr. 
 
 W so i. 
 
 WsaU. W H *0. 
 
 Per cent of 
 correction. 
 
 o 
 
 .0125 
 
 i 
 
 .001846 
 
 1001 
 
 .846 
 
 2 
 
 .052 
 
 999- 
 
 794 
 
 
 
 .021 
 
 
 
 .025 
 
 i 
 
 .003166 
 
 1003 
 
 .166 
 
 4 
 
 .104 
 
 999 
 
 062 
 
 O 
 
 094 
 
 
 
 05 
 
 i 
 
 .00604 
 
 1006 
 
 .04 
 
 8 
 
 .209 
 
 997 
 
 831 
 
 O 
 
 .217 
 
 
 
 125 
 
 i 
 
 01523 
 
 1015 
 
 .23 
 
 20 
 
 .520 
 
 994 
 
 71 
 
 o 
 
 529 
 
 
 
 25 
 
 i 
 
 .03074 
 
 1030 
 
 74 
 
 41 
 
 .04 
 
 989 
 
 70 
 
 I 
 
 03 
 
 
 
 5 
 
 i 
 
 .06011 
 
 1060 
 
 . ii 
 
 82 
 
 .09 
 
 978 
 
 02 
 
 2 
 
 .198 
 
 
 
 75 
 
 i 
 
 .08874 
 
 1008 
 
 74 
 
 123 
 
 13 
 
 965 
 
 61 
 
 3 
 
 439 
 
 I 
 
 .00 
 
 i 
 
 .11751 
 
 1117 
 
 .51 
 
 164 
 
 .18 
 
 953 
 
 33 
 
 4 
 
 .66 
 
 I 
 
 5 
 
 i 
 
 17375 
 
 1173 
 
 75 
 
 246 
 
 27 
 
 927 
 
 48 
 
 7 
 
 25 
 
 Table XX. Hydrates. 
 
 m. a. L. A/w. L f . M. H. 
 
 0.025 81.13 4.8780 5.2120 5.2072 3.511 140.4 
 
 0.05 
 
 76.00 
 
 4.6872 
 
 4 . 8090 
 
 4.7986 
 
 1.288 
 
 25-7 
 
 0.125 
 
 67.66 
 
 4-3769 
 
 4.6019 
 
 4-5776 
 
 2.437 
 
 19.5 
 
 0.25 
 
 61.28 
 
 4-139 
 
 4-569 
 
 4-522 
 
 4.703 
 
 18.8 
 
 0.5 
 
 52.52 
 
 3-813 
 
 4-572 
 
 4.471 
 
 8.173 
 
 16.3 
 
 0.75 
 
 46.03 
 
 3-572 
 
 4-645 
 
 4-485 
 
 11.312 
 
 15.07 
 
 I.OO 
 
 40.49 
 
 3.366 
 
 4.766 
 
 4-544 
 
 14.490 
 
 14.49 
 
 i-5 
 
 31-75 
 
 3-041 
 
 5-077 
 
 4.709 
 
 19.683 
 
 13.12 
 
 Nothing special need be said regarding the data for this 
 salt, except to call attention to the fact that the amounts of 
 water combined with calcium chloride in solution are, in 
 general, higher than the amounts combined with calcium ni- 
 trate. This is just what we should expect when we consider 
 that calcium chloride crystallizes with 6 molecules of water, 
 while calcium nitrate crystallizes with 4. 
 
 Strontium Nitrate. 
 
 The strontium was precipitated and weighed as the car- 
 bonate. Unlike the other salts thus far studied, the freezing 
 point lowerings show no minimum within the range of con- 
 centrations used, the molecular lowering constantly decreas- 
 ing in value. A minimum was, however, obtained by Jones 
 and Bassett 1 at a concentration of about 1.5 normal. 
 
 i Am. Chem. J., 34, 305 (1905). 
 
39 
 Table XXL Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/w. 
 
 i. 
 
 a. 
 
 O.OI 
 
 0.05717 
 
 5.7170 
 
 3.0736 
 
 103.68 
 
 0.025 
 
 0.1304 
 
 5.2180 
 
 2.8053 
 
 90.27 
 
 0.05 
 
 o . 2402 
 
 4-8050 
 
 2.5833 
 
 79.16 
 
 0.075 
 
 0.3492 
 
 4.6567 
 
 2.5036 
 
 75-iS 
 
 O.IO 
 
 0.4587 
 
 4.5875 
 
 2.4664 
 
 73-32 
 
 0.25 
 
 I.08I7 
 
 4.326 
 
 2.3263 
 
 66.31 
 
 0.5 
 
 2.0849 
 
 4.169 
 
 2.2418 
 
 62.09 
 
 0.75 
 
 3.0453 
 
 4.060 
 
 2. 1829 
 
 59-15 
 
 I.OO 
 
 
 3.9983 
 
 2.1496 
 
 57.48 
 
 
 Table XXII. 
 
 Conductivity 
 
 Measurements. 
 
 /*oo == 125.62. 
 
 V. 
 
 
 Hv. 
 
 
 a. 
 
 IOO 
 
 
 III.I4 
 
 
 88.47 
 
 40 
 
 
 100.95 
 
 
 80.36 
 
 20 
 
 
 94.12 
 
 
 74.92 
 
 13 
 
 34 
 
 89.26 
 
 
 71.06 
 
 IO 
 
 
 86.16 
 
 
 68.59 
 
 4 
 
 
 73-59 
 
 
 58.58 
 
 2 
 
 
 61.34 
 
 
 48.83 
 
 I 
 
 33 
 
 52.77 
 
 
 42.01 
 
 I 
 
 
 45.69 
 
 
 36.37 
 
 Table XXIII. Specific Gravity Measurements. 
 
 m. Sp. gr. Wsoi. 
 
 Wtalt. Wl 
 
 , _ Per cent of 
 ** u ' correction. 
 
 o.oi 1.001525 
 
 1001 
 
 .525 
 
 2 
 
 .116 
 
 999 
 
 .409 
 
 
 
 .059 
 
 O 
 
 .025 1.004207 
 
 1004 
 
 .207 
 
 5 
 
 .292 
 
 998 
 
 .915 
 
 
 
 .108 
 
 
 
 .05 
 
 .008391 
 
 1008 
 
 .391 
 
 IO 
 
 .584 
 
 997 
 
 .807 
 
 
 
 .219 
 
 
 
 075 
 
 .012646 
 
 IOI2 
 
 .646 
 
 15 
 
 .876 
 
 996 
 
 77 
 
 o 
 
 323 
 
 
 
 . IO 
 
 .016834 
 
 1016 
 
 834 
 
 21 
 
 .168 
 
 995 
 
 .666 
 
 
 
 -433 
 
 
 
 .25 
 
 .04201 
 
 1042 
 
 .01 
 
 52 
 
 .92 
 
 989 
 
 09 
 
 I 
 
 .09 
 
 
 
 .5 
 
 .08312 
 
 1088 
 
 . 12 
 
 105 
 
 .84 
 
 977 
 
 .28 
 
 2 
 
 .27 
 
 
 
 .75 
 
 .12386 
 
 1123 
 
 .86 
 
 158 
 
 .76 
 
 965 
 
 .11 
 
 3 
 
 .48 
 
 I 
 
 .00 
 
 16354 
 
 1163 
 
 .54 
 
 211 
 
 .68 
 
 95i 
 
 .86 
 
 4 
 
 .814 
 
40 
 
 Table XXIV .Hydrates. 
 
 m. a. L. A/w. L> '. M. H. 
 
 0.025 80.36 4-8493 5-7i8o 5-7I24 3-870 154-8 
 
 0.05 
 
 74.92 
 
 4.6470 
 
 4 . 8050 
 
 4-7945 
 
 1.710 
 
 34.20 
 
 0.075 
 
 71.06 
 
 4-5034 
 
 4.6567 
 
 4.6418 
 
 1-657 
 
 22.09 
 
 O.IO 
 
 68.59 
 
 4-4115 
 
 4-5875 
 
 4-5677 
 
 1.900 
 
 19.00 
 
 0.25 
 
 58.58 
 
 4.0391 
 
 4.3269 
 
 4.2798 
 
 3.124 
 
 12.49 
 
 0.5 
 
 48.83 
 
 3.676 
 
 4.169 
 
 4-075 
 
 5-437 
 
 10.87 
 
 0.75 
 
 42.01 
 
 3.422 
 
 4.060 
 
 3.9i8 
 
 7-030 
 
 9.37 
 
 1. 00 
 
 36.37 
 
 3-213 
 
 3-998 
 
 3.806 
 
 8.607 
 
 8.65 
 
 The values for the combined water show a minimum at 0.075 
 normal, just as calcium nitrate does. 
 
 The hydration per ion and molecule also shows no tendency 
 to become constant. 
 
 The curves are plotted in Figs. III. and IV. 
 
 Magnesium Nitrate. 
 
 The nitrate of magnesium, like the chloride, shows a much 
 greater power to combine with water, throughout the range 
 of concentration studied, than do the nitrates of the alkali 
 earth metals. 
 
 Table XXV. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/w. 
 
 i. 
 
 a. 
 
 0.02 
 
 O.IO78 
 
 5-3903 
 
 2 . 8980 
 
 94.90 
 
 0.05 
 
 0.24968 
 
 4-9938 
 
 2.6848 
 
 84-24 
 
 O.IO 
 
 0.49085 
 
 4.9085 
 
 2.6390 
 
 81-95 
 
 0.15 
 
 o . 74486 
 
 4.9671 
 
 2.6705 
 
 83.52 
 
 O.2O 
 
 0.99875 
 
 4-9937 
 
 2.6848 
 
 
 0.50 
 
 2 . 74280 
 
 5-4856 
 
 2.9492 
 
 
 1. 00 
 
 6.5H5 
 
 6.5H5 
 
 3.5024 
 
 
 Table XXVI. Conductivity Measurements. 
 
 /KOO o = 119.90. 
 
 V. PV. a. 
 
 50 102.06 85.12 
 
 20 94.48 78.80 
 
 10 89.66 74.78 
 
 6.666 85.61 71.40 
 
 5 83.04 69.25 
 
 2 72.03 60.07 
 
 I 59-27 49-43 
 
4i 
 Table XXVII. Specific Gravity Measurements. 
 
 m. Sp. gr. 
 
 W 50 l. 
 
 malt. Wi 
 
 Per cent of 
 /jG>. correction. 
 
 O 
 
 .02 1.00224 
 
 1002.224 
 
 2 
 
 .968 
 
 999 
 
 255 
 
 
 
 .074 
 
 
 
 .05 I . 005626 
 
 1005.626 
 
 7 
 
 .422 
 
 998 
 
 .204 
 
 
 
 179 
 
 
 
 . IO 
 
 .011118 
 
 1011.118 
 
 H 
 
 .844 
 
 996 
 
 .274 
 
 
 
 372 
 
 
 
 .15 
 
 016557 
 
 1016.557 
 
 22 
 
 .266 
 
 994 
 
 .291 
 
 
 
 571 
 
 
 
 .20 
 
 .022026 
 
 1022.026 
 
 29 
 
 .688 
 
 992 
 
 .338 
 
 
 
 .766 
 
 
 
 50 
 
 . 054804 
 
 1054.804 
 
 74 
 
 .220 
 
 980 
 
 .584 
 
 I 
 
 .941 
 
 I 
 
 .00 
 
 . 107865 
 
 1107.865 
 
 148 
 
 .440 
 
 959 
 
 425 
 
 4 
 
 057 
 
 I 
 
 .274 
 
 .136615 
 
 1136.615 
 
 189 
 
 . 112 
 
 947 
 
 502 
 
 5 
 
 .249 
 
 Table XXVIII. 
 
 Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 A/w. 
 
 L'. 
 
 
 M. 
 
 H. 
 
 0.05 
 
 7 8. 
 
 ,80 
 
 4 
 
 7913 
 
 4- 
 
 9938 
 
 4 
 
 .9849 
 
 2 
 
 .157 
 
 43-14 
 
 O. 10 
 
 74 
 
 ,78 
 
 4 
 
 .6418 
 
 4- 
 
 9085 
 
 4 
 
 .8903 
 
 2 
 
 .817 
 
 28.17 
 
 0.15 
 
 7i 
 
 40 
 
 4 
 
 .5161 
 
 4- 
 
 9671 
 
 4 
 
 .9388 
 
 4 
 
 759 
 
 31-73 
 
 O.20 
 
 69 
 
 25 
 
 4 
 
 .4361 
 
 4- 
 
 9937 
 
 4 
 
 9555 
 
 5 
 
 .819 
 
 29.09 
 
 0.50 
 
 60 
 
 07 
 
 4 
 
 .0946 
 
 5- 
 
 4856 
 
 5 
 
 3792 
 
 13 
 
 .260 
 
 26.52 
 
 I. 00 
 
 49 
 
 43 
 
 3 
 
 .6988 
 
 6. 
 
 5H5 
 
 6 
 
 .2507 
 
 22 
 
 .672 
 
 22.67 
 
 1.274 
 
 44. 
 
 46 
 
 3 
 
 5139 
 
 7- 
 
 1032 
 
 6 
 
 7303 
 
 29 
 
 .006 
 
 22.76 
 
 The amount of water decreases with increase in concentra- 
 tion in the dilute solutions, reaches a minimum at 0.05 to 
 0.075 normal, and then increases regularly with increase in 
 concentration. 
 
 The values of H do not approach a constant until normal 
 concentration is reached. 
 
 It is very probable that the relatively low values of H for 
 0.05 and o.i normal are due to errors in measuring the freez- 
 ing points of those solutions. 
 
 The curves for magnesium nitrate are given in Figs. III. 
 and IV. 
 
 Barium Nitrate. 
 
 Owing to the very small solubility of this salt I did not at- 
 tempt to make measurements beyond 0.15 normal. Barium 
 nitrate has special interest in that it is the first salt thus far 
 studied in this investigation which, under ordinary condi- 
 tions, crystallizes without water. 
 
42 
 
 Table XXIX. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/I*. 
 
 i. 
 
 . 
 
 O.OI 
 
 0.05545 
 
 5-5450 
 
 2.9812 
 
 99.06 
 
 0.025 
 
 0.12482 
 
 4.9928 
 
 2.6838 
 
 84.19 
 
 0.05 
 
 0.23281 
 
 4-6566 
 
 2 5035 
 
 75-18 
 
 0.075 
 
 0.32704 
 
 4 3606 
 
 2 . 3440 
 
 67.20 
 
 O. IO 
 
 O.420I8 
 
 4.2018 
 
 2.2590 
 
 62.95 
 
 0.15 
 
 0-59935 
 
 3-9955 
 
 2.1481 
 
 57-40 
 
 Table XXX. Conductivity Measurements. 
 
 /AGO o = 128.08. 
 V. PV. a. 
 
 loo 110.62 86.37 
 
 40 99.04 77.32 
 
 20 90.26 70.47 
 
 13.34 83.92 65.51 
 
 10 78.59 61.36 
 
 6.67 71.05 55.47 
 
 Table XXXI. Specific Gravity Measurements. 
 
 m. 
 
 Sp. gr. 
 
 Wsoi. Wsait. WH^O- 
 
 Per cent of 
 correction. 
 
 O 
 
 .01 
 
 I 
 
 .OO2O3I 
 
 1002 
 
 .031 
 
 2 
 
 .14 
 
 999 
 
 .891 
 
 O 
 
 .088 
 
 
 
 .025 
 
 I 
 
 .005224 
 
 1005 
 
 .224 
 
 6 
 
 537 
 
 998 
 
 .687 
 
 
 
 131 
 
 
 
 .05 
 
 I 
 
 .010591 
 
 1010 
 
 591 
 
 13 
 
 .074 
 
 997 
 
 .517 
 
 
 
 .248 
 
 
 
 .075 
 
 I 
 
 .015671 
 
 1015 
 
 .6 7 I 
 
 19 
 
 .611 
 
 996 
 
 .060 
 
 
 
 .394 
 
 
 
 .10 
 
 I 
 
 .021143 
 
 102 1 
 
 143 
 
 26 
 
 .148 
 
 994 
 
 -995 
 
 
 
 .500 
 
 
 
 .15 
 
 I 
 
 .031770 
 
 1031 
 
 770 
 
 39 
 
 .222 
 
 992 
 
 .548 
 
 
 
 745 
 
 Table XXXII. Hydrates. 
 
 m. a. 
 
 L. 
 
 
 A/w. 
 
 
 L'. 
 
 M. 
 
 H. 
 
 0.05 
 
 70 
 
 47 
 
 4 
 
 4814 
 
 4 
 
 .6566 
 
 4 
 
 .6451 
 
 I . 
 
 957 
 
 39.15 
 
 0.075 
 
 65 
 
 .51 
 
 4 
 
 2969 
 
 4 
 
 .3606 
 
 4 
 
 3434 
 
 o. 
 
 595 
 
 7.93 
 
 O.IO 
 
 61 
 
 30 
 
 4 
 
 1425 
 
 4 
 
 .2018 
 
 4 
 
 .1808 
 
 
 
 509 
 
 5-09 
 
 O.IO 
 
 55 
 
 47 
 
 O ' 
 
 9234 
 
 3 
 
 9955 
 
 3 
 
 .9648 
 
 0, 
 
 5805 
 
 3-87 
 
 It will be seen that, like strontium nitrate, the molecular 
 lowering of the freezing point decreases regularly as the con- 
 centration increases, without showing a minimum value. 
 
 The amount of water held in combination decreases rapidly 
 and reaches a minimum at o.i normal. 
 
 The hydration per molecule is very small, as we should ex- 
 pect, since the salt in its solid state is anhydrous. In the 
 more dilute solutions, however, where the ions predominate, 
 the hydration is of the same order as that of the other nitrates 
 of the alkali earths. 
 
"\> "* ^K 
 
 OF THE \ 
 
 UNIVERSITY J 
 
 43 
 
 This is, indeed, convincing proof that the ions themselves 
 have great hydrating power. 
 
 It was pointed out in the introduction that if there were 
 no hydration the corrected molecular lowering of the freezing 
 point should be equal to the corrected lowering. A glance 
 at Table XXXII. will show how closely the assumption agrees 
 with facts. The values for the corrected freezing point low- 
 erings for the three most concentrated solutions, in which the 
 hydration is least, are only about one per cent higher than the 
 calculated values. Moreover, if there is no hydration and 
 if we may disregard the effect of viscosity upon the velocity 
 of the ions, we should expect the dissociation as measured by 
 the conductivity and freezing point methods to be the same. 
 That this is true may be seen by consulting the values of a 
 for 0.075, o.io, and 0.25 normal in Tables XXIX. and XXX. 
 Owing to slight hydration, the amounts of dissociation, as 
 measured by the freezing point method, are slightly higher 
 than those measured by the conductivity method. 
 
 The curves for barium nitrate are given in Figs. III. and 
 IV. 
 
 Since the two barium salts studied are so slightly soluble, 
 it was thought best to add the tables for the hydrates of bar- 
 ium bromide and barium iodide which were prepared by 
 Jones and Bassett. 1 Both of these salts crystallize with two 
 molecules of water of crystallization. 
 
 Table XXXIII. Hydrates. 
 
 m. 
 
 . 
 
 L. 
 
 A/ra. 
 
 L 1 . 
 
 M. 
 
 H. 
 
 O. 10 
 
 79-3 
 
 4.81 
 
 5.06 
 
 5-04 
 
 2-54 
 
 25.4 
 
 0.15 
 
 77-7 
 
 4-75 
 
 4.91 
 
 4.88 
 
 1.48 
 
 9-9 
 
 0.25 
 
 73-8 
 
 4.60 
 
 5-oo 
 
 4.96 
 
 4-03 
 
 16.1 
 
 0.40 
 
 71-3 
 
 4-52 
 
 5-09 
 
 5-03 
 
 5.63 
 
 14.1 
 
 0.50 
 
 68.8 
 
 4.42 
 
 5. 18 
 
 5-09 
 
 6.22 
 
 12.5 
 
 0.6774 
 
 65-3 
 
 4.29 
 
 5-74 
 
 5-59 
 
 12.92 
 
 19.1 
 
 0.9032 
 
 64.8 
 
 4.27 
 
 5-87 
 
 5 66 
 
 13.64 
 
 15-1 
 
 I. 1290 
 
 61.1 
 
 4-13 
 
 6.24 
 
 5-93 
 
 16.88 
 
 14.9 
 
 I 3548 
 
 58.4 
 
 4-03 
 
 6.66 
 
 6.28 
 
 19.90 
 
 14.7 
 
 1.5806 
 
 55-6 
 
 3-93 
 
 7.12 
 
 6.63 
 
 22.66 
 
 14-3 
 
 1.884 
 
 50.90 
 
 3-75 
 
 7.67 
 
 7.06 
 
 26.05 
 
 14.4 
 
 2.258 
 
 41.1 
 
 3-39 
 
 8-343 
 
 7-58 
 
 30.71 
 
 13-6 
 
 i Am, Chem. J., 33, 553 (1905); 34, 306 (1905). 
 
44 
 Table XXXIV. Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 A/m. 
 
 L'. 
 
 M. 
 
 H. 
 
 0.076 
 
 78.6 
 
 4.78 
 
 4.92 
 
 4.91 
 
 1-47 
 
 19.3 
 
 0.153 
 
 75-9 
 
 4.68 
 
 5.00 
 
 4.96 
 
 3-14 
 
 20.5 
 
 0.306 
 
 74-9 
 
 4.65 
 
 5-17 
 
 5-o8 
 
 4.70 
 
 15-4 
 
 0.612 
 
 71.0 
 
 4-54 
 
 6.08 
 
 5-86 
 
 12.51 
 
 20.4 
 
 0.917 
 
 64.8 
 
 4-27 
 
 6.69 
 
 6.29 
 
 17.84 
 
 19-5 
 
 I .222 
 
 6k. i 
 
 4 13 
 
 7-54 
 
 6.98 
 
 22.70 
 
 18.1 
 
 1.528 
 
 55-5 
 
 3-92 
 
 8.67 
 
 7-83 
 
 27.74 
 
 18.2 
 
 1.834 
 
 51.1 
 
 3-76 
 
 9.54 
 
 8-44 
 
 31.92 
 
 17.4 
 
 2.139 45.0 3.53 11.22 9.67 35-28 16.5 
 
 The solubilities of these two salts are nearly equal to that 
 of the other halides of the calcium group. It is very probable, 
 owing to the fact that Jones and Bassett used a thermometer less 
 sensitive than the one employed in this work, that the observed 
 freezing point lowerings for the most dilute solutions are too low. 
 This would, of necessity, give low values for the total com- 
 bined water and for the hydration. 
 
 The values of M for these salts increases regularly with 
 increase in concentration. The magnitude of hydration 
 for each salt is approximately constant. If we compare the 
 values of H for the four barium salts in Tables XVI., XXXII., 
 XXXIII., and XXXIV., we see that of the halides the iodide has 
 the greatest hydrating power, and the chloride the least, while 
 the bromide stands intermediate between the other two. 
 The nitrate has the least hydrating power. 
 
 Since the chloride, bromide, and iodide crystallize each with 
 two molecules of water, we should expect the observed molec- 
 ular lowering to be greater than the calculated. Experimen- 
 tal results confirm this. 
 
 Cobalt Chloride. 
 
 An approximately two normal solution was first made 
 up. A portion of this was diluted to convenient strength, 
 and the cobalt determined electrolytically. 
 
 Cobalt chloride crystallizes with 6 molecules of water, and, 
 like the other chlorides with the same amount of water of 
 crystallization, has a large hydrating power. The results are 
 just what we should expect. 
 
45 
 Table XXXV. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/w. 
 
 i. 
 
 a. 
 
 O.OI 
 
 0.06241 
 
 6 24.1 
 
 
 
 0.025 
 
 0.1394 
 
 vy . ^f-*- 
 5-5786 
 
 2.9992 
 
 99.96 
 
 0.05 
 
 o . 2609 
 
 5.2186 
 
 2.8057 
 
 90.28 
 
 0.075 
 
 0.3356 
 
 5.I4I3 
 
 2.7641 
 
 88.20 
 
 O. 10 
 
 0.5110 
 
 5-IIOO 
 
 2 . 7473 
 
 87.36 
 
 0.25 
 
 I . 3040 
 
 5.2160 
 
 2.8043 
 
 
 0.50 
 
 2.8371 
 
 5^743 
 
 3-0507 
 
 
 0.75 
 
 4.5860 
 
 6.II47 
 
 3-2874 
 
 
 I.OO 
 
 6.7157 
 
 6.7157 
 
 3-6105 
 
 
 i-5 
 
 12.1308 
 
 8.0871 
 
 4.3532 
 
 
 2.0 
 
 17.7342 
 
 8.8671 
 
 4-7672 
 
 
 Table XXXVI. Conductivity Measurements. 
 
 /*oo o = 117 (Jones and Bassett) 1 . 
 
 F. 
 
 Hv. 
 
 a. 
 
 IOO 
 
 113.06 
 
 96.63 
 
 40 
 
 104 . 86 
 
 89.62 
 
 20 
 
 99.30 
 
 84.80 
 
 13-34 
 
 96.00 
 
 82.05 
 
 IO 
 
 92.26 
 
 78.85 
 
 4 
 
 83.79 
 
 7I.6l 
 
 2 
 
 73-86 
 
 63.I4 
 
 1-334 
 
 66.15 
 
 56.54 
 
 i 
 
 59-58 
 
 50.92 
 
 0.667 
 
 48.59 
 
 4L53 
 
 0-5 
 
 38.51 
 
 32.91 
 
 Table XXXVII. Specific Gravity 
 
 Measurements . 
 
 m. Sp. gr. 
 
 W 50 l. Wsalt. 
 
 TTT Per cent of 
 w H z o- correction. 
 
 o.oi 1.001159 
 
 IOOI.I59 L299 
 
 999.860 0.014 
 
 0.025 1.003052 
 
 1003.052 3.247 
 
 999.805 0.019 
 
 o . 05 i . 006065 
 
 IOO6.065 6.495 
 
 999-5703 0.043 
 
 0.075 1.009190 
 
 1009.190 9-742' 
 
 5 999-447 0.055 
 
 o.io .012386 
 
 1012.386 12.990 
 
 999 - 396 o . 060 
 
 0.25 .03049 
 
 1030.491 32.475 
 
 998.016 0.19 
 
 0.50 .05492 
 
 1054.924 64.95 
 
 989.974 i.oo 
 
 0.75 .09118 
 
 1089.180 97.425 
 
 991.655 0.83 
 
 i.oo .11847 
 
 III8.47I 129.90 
 
 988.571 1.14 
 
 i-5 -17502 
 
 1175.026 194.85 
 
 980.176 1.98 
 
 2.0 .23637 
 
 1236.376 25.98 
 
 976.576 2.34 
 
 i Am. Chem. J., 33, 567 (1905). 
 
4 6 
 
 m. 
 
 0.025 
 0.05 
 0.075 
 
 O. 10 
 
 0.25 
 0.50 
 0.75 
 
 I.OO 
 
 1.5 
 
 2.0 
 
 a. 
 
 89.62 
 84.87 
 82.05 
 78.85 
 71.61 
 63.41 
 
 56.54 
 50.92 
 
 41-53 
 32.91 
 
 Table XXXVIII.. 
 
 L. 
 
 5.1938 
 5-0717 
 4.9122 
 
 4.7932 
 4.7098 
 4.2088 
 3.9632 
 3.7542 
 3.4049 
 
 3.0842 
 
 5.5786 
 5.2186 
 5-I4I3 
 
 5. i ioo 
 5.2160 
 
 5.6743 
 6.1417 
 
 6.7157 
 
 8.0871 
 8.8671 
 
 -Hydrates. 
 
 L'. 
 
 M. 
 
 5.5776 
 
 3-822 
 
 5.2164 
 
 2.122 
 
 5-1385 
 
 2.444 
 
 5 1070 
 
 3.413 
 
 5-2057 
 
 5.292 
 
 5.6176 
 
 13-93 
 
 5-9937 
 
 18.22 
 
 6.6394 
 
 24.14 
 
 7.9270 
 
 3L69 
 
 8.6594 
 
 35-76 
 
 H. 
 
 152.88 
 42.44 
 33-68 
 
 34-13 
 28.31 
 27.86 
 
 25.09 
 24.14 
 
 21. I 
 
 17.88 
 
 It will be noted, first of all, that the freezing point lower- 
 ings for all concentrations are greater than for any of the salts 
 
 AICI 
 
 5T 
 
 0.75 i 
 
 Concen tratlon . 
 Fig. V. 
 
47 
 
 thus far studied, and hence there is a correspondingly greater 
 difference between the observed and calculated lowerings. The 
 amount of water combined with the salt increases regularly 
 from 0.05 normal to the most concentrated solution, as shown 
 by Fig. VI. The hydration per molecule decreases rapidly 
 in the most dilute solutions, and approaches a constant value 
 at 0.25 normal. For the curve for hydrates, see Fig. V. 
 
 4-0 
 
 fl.5 
 
 0-75 1. 
 
 Concentration. 
 Fig. VI. 
 
 2.5 
 
 Cobalt Nitrate. 
 
 Cobalt nitrate, like cobalt chloride, crystallizes with 6 mole- 
 cules of water, and we should expect it to have hydrating 
 power of the same order of magnitude. The data given in 
 the following tables show that such is the case. What has 
 been said regarding cobalt chloride applies equally well to 
 the nitrate. 
 
 The curves for the values of H and M are found in Figs. 
 VII. and VIII., respectively. 
 
4 8 
 
 6 
 
 r 
 
 z 
 
 4.5 
 
 Concentration . 
 Fig. VII. 
 
 XXXIX. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/w. 
 
 it 
 
 a. 
 
 O.IO 
 
 0.0553 
 
 5-5300 
 
 2.9731 
 
 98.65 
 
 0.025 
 
 O.I34I 
 
 5-3640 
 
 2.8731 
 
 93.65 
 
 0.05 
 
 0.2572 
 
 5.1434 
 
 2.7652 
 
 88.26 
 
 0.075 
 
 0.3812 
 
 5.0826 
 
 2.7218 
 
 86.09 
 
 O.IO 
 
 0.5005 
 
 5.0050 
 
 2 . 7096 
 
 85.48 
 
 0.25 
 
 I . 2705 
 
 5.0082 
 
 2.7323 
 
 
 0.50 
 
 2.708 
 
 5-4I7 
 
 2.9125 
 
 
 0.75 
 
 4.338 
 
 5.784 
 
 3.1099 
 
 
 I.OO 
 
 6.22O 
 
 6.22O 
 
 3-3441 
 
 
 1.5 
 
 10.888 
 
 7.192 
 
 3.8668 
 
 
 2.0 
 
 18.863 
 
 9-431 
 
 5.0701 
 
 
49 
 
 10 
 
 Concentratl on . 
 Fig. VIII. 
 
 Table XL. Conductivity. 
 
 V. 
 ioo 
 
 40 
 
 20 
 
 13-334 
 10 
 4 
 
 2 
 
 1-333 
 i 
 
 0.668 
 0-5 
 
 117. 6. * 
 
 108 .66 
 100.69 
 96.12 
 91-67 
 89 .94 
 81.48 
 
 72.94 
 
 65.32 
 58.89 
 47.57 
 37-io 
 
 92 . 40 
 85.62 
 81.73 
 
 77-95 
 76 . 48 
 69.28 
 
 62.02 
 
 55.54 
 50.08 
 40.45 
 31-55 
 
 J. U/Ul'C- J\.J-i . 
 
 m. Sp. gr. 
 
 wj^xt'^f'yux \J 
 W SO l, 
 
 f U/ V flsj/ J. VJ. C-U/O */ C- II trf, JM-0 . 
 
 WsaU. WH^O. 
 
 Per cent of 
 correction. 
 
 
 
 .OI I.OOI496 
 
 1001 
 
 .496 
 
 I 
 
 830 
 
 999 
 
 .652 
 
 
 
 .033 
 
 
 
 .025 1.003863 
 
 1003 
 
 863 
 
 4 
 
 577 
 
 999 
 
 .286 
 
 
 
 .071 
 
 
 
 05 1-007579 
 
 1007 
 
 579 
 
 9 
 
 .154 
 
 998 
 
 425 
 
 
 
 157 
 
 
 
 .075 I.OII289 
 
 ion 
 
 .289 
 
 13 
 
 731 
 
 997 
 
 .558 
 
 
 
 .244 
 
 
 
 . IO 
 
 .015084 
 
 1015 
 
 .084 
 
 18 
 
 .308 
 
 996 
 
 .776 
 
 
 
 .322 
 
 
 
 25 
 
 03737 
 
 1037 
 
 .37 
 
 45 
 
 -77 
 
 991 
 
 .603 
 
 
 
 83 
 
 
 
 5 
 
 .07415 
 
 1074 
 
 15 
 
 9 1 
 
 54 
 
 982 
 
 .61 
 
 I 
 
 73 
 
 
 
 -75 
 
 . II204 
 
 mo 
 
 .04 
 
 137 
 
 .31 
 
 972 
 
 -73 
 
 2 
 
 .72 
 
 i 
 
 .00 
 
 . 14612 
 
 1146 
 
 . 12 
 
 183 
 
 .08 
 
 963.04 
 
 3 
 
 -69 
 
 i 
 
 .5 
 
 .21720 
 
 1217 
 
 .20 
 
 274 
 
 .62 
 
 942 
 
 58 
 
 5-74 
 
 2 
 
 .0 1.28576 
 
 1285 
 
 -76 
 
 366 
 
 .16 
 
 919.60 
 
 8 
 
 .04 
 
 i 
 
 Am. Chem. J., S3, 569 
 
 (1905). 
 
 
 
 
 
 
 
 
50 
 Table XLIL Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 A/m. 
 
 
 L'. 
 
 
 M. 
 
 ff. 
 
 0. 
 
 025 
 
 85 
 
 .62 
 
 5- 
 
 0451 
 
 5-3640 
 
 5 
 
 .3602 
 
 3 
 
 .266 
 
 130.6 
 
 0. 
 
 05 
 
 81 
 
 73 
 
 4- 
 
 9003 
 
 5-1434 
 
 5 
 
 1354 
 
 2 
 
 -544 
 
 50.8 
 
 0. 
 
 075 
 
 77 
 
 95 
 
 4- 
 
 7597 
 
 5.0826 
 
 5 
 
 .0702 
 
 3 
 
 .402 
 
 45-3 
 
 0. 
 
 10 
 
 76 
 
 48 
 
 4- 
 
 7050 
 
 5-0050 
 
 4 
 
 .9889 
 
 3 
 
 .161 
 
 31-6 
 
 0. 
 
 25 
 
 69 
 
 .28 
 
 4- 
 
 437 
 
 5.082 
 
 5 
 
 .0296 
 
 6 
 
 445 
 
 25-8 
 
 0. 
 
 5 
 
 62 
 
 .02 
 
 4- 
 
 167 
 
 5-4I7 
 
 5 
 
 .323 
 
 12 
 
 .070 
 
 24.1 
 
 0. 
 
 75 
 
 55 
 
 54 
 
 3- 
 
 926 
 
 5.784 
 
 5 
 
 .627 
 
 16 
 
 .880 
 
 22.5 
 
 I. 
 
 oo 
 
 50 
 
 .08 
 
 3- 
 
 723 
 
 6.220 
 
 5 
 
 990 
 
 21 
 
 .020 
 
 21. O 
 
 I . 
 
 5 
 
 40 
 
 45 
 
 3- 
 
 364 
 
 7.192 
 
 6 
 
 .779 
 
 27 
 
 .980 
 
 I8. 7 
 
 2.0 31.55 3-033 9-43 1 8.607 30.123 18.0 
 
 Copper Chloride. 
 
 Diluted portions of the mother solution were taken and 
 the copper in them determined electrolytically. 
 
 While copper chloride crystallizes with two molecules of 
 water, its power to combine with water is of the same order 
 of magnitude as that of cobalt chloride and cobalt nitrate, 
 as may be seen in the curves, Figs. V. and VII. 
 
 The total amount of water combined with the electrolyte 
 passes through a minimum at about 0.05 normal and then 
 increases rapidly with increase in concentration. This is 
 seen in Fig. VI. 
 
 Table XL/77. Freezing Point Measurements. 
 
 a. 
 
 m. 
 
 A. 
 
 A/w. 
 
 (. 
 
 O.OI 
 
 O.OS7O1 
 
 5 . 7OV) 
 
 
 0.05 
 
 " v \j / ^^O 
 
 0.24944 
 
 \} i ^"^O 
 
 4.9888 
 
 2.6821 
 
 0.075 
 
 0.37075 
 
 4-9433 
 
 2.6576 
 
 O.IOO 
 
 o . 48665 
 
 4-8665 
 
 2.6164 
 
 0.25 
 
 1.2237 
 
 4-894 
 
 2.6316 
 
 0.50 
 
 2.669 
 
 5-338 
 
 2.8701 
 
 0.75 
 
 4-245 
 
 5-66i 
 
 3-0436 
 
 I.OO 
 
 5-994 
 
 5-994 
 
 3.2228 
 
 1.50 
 
 10.105 
 
 6.737 
 
 3.6220 
 
 2.0 
 
 15-294 
 
 7.647 
 
 4. III2 
 
 84. 10 
 
 80.82 
 
Table XLIV. Conductivity Measurements. 
 
 /AOO o = 1 20 (Jones and Bassett). 1 
 
 F. /*. a. 
 
 loo 110.55 92.12 
 
 20 95-88 79-98 
 
 13.34 93.27 77.72 
 
 10 90.21 75-17 
 
 4 80.20 66.83 
 
 2 6908 57.56 
 
 1.334 61.03 50.86 
 
 I 54.01 45.00 
 
 0.6666 41.81 34.84 
 
 0.5 31.56 26.30 
 
 Table XLV. Specific Gravity Measurements. 
 
 m. 
 
 Sp. gr. 
 
 Wsol. 
 
 Wsalt. 
 
 
 Per cent of 
 correction. 
 
 O.OI 
 
 .OOI208 
 
 1001.208 
 
 1-345 
 
 999.863 
 
 0.013 
 
 0.05 
 
 .006370 
 
 1006.370 
 
 6.725 
 
 999-645 
 
 0.035 
 
 0.075 
 
 .009264 
 
 1009 . 264 
 
 10.0875 
 
 999.176 
 
 0.084 
 
 O. IO 
 
 .012614 
 
 1012.614 
 
 I3-450 
 
 999.164 
 
 0.263 
 
 0.20 
 
 .030991 
 
 1030.991 
 
 33-625 
 
 997.366 
 
 0.263 
 
 0.50 
 
 051479 
 
 1061.479 
 
 67.25 
 
 994.229 
 
 0-57 
 
 0-75 
 
 .090912 
 
 1090.91 
 
 100.87 
 
 990-037 
 
 0-99 
 
 I.OO 
 
 . 120249 
 
 1120.24 
 
 134-5 
 
 985 - 749 
 
 1.42 
 
 1.50 
 
 .177618 
 
 1177.61 
 
 201.75 
 
 975.868 
 
 2.41 
 
 2.0 
 
 234551 
 
 1234.55 
 
 269.0 
 
 965.55 
 
 3-44 
 
 Table XLV I. Hydrates. 
 
 m. 
 
 a. 
 
 L. 
 
 
 b\m. 
 
 L'. 
 
 
 M. 
 
 H. 
 
 O. 
 
 05 
 
 79 
 
 98 
 
 4 
 
 8352 
 
 4 
 
 9888 
 
 4.9871 
 
 i 
 
 693 
 
 33-85 
 
 0. 
 
 075 
 
 77 
 
 .72 
 
 4 
 
 
 4 
 
 9433 
 
 4.9392 
 
 2 
 
 .116 
 
 28.21 
 
 0. 
 
 IO 
 
 75 
 
 17 
 
 4 
 
 6563 
 
 4 
 
 8665 
 
 4.8695 
 
 2 
 
 354 
 
 23-54 
 
 0. 
 
 20 
 
 66 
 
 -83 
 
 4 
 
 3460 
 
 4 
 
 8949 
 
 4.8821 
 
 6 
 
 .091 
 
 24-36 
 
 0. 
 
 50 
 
 57 
 
 .56 
 
 4 
 
 0012 
 
 5. 
 
 3384 
 
 5 - 3076 
 
 13 
 
 .67 
 
 27-34 
 
 0. 
 
 75 
 
 50 
 
 .86 
 
 3 
 
 7519 
 
 & 
 
 6611 
 
 5-5748 
 
 18 
 
 -17 
 
 24.22 
 
 I . 
 
 oo 
 
 45 
 
 .00 
 
 3 
 
 5340 
 
 5- 
 
 9945 
 
 5.9088 
 
 22 
 
 -33 
 
 22.33 
 
 I . 
 
 50 
 
 34 
 
 .84 
 
 3 
 
 1560 
 
 6. 
 
 7370 
 
 6.5747 
 
 26 
 
 .66 
 
 17.78 
 
 2. 
 
 00 
 
 26 
 
 30 
 
 2. 
 
 8383 
 
 7- 
 
 6470 
 
 7-3836 
 
 34 
 
 .20 
 
 17.10 
 
 I 
 
 Am. Chem. 
 
 J.,35 
 
 \, 576 (1905). 
 
52 
 
 Copper Nitrate. 
 
 The mother solution of the salt was diluted to convenient 
 strength and the copper determined electrolytically. 
 
 Copper nitrate crystallizes with 6 molecules of water and, 
 therefore, should give us hydration of the same order of mag- 
 nitude as that found for the nitrate of cobalt and nickel, 
 which crystallize with the same amount of water. Refer- 
 ence to Table L. will show that this is the fact. The minimum 
 for the total amount of combined water is pronounced and 
 lies between 0.075 and 0.25 normal. The hydration per mole- 
 cule decreases rapidly with increase in concentration to 0.25 
 normal, and then becomes approximately constant. 
 
 The curves representing the values of H and M are given 
 in Figs. VII. and VIII., respectively. 
 
 Table XLVII. Freezing Point Measurements. 
 m. A. Ajm. i. a. 
 
 0.025 
 
 0.13852 
 
 o / o v j 
 5-5401 
 
 o - 
 
 2.9785 
 
 98.92 
 
 0.05 
 
 0.25540 
 
 5.I08I 
 
 2.7463 
 
 87.31 
 
 0.075 
 
 0.36979 
 
 4.9306 
 
 2.6508 
 
 82.54 
 
 0.25 
 
 I. 221 
 
 4.885 
 
 2.6264 
 
 81.32 
 
 0.5 
 
 2.589 
 
 5.178 
 
 2.7841 
 
 
 0.75 
 
 4.190 
 
 5.587 
 
 3.0039 
 
 
 0-935 
 
 5-512 
 
 5.895 
 
 3.1696 
 
 
 1.50 
 
 10.284 
 
 6.856 
 
 3.6861 
 
 
 2.0 16.89 8.44 4-54I9 
 
 Table XLVIII. Conductivity Measurements. 
 /*oo o = nS. 1 
 
 V. Mr. a. 
 
 loo 108.84 92.24 
 
 40 IOI.2 85.76 
 
 2O 95.7 Sl.IO 
 
 13-34 91-86 77.85 
 
 4 79.4 57.29 
 
 69.8 
 
 1-334 62.0 52.54 
 
 1.0695 56.89 48.21 
 
 0.667 44-0 37-29 
 
 0.5 33-47 28.36 
 
 Am. Chem. J., 88, 578 (1905). 
 
53 
 Table XLIX. Specific Gravity Measurements. 
 
 m. 
 
 Sp. gr. 
 
 Wsol. 
 
 Wsalt. 
 
 WH Z O. 
 
 Per cent, of 
 correction 
 
 O.OI 
 
 1.001504 
 
 iooi . 5049 
 
 1.876 
 
 999.628 
 
 0.037 
 
 0.025 
 
 I . 004076 
 
 1004 . 0764 
 
 4.692 
 
 999.384 
 
 0.061 
 
 0.05 
 
 1.007859 
 
 1007.8599 
 
 9.384 
 
 998.4759 
 
 0.152 
 
 0.075 
 
 I.OII7I5 
 
 IOII.7I55 
 
 14.076 
 
 997.6395 
 
 0.236 
 
 0.25 
 
 I . 040290 
 
 1040.2903 
 
 46 . 920 
 
 993.370 
 
 0.663 
 
 0.50 
 
 1.07723 
 
 1077.230 
 
 93.840 
 
 983.390 
 
 1.66 
 
 0-75 
 
 1 . 1 1469 
 
 III4.699 
 
 140.76 
 
 973-930 
 
 2.607 
 
 0-935 
 
 I. 14262 
 
 1142.627 
 
 174.48 
 
 968 . 140 
 
 3.188 
 
 1-5 
 
 I.226l8 
 
 1226. 183 
 
 281.52 
 
 944 . 660 
 
 5-53 
 
 2.0 
 
 I .29262 
 
 1292.623 
 
 375.36 
 
 917.26 
 
 8.27 
 
 Table L. -Hydrates. 
 
 m. 
 
 a 
 
 
 
 L. 
 
 A/w. 
 
 
 L'. 
 
 M. 
 
 H, 
 
 
 0.025 
 
 75- 
 
 76 
 
 5 
 
 .0502 
 
 5-5401 
 
 5 
 
 .5368 
 
 4- 
 
 882 
 
 195 
 
 .2 
 
 0.05 
 
 81. 
 
 10 
 
 4 
 
 .8769 
 
 5.1081 
 
 5 
 
 .1005 
 
 2. 
 
 435 
 
 48 
 
 7 
 
 0.075 
 
 77- 
 
 85 
 
 4 
 
 756o 
 
 4.9306 
 
 4 
 
 .9188 
 
 I . 
 
 839 
 
 24 
 
 5 
 
 0.25 
 
 67. 
 
 29 
 
 4 
 
 363 
 
 4.885 
 
 4 
 
 852 
 
 5. 
 
 607 
 
 22 
 
 4 
 
 0.50 
 
 59. 
 
 15 
 
 4 
 
 .060 
 
 5.178 
 
 5 
 
 .092 
 
 II. 
 
 261 
 
 22 
 
 5 
 
 0-75 
 
 52. 
 
 54 
 
 3 
 
 .814 
 
 5.587 
 
 5 
 
 .441 
 
 16. 
 
 612 
 
 22 
 
 15 
 
 0-935 
 
 48. 
 
 21 
 
 3 
 
 .653 
 
 5.895 
 
 5 
 
 .708 
 
 19- 
 
 953 
 
 21 
 
 3 
 
 1.50 
 
 37- 
 
 29 
 
 3 
 
 .247 
 
 6.856 
 
 6 
 
 447 
 
 27. 
 
 575 
 
 18 
 
 .38 
 
 2.0 
 
 28. 
 
 36 
 
 2 
 
 .914 
 
 8.44 
 
 7 
 
 749 
 
 34- 
 
 65 
 
 17 
 
 32 
 
 Nickel Nitrate. 
 
 The nickel was determined electrolytically in diluted por- 
 tions of the mother solution. 
 
 The hydrating power of nickel nitrate is of the same order 
 of magnitude as that of cobalt and copper nitrates, which crys- 
 tallize with the same amounts of water (see Fig. IX.). The 
 total combined water passes through a minimum at 0.05 nor- 
 mal and then increases rapidly with increasing concentra- 
 tion (see Fig. X.). 
 
54 
 
 Table LI. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/w. 
 
 i. 
 
 a. 
 
 O.OI 
 
 0.0550 
 
 5.5070 
 
 2 . 9607 
 
 98.03 
 
 0.025 
 
 0.1299 
 
 5 - 1960 
 
 2 . 7950 
 
 89.75 
 
 0.05 
 
 0.2487 
 
 4-9745 
 
 2.6744 
 
 83.72 
 
 0.075 
 
 o . 3664 
 
 4.8854 
 
 2.6265 
 
 81.32 
 
 0. 10 
 
 o . 4960 
 
 4.9602 
 
 2.6667 
 
 
 0.25 
 
 1.251 
 
 5-003 
 
 2.69OI 
 
 
 0.5 
 
 2.652 
 
 5-305 
 
 2.8524 
 
 
 0.75 
 
 4-213 
 
 5-6i8 
 
 3.0205 
 
 
 1. 00 
 
 6.101 
 
 6. 101 
 
 3.2801 
 
 
 1.5 
 
 10.576 
 
 7-051 
 
 3.7910 
 
 
 2.0 
 
 17-050 
 
 8.523 
 
 4-5334 
 
 
 Table LII. Conductivity Measurements. 
 
 117. 2 
 
 V. 
 100 
 
 40 
 
 20 
 13.34 
 
 10 
 4 
 
 2 
 
 a. 
 
 1-334 
 
 i.o 
 
 0.667 
 0-5 
 
 106.77 
 100.31 
 
 93.57 
 89.74 
 
 87.84 
 80 . 07 
 
 71-44 
 64.06 
 
 57.38 
 
 45-79 
 35.61 
 
 91.10 
 85.58 
 79-83 
 76.77 
 74-94 
 68.31 
 60.95 
 54-65 
 48.95 
 39-06 
 
 30.38 
 
 Table LIII. Specific Gravity Measurements. 
 
 ,,'JI 
 
 w. 
 
 Sp. gr. 
 
 w* 
 
 oL 
 
 
 Wsalt. 
 
 Wi 
 
 7 2 0. 
 
 Per 
 cor 
 
 cent c 
 rectioi 
 
 
 
 .01 
 
 .OOI52I 
 
 IOOI 
 
 521 
 
 i 
 
 .8278 
 
 999 
 
 .693 
 
 
 
 .030 
 
 
 
 .025 
 
 .003882 
 
 1003 
 
 .882 
 
 4 
 
 .5695 
 
 999 
 
 .312 
 
 
 
 .068 
 
 
 
 05 
 
 .007792 
 
 1007 
 
 .792 
 
 9 
 
 139 
 
 998 
 
 653 
 
 
 
 134 
 
 
 
 .075 
 
 .011541 
 
 IOII 
 
 541 
 
 13 
 
 .7085 
 
 997 
 
 .029 
 
 
 
 .216 
 
 
 
 .10 
 
 .015307 
 
 1015 
 
 377 
 
 18 
 
 .278 
 
 997 
 
 .029 
 
 
 
 .291 
 
 
 
 .25 
 
 .03837 
 
 1038 
 
 -37 
 
 45 
 
 695 
 
 992 
 
 .68 
 
 
 
 .732 
 
 
 
 5 
 
 .07611 
 
 1076 
 
 . ii 
 
 9i 
 
 390 
 
 984 
 
 .72 
 
 r 
 
 .527 
 
 
 
 75 
 
 .11310 
 
 1113 
 
 . 10 
 
 137 
 
 .08 
 
 976 
 
 .01 
 
 2 
 
 39 
 
 I 
 
 .0 
 
 . 14562 
 
 1145 
 
 .62 
 
 182 
 
 78 
 
 962 
 
 .88 
 
 3 
 
 .71 
 
 I 
 
 5 
 
 .22134 
 
 1221 
 
 -34 
 
 274 
 
 17 
 
 947 
 
 17 
 
 5 
 
 .28 
 
 2 
 
 .0 
 
 t 29459 
 
 1294 
 
 59 
 
 365 
 
 .56 
 
 929 
 
 03 
 
 7 
 
 .09 
 
 * Am. Chem. J., 33, 574 (1905). 
 
55 
 
 Table LIV. Hydrates, 
 m. a. L. A/m. L' . M. H. 
 
 0.05 
 
 79 
 
 83 
 
 4 
 
 .8296 
 
 4- 
 
 9745 
 
 4 
 
 .9679 
 
 i. 
 
 545 
 
 30.9 
 
 0.075 
 
 76 
 
 .0 
 
 4 
 
 .7084 
 
 4- 
 
 8854 
 
 4 
 
 8749 
 
 i. 
 
 797 
 
 25-3 
 
 0.075 
 
 76 
 
 57 
 
 4 
 
 .7084 
 
 4- 
 
 8854 
 
 4 
 
 .8749 
 
 i . 
 
 897 
 
 25-3 
 
 O. 10 
 
 74 
 
 94 
 
 A 
 
 .6477 
 
 4- 
 
 9675 
 
 4 
 
 .8721 
 
 2. 
 
 560 
 
 25.6 
 
 0.25 
 
 68 
 
 3i 
 
 4 
 
 .401 
 
 5- 
 
 0036 
 
 4 
 
 .9670 
 
 6. 
 
 329 
 
 25-3 
 
 0.50 
 
 60 
 
 95 
 
 4 
 
 .127 
 
 5- 
 
 305 
 
 5 
 
 .225 
 
 ii . 
 
 672 
 
 23-3 
 
 0.75 
 
 54 
 
 65 
 
 3 
 
 .894 
 
 5- 
 
 618 
 
 5 
 
 .484 
 
 16. 
 
 IO2 
 
 21.4 
 
 I.OO 
 
 48 
 
 95 
 
 3 
 
 .700 
 
 6. 
 
 102 
 
 5 
 
 875 
 
 20. 
 
 561 
 
 20.5 
 
 1.5 
 
 39 
 
 .06 
 
 3 
 
 313 
 
 7- 
 
 051 
 
 6 
 
 .679 
 
 27. 
 
 99 8 
 
 18.6 
 
 2.O 
 
 30 
 
 38 
 
 2 
 
 990 
 
 8. 
 
 525 
 
 7 
 
 .921 
 
 34- 
 
 58 
 
 17-3 
 
 Before going farther, it will be interesting to note the great 
 similarity between the salts of cobalt, copper, and nickel which 
 we have just studied. Solutions of the same concentrations 
 were used in all five salts. 
 
 Reference to Figs. VI., VIII., and X. will show at a glance 
 the close relation between the amounts of water held in com- 
 bination by these salts, whether they are chlorides or nitrates. 
 We are not surprised at this, since, with the exception of cop- 
 per chloride, all crystallize with 6 molecules of water. In 
 fact, we found it impossible to put more than two curves on 
 one sheet, so closely did the values agree. From the min- 
 imum in the most concentrated solutions studied, the magni- 
 tude of the hydrating power is a linear function of the concen- 
 tration. In other words, each hydrate has its own definite 
 composition, which varies with every concentration. 
 
 The curves representing the hydration per molecule (Figs. 
 V., VII., and IX.) show the same striking similarity. They are 
 almost asymptotic with the two coordinates. The hydration 
 per molecule decreases very rapidly, for the very dilute solu- 
 tions, to approximately the same concentration, when they 
 become nearly constant for further increase in concentration. 
 
 Two conclusions are to be drawn from these relations. It 
 will be noted that the molecular hydration and the total amount 
 of water held in combination are the same for any two salts 
 containing a common cation. It seems most probable that 
 
 if the two anions, Cl and NO 3 , possess very different hydra- 
 
0.1 0..25 0-5 
 
 Concentration. 
 Fig. IX. 
 
 ting power, this influence would manifest itself. It is a well- 
 known fact that organic acids possess little or no hydrating 
 power, and in the work which I have done upon the strong 
 acids hydrochloric, nitric, and sulphuric this has been found 
 to hold in the dilute solutions, where the dissociation is prac- 
 tically complete. 
 
 This would lead us to conclude that the hydrating power 
 of any salt is primarily a function of the cation. 
 
 In the discussion of the nitrates and chlorides of the alkaline 
 earth group, attention was called to the fact that the hydra- 
 ting power of those salts is an inverse function of the atomic 
 volumes. 
 
57 
 
 In the case of the salts of cobalt, copper, and nickel which 
 we have studied, we have to do with cations which have ap- 
 proximately the same atomic volumes. 
 
 As stated by Ostwald, 1 the migration velocity of an organic 
 acid decreases with increase in the mass of the anion, as well 
 as with increase in the mass of the cation in case of the organic 
 bases. We should expect, then, to obtain larger values for 
 conductivity than those given by the alkaline earth metals. 
 Experiment shows the opposite to be the fact. We are, there- 
 fore, forced to believe that the effect of the atomic volume 
 of the ions upon the conductivity is more than compensated 
 for by the relatively large volume of the ionic complex. 
 
 Bredig 2 pointed out the fact that the migration velocities 
 of elementary cations are a periodic function of the atomic 
 weights. When plotted in a curve, where the ordinates rep- 
 resent velocities and the abscissas the atomic weights, it will 
 be seen that the alkali metals lie very near the maxima of 
 the curve, along with the halogens. At the extreme minima 
 we find aluminium and chromium. Slightly above these lie 
 the metals of the copper group, zinc, and cadmium; while 
 still higher are to be found the metals of the alkaline earths. 
 
 The significance of this periodic relation between the migra- 
 tion velocities of the cations and the atomic weights has never 
 been satisfactorily explained. 
 
 We believe that we have found the cause of this phenomenon. 
 Of two ions or ionic complexes of different volumes, that one 
 will meet with less friction on moving through the solution 
 which has the smaller volume. Consequently, it will have 
 the greater velocity. On the other hand, the greater the vol- 
 ume, the greater will be the friction to be overcome by the 
 ion, and, hence, the smaller the velocity. Therefore, we should 
 expect to find that those salts which crystallize with little 
 or no water of crystallization give greater values for conduc- 
 tivity than those crystallizing with a greater amount. 
 
 It is a well-known law that the conductivity of an electro- 
 lyte depends upon the velocities of the ions. These veloci- 
 ties, in turn, depend upon the fluidity and the volume of the 
 
 1 Lehrbuch, 2, 679. 
 
 Z. physik. Chem., 13, 242 (1894). 
 
58 
 
 ion. The greater the volume, the greater will be the resist- 
 ance offered to the movement of the ions. 
 
 If we consider the alkalis we find that potassium, rubidium, 
 and caesium, which have the largest atomic volumes and 
 whose salts generally crystallize without water, have the great- 
 est migration velocities, while lithium and sodium, which have 
 smaller atomic volumes and whose salts crystallize with two 
 or three molecules of water, have very much smaller migra- 
 tion velocities. 
 
 Comparing the members of the calcium group, we find that 
 the atomic volumes increase with increasing atomic weight. 
 The migration velocities of the cations calcium and strontium, 
 whose salts usually crystallize with 6 molecules of water, are 
 approximately equal to that of the barium cation, whose 
 salts crystallize either with two molecules of water, or water- 
 free. On the other hand, the magnesium cation, of smaller 
 atomic volume, has a slightly smaller migration velocity, due 
 to the more complex composition of its hydrates. 
 
 The cations of cobalt, copper, and nickel have approximately 
 'the same atomic weights, the same atomic volume, and the same 
 hydrating power. Since these cations have the greatest 
 hydrating power of any which we have studied, we should 
 expect them to have the smallest migration velocities, and 
 such is the case. 
 
 Aluminium Chloride. 
 
 Special interest is attached to the study of aluminium 
 chloride, owing to the fact that it is a quaternary electrolyte 
 and crystallizes with six molecules of water. 
 
 The hydrolytic effect of water upon this salt, in dilute solu- 
 tions, can be noted in the first two concentrations. The hy- 
 drochloric acid liberated is almost completely dissociated 
 at the dilutions in question, thus giving values for L which are 
 considerably higher than would be obtained if the salt were 
 not hydrolyzed. This may be attributed to one of two causes : 
 the very high migration velocity of the hydrogen ion; its ina- 
 bility to form hydrates; or both. It is at about 0.075 
 normal that the influence due to the hydration of the alumin- 
 ium cation begins to predominate. Just as we should ex- 
 
59 
 
 pect, the number of molecules of water held in combination 
 by one molecule of the electrolyte is large and increases very 
 rapidly with increase in concentration (see Fig. VI.). In the 
 curve representing the hydration per molecule (Fig. V.), 
 that part representing concentrations between 0.075 an d 0.5 
 normal represents the abnormality in the hydration due to 
 hydrolysis. 
 
 A glance at column a (Table LVIII.) shows us that, in spite 
 of the tendency of this salt to hydrolyze, the dissociation de- 
 creases very rapidly with increase in concentration. This 
 is just what might be predicted. Its atomic volume is very 
 small and the hydrating power of its cation very large. There- 
 fore, it should have a very small migration velocity. 
 
 Table LV. Freezing Point Measurements, 
 m. A. A/*. i. a. 
 
 o.oi 0.712 7.1200 3.8279 94.26 
 
 0.025 0.1623 6.4940 3.4193 80.64 
 
 0.05 0.3053 6.1060 3.2827 76.09 
 
 0.075 0.4511 6.0153 3.2340 74-46 
 
 o.io 0.4511 6.0850 3.2704 
 
 0.25 1.6604 6.641 3.5708 
 
 0.50 3-9446 7.889 4-2415 
 
 0-75 7-1339 9-5H 5-H37 
 
 i. oo n.795 n-795 6.341 
 
 1.5 25. 5 1 17.000 9-I398 
 
 2.0 48. 5 1 24.25 13-037 
 
 Table LVI. Conductivity Measurements. 
 
 Poo o = i7o. 2 
 
 V. fj. v . a. 
 
 100 156.48 92.04 
 
 40 141.24 83.08 
 
 20 130.44 76.72 
 
 13.334 126.66 74-50 
 
 10 122.07 71.80 
 
 4 106 .90 62 . 88 
 
 2 88.60 52.11 
 
 1-333 75-02 44.12 
 
 i 61.93 36.42 
 
 1.6667 41.62 24.48 
 
 0.5 25.47 14.98 
 
 1 These freezing points were determined by means of an alcohol thermometer 
 and freezing mixtures of solid carbon dioxide and ether. 
 * Am. Chem. J., 31, 333 (1904). 
 
6o 
 
 Table LVH. Specific 
 
 Sp.gr. Wsol. 
 
 Gravity Measurements. 
 
 Wsalt. 
 
 Per cent of 
 correction. 
 
 
 
 .OI 
 
 .00104 
 
 IOOI 
 
 .04 
 
 i 
 
 3345 
 
 999 
 
 7i 
 
 
 
 .029 
 
 
 
 025 
 
 .00282 
 
 IOO2 
 
 .82 
 
 3 
 
 3625 
 
 999 
 
 49 
 
 
 
 051 
 
 
 
 05 
 
 .00588 
 
 1005 
 
 .88 
 
 6 
 
 .6725 
 
 999 
 
 .21 
 
 
 
 .079 
 
 
 
 075 
 
 .00870 
 
 1008 
 
 .70 
 
 10 
 
 .0087 
 
 998 
 
 .70 
 
 
 
 .130 
 
 
 
 . I 
 
 .01158 
 
 IOII 
 
 .58 
 
 13 
 
 345 
 
 998 
 
 .24 
 
 
 
 .176 
 
 
 
 25 
 
 .02911 
 
 1029 
 
 . ii 
 
 33 
 
 36 
 
 995 
 
 75 
 
 
 
 425 
 
 
 
 55 
 
 .05706 
 
 1057 
 
 .06 
 
 66 
 
 725 
 
 990 
 
 33 
 
 
 
 .966 
 
 
 
 .08431 
 
 1084 
 
 31 
 
 IOO 
 
 .087 
 
 988 
 
 .22 
 
 I 
 
 57 
 
 I 
 
 .00 
 
 .11054 
 
 1 1 10 
 
 54 
 
 133 
 
 45 
 
 977 
 
 .09 
 
 2 
 
 .29 
 
 I 
 
 5 
 
 . 16308 
 
 1163.08 
 
 200 
 
 175 
 
 962 
 
 905 
 
 3 
 
 .70 
 
 2 
 
 .00 1.21378 
 
 1213 
 
 .78 
 
 266 
 
 .90 
 
 946 
 
 .88 
 
 5 
 
 3i 
 
 Table LV III. Hydrates. 
 
 1 
 
 o 
 
 m. 
 .01 
 
 1 
 
 Q2 
 
 a. 
 .04 
 
 L. 
 6.9958 
 
 7 
 
 A/w. 
 . I2OO 
 
 7 
 
 L'. 
 
 .1180 
 
 
 M. 
 
 H. 
 
 o 
 
 .025 
 
 -7 
 
 8^ 
 
 T^ 
 
 .08 
 
 J7Z7 \j 
 
 6.4QS8 
 
 6 
 
 .4Q4O 
 
 6 
 
 .4007 
 
 
 
 
 o 
 
 \^** ^j 
 
 .OS 
 
 O 
 
 76 
 
 . 72 
 
 *T;7_/ 
 
 6. I4OQ 
 
 6 
 
 i ^7^^^ 
 
 . 1060 
 
 6 
 
 T^ X / 
 
 . IOI2 
 
 
 
 
 o 
 
 **vP 
 
 .075 
 
 / 
 
 74 
 
 / 
 
 . so 
 
 V A .i-f-V^^ 
 
 6.0111 
 
 6 
 
 1526 
 
 6 
 
 1447 
 
 
 
 
 
 
 
 
 I 
 
 2 
 
 ^* / \J 
 
 . IO 
 
 25 
 
 5 
 .00 
 
 .0 
 
 / T^ 
 
 71 
 62 
 
 44 
 36 
 24 
 14 
 
 *-J 
 
 .80 
 .88 
 
 . 12 
 
 42 
 .48 
 .98 
 
 5.8664 
 
 5-368 
 
 4.321 
 3.892 
 3-225 
 2.695 
 
 6 
 6 
 
 ii 
 17 
 24 
 
 .1560 
 .641 
 
 -795 
 .000 
 
 -25 
 
 6 
 6 
 
 9 
 ii 
 16 
 
 22 
 
 fcj-fef. ^ 
 
 .1452 
 .613 
 .362 
 523 
 369 
 963 
 
 2 
 10 
 
 9 
 
 36 
 
 44 
 49 
 
 52 
 54 
 9i 
 .78 
 .60 
 03 
 
 25.2 
 42.16 
 39.88 
 36.78 
 29-33 
 24-5I 
 
 Sodium Bromide. 
 
 Dilute portions of the mother solution were standardized 
 volumetrically by Volhard's method, This salt differs from 
 those preceding in that it is a binary electrolyte and crystal- 
 lizes with two molecules of water. A study of Table LXII. 
 brings out the same general results. The observed molecular 
 lowering passes through a minimum between 0.5 and 0.75 
 normal. The minimum in the total amount of combined 
 water occurs at o.io normal. From the amounts of water 
 which combine with one gram molecule of the salt, it will be 
 seen that the sodium cation has nearly the same hydrating 
 power in dilute solutions as do the cations of the calcium and 
 copper groups. 
 
 The atomic volume of sodium is slightly more than half 
 
6i 
 
 that of potassium. Its hydrating power, however, for the 
 more dilute solutions is much greater. If, then, the amount 
 of hydration of the sodium ion is more than sufficient to com- 
 pensate for the inverse volume relations, we should expect the 
 migration velocity of sodium to be less than that of potassium. 
 This has been found to be the case. 1 
 
 The atomic volume of sodium is also slightly less than that 
 of calcium, and considerably less than those of strontium and 
 barium; yet, owing to the greater hydration of the cations 
 of the calcium group, its migration velocity is greater. 
 
 For the curves representing the values of H and M, see Figs. 
 IX. and X. 
 
 Table LIX. Freezing Point Measurements, 
 m. A. A/w. i. a. 
 
 0.025 
 
 0.0952 
 
 3 . 8090 i 
 
 i . 0478 
 
 104.78 
 
 0.05 
 
 0.1863 
 
 3.7260 ; 
 
 2 . 0032 
 
 100.32 
 
 0.075 
 
 0.2727 
 
 3-636 
 
 .9548 
 
 95.48 
 
 O. IO 
 
 0.3572 
 
 3-572 
 
 .9204 
 
 92.04 
 
 0.25 
 
 0.885 
 
 3-543 
 
 .9049 
 
 90.49 
 
 0.50 
 
 1.787 
 
 3-574 
 
 .9215 
 
 
 0.75 
 
 2.696 
 
 3-595 
 
 .9327 
 
 
 I. 00 
 
 3-633 
 
 3.633 
 
 .9481 
 
 
 1.5 
 
 5-654 
 
 3.769 < 
 
 2.0263 
 
 
 2.OO 7.746 3-873 2.O822 
 
 Table LX. Conductivity Measurements. 
 
 /*oo o = 64. 48. 2 
 V. to. . 
 
 94-78 
 
 9L53 
 89.44 
 
 87.36 
 
 85.73 
 79.21 
 
 76.78 
 76.08 
 
 73.83 
 70.56 
 
 66.22 
 
 IOO 
 
 6l . 12 
 
 40 
 
 59-02 
 
 20 
 
 57.67 
 
 13-334 
 
 56.33 
 
 10 
 
 55.28 
 
 4 
 
 51.08 
 
 2 
 
 49-51 
 
 1-333 
 
 49.06 
 
 I 
 
 47.61 
 
 0.6667 
 
 45-50 
 
 0-5 
 
 42.70 
 
 1 Bredig: Z. physik. Chem., 13, 
 
 242 (1894). 
 
 Am. Chem. J., 34, 375 (1905). 
 
 
62 
 
 o.oi 
 0.025 
 0.05 
 0.075 
 
 O.IO 
 
 0.25 
 
 0.50 
 
 0.75 
 
 1. 00 
 
 i-5 
 
 2.OO 
 
 4-0 
 
 30 
 
 20 
 
 O-75 1. 
 
 Concentration. 
 Fig. X. 
 
 1.5 
 
 Table LXI. Specific Gravity Measurements. 
 Sp.gr. Wsoi. W S ait. 
 
 Per cent of 
 correction. 
 
 .000732 
 .002177 
 . 004074 
 .005972 
 .00788 
 .01964 
 .03908 
 .05811 
 .07632 
 .11963 
 .15240 
 
 IOOO 
 1002 
 1004 
 1005 
 IOO7 
 1019 
 1039 
 1058 
 1076 
 III9 
 1152 
 
 732 
 .177 
 .074 
 972 
 
 .88 
 .64 
 .08 
 . ii 
 32 
 63 
 .40 
 
 i. 
 
 2. 
 5- 
 7- 
 10. 
 
 25- 
 
 77- 
 103. 
 
 154- 
 206. 
 
 030 
 
 575 
 150 
 725 
 30 
 75 
 50 
 25 
 
 01 
 02 
 
 999 
 999 
 998 
 998 
 997 
 993 
 987 
 980, 
 
 973 
 965 
 946. 
 
 70 
 602 
 924 
 
 247 
 58 
 89 
 58 
 86 
 
 12 
 
 38 
 
 O. 
 O. 
 0. 
 
 o. 
 
 0. 
 
 o. 
 I. 
 I. 
 
 2. 
 
 3- 
 
 5- 
 
 030 
 040 
 
 107 
 175 
 24 
 
 61 
 24 
 
 66 
 48 
 36 
 
 Table LXIL Hydrates. 
 
 nt. 
 
 a. 
 
 L. 
 
 A/w. 
 
 Z'. 
 
 M. 
 
 H. 
 
 0.025 
 
 91 
 
 53 
 
 3 
 
 .5624 
 
 3 
 
 .805 
 
 3- 
 
 8075 
 
 3- 
 
 575 
 
 143-0 
 
 0.05 
 
 89 
 
 44 
 
 3 
 
 .5235 
 
 3 
 
 .7260 
 
 3- 
 
 7221 
 
 2. 
 
 963 
 
 59-2 
 
 0.075 
 
 87 
 
 .36 
 
 3 
 
 .4848 
 
 3 
 
 636 
 
 3- 
 
 6297 
 
 2. 
 
 217 
 
 24.29 
 
 O.IO 
 
 85 
 
 73 
 
 3 
 
 4545 
 
 3 
 
 572 
 
 3- 
 
 5635 
 
 I . 
 
 700 
 
 17.00 
 
 0.25 
 
 79 
 
 .21 
 
 3 
 
 333 
 
 3 
 
 543 
 
 3- 
 
 521 
 
 2. 
 
 974 
 
 11.89 
 
 0.50 
 
 76 
 
 .78 
 
 3 
 
 .288 
 
 3 
 
 574 
 
 3- 
 
 529 
 
 3- 
 
 803 
 
 7.60 
 
 0.75 
 
 76 
 
 .08 
 
 3 
 
 275 
 
 3 
 
 595 
 
 3- 
 
 526 
 
 3- 
 
 961 
 
 5-28 
 
 1. 00 
 
 72 
 
 .83 
 
 3 
 
 233 
 
 3 
 
 633 
 
 3- 
 
 536 
 
 4- 
 
 763 
 
 4.76 
 
 1.5 
 
 70 
 
 -56 
 
 3 
 
 .172 
 
 3 
 
 769 
 
 3- 
 
 637 
 
 7- 
 
 103 
 
 4-73 
 
 2.OO 
 
 66 
 
 .22 
 
 3 
 
 . IOI 
 
 3 
 
 873 
 
 3- 
 
 665 
 
 8. 
 
 547 
 
 4-27 
 
63 
 Hydrochloric Acid. 
 
 Having investigated fifteen salts, I next turned my at- 
 tention to the study of some of the more common acids. 
 
 An approximately three normal solution of hydrochloric 
 acid was prepared. Dilute portions of the mother solution 
 were then titrated against a standard solution of potassium 
 hydroxide free from carbonate. This, in turn, had been stand- 
 ardized by means of a tenth normal solution of freshly pre- 
 pared oxalic acid. The results are given in Tables LXIII. 
 to LXVI. 
 
 A glance at Table LXVI. shows that, for the more dilute 
 solutions, the corrected observed freezing point lowering (L f ) 
 is less than that calculated from the dissociation. This is 
 due to one of two causes: the very high migration velocity 
 of the hydrogen ion, or its inability to form hydrates. 
 
 The minimum in the freezing point lowering occurs at about 
 0.25 normal. For dilutions greater than 0.5 normal, there 
 is no evidence of hydration. At 0.5 normal, however, the 
 hygroscopic property of the molecular hydrochloric acid be- 
 gins to predominate over the effect of decrease in dissociation. 
 From this point the amount of combined water increases 
 with increase in concentration. The corresponding values 
 of H differ from those of the other electrolytes thus far studied 
 in that they, also, increase as the concentration increases. 
 
 The values of H and M, for hydrochloric acid, are plotted 
 in Figs. I. and II. 
 
 Table LXIII. Freezing Point Measurements, 
 m. A. A/w. /. a. 
 
 0.025 
 
 o . 0902 
 
 3.6080 
 
 9377 
 
 93-97 
 
 0.05 
 
 0.1799 
 
 3 59 8 o 
 
 -9344 
 
 93-44 
 
 0.075 
 
 0.2681 
 
 3-5752 
 
 .9221 
 
 92.21 
 
 0. IO 
 
 0.3567 
 
 3-5670 
 
 .9177 
 
 91.77 
 
 0.25 
 
 0.8862 
 
 3-5450 
 
 -9059 
 
 90.59 
 
 0.50 
 
 I.84I 
 
 3.682 ] 
 
 9794 
 
 
 0.75 
 
 2.852 
 
 3.804 : 
 
 2.0450 
 
 
 1. 00 
 
 3-975 
 
 3-975 2 
 
 1.1372 
 
 
 1.50 
 
 6.452 
 
 4-301 2 
 
 J-3I23 
 
 
 2.0O 
 
 9.367 
 
 4-683 2 
 
 '5177 
 
 
6 4 
 
 Table LXIV. Conductivity Measurements. 
 
 
 /^oo = 236.92. 
 
 
 y. 
 
 A*z>. 
 
 a. 
 
 40 
 
 233.95 
 
 98.75 
 
 20 
 
 232.60 
 
 98.18 
 
 13-33 
 
 231.87 
 
 97.87 
 
 10 
 
 228.61 
 
 96.49 
 
 4 
 
 222. 17 
 
 93-77 
 
 2 
 
 211.79 
 
 89.39 
 
 1-333 
 
 203.28 
 
 85.80 
 
 i 
 
 199.85 
 
 84.35 
 
 0.667 
 
 l8l.79 
 
 76.73 
 
 0.5 
 
 I68.O4 
 
 70.93 
 
 Table LXV. Specific Gravity Measurements. 
 
 m. 
 0.025 
 
 Sp. gr. 
 [.00034 
 
 1000.34 
 
 W 5 alt. 
 O.9II 
 
 999.429 
 
 Per cent of 
 correction. 
 
 0.057 
 
 0.05 
 
 [.OOIOI 
 
 IOOI.OI 
 
 1.822 
 
 999.188 
 
 O.oSl 
 
 0.075 
 
 .00135 
 
 1001.35 
 
 2.734 
 
 998.616 
 
 0.138 
 
 O.IO 
 
 .00180 
 
 1001.80 
 
 3-645 
 
 998.155 
 
 o. 184 
 
 0.25 
 
 .00425 
 
 1004.25 
 
 9.II4 
 
 999.136 
 
 0.486 
 
 0.50 
 
 .00849 
 
 1008.49 
 
 18.229 
 
 99O.26I 
 
 0-973 
 
 0.75 
 
 .01264 
 
 1012.64 
 
 27-343 
 
 985.297 
 
 i-47 
 
 I.OO 
 
 .01749 
 
 1017.49 
 
 36.458 
 
 981.032 
 
 1.896 
 
 1.5 
 
 .02542 
 
 1025.42 
 
 54-687 
 
 970-733 
 
 2.92 
 
 2.O 
 
 03414 
 
 1034.14 
 
 72.916 
 
 961.224 
 
 3.87 
 
 Table LXV I. Hydrates. 
 
 m. 
 0.025 
 0.05 
 0.075 
 O.IO 
 
 0.25 
 o. 20 
 
 a. 
 
 98.75 
 98.18 
 
 97-87 
 96.40 
 
 93-77 
 
 L. 
 
 3.6967 
 3.6861 
 3.6803 
 
 3-6547 
 3-604I 
 
 1 CQ2I 
 
 3.6080 
 3-598o 
 3-5752 
 3-5670 
 
 T. C'Jio 
 
 L'. 
 3.6060 
 
 3-5702 
 3-56IO 
 3.5280 
 36260 
 
 0.75 
 
 I.OO 
 
 1.5 
 
 2.0 
 
 85.80 
 84.35 
 76.73 
 70.93 
 
 O O v/< * J 
 
 3-455 
 3.428 
 3.287 
 3-179 
 
 O - OO AV ^ 
 
 3.803 
 
 3-975 
 4-301 
 4-683 
 
 * v/Av^vy 
 
 3-747 
 3.899 
 4.176 
 4.502 
 
 M. 
 
 H. 
 
 1.580 3.16 
 
 3-33 5-77 
 
 6.707 6.70 
 
 11.820 7.88 
 
6 5 
 
 Nitric Acid. 
 
 A moderately concentrated solution was first made up, 
 care having been taken that the acid used contained none 
 of the oxides of nitrogen in solution. 
 
 Dilute portions of this were standardized volumetrically 
 against a solution of potassium hydroxide. 
 
 Like hydrochloric acid, dilute solutions of nitric acid ex- 
 hibit no tendency to form hydrates. No appreciable power 
 to combine with water is manifested until the concentration 
 0.75 normal is reached. The amount of total combined water, 
 then, increases with increase in concentration. The same re- 
 sults are obtained for the values of H. For curves repre- 
 senting the values of H and M see Figs. III. and IV. 
 
 Table LXVII. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/w. 
 
 t. 
 
 a. 
 
 0.025 
 
 0.09035 
 
 3.6140 3 
 
 9430 
 
 94-30 
 
 0.05 
 
 O.I79I 
 
 3.5830 '1 
 
 9263 
 
 92.63 
 
 0.075 
 
 0.2678 
 
 3-5713 "1 
 
 .9200 
 
 92.00 
 
 O. IO 
 
 0-3547 
 
 3 5470 l 
 
 .9069 
 
 90.69 
 
 0.25 
 
 0.8869 
 
 3-4576 ,J 
 
 9073 
 
 90.73 
 
 0.50 
 
 1.798 
 
 3-597 ,.J 
 
 9341 
 
 
 0.75 
 
 2.766 
 
 3.681 
 
 9736 
 
 
 I.OO 
 
 3-749 
 
 3-749 i 
 
 2.0156 
 
 
 i-5 
 
 5-955 
 
 3-970 : 
 
 2.1344 
 
 
 2.O 
 
 8-383 
 
 4.191 : 
 
 2.2532 
 
 
 Table LXVIII. Conductivity Measurements. 
 
 ^oo o = 237.07. 
 
 V. itv. a. 
 
 40 234.89 99.08 
 
 20 233.88 98.65 
 
 13-33 229.66 96.87 
 
 10 226.24 95-43 
 
 4 222.82 93-99 
 
 2 216.63 9I-38 
 
 1.334 211.43 89.17 
 
 i.o 203.72 85.93 
 
 0.5 177.15 74.71 
 
66 
 
 Table LXIX. Specific Gravity Measurements. 
 
 m. Sp. gr. 
 
 Wsol. 
 
 Wsalt. WH&. 
 
 Per cent of 
 correction. 
 
 O. 
 
 025 1.000926 
 
 1000 
 
 .926 
 
 I. 
 
 576 
 
 999 
 
 35 
 
 O 
 
 .065 
 
 0. 
 
 05 1.001798 
 
 IOOI 
 
 .798 
 
 3- 
 
 152 
 
 998 
 
 .64 
 
 
 
 134 
 
 0. 
 
 075 
 
 .002653 
 
 IOO2 
 
 .653 
 
 4- 
 
 728 
 
 997 
 
 -92 
 
 
 
 .207 
 
 O. 
 
 10 
 
 .003496 
 
 1003 
 
 .496 
 
 6. 
 
 304 
 
 997 
 
 J 9 
 
 
 
 .281 
 
 0. 
 
 25 
 
 .008481 
 
 I008 
 
 .48 
 
 15- 
 
 762 
 
 992 
 
 .71 
 
 
 
 .728 
 
 0. 
 
 5 
 
 .01686 
 
 1016 
 
 .86 
 
 3i. 
 
 524 
 
 985 
 
 34 
 
 I 
 
 465 
 
 0. 
 
 75 
 
 .02503 
 
 1025 
 
 03 
 
 48. 
 
 280 
 
 976 
 
 -75 
 
 2 
 
 -325 
 
 I . 
 
 oo 
 
 .03360 
 
 1033 
 
 .60 
 
 63- 
 
 050 
 
 970 
 
 55 
 
 2 
 
 -945 
 
 2. 
 
 00 
 
 .06700 
 
 1067 
 
 .00 
 
 126. 
 
 090 
 
 940 
 
 9 1 
 
 5 
 
 .909 
 
 Table LXX. Hydrates. 
 
 nt. 
 
 0.025 
 0.05 
 0.075 
 O. IO 
 
 0.25 
 
 0.5 
 
 0.75 
 
 I.OO 
 2.OO 
 
 a. 
 
 99.08 
 98.65 
 96.87 
 
 95-43 
 93-99 
 91-38 
 89.17 
 85.93 
 74-71 
 
 L. 
 3.7028 
 
 A/w. 
 3.6140 
 
 L'. 
 
 3.6124 
 3-5790 
 3-5640 
 3-5370 
 3-5210 
 3-544 
 3-595 
 3-639 
 3-944 
 
 M. 
 
 H. 
 
 3.6948 3.5830 
 
 3.6617 3-57I3 
 
 3.6348 3.5470 
 
 3.6062 3.5476 
 
 3-559 3-597 
 
 3.518 3.680 3.595 1.180 1.57 
 
 3.450 3.749 3-639 2.880 2.88 
 
 3.249 4.191 3.944 9.78 4.89 
 
 Sulphuric Acid. 
 
 Dilute portions of the mother solution were titrated against 
 the standard potassium hydroxide used for the previous acids. 
 
 The results are given in Tables LXXI. to LXXIV. ; the curves 
 in Figs. IX. and X. 
 
 In dilute solutions no water is held in combination. The 
 total amount of water held in combination by the acid, and 
 the hydration per molecule, increases with concentration from 
 0.75 to 2 normal. 
 
 Table LXXI. Freezing Point Measurements. 
 
 m. 
 
 A. 
 
 A/*v. 
 
 i. 
 
 a. 
 
 O.OI 
 
 0.04872 
 
 4.8720 
 
 2.6193 
 
 80.96 
 
 0.025 
 
 0.1179 
 
 4.7184 
 
 2.5367 
 
 76.84 
 
 0.050 
 
 0.2182 
 
 4.3640 
 
 2 3462 
 
 67.31 
 
 0.075 
 
 0.3157 
 
 4.2099 
 
 2 2634 
 
 63.17 
 
 O. IO 
 
 0.4043 
 
 4-0434 
 
 2.1738 
 
 58.69 
 
 0.25 
 
 0.9865 
 
 3-946o 
 
 2.I2I5 
 
 56.07 
 
 0.50 
 
 2.0033 
 
 4.0066 
 
 2.I54I 
 
 
 o.75 
 
 3-H74 
 
 4-I56 
 
 2.2346 
 
 
 I.OO 
 
 4-379 
 
 4-379 
 
 2 - 3544 
 
 
 1.50 
 
 7.265 
 
 4.843 
 
 2.6042 
 
 
 2.0 
 
 11.296 
 
 5.648 
 
 3-0365 
 
 
6 7 
 
 Table LXXII. Conductivity Measurements. 
 
 V. 
 
 100 
 
 40 
 
 20 
 
 13-34 
 IO 
 
 4 
 
 2 
 
 1-334 
 
 I.OO 
 
 0.6667 
 0.5 
 
 = 485-42- 
 
 (*v. 
 
 398.34 
 353-41 
 335.56 
 323.43 
 314.42 
 296:30 
 281.52 
 271.25 
 259.05 
 234.38 
 
 209 . 28 
 
 a. 
 
 82.06 
 72.80 
 
 69-13 
 66.63 
 64.78 
 61.04 
 
 57-99 
 
 55-88 
 
 53-37 
 48.28 
 
 43-n 
 
 Table LXXIII. Specific 
 m. Sp. gr. Wsoi. 
 
 Gravity Measurements. 
 
 W n U/tr r* Per cent f 
 Wsalt. WH&. correction. 
 
 O.OI 
 
 .000719 
 
 IOOO 
 
 .719 
 
 O. 
 
 980 
 
 999- 
 
 74 
 
 
 
 .026 
 
 O. 
 
 025 
 
 .001907 
 
 1001 
 
 9i 
 
 2. 
 
 45i 
 
 999- 
 
 45 
 
 
 
 054 
 
 0. 
 
 05 
 
 003551 
 
 1003 
 
 55 
 
 4- 
 
 902 
 
 998. 
 
 65 
 
 
 
 135 
 
 0. 
 
 075 
 
 005152 
 
 1005 
 
 15 
 
 7- 
 
 353 
 
 997- 
 
 79 
 
 
 
 .220 
 
 0. 
 
 I 
 
 .00677 
 
 1006 
 
 77 
 
 9- 
 
 807 
 
 996. 
 
 97 
 
 
 
 303 
 
 o. 
 
 25 
 
 .01618 
 
 1016 
 
 .18 
 
 24- 
 
 51 
 
 991. 
 
 67 
 
 
 
 832 
 
 0. 
 
 5 
 
 .03218 
 
 1032 
 
 .18 
 
 49- 
 
 03 
 
 983- 
 
 H 
 
 I 
 
 .68 
 
 0. 
 
 75 
 
 .04760 
 
 1047 
 
 .60 
 
 73- 
 
 53 
 
 974- 
 
 07 
 
 2 
 
 59 
 
 I . 
 
 00 
 
 .06307 
 
 1063 
 
 07 
 
 98. 
 
 07 
 
 964. 
 
 99 
 
 3 
 
 50 
 
 I . 
 
 5 
 
 09345 
 
 1093 
 
 45 
 
 147. 
 
 ii 
 
 946. 
 
 34 
 
 5 
 
 -36 
 
 2. 
 
 o 
 
 .12316 
 
 1123 
 
 51 
 
 196. 
 
 15 
 
 926. 
 
 99 
 
 7 
 
 30 
 
 Table LXXIV. Hydrates. 
 
 
 
 
 
 o 
 
 
 
 
 
 
 I 
 I 
 
 2 
 
 m. 
 
 .01 
 
 .025 
 05 
 .075 
 
 . IO 
 
 .25 
 
 -5 
 
 75 
 
 .0 
 
 5 
 
 .0 
 
 a 
 82. 
 72. 
 69. 
 66. 
 
 61. 
 
 57- 
 55- 
 53- 
 48. 
 43- 
 
 06 
 80 
 
 04 
 99 
 
 88 
 
 37 
 28 
 ii 
 
 4- 
 4- 
 4- 
 4- 
 4- 
 4- 
 
 3- 
 3- 
 3- 
 3. 
 
 L. 
 9126 
 5681 
 43i6 
 3386 
 2698 
 
 017 
 938 
 845 
 656 
 464 
 
 4 
 4 
 4 
 4 
 4 
 3 
 4 
 4 
 4 
 4 
 5 
 
 A/w. 
 .8720 
 .7184 
 .3640 
 .2099 
 
 0434 
 .9460 
 .266 
 .156 
 379 
 844 
 .648 1 
 
 4 
 4 
 4 
 4 
 4 
 3 
 3 
 4 
 4 
 4 
 5 
 
 .8708 
 
 .2007 
 .0312 
 .9132 
 
 939 
 .048 
 .226 
 
 -585 
 236 
 
 M. 
 
 H. 
 
 I.5I2 2.00 
 
 5.004 5.00 
 
 11.257 7-50 
 
 18.801 9.40 
 
 1 Jones and Getman: Z. physik. Chem., 46, 272 (1903). 
 
68 
 
 A comparison of Figs. L, III., and IX. shows that the hy- 
 drating powers of hydrochloric and sulphuric acids are of ap- 
 proximately the same order of magnitude, while that of nitric 
 acid is slightly less. 
 
 Figs. II., IV., and X., representing the total amounts of 
 combined water for the three acids, show that the same re- 
 lation holds here as for the hydrates. 
 
 Discussion. 
 
 Fifteen salts and three strong acids have been studied in 
 this investigation. I have worked with solutions cover- 
 ing a range of concentration from o.oi to 2.0 normal ; at one 
 extremity are found to predominate, in a very pronounced 
 manner, those influences due to the ions; at the other, those 
 due to the molecules also manifest themselves. In this way 
 I have attempted to compare the relative effects of the ions 
 and the molecules upon the molecular lowering of the freezing 
 point and the dissociation. 
 
 Comparing, first of all, the freezing point lowerings for any 
 given solution, it is found that, without exception, the molec- 
 ular lowering calculated from the dissociation decreases regu- 
 larly with increasing concentration. Naturally, this follows 
 from the fact that the decrease in dissociation is regular 
 throughout. On the other hand, the corrected observed 
 freezing point lowering decreases very rapidly in the dilute 
 solutions, passes through a very pronounced minimum, and 
 then increases as the concentration increases. A glance at 
 the tables of the hydrates shows that in every case the ob- 
 served molecular lowering produced by any salt is greater 
 than the calculated lowering based on conductivity measure- 
 ments. 
 
 If there were no hydration, we should expect the observed 
 and the calculated molecular lowerings to be equal, except 
 for the difference due to the influence of the friction between 
 the ion and the solvent. The nearest approach to this con- 
 dition which we have met is found in the most concentrated 
 solutions of barium nitrate. Here the observed molecular low- 
 ering is about one per cent greater than the calculated value^ 
 
6 9 
 
 An equally satisfactory agreement was found by Jones and Stine 
 for solutions of potassium chloride, which, likewise, crystallizes 
 without water. 
 
 The values of M and H also show that the abnormality of 
 the freezing point lowering in the dilute solutions is greatly 
 augmented by the relatively great hydrating power of the 
 ions. 
 
 Since, then, the hydration of the ion increases with increase 
 in dilution, the volume and mass of the ionic complex is greater, 
 the more dilute the solution; and, therefore, the greater will 
 be the resistance to be overcome by the ion as it moves through 
 the solvent. This being the case, the dissociation as meas- 
 ured by the conductivity method will be less than the true 
 dissociation, and the abnormality in the dissociation meas- 
 ured will increase with increasing dilution. 
 
 The effect produced by adding more of the given electro- 
 lyte will be to break down these larger hydrates into simpler 
 ones with smaller volume, thus decreasing the resistance to 
 the motion of the hydrated ion. 
 
 This agrees well with the results of Jones and Uhler. 1 They 
 found that the number of ether waves of different wave 
 length with which a given particle will vibrate in resonance 
 decreases with increasing dilution, thereby producing a nar- 
 rowing of the absorption bands. On the other hand, the ad- 
 dition of more of the same electrolyte, or a strong dehydra- 
 ting agent, decreases the complexity of the hydrate, thereby 
 decreasing its period. As a result, the particles are free to 
 vibrate in resonance with a greater number of wave lengths, 
 and the absorption bands widen. 
 
 It will be seen that, with the exception of magnesium chlor- 
 ide, the value of M, the total amount of water held in com- 
 bination by one molecule of the electrolyte, decreases rapidly 
 in the dilute solutions, passes through a minimum, and then 
 becomes a linear function of the concentration. 
 
 The hydration per molecule decreases rapidly, to approxi- 
 mately the same concentration which corresponds to a min- 
 imum in the freezing point lowering, and then remains 
 practically constant as the concentration increases. 
 
 1 Am. Chem. J., 37, 126 (1907); Carnegie Inst. (Washington), Memoir No. 60. 
 
70 
 
 Eliminating the hydration due to the ions, the hydration per 
 molecule in solution over a given range of temperature is con- 
 stant, just as the amount of water with which that same salt 
 will crystallize from solution is constant for a given range of 
 temperature. This relation is best illustrated by the curves 
 representing the values of H. They are almost asymptotic 
 to the coordinates. 
 
 Having found that the ions of a salt are hyd rated, the next 
 question which arises is this: Is it the cation or the anion 
 which has the greater hydrating power? 
 
 Nernst, Garrard, and Oppermann, 1 in a study of the con- 
 centration changes which take place in an indifferent sub- 
 stance during electrolysis, have calculated that the ions SO 4 , 
 
 Cl, Br, and NO 3 drag with them 9, 5, 4, and 2.5 molecules of 
 water, respectively. 
 
 It is seen from a study of the chlorides and nitrates of the 
 copper group, each of which crystallizes with 6 molecules 
 of water (copper chloride alone separating with two mole- 
 cules), that the hydration per molecule is approximately the 
 same for all of these salts. If, as Nernst and his coworkers 
 
 have found, the hydrating power of the NO 3 ion is only one- 
 half that of the Cl ion, then we should expect the influence 
 of the hydrating power of these two anions to manifest itself 
 in the hydrating power of the salts in question, and especially 
 so since the three cations are so nearly alike chemically. On 
 the basis of this reasoning we are forced to conclude that the 
 hydrating power of any salt is primarily a function of the cation. 
 
 We do not deny that the anions are capable of forming hy- 
 drates ; but, if they do, experiments lead us to believe that 
 they have this power only to a relatively slight degree. 
 
 We have noted also this striking relation. It is well known 
 that if the atomic volumes of the elements are plotted as or- 
 dinates against the atomic weights as abscissas, there exists 
 between them a periodic relation. At the maxima of the curve 
 are the alkali metals. The three elements having the largest 
 
 1 Gottingen Nachr., 1900, p. 86. 
 
atomic volumes are potassium, rubidium, and caesium. Salts 
 of these metals usually crystallize from aqueous solution in 
 the anhydrous form, and as experiments have shown, they 
 have very slight hydrating power in solution. Lithium and 
 sodium, some of Whose salts crystallize with two and three 
 molecules of water, have much smaller atomic volumes. 
 
 At the minimum of the third section of the atomic weight 
 curve we find the elements strontium, iron, cobalt, copper, 
 and nickel. The salts of these metals crystallize with large 
 amounts of water and show great hydrating power in solu- 
 tion. Aluminium, which has less than half the atomic weight 
 of iron, but slightly greater atomic volume, lies at the second 
 minimum. Its salts crystallize with 8 and 9 molecules of 
 water and show great hydrating power in solution. 
 
 Comparing the metals of the alkaline earth group we find 
 that barium, whose salts crystallize with two molecules of 
 water or water-free, has the largest atomic volume. The 
 other members of this group form salts which crystallize 
 with 6 molecules, calcium nitrate excepted. The magne- 
 sium cation, which has the smallest atomic volume, has the 
 greatest hydrating power in solution; the strontium cation, 
 which has the largest atomic volume, has a smaller hydra- 
 ting power than does the calcium cation, whose atomic vol- 
 ume is slightly less. 
 
 This is conclusive evidence that the hydrating power of the 
 cation is an inverse function of its atomic volume. 
 
 That the velocities of the ions are an inverse function of 
 their mass (and perhaps of their volumes) is an established 
 fact. Experimental evidence, however, seems at variance 
 with this statement. We should expect those ions which 
 have the smallest atomic volumes to have the greatest migra- 
 tion velocities. On the contrary, we find that potassium, 
 rubidium, and caesium have the greatest migration veloci- 
 
 + 
 ties (H and OH excepted), while the ions of the iron and 
 
 copper groups, with very small atomic volumes, have the 
 smallest migration velocities. 
 
 A glance at the two curves representing the relation be- 
 tween atomic volume and atomic weights, and between migra- 
 
72 
 
 tion velocities and atomic weights, shows at once the cause 
 of this apparent anomaly. It has been shown that those 
 elements which have the smallest atomic volumes have the 
 greatest hydrating power, and vice versa. We see, then, that 
 those ions which have the smallest migration velocities have also 
 the greatest hydrating power. 
 
 A somewhat detailed comparison of the members of the 
 different groups will bring out this idea more clearly. 
 
 The atomic volumes of potassium, rubidium, and caesium 
 increase rapidly with increasing atomic weights, and, as a 
 rule, their salts crystallize without water. We should ex- 
 pect, then, the potassium ion to have the greatest migration 
 velocity, and the caesium ion to have the smallest. Ex- 
 periments show that they have approximately the same migra- 
 tion velocities. Sodium and lithium, whose atomic volumes 
 are less than half that of potassium, have migration veloci- 
 ties which are only about two-thirds that of potassium. 
 It will be remembered that sodium and lithium form salts 
 which may crystallize with 2 and 3 molecules of water, re- 
 spectively. Hence we may assume that the increase in vol- 
 ume of the sodium and lithium ions, due to the formation 
 of a relatively large hydrate, decreases the velocity of those 
 ions to a far greater extent than the slight hydration of the 
 large potassium ion decreases the velocity of that ion. 
 
 The atomic volume of lithium is about one-half that of 
 sodium, and the maximum amount of water with which lith- 
 ium salts crystallize from solution is 3 molecules, whereas 
 the maximum for sodium salts is 2 molecules. Since the 
 ratio of 2 : 3 represents approximately the ratio of the hydra- 
 ting power of the two ions in solution, we should expect the 
 effect, upon the velocity, of the greater increase in the vol- 
 ume of the small lithium ion, due to its hydration, to compen- 
 sate somewhat for the smaller increase in the volume of the 
 larger sodium ion. Experiment shows that the migration 
 velocities are nearly equal. 
 
 The same relation holds for the metals of the alkaline 
 earth group. The atomic volumes increase with increasing 
 atomic weight. The migration velocities of the cations cal- 
 
73 
 
 cium and strontium, whose salts crystallize with 6 molecules 
 of water, are approximately equal to that of the barium 
 cation, whose salts crystallize either with 2 molecules of water, 
 or water-free. On the other hand, the magnesium cation, 
 which has one-half the atomic volume of the calcium ion, 
 has nearly the same migration velocity, due to compensation 
 between the atomic volumes and the hydration of the ions. 
 
 The calcium ion has a slightly greater atomic volume than 
 sodium, yet, owing to its much greater hydrating power, its 
 migration velocity is considerably less. 
 
 The cations of copper, cobalt, and nickel have nearly the 
 same atomic volumes and the same hydrating power. We 
 should expect them to have the same migration velocity, 
 and such is the case. 
 
 The atomic volumes of the halogens, chlorine, bromine, and 
 iodine, are approximately the same. If their ions are hy- 
 drated we should expect them to combine with the same amount 
 of water, and, therefore, they should give migration veloci- 
 ties of the same order of magnitude. This has been found to 
 be the case. The atomic volume of fluorine has not been de- 
 termined, but from its position on the migration velocity 
 curve we should infer that its atomic volume is smaller than 
 that of the halogens, and that its ion possesses a considera- 
 ble degree of hydrating power. 
 
 Further, it will be noted that the migration velocities of 
 the halogens are almost identical with those of the alkalis 
 standing next above them in order of atomic weights, whereas 
 their atomic volumes are very much smaller. This leads us 
 to believe that the compensation, which brings about an 
 equalization of the migration velocities of the two groups, is 
 due to the increase in volume of the alkali ions by hydration. 
 
 The silver ion alone of all the metallic elements for which 
 satisfactory data can be found presents an exception. It 
 has a small atomic volume, and its salts crystallize from solu- 
 tion without water. We should expect it to have but slight 
 hydrating power in solution and it should, therefore, have a 
 high migration velocity, but this has been found to be slightly 
 less than that of the halogens. 
 
74 
 
 According to the law of Raoult, the lowering of the freez- 
 ing point of a given weight of solvent by a dissolved substance 
 is directly proportional to the amount of the substance dis- 
 solved, providing that substance is a non electrolyte. In 
 the case of electrolytes the lowering produced by gram molec- 
 ular weights of the dissolved substances are greater than those 
 produced by gram molecular weights of non-electrolytes. 
 This abnormality in the case of electrolytes is explained by 
 the fact that an ion and a molecule lower the freezing point 
 to the same extent. 
 
 The fact is that the freezing point method gives us a rela- 
 tion between the amount of solvent acting as such and the 
 number of dissolved particles, whether they are molecules 
 or ions. 
 
 Having determined the freezing point lowering for any 
 concentration of a given electrolyte, it is an easy matter to- 
 calculate the amount of dissociation. For binary electro- 
 lytes a is obtained from the expression a = i i, where i is 
 
 the van't Hoff i. For ternary electrolytes, a = - , and 
 
 i i 
 
 for quaternary electrolytes a = . 
 
 o 
 
 We have calculated the values of a from the molecular 
 lowerings of all the solutions studied, for the dilute solutions 
 up to the concentration at which the molecular lowering 
 passes through a minimum. Beyond this concentration 
 the molecular lowering of the freezing point increases, due to 
 hydration, and, consequently, the calculated dissociation 
 would increase. For that reason the values of a have not 
 been calculated. 
 
 In the case of every salt studied, without exception, the 
 dissociation as calculated from the freezing point lowering is 
 higher than the dissociation as calculated from the conductivity 
 measurements. 
 
 This will be seen by comparing the values obtained for a 
 in the tables representing the freezing point and conductivity 
 measurements for each salt. 
 
 If there were no hydration, these values should be equaL 
 Since the freezing point measurements give us the most ac- 
 
75 
 
 curate relation between the amount of the actual solvent 
 and the number of dissolved particles, it, therefore, must give 
 us the most accurate measure of the dissociation, when hy- 
 dration is taken into account. 
 
 The conductivity of a solution is, as we have seen, depend- 
 ent upon the number of ions present, their velocity, their 
 mass and volume, and the viscosity of the solution. Since 
 the temperatures at which the dilute solutions freeze are ap- 
 proximately only one-fourth of a degree or less below the 
 freezing point of pure water the temperature at which the 
 conductivity measurements were made we must conclude 
 that the number of ions present and their velocities are in the 
 two cases the same. Similarly, the viscosity of the solutions 
 is the same in both measurements and, therefore, the fric- 
 tion between solvent and ion will vary directly as the sur- 
 face of the latter. 
 
 We have shown that most metallic ions in solution have 
 great hydrating power, and that the degree of hydration varies, 
 inversely with the atomic volume of the ion. Those ions which, 
 have the greatest hydrating power are those which have the 
 smallest atomic volumes, and should, therefore, if there were 
 no hydration, meet with less friction in their movements 
 through the solution. They should have greater migration 
 velocities, while exactly the opposite results are found. 
 
 A comparison of the values of a for a dilute solution of the- 
 strong acids shows that the dissociation as measured by con- 
 ductivity is greater in every case than the dissociation meas- 
 ured by the freezing point method. In the more concentra- 
 ted solutions the observed freezing point lowerings are higher 
 than the molecular lowerings calculated from conductivity.. 
 This is due to the fact that the molecules or ions of those 
 acids have considerable hydrating power, and we obtain in 
 concentrated solutions results of the same character as with 
 the salts. * 
 
 Summary. 
 
 i. The freezing point lowerings and the conductivities of 
 solutions of a number of electrolytes, over a wide range of 
 concentration, have been carefully redetermined. 
 
7 6 
 
 2. We observe that the molecular lowerings of the freezing 
 point of all the electrolytes studied passes through a very 
 pronounced minimum at concentrations ranging from o.i 
 to 0.25 normal. The molecular lowerings calculated from 
 the dissociation, as measured by conductivity, decrease regu- 
 larly from the most dilute to the most concentrated solutions. 
 
 3. The magnitude of the molecular lowerings produced by 
 molecular quantities of different salts varies directly as the 
 number of molecules of water with which those salts crystal- 
 lize from solution. The magnitude of the hydrating power of 
 salts in solution is, in turn, proportional to the amount of 
 water of crystallization. 
 
 4. That the ions have very great hydrating power is shown 
 by the values of M and H for the different salts. The total 
 amount of combined water decreases with increase in concen- 
 tration, passes through a minimum, and then increases regu- 
 larly with increase in concentration. The amount of water 
 held in combination by one molecule of a salt is very large in 
 the more dilute solutions where the ions predominate. It 
 decreases rapidly with decrease in dissociation, and approaches 
 a constant value at greater concentration. 
 
 5. The hydrating power of a salt is, primarily, a function of 
 the cation. The results show that two salts which crystal- 
 lize with the same amounts of water of crystallization and 
 contain a common cation exhibit hydrating power of the 
 same order of magnitude. 
 
 6. It has been found that the hydrating power of a cation 
 is an inverse function of its atomic volume. Those cations 
 which have the smallest atomic volumes have the greatest 
 hydrating power, and vice versa. We may state the relations 
 thus : The hydrating power of the ions is an inverse function of 
 their atomic volumes, and a periodic function of their atomic 
 weights. 
 
 7. Furthermore, we have found that those cations which 
 have the greatest migration velocities exhibit, also, the small- 
 est hydrating power, and vice versa. This probably accounts 
 for the apparent anomaly which exists in the relation between 
 the migration velocities of the ions and their atomic weights 
 and atomic volumes. The influence upon the migration 
 
77 
 
 velocity of the hydration of those ions with small atomic 
 volumes is greater than that of the small hydration of those 
 ions which have large atomic volumes. 
 
 8. In the case of every salt it has been found that the disso- 
 ciation in the dilute solutions, as measured by the conduc- 
 tivity method, is less than that calculated from the freezing 
 point lowering. Since the freezing point and conductivity 
 measurements of the dilute solutions were made at approx- 
 imately the same temperature, the number of the ions pres- 
 ent,- their velocities, and their hydration are practically the 
 same in both cases. The solutions have, likewise, the same 
 viscosity. Therefore, the friction between the solvent and 
 ion will vary directly as the surface of the latter. This being 
 the case, the greater the dilution, the greater will be the com- 
 plexity of the hydrate, and, consequently, its surface. We 
 should expect to find, therefore, a greater abnormality in the 
 dissociation, as measured by the two methods, the greater 
 the dilution at which the measurements are made. The re- 
 sults show this to be the fact. 
 
 It is only in case of those salts which crystallize in the an- 
 hydrous condition that we obtain comparable values for the 
 dissociation, as measured by the two methods. These values 
 are found only in those concentrations which lie close to that, 
 concentration which gives the minimum molecular lowering. 
 
BIOGRAPHY. 
 
 James Newton Pearce, the author of this dissertation, was 
 born in Oswego, Illinois, December 21, 1873. His early edu- 
 cation was obtained in the public schools of his native vil- 
 lage. In 1891, at the age of 17, he entered the Academy of 
 Northwestern University, at Evanston, 111., where he com- 
 pleted his preparation for college. In 1892 he matriculated 
 in Northwestern University, graduating in 1896 with the de- 
 gree of Ph.B., and the following year he took his Master's de- 
 gree in Chemistry from the same institution. 
 
 From June, 1897, to January, 1900, he was head chemist 
 for James S. Kirk & Co., soap manufacturers at Chicago, 
 111. In January, 1900, he entered Chicago University to pur- 
 sue graduate work in chemistry. In September of the same 
 year he was appointed Instructor in Chemistry and Physics 
 in the La Salle-Peru Township High School at La Salle, 111., 
 where he remained for two years. In 1902 he was appointed 
 Instructor in Chemistry in Northwestern University and re- 
 mained there until 1905, when he entered Johns Hopkins 
 University as a graduate student in Chemistry. His subor- 
 dinate subjects were Physical Chemistry and Physics. 
 
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