VIII. On the Relation of the Physical Properties of Aqueous Solutions to their state of Ionization. By Prof. J. G. MACGREGOR, Dalhousie College, Halifax, N.S.* IT T has often been pointed out that, according to the dissociation or ionization conception of the constitution of a solution of an electrolyte, the difference between the physical properties of one in which ionization is complete and those of the solvent must be compounded additively of the differences produced by the two ions. It would seem to be equally obvious that, in the case of solutions in which the ionization is not complete, the differences referred to must be similarly compounded of those produced by the undissociated molecules and by the free ions; and if so, it should be possible to express the numerical values of the various properties in terms of the state of ionization. Such an expression would take its simplest form in the case of solutions so dilute that the molecules, dissociated or undissociated, might be regarded as sufficiently far apart to render mutual action between them impossible, and in these circumstances the change produced in the properties of the solvent by the undissociated and the dissociated molecules respectively might be expected to be simply proportional to their respective numbers per unit of volume. It is the object of this paper to test the applicability to sufficiently dilute solutions of such an expression, viz., 20 P=Pu+k(1-a)n+lan, (1) where P is the numerical value of any property (density &c.), Pw that of the same property for water under the same physical conditions, n the molecular concentration of the solution, i. e., the number of gramme-equivalents of the dissolved substance per unit volume of the solution, a the ionizationcoefficient, an and (1-a)n consequently the numbers of dissociated and undissociated gramme-equivalents per unit of volume respectively, and k and I constants, which may be spoken of as ionization-constants, which will vary with the solvent, the substance dissolved, the property to which they apply, the temperature, and the pressure, but not with the concentration of the solution. w The formula can obviously apply only to properties for which P has a finite value. Thus it is inapplicable to electrical resistance, for which Pu would have a practically infinite value. Abstract of a paper read before the Nova Scotian Institute of Science. Communicated by the Author. Simple Solutions. I In order to test the applicability of the above expression I have determined the ionization-constants for the density, thermal expansion, viscosity, surface-tension, and refractive index of solutions of Sodium and Potassium Chlorides, by the aid of observations made by Bender*, Brückner †, and Rother‡. I selected these observations as a first instalment not because of their precision (for in one or two cases more exact observations are available), but because these observers, in all cases but one, determined the values of the above properties for mixtures of solutions as well as for simple solutions. selected the above chlorides partly because I thought it well to begin with salts of simple molecular structure, but largely also because, for the purpose of calculating the conductivity of mixtures of them (as described in my paper on this subject §), I had already obtained interpolation formulæ and curves which, judged by the results of that paper, gave with considerable accuracy the ionization-coefficients of the simple solutions of these salts in terms of their molecular concentration. To save space I may tabulate here the values of the ionization-coefficients used in the calculations for simple solutions. They are as follows: * Wied. Ann. vol. xxii. (1884) p. 184, and vol. xxxix. (1890) p. 89. † Ibid. vol. xlii. (1891) p. 293. Phil. Mag. [5] xli. p. 276 (1896); (1896) p. 101. ‡ Ibid. vol. xxi. (1884) p. 576. and Trans. N.S. Inst. Sci. ix. These coefficients were obtained from Kohlrausch and Grotrian's and Kohlrausch's observations of conductivity at 18° C.* In obtaining them I took the specific molecular conductivity (referred to mercury) at infinite dilution to be 1216 x 10-8 for KCl, and 1028 x 10-8 for NaCl, not being aware at the time that Kohlrausch had given 1220 and 1030 respectively as more exact values. Nevertheless, to save labour I have used the above values of a in the calculations of this paper, having satisfied myself by a re-calculation in one case that no appreciable difference in the results would be produced by the employment of more exact values. It will be noticed that in one or two cases the above values of a are obviously a little out; but they would seem to be sufficiently accurate for my purpose. I did not foresee the extent of the calculations, or I should have determined all the values of a required at the outset, and checked them by comparison with one another. I have determined the ionization-constants (k and 7) in all cases in which more than two observations of a property on solutions of sufficient dilution were available by the method of least squares. The constants thus determined and used in the calculations are tabulated below. In all cases the available observations had been made on solutions of such great concentration that the values of the constants obtained cannot be regarded as exact; but the calculations may serve as a test of the general applicability of the expression referred to above. The only available observations, so far as I know, on solutions of sufficient dilution for the determination of the ionization-constants and the limits of concentration within which the above expression is applicable, are those by Kohlrausch and Hallwachs † on the specific gravity of dilute solutions, from which two of my students have undertaken to determine the density-constants for the salts and acids examined. With regard to the observations which I used in determining the various ionization-constants, the following statements should be made: - Bender's determinations of density (i. e. specific gravity referred to water at 4° C.) were made at 15° C., but were readily reduced to 18° by the aid of his observations on the thermal expansion between 15° and 20° of the same solutions. According to his statement, the fourth place of decimals in his values may be in error by +2 or 3. The density of water was taken to be 0.99863. * Wied. Ann. vi. (1879) p. 37, and xxvi. (1885) p. 195. Bender's determinations of thermal expansion are for the interval between 15° and 20° C.; and will therefore be sufficiently nearly proportional to the coefficients of expansion at 18° for my purpose. He considers that they may be in error by 2 in the sixth place of decimals. On plotting his observations, however, it becomes obvious that they do not all attain this degree of accuracy. The expansion of water was taken, according to his observations, to be 0.0,878 for the same interval. Brückner's observations of viscosity were made at 15° C.; but he gives an interpolation formula, applicable between 15° and 20°, by means of which at least approximate values for 18° were obtained. His values for water at 15° and 20° do not agree well with those given by Landolt and Börnstein. I have therefore taken 0.010613 as the viscosity at 18° of the water used by him, a value which has to his value at 15° the same ratio as Landolt and Börnstein's for the same temperatures. The actual concentrations of Brückner's solutions differed from those given in the tables below by about 0.1 per cent.; but so small a difference could produce no appreciable error in the result. He gives as his "mean probable error of observation," +24 in the fifth place of decimals for sodium-chloride solutions, and +1.8 for those of potassium chloride. Rother's observations of surface-tension were made at 15°, and are therefore not precisely comparable with calculated values based on the values of ionization-coefficients for 18°. From Kohlrausch's data*, however, it would appear that between 15° and 18° in the case of potassium-chloride solutions containing 0.5 and 3 gramme-molecules per litre, the ionization-coefficient changes only by about 0.13 and 1.3 per cent. respectively; and in the case of sodium-chloride solutions of the same concentrations only by about 04 and 0.6 per cent. respectively. For the more dilute solutions, therefore, my calculations will be practically comparable with Rother's observations. He seems to regard his determinations as possibly in error by + 5 to 8 in the third place of decimals. The surface-tension of the water he used he found to be 7.357. Bender's observations of refractive index were made at 15° C., but were reduced to 18° by means of data provided in his paper, based on observations made by Fouquét. The refractive index of the water he used he found to be 1.33310 * Wied. Ann. xxvi. (1885) p. 223. Phil, Mag. S. 5. Vol. 43. No. 260. Jan. 1897. |