A STUDY OF THE HEATS OF DILUTION OF 
 CERTAIN AQUEOUS SALT SOLUTIONS 
 
 BY 
 
 ALLEN EDWIN STEARN 
 
 A.B. Stanford University, 1915 
 A.M. Stanford University, 1916 
 M. S. University of Illinois, 1917 
 
 THESIS 
 
 Submitted in Partial Fulfillment of the Requirements for the 
 
 Degree of 
 DOCTOR OF PHILOSOPHY 
 
 IN CHEMISTRY 
 
 / 
 
 
 SB I 
 
 IN 
 
 THE GRADUATE SCHOOL 
 
 OF THE 
 
 UNIVERSITY OF ILLINOIS 
 
 1919 
 
 - 
 
 KASTON, PA.: 
 
 BSCHSNBACH PRINTING COMPANY 
 1919 
 
A STUDY OF THE HEATS OF DILUTION OF 
 CERTAIN AQUEOUS SALT SOLUTIONS 
 
 BY 
 
 ALLEN EDWIN STEARN 
 
 l! 
 
 A.B. Stanford University, 1915 
 A.M. Stanford University, 1916 
 M. S. University of Illinois, 1917 
 
 THESIS 
 
 Submitted in Partial Fulfillment of the Requirements for the 
 
 Degree of 
 DOCTOR OF PHILOSOPHY 
 
 IN CHEMISTRY 
 
 IN 
 
 THE GRADUATE SCHOOL 
 OF THE 
 
 UNIVERSITY OF ILLINOIS 
 1919 
 
 EASTON, PA.: 
 
 ESCHENSACH PRINTING COMPANY 
 1919 
 
ACKNOWLEDGMENT. 
 
 I wish to express my appreciation of the suggestions of Dr. G. McP. 
 Smith under whose supervision this investigation was carried on. To Dr. 
 J. M. Braham I am also indebted for the use of his calorimeter and his 
 suggestions regarding its manipulation, and to Dr. D. A. Maclnnes for 
 permission to reproduce his drawings of the apparatus. Acknowledgment 
 is also due Mr. R. F. Schneider for assistance during the research. 
 
 464191 
 
A Study of the Heats of Dilution of Certain 
 Aqueous Salt Solutions* 
 
 A. Introduction. 
 
 i. Purpose of the Investigation. A series of investigations 1 under- 
 taken in this laboratory with the object of studying ionic relationships 
 in aqueous solutions of mixed strong electrolytes has indicated the forma- 
 tion of higher order compounds in the ionization process, in harmony 
 with Werner's ideas in regard to its mechanism. 
 
 The method of investigation in the papers referred to has been to study 
 the equilibria between aqueous and metallic solutions, using mixed salt 
 
 1 G. McP. Smith, Am. Chem. J., 37, 506 (1907); /. Am. Chem. Soc., 32, 502 (1910); 
 35> 39 (1913); Smith and Ball, Ibid., 39, 179 (1917); Smith and Braley, Ibid., 39, 1545 
 (1017); 40, 197 (1918); Smith and Rees, Ibid., 40, 1802 (1918). 
 
solutions and liquid amalgams. The measurement of some colligative 
 property of aqueous solutions seemed to offer a means of testing these 
 ideas from another point of attack, and consequently it was planned in 
 this investigation to measure the reversible molal heats of dilution of 
 certain mixed salt solutions and to compare these with the heats of dilu- 
 tion of solutions of the single salts. 
 
 2. Heats of Dilution. The reversible molal heat of dilution, L D , 
 of an aqueous solution at any concentration is represented by the differ- 
 ence in the heats of vaporization of one mol of water from a solution of 
 that concentration and from pure water. 
 
 Thus: L D = L v -- L v . 
 
 Here L D is the reversible molal heat of dilution, L v is the heat of vapor- 
 ization of one mol of water from the solution in question, and L v is the 
 heat of vaporization of one mol of water from pure water. 
 
 But 
 
 
 dT 
 
 Or _ d In P /p 
 
 L D - Kl dT . 
 
 Without a large mass of experimental data on the partial vapor pressure 
 of water in solutions of various concentrations and at various temperatures, 
 there is no method of calculating the value of L D without assuming 
 Raoult's law for cases for which we know it does not hold. For dilute 
 solutions where Raoult's law does hold the ratio p/p approaches unity 
 so that LD is zero. In concentrated solutions, however, "or in dilute 
 solutions where the process of dilution is associated with the formation 
 of new molecular complexes, or with the decomposition of those already 
 occurring, the heat of dilution may have a positive or negative value." 2 
 
 If, now, one should measure the reversible molal heat of dilution for a 
 given concentration of solutions of single salts, and then for an equiva- 
 lent concentration of a solution of the mixed salts, one might expect to 
 find the value in the latter case to be somewhere near the sum of the other 
 values unless affected by the formation of new molecular complexes. 
 
 B, Materials. 
 
 The strontium chloride was in the form of "pure crystals." Most of 
 the material was recrystallized once from water. This procedure in the 
 light of our results seems unnecessary when it is considered that the heat 
 effects in solutions as concentrated as 0.2 N are so small as to be hardly 
 measureable. The sodium and potassium chlorides were of various 
 brands, all labeled c. P. These materials are easy to obtain in a state of 
 high purity, and inasmuch as small amounts of impurities have no effect 
 
 1 Kirchhoff, Pogg. Ann., 104 (1856); Ges. Abh., p. 492. 
 
 2 Nernst, "Theoretical Chemistry," Trans. 6th Ger. Ed., p. 143. 
 
on the results in this work, it was considered unnecessary to purify them 
 further. 
 
 C. Apparatus. 
 
 The apparatus was a very slight modification of the adiabatic calorim- 
 eter of Maclnnes and Braham. 1 The instrument itself was that actually 
 employed by Braham, as were the thermometers, Wheatstone bridge, 
 standard cells, etc. 
 
 A calorimetric determination of a positive heat effect consisted of 
 measuring the change in resistance of a coil of platinum wire due to the 
 direct dilution of a certain quantity of solution of a certain concentra- 
 tion with a certain quantity of water. Next, a carefully measured quan- 
 tity of electrical energy was introduced into the solution and the corre- 
 sponding change in resistance of the same coil measured. For negative 
 heats a slightly different procedure was followed where these heats were 
 comparatively large. In such cases the procedure was to introduce elec- 
 trical energy into the solution at a carefully measured rate slightly more 
 rapidly than it was taken up in dilution, so that the solution did not cool 
 down below the temperature of the surroundings. The reason for this 
 is that it is much easier to adjust the surroundings to a rising tempera- 
 ture in the calorimeter by means of heating coils, than to a decreasing 
 temperature in the calorimeter where the cooling of the surroundings could 
 not be closely regulated with any degree of satisfaction. After finishing 
 the run as described above, one can calculate the number of calories cor- 
 responding to the electrical energy introduced, and the actual number 
 of calories corresponding to the increase in temperature as measured by 
 the change in resistance of the thermometer. The difference is the num- 
 ber of calories due to the heat of dilution. By this procedure the heat 
 capacity of the calorimeter is measured as a part of every determina- 
 tion, and thus inaccuracies due to calculations from questionable data 
 on specific heats of solutions, water equivalent of the calorimeter, slightly 
 varying conditions of the experiments, uncertainties arising from the 
 calibration of the thermometer, etc., are eliminated. Thus by a simple 
 proportion the heat of dilution can be obtained at once. For if H D is 
 the heat due to dilution, expressed in joules, then 
 
 H D : EIT = R D : RE, 
 
 where E is electromotive force, / the current, and T the time in seconds 
 during which the current is passed through the calorimeter heater. R D 
 and R E are the changes in temperature, in resisting units, due, respec- 
 tively, to the dilution and to the electrical heating. 
 
 H D (in calories) : = RD ' RE 
 
 where J represents Joule's equivalent, 4.184 joules per calorie. 
 1 Maclnnes and Braham, /. Am. Chem. Soc., 39, 2110 (1917)- 
 
8 
 
 Since the relation between the change in resistance and the tempera- 
 ture change is not linear, any large values of R D or R E would have to be 
 corrected by means of the relation 
 
 100 100' 
 
 in which -Rioo is the resistance of the thermometer in steam at 760 mm. 
 pressure, RQ is its resistance in melting ice, and d' is an empirical constant. 
 Maclnnes and Braham determined RI OO and R for the thermometers 
 employed, and used for d' the value 1.47, recommended by the Bureau 
 of Standards. They found, however, that with the values of R D and R E 
 of the magnitude met with in their work, which were even greater than 
 those met with in this investigation, the correction was too small to affect 
 their numerical results in any way; so that if AR = 0.02395, then At = 
 0.2395, just 10 times the numerical value of &R. 
 
 D. Method. 
 
 The salt solutions were made on the basis of gram equivalents of an- 
 hydrous salt per 1000 g. of water. Their concentration was ascertained 
 by a Volhard determination of the chlorine. The salts used were sodium 
 chloride, potassium chloride and strontium chloride; and the concentra- 
 tions at which the heats of dilution were determined were 0.2, 0.4, 0.8, 
 1.6 and 3.2 weight normal. 1 Points on the strontium chloride curve were 
 also obtained for concentrations of 1.2, 2.0, 2.4 and 2.8 wt. N. Mixed 
 salt solutions of NaCl : l / 2 SrCl 2 ,NaCl : KC1, KC1 : l / 2 SrCl 2 , and KC1 : 
 SrCl 2 were also run at the above mentioned concentrations. These solu- 
 tions were prepared by diluting a volume of the solution of one of the salts 
 with an equal volume of the solution of the same concentration of the 
 other salt. Thus one volume of 0.8 wt. N potassium chloride and one 
 volume of 0.8 wt. N sodium chloride were mixed and called 0.8 wt. N 
 of the mixed salt. 
 
 The value of the reversible molal heat of dilution was obtained by di- 
 luting the solution of a definite concentration with decreasing amounts of 
 water, and plotting the heat effects obtained against the number of mols 
 of water added. The curve was found to be a straight line (within this 
 region) so that, by extrapolation to zero mols of water added, the value 
 of the reversible molal heat of dilution at the particular concentration 
 could be obtained. 
 
 Accuracy. The very small values of the heat effects in the case of 
 the more dilute solutions necessitated only approximate results here. 
 Maclnnes and Braham state that heat effects of from 50 to 60 calories 
 
 1 Weight normal or wt. N is the number of gram equivalents of anhydrous salt 
 per 1000 g. of water. 
 
-30 
 
 
 
 r 
 
 \ 
 
 _ Vpptr Curve.- 3./6 /nob tfCt 
 
 
 \ 
 
 \ 
 
 
 
 
 
 ^ 
 
 i^ 
 
 
 !' 
 
 x. 
 
 ^ 
 
 
 3 
 
 
 
 * < 
 
 -- 
 
 IOO ISO 
 Water of Di\ui.ion 
 
 can be measured with an accuracy of from 4 to 5%.* With a total heat 
 effect of from 5 to 20 calories one should not expect much more than 30 
 to 50% accuracy. In these cases, however, an error of even 100% would 
 change the point on the curve of the concentration plotted against the 
 molal heat effect to such a slight extent that the curve itself would be 
 unaffected. In the case of the larger heat effects, running as high as 
 600 to 700 calories, the heat change can be measured to within 0.25 to 
 0.5%, so that the error of the reversible heat value should not be greater 
 than i to 2%. 
 
 Some justification for the assumption that the molal heat values ob- 
 tained by diluting a certain quantity of solution with varying amounts of 
 water give a straight line when plotted against the number of mols of 
 
 water of dilution is given in Fig. i. 
 The data for these curves are taken 
 from Tables IV and VII. Accord- 
 ing to Thomsen 2 "the value of the 
 thermal change on dilution always 
 varies with variations in the quantity 
 of water of dilution, and this varia- 
 tion, whether positive or negative, 
 seems to have the character of a 
 hyperbolic function of the quantity 
 of water added." As will be seen, 
 the region of the curve on which the 
 experimental data represented in all the subsequent curves fall is so far 
 from the vertex that the change of slope of the curve has become vanish- 
 ingly small, and it is practically a straight line. (In Fig. i , mols of water 
 of dilution per 10,000 g. of solution are plotted as abscissas, and the molal 
 heat effects as ordinates.) 
 
 E. Experimental Results. 
 
 Tables I to VIII give the data for the heats of dilution of various salt 
 solutions and mixtures. Table I gives in considerable detail the results 
 of a run including resistance readings, results of potentiometer readings, 
 etc. Table I is for the case of a negative heat effect, and a sample calcu- 
 lation from the data included in the table is appended. 
 
 In this table, "Time" is the time in seconds during which heat is passed through 
 the calorimeter heater; "Res." is the resistance of the thermometer in ohms; "R" 
 is the change of resistance of the thermometer in ohms multiplied by io 5 ; "Sol. G." 
 represents the number of grams of solution to be diluted; "Mols H 2 O" represents the 
 number of mols of water (assuming 18 g. to the mol) with which the solution was diluted; 
 
 1 It may be stated that to measure the change of resistance due to dilution or to 
 the electrical energy passed into the calorimeter it was not necessary to shift a plug in 
 the resistance box. 
 
 2 Pattison Muir, "Elements of Thermal Chemistry," p. 167. 
 
 Fig. i. Change of molal heat effect with 
 
 the number of mols of water of 
 
 dilution over a wide range. 
 
10 
 
 "Amp." is the current in amperes through the heating coil of the calorimeter; "E. M. 
 F." is the voltage drop across the terminals of this same coil; "Cal." is the number of 
 calories of electrical energy introduced. 
 
 The total heat effect of the dilution is given in calories as well as the 
 molal heat effect. The latter value is obtained from the former by dividing 
 it by the number of mols of water of dilution. 
 
 A few curves representative of the 
 method of extrapolation are given. 
 Mols of water of dilution are plotted 
 as abscissas and molal heat effects as 
 ordinates. Fig. 2 gives the curve for 
 2.9 wt. N SrCl 2 and that for 0.8 wt. N 
 KC1. The size of the plotted point 
 gives an estimate of the probable ac- 
 curacy of each point. The radius 
 of the circle represents the variation in 
 the molal heat of dilution due to a 
 variation of o.ooooi ohm in the re- 
 sistance measurement. In the remainder of the data, the values obtained 
 by drawing similar curves are given but the curves themselves are not 
 included. 
 
 Tables III to IX give a condensed summary of some 50 tables of the 
 type of Table I. 
 
 I. HEAT OF DILUTION OF 3.2 WT. N NaCl. 
 
 IS 20 2o 50 
 W<aier of Di/ut./on 
 
 Fig. 2. Molal heat effect as a function 
 
 of the amount of water of dilution. 
 
 (NOTE : Read the ordinates as negative 
 
 for the NaCl curve.) 
 
 Time. 
 Sec. 
 
 300 
 
 300 
 
 300 
 
 300 
 
 300 
 
 300 
 
 Res. d 
 Ohms. 
 
 27.41500 
 3205 
 
 3875 
 
 5190 
 
 27.43500 
 
 2795 
 
 3605 
 
 4865 
 
 27.44500 
 2862 
 
 3808 
 5043 
 
 X 105. 
 Ohms. 
 
 670 
 
 1315 
 
 810 
 
 1260 
 
 946 
 
 1235 
 
 Sol. 
 G. 
 
 H 2 0. 
 Mols. 
 
 Free 
 Current. E. M. F. energy. 
 
 Amp. Volts. Ca 
 
 Total ht. 
 
 effect. 
 
 Cal. 
 
 Heat 
 
 effect 
 
 per mol. 
 
 Cal. 
 
 10,586 27.4 
 
 2.322 6.635 
 
 105 
 
 10,586 18.45 
 
 10,586 I I . 22 
 
 2.305 6.58 IOQ9 
 
 2-335 6.66 1115 
 
 2.334 6.66 1115 
 
 2-33 6.65 
 
 2-335 6.66 1115 
 
 546 19-9 
 
 398 21.6 
 
 Reversible Molal Heat of Dilution, 
 
 258 22 . 
 25.0 cal. 
 
 Sample Calculation. If 1115 cals. produce a change in resistance of 1235 units, 
 
1 1 
 
 then 1 1 1 1 cals. would produce in the same amount of the same .solution a change of 
 resistance of 1231 units. The change measured, however, was only 946 units. A 
 quantity of heat, therefore, equivalent to that represented by a change of resistance of 
 123 1 minus 946 or 285 units was used up by dilution. Therefore if 1235 units are equiv- 
 alent to 1115 cals., 285 units would be equivalent to 258 cals. This value, then, would 
 represent the heat effect due to dilution with 11.22 mols of water. The molal heat 
 effect would then be 258 divided by 11.22, or 22.95 cals. The sign would, of course, 
 be negative. 
 
 TABLE II. HEAT OF DILUTION OF NaCl SOLUTIONS. 
 
 
 
 
 
 Reversible 
 
 Concen- 
 
 Water of 
 
 Total heat 
 
 Molal heat 
 
 molal heat 
 
 tration. 
 
 Solution. dilution. 
 
 of dilution. 
 
 of dilution. 
 
 of dilution. 
 
 Wt. N. 
 
 G. Mols. 
 
 Cal. 
 
 Cal. 
 
 L D cal. 
 
 3-2 
 
 10,586 27.4 
 
 -546 
 
 19 9 
 
 
 
 18-45 
 
 398 
 
 21.6 
 
 
 
 II .22 
 
 258 
 
 22.95 
 
 25.0 
 
 1.6 
 
 8,280 34.83 
 
 245 
 
 7.04 
 
 
 
 22.06 
 
 179 
 
 8.06 
 
 
 
 n-75 
 
 IO2 
 
 8.67 
 
 
 
 7-83 
 
 7I-I 
 
 9.08 
 
 9.80 
 
 0.8 
 
 7,986 36-45 
 
 7O.O 
 
 1.92 
 
 
 
 32-86 
 
 77-8 
 
 2.37 
 
 
 
 25.65 
 
 70.9 
 
 2.76 
 
 
 
 16-75 
 
 48 44 
 
 2.89 
 
 3-93 
 
 0.4 
 
 7,900 37-72 
 
 29.62 
 
 0.79 
 
 
 
 25-58 
 
 24.09 
 
 0.94 
 
 
 
 21.5 
 
 25.38 
 
 1.18 
 
 
 
 16.5 
 
 21.15 
 
 1.28 
 
 
 
 12.47 
 
 17.16 
 
 1.38 
 
 
 
 8.86 
 
 12.48 
 
 1.41 
 
 1. 60 
 
 O.2 
 
 9,300 28.8 
 
 17.64 
 
 0.61 
 
 
 
 23-4 
 
 17.9 
 
 0.765 
 
 
 
 18. ii 
 
 13-4 
 
 0-74 
 
 
 
 14.6 
 
 10.0 
 
 0.69 
 
 0.85 
 
 
 TABLE III. HEAT OF 
 
 DILUTION OF 
 
 KC1 SOLUTIONS. 
 
 
 
 
 
 Reversible 
 
 Concen- 
 
 Water of 
 
 Total heat 
 
 Molal heat 
 
 molal heat 
 
 tration. 
 
 Solution. dilution. 
 
 of dilution. 
 
 of dilution. 
 
 of dilution. 
 
 Wt. N. 
 
 G. Mols. 
 
 Cal. 
 
 Cal. 
 
 L D cal. 
 
 3-16 
 
 8,410 39.0 
 
 781.0 
 
 20 . 03 
 
 
 
 26.55 
 
 604 . 3 
 
 22 . 76 
 
 
 
 19 4 
 
 484.0 
 
 24 94 
 
 
 
 14.4 
 
 382 . 2 
 
 26.48 
 
 
 
 94 
 
 26l .2 
 
 27.79 
 
 30.0 
 
 1.6 
 
 8 , ooo 40 . o 
 
 289.5 
 
 7.24 
 
 
 
 30.0 
 
 246 . 7 
 
 8.22 
 
 
 
 20.0 
 
 177.2 
 
 8.87 
 
 
 
 10. 
 
 103.3 
 
 10.33 
 
 10. 80 
 
 0.8 
 
 8 , ooo 40 . o 
 
 70 . 68 
 
 i 77 
 
 
 
 30.0 
 
 64.9 
 
 2.16 
 
 
 
 20. o 
 
 48.8 
 
 2.44 
 
 
 
 IO.O 
 
 27.8 
 
 2.78 
 
 3-30 
 
12 
 
 TABLE III (continued). 
 
 
 
 
 
 Reversible 
 
 Concen- 
 tration. Solution. 
 Wt. N. G. 
 
 Water of 
 dilution. 
 Mols. 
 
 Total heat 
 of dilution. 
 Cal. 
 
 Molal heat 
 of dilution. 
 Cal. 
 
 molal heat 
 of dilution. 
 L D cal. 
 
 0.4 8 , ooo 
 
 34-95 
 
 15 o 
 
 0-43 
 
 
 
 30.0 
 
 13 42 
 
 0-45 
 
 
 
 25 o 
 
 I4.I 
 
 -0-564 
 
 
 
 20.0 
 
 12.44 
 
 O.622 
 
 
 
 15.0 
 
 IO.O 
 
 0.67 
 
 0.95 
 
 0.2 7,850 
 
 40.0 
 
 2.74 
 
 0.069 
 
 
 
 38-2 
 
 2 .92 
 
 o . 076 
 
 
 
 34-0 
 
 2-32 
 
 0.094 
 
 
 
 30.0 
 
 3-1 
 
 o. 103 
 
 
 
 30.0 
 
 3-25 
 
 o. 108 
 
 o. 24 
 
 TABLE IV. HEAT OF DILUTION OF SrCl 2 SOLUTIONS. 
 
 
 
 
 
 
 Reversible 
 
 Concen- 
 tration. 
 Wt. N. 
 
 Solution. 
 G. 
 
 Water 
 of dilution. 
 Mols. 
 
 Total heat 
 of dilution. 
 Cal. 
 
 Molal heat 
 of dilution. 
 Cal. 
 
 molal heat 
 of dilution. 
 L D cal. 
 
 3-2 
 
 10,000 
 
 35-0 
 
 189.0 
 
 5-4 
 
 
 
 
 15-0 
 
 95-7 
 
 6-4 
 
 7-2 
 
 2.9 
 
 9,500 
 
 37-2 
 
 129.8 
 
 3-49 
 
 
 
 
 30.0 
 
 I 12 .4 
 
 3-75 
 
 
 
 
 30.0 
 
 II4.I 
 
 3-8o 
 
 
 
 
 27-7 
 
 109.2 
 
 3 95 
 
 
 
 
 20. o 
 
 86.33 
 
 4-3i 
 
 
 
 
 19.5 
 
 85-44 
 
 4-38 
 
 
 
 
 IO.O 
 
 48-5 
 
 4-85 
 
 5 40 
 
 2-4 
 
 IO,OOO 
 
 35-0 
 
 33-7 
 
 . 0.96 
 
 
 
 
 25-0 
 
 32-5 
 
 1.29 
 
 2. 10 
 
 2.0 
 
 IO,OOO 
 
 35-0 
 
 35-5 
 
 i .01 
 
 
 
 
 25.0 
 
 31.0 
 
 1.23 
 
 i-75 
 
 i-55 
 
 10,000 
 
 40.0 
 
 23.64 
 
 0-59 
 
 
 
 
 30.0 
 
 21.4 
 
 0.71 
 
 
 
 
 30.0 
 
 20.92 
 
 0.70 
 
 
 
 
 20. o 
 
 17-3 
 
 0.86 
 
 i . ii 
 
 1.2 
 
 10,000 
 
 35-0 
 
 18.9 
 
 0-54 
 
 
 
 
 25-0 
 
 16.3 
 
 0.65 
 
 0.90 
 
 0.8 
 
 10,000 
 
 40.0 
 
 15-4 
 
 0.38 
 
 
 
 
 30.0 
 
 13.0 
 
 0.44 
 
 
 
 
 20.0 
 
 IO.O 
 
 0.50 
 
 0.62 
 
 0.425 
 
 10,000 
 
 4O.O 
 
 11.16 
 
 0.28 
 
 
 
 
 30.0 
 
 10.07 
 
 0-34 
 
 
 
 
 20.0 
 
 7-4 
 
 o.37 
 
 0.50 
 
 0.2 
 
 10,000 
 
 4O.O 
 
 7.88 
 
 O.2O 
 
 
 
 
 30.0 
 
 6.81 
 
 0.23 
 
 
 
 
 20.0 
 
 4.0 + 
 
 0.2 + 
 
 0.25 = 
 
TABLE V. HEAT OF DILUTION OF NaCl : KC1 SOLUTIONS. 
 
 Concen- Water of 
 tration. Solution. dilution. 
 Wt. N. G. Mols. 
 
 Total heat Molal heat 
 of dilution. of dilution. 
 Cal. Cal. 
 
 3.2 10,000 40.0 
 
 780 . o 
 
 19-5 
 
 30.0 
 
 658.0 
 
 21.9 
 
 2O. O 
 
 468 . 
 
 23-4 
 
 IO.O 
 
 256.0 
 
 -25-6 
 
 1.6 10,000 40.0 
 
 286.6 
 
 7.16 
 
 30.0 
 
 230.7 
 
 7.70 
 
 20.0 
 
 165. I 
 
 8.30 
 
 IO.O 
 
 88.6 
 
 8.86 
 
 0.8 10,000 40.0 
 
 58.54 
 
 i .46 
 
 30.0 
 
 52-6 
 
 1-75 
 
 20.0 
 
 39-25 
 
 1.96 
 
 IO.O 
 
 23-8 
 
 2.38 
 
 0.4 10,000 35.0 
 
 21 .O 
 
 0.60 
 
 25.0 
 
 16.0 
 
 0.65 
 
 15.0 
 
 10.4 
 
 0.70 
 
 27.8 
 
 20.6 
 
 9.40 7-13 
 
 2.60 2.55 
 
 77 i. 01 
 
 0.2 10,000 40.0 7.2 o.i 8 
 
 30.0 58 0.19 0.2 0.55 
 
 a Another run gave a non-measurable result probably due to the fact that equi- 
 librium between the solution and the dilution water had not been reached. 
 
 TABLE VI. HEAT OF DILUTION OF NaCl : 1/2 SrCl 2 SOLUTIONS. 
 
 Concen- Water of 
 
 Total heat 
 
 Molal heat Reversible molal heat of dil. 
 
 tration. Solution. dilution. 
 Wt. N. G. Mols. 
 
 of dilution. 
 Cal. 
 
 of dilution. - - 
 Cal. Obs. 
 
 Calc. 
 
 3.2 IO,OOO 40 
 
 .0 
 
 303 
 
 .0 
 
 7 
 
 -58 
 
 
 30 
 
 .0 
 
 -2 4 6 
 
 .6 
 
 8 
 
 .22 
 
 
 20 
 
 .0 
 
 177 
 
 .0 
 
 8 
 
 85 
 
 
 10 
 
 .0 
 
 95 
 
 .0 
 
 9 
 
 .50 IO.2O 
 
 8.70 
 
 1.6 10,000 40 
 
 .0 
 
 i 08 
 
 .8 
 
 2 
 
 .72 
 
 
 30 
 
 .0 
 
 93 
 
 .8 
 
 3 
 
 13 
 
 
 20 
 
 
 
 70 
 
 .2 
 
 3 
 
 51 
 
 
 10 
 
 .0 
 
 36 
 
 .6 
 
 3 
 
 .65 4.20 
 
 3-30 
 
 0.8 10,000 40 
 
 .0 
 
 28 
 
 .2 
 
 o 
 
 .70 
 
 
 30 
 
 o 
 
 25 
 
 7 
 
 o 
 
 .86 
 
 
 15 
 
 
 
 16 
 
 . i 
 
 I 
 
 .07 1.30 
 
 1.18 
 
 0.4 10,000 40 
 
 
 
 8 
 
 65 
 
 o 
 
 .22 
 
 
 20 
 
 
 
 6 
 
 .0 
 
 o 
 
 . 30 o . 40 
 
 0.60 
 
 O.2 IO,OOO 40 
 
 
 
 5 
 
 .0 
 
 o 
 
 . 12 
 
 
 25 
 
 .0 
 
 3 
 
 .0 
 
 o 
 
 .12 O.I 
 
 0.2 
 
H 
 TABLE VII. HEAT OF DILUTION OF KC1 : 1/2 SrCl 2 SOLUTIONS. 
 
 Reversible molal heat of dil. 
 Obs. Cals. 
 
 Concen- 
 tration. 
 Wt. N. 
 
 Solution. 
 G. 
 
 Water of 
 dilution. 
 Mols. 
 
 Total heat 
 of dilution. 
 Cal. 
 
 Molal heat 
 of dilution. 
 Cal. 
 
 3-2 
 
 10,000 
 
 40.0 
 
 575-0 
 
 14-37 
 
 
 
 30.0 
 
 472.0 
 
 15-70 
 
 
 
 2O. O 
 
 343 - 5 
 
 17.2 
 
 
 
 10. 
 
 189.0 
 
 18.9 
 
 20.5 9.7 
 
 (Duplicate Run) 
 
 3.2 10,000 
 
 25.0 412.0 16.48 
 
 20.7 
 1.6 10,000 
 
 35-0 
 
 514-8 
 
 14.72 
 
 25.0 
 
 412.0 
 
 16.48 
 
 15.0 
 
 269.3 
 
 17-95 
 
 40.0 
 
 168.5 
 
 4.21 
 
 30.0 
 
 142.0 
 
 4 75 
 
 20. o 
 
 IO2 .O 
 
 5-io 
 
 10. 
 
 54-3 
 
 5-43 
 
 6 . o 2 . 6 
 (Duplicate Run) 
 
 1.6 10,000 35.0 150.5 4.30 
 
 25.0 121.3 4-86 
 
 15.0 77.0 5.15 6.0 
 
 0.8 10,000 40.0 32.4 0.8 1 
 
 30.0 27.9 0.93 
 
 2O. O - 2O. 2 - I.OI 1.22 - O.53 
 
 0.4 On four dilutions there wa$ no certain effect measured. 
 
 o . oo o . oo 
 
 o . 2 Since the 0.4 wt. N solution gave a value which was too small to be measured, 
 no dilutions were made on this solution. The observed value may be safely assumed 
 tojDe zero. The calculated value is zero. 
 
 TABLE VIII. HEAT OF DILUTION OF KC1 : SrCl 2 SOLUTIONS. 
 
 Reversible molal heat of dil. L 
 
 Concen- 
 tration. 
 Wt. N. 
 
 Solution. 
 G. 
 
 Water of 
 dilution. 
 Mols. 
 
 Total heat 
 of dilution. 
 Cal. 
 
 Molal heat 
 of dilution. 
 
 Cal. 
 
 3-2 
 
 IO,OOO 
 
 35-0 
 
 375-0 
 
 10.66 
 
 
 
 25.0 
 
 297 . I 
 
 11.88 
 
 
 
 15.0 
 
 184.6 
 
 12.30 
 
 1.6 
 
 IO,OOO 
 
 35-0 
 
 96 . 06 
 
 2-75 
 
 
 
 25.0 
 
 86.47 
 
 -3-46 
 
 
 
 15.0 
 
 60 . 80 
 
 4.06 
 
 0.8 
 
 10,000 
 
 35-0 
 
 18.6 
 
 0.53 
 
 
 
 25.0 
 
 -16.5 
 
 0.66 
 
 
 
 15.0 
 
 15 6 
 
 i .04 
 
 Obs. Calc. 
 
 14.0 3.9 
 
 5.2 
 
 1.3 o.o 
 
 F. Discussion. 
 
 Figs. 3 to 7 show graphically the change of the reversible molal heat of 
 dilution with the concentration for the various solutions studied. The 
 concentrations expressed in terms of weight normality are plotted as 
 abscissas, while the heats of dilutions in calories per mol of water of dilu- 
 tion are plotted as ordinates. Fig. 3 shows this for the 3 single salts, 
 by means of curves, plotted to the same scale. Figs. 4 to 7 show the 
 change of the heat of dilution of the various salt mixtures with their con- 
 
centrations. There are 2 curves in each of these 4 figures. The one 
 labeled "Obs." gives the curve as it was observed experimentally, while 
 the one marked "Calc." is plotted from data calculated on the assump- 
 tion that the heat of dilution of a mixed 
 salt solution is equal to the sum of -the 
 heats of dilution of solutions of the 
 various constituents at concentrations 
 equivalent to their concentrations in the 
 mixed solution. 
 
 It will be noted at once that, without 
 exception, the observed values lie on a 
 curve which, except at low concentra- 
 tions, is significantly lower than the 
 curve for the calculated values. This 
 holds even in the case of the mixed 
 sodium and potassium salts where one 
 might expect the least deviation from the 
 thfcon' calculated values; and is in harmony with 
 centration for solution of the salts the conclusion 1 that the ion-fraction of 
 SrCl,, NaCl and KG Qne of ^ metallic constituents increases 
 
 with increasing total salt concentration, since the two curves, which prac- 
 tically coincide at low concentrations, diverge more and more as the total 
 salt concentration increases. The curve, to be sure, does not indicate 
 which of the ion-fractions increases. 
 
 There seems to be no simple relation between the two curves. In the 
 case of the mixture NaCl : 1/2 SrCls the divergence is even less than in 
 the case of NaCl : KC1 where the least divergence might be expected. 
 These experimental curves, then, seem to be influenced by 3 factors. 
 There are the specific effects of the two salt components, and there is also 
 the very apparent effect of a third species of molecular aggregate, in all 
 probability a molecular complex of the two salts with varying amount 
 of water. The concentration of these complexes, in equilibrium with 
 their simple components, will be low at low total salt concentrations, 
 and the specific effect on the curve will be slight in that region so that the 
 two curves should tend to come together at low concentrations. This is, 
 as is observed, the case. As the total salt concentration increases, the 
 concentration of these complexes correspondingly increases and the curve 
 is given a component of slope characteristic of them and depending on 
 two things; namely, their individual "heats of dilution" at the concentra- 
 tion at which they occur, which will depend primarily perhaps on their 
 heats of formation; and the rate of change of their concentration with 
 
 1 Smith and Ball, J. Am. Chem. Soc., 39, 179 (1917). 
 
i6 
 
 the total salt concentration, or, in other words, the value of their equi- 
 librium constant. 
 
 Thus, if the value of k in the expression 
 [(Kd), . (NaCl) y ] 
 
 (KCl),(NaCl y ) 
 
 is large, and if the complex [(KC1)* . (NaCl) y ] has a high heat of dilu- 
 tion we would expect the slope of the experimental curve to be widely 
 divergent from that of the calculated curve, since a substance of high heat 
 
 0/23 0/23 
 
 -30 
 
 Fig. 4. Reversible molal heat of dilution 
 as a function of the concentration for the 
 mixed salt solution NaClrKCl. 
 
 Fig. 6. Reversible molal heat of dilution 
 as a function of the concentration for the 
 mixed salt solution KCl:i/2 SrCl 2 . 
 
 Fig. 5. Reversible molal heat of dilu- 
 tion as a function of the concentration for 
 the mixed salt solution NaCl:i/2 SrCl 2 . 
 
 Fig. 7. Reversible molal heat of dilu- 
 tion as a function of the concentration for 
 the mixed salt solution KCl:SrCl 2 . 
 
 of dilution is being rapidly produced with increasing total salt concentra- 
 tion. If the value of k is small the curves will diverge less rapidly. 
 
 Table IX gives the results of a short series of experiments in which very 
 large quantities of water of dilution, 5.555 mols E^O and 10,000 g. of 
 
17 
 
 solution, were used. The same tendencies will be noticed as before. In 
 each of the 3 cases of mixed salt solutions the observed value of the 
 molal heat effect is greater (negatively) than the calculated value, a rela- 
 tionship which agrees with those brought out in the curves. 
 
 IX. 
 
 Salt. 
 
 SrCl 2 
 
 Cone. 
 
 3.2 wt. N 
 
 KC1 
 
 32 wt. N 
 
 NaCl 
 
 3 2 wt N 
 
 NaCl : KC1 
 
 3.2 wt. N 
 
 NaCl : 1/2 SrCl 2 
 KC1 : 1/2 SrCl9.. 
 
 3.2 wt. N 
 
 1 . 2 Wt. N 
 
 The assumption of these complexes is not out of harmony with experi- 
 mental data. The substances 2KCl.SrCl 2 and 2NaCl.SrCl 2 have both 
 been prepared and isolated 1 and ions of the type (SrCU)"" and (BaCU)" 
 have been referred to as probably existing in solution. 2 Indeed it seems 
 probable that there are very few types of compounds which do not tend 
 to form "higher order compounds." 3 
 
 As was stated in the introduction, according to Nernst the existence of 
 a measurable heat of dilution seems due to the existence of complexes 
 which are formed or decomposed with dilution. 4 
 
 The thermodynamic expression for the reversible molal heat of dilu- 
 tion, L D , is 
 
 = RT2 dlnp/ Po 
 dT 
 
 where p is the vapor pressure of the solution, and p is the vapor pressure 
 of the pure solvent at the same temperature. For a negative value of L D , 
 as in the case of potassium and sodium chlorides, the equation tells us that 
 the ratio p/p decreases with the temperature. Thus, if p/p de- 
 creases with increasing temperature, it means that p increases more 
 slowly than p with the temperature, and from Raoult's law this would 
 indicate that at higher temperatures there is an increase in the degree of 
 ionization of the salt. A. A. Noyes 5 found experimentally, however, that 
 for salts of this type the opposite was true, namely, that the degree of 
 ionization actually decreased with the temperature. There must, there- 
 fore, be some factor which aids in determining what this value shall be, 
 other than simple ionization. The heats of ionization can be obtained 
 from a knowledge of the rate of change of the degree of ionization with 
 the temperature, from the relation 
 
 1 Berthelot and Ilosvay, Ann. chim., [5] 29, 318 (1885). 
 
 2 Noyes and Falk, /. Am. Chem. Soc., 33, 1455 (1911). 
 
 3 A. Werner, Neuere Anschanungen a. d. Gebiete d. Anorg. Chemie (1913). 
 
 4 Loc. cit. 
 
 5 A. A. Noyes, Carnegie Inst. Pub., 63, 339 (1907). 
 
i8 
 din K Q 
 
 dT RT 2 ' 
 
 The values calculated from this relationship, however, do not seem to 
 agree with those observed. For instance, Arrhenius gives the energy 
 equation for the ionization of dissolved potassium chloride 1 as 
 
 KC1 = K+ + Cl- + 362 cal., 
 
 whereas, when calculated, the value of the heat of ionization is found to be 
 2,000 calories. According to Senter, "it seems that the process of ion- 
 ization must be attended by some exothermic reaction which more than 
 compensates for the heat presumably absorbed in splitting up the mole- 
 cules." Van der Waals, 2 as well as Werner, has suggested that ioniza- 
 tion in aqueous solution is essentially a hydration process and thus the 
 energy necessary for its completion may come from the combination be- 
 tween the ions and water. The heats of ionization are small in com- 
 parison with the heats of hydration. Thomsen 3 has found values as high 
 as 8,000 calories per mol of water combining to form a hydrate. Of the 
 two effects, therefore, this one would predominate. The order of magni- 
 tude of the heats of formation of higher order complexes of mixed salts 
 is also great enough to overshadow any ionization effect. A few examples 
 are taken from Pattison Muir's, "Elements of Thermal Chemistry," Ap- 
 pendix I: 
 
 SiF 4 (aq) + 2KF(aq) = K 2 SiF 6 (aq) + 23,000 cal. 
 
 NaF + HF = NaHF 2 + 17,000 cal. 
 
 NH 3 + HC1 = NH 4 C1 + 42,000 cal. 
 
 AuBr 3 (aq) + HBr(aq) = HAuBr 4 (aq) + 7,700 cal. 
 These heats are all positive. Now it will be noted in the curves in 
 Figs. 4 to 7 that the deviations of the observed values from those calculated 
 are always toward a larger negative heat. That is, with dilution, the 
 complexes existing in the solution are broken up with the absorption of 
 heat. 
 
 G. Summary. 
 
 1. The reversible molal heat of dilution has been determined for solu- 
 tions of the single salts, sodium, potassium and strontium chlorides at 
 various concentrations ranging from 3.2 wt. N to 0.02 wt. N, and also for 
 solutions of the mixed salts NaCl : KC1, NaCl : l /&rC\* KC1 : l /i SrCl 2 , 
 and KC1 : SrCk for the above-mentioned range of concentration. 
 
 2. The heats of dilution of sodium and potassium chlorides are nega- 
 tive. This fact in the light of the equation 
 
 dT 
 
 1 Senter, "Outlines of Physical Chemistry," p. 344. 
 
 2 Van der Waals, Z. physik. Chem., 8, 215 (1891). 
 
 3 Pattison Muir, "Elements of Thermal Chemistry," p. 167. 
 
19 
 
 in which L# is the molal heat of dilution, indicates an increase in the de- 
 gree of ionization with the temperature, contrary to the experimental 
 results of A. A. Noyes, unless explained on the basis of the decomposi- 
 tion with dilution, of complexes existing in the solution. 
 
 3. The heats of dilution for the solutions of the mixed salts bear no 
 simple additive relation to the heat effects of the single components at 
 equivalent concentrations. 
 
 4. The results have been explained on the basis of the conception of 
 higher order compounds as put forth by A. Werner. 
 
BIOGRAPHY. 
 
 The writer of this thesis received his early education in the public 
 schools of Eldon, Missouri, and St. Louis, Missouri. He entered Leland 
 Stanford Junior University in the autumn of 1912 and graduated with the 
 degree of Bachelor of Arts in Chemistry in the spring of 1915. The follow- 
 ing year, 1916, he received the degree of Master of Arts. The thesis con- 
 sisted of "A Study of the Basic Sulfates of Copper" (/. Am. Ghent Soc., 
 38, 1947 (1916)), and was carried out under the direction of Prof. S. W. 
 Young. During the academic year 1914-1915 he held the position of 
 Teaching Assistant in Chemistry in Stanford University, and during 1915- 
 1916 that of Lecture Preparation Assistant, and Assistant in Toxicology 
 and Medical Organic, respectively. 
 
 In 1916 he entered the graduate school of the University of Illinois as a 
 Fellow in Chemistry, and received in June, 1917, the degree of Master of 
 Science. The thesis was on the "Mechanism of Colloidal Behavior. I. 
 The Swelling of Fibrin in Acids" (J. Am. Ckem, Soc., 40, 264 (1918)), and 
 was carried out under the direction of Major Richard C. Tolman. During 
 the academic year 1917-1918 he held the position of Research and Teach- 
 ing Assistant in Physical Chemistry in the University of Illinois, and 
 during 1918-1919 that of Assistant in Chemistry at the same place. He 
 is a member of Phi Beta Kappa, Sigma Xi, Phi Lambda Upsilon, and 
 Alpha Chi Sigma. 
 
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