Properties of Aqueous Solutions to their State of Ionization. 105 



data were available the absorption-spectra were similarly 

 affected by elevation of temperature and increase of concen- 

 tration. 



The occasional constancy in the Difference between the Molecular 

 Values of Properties of Solutions having the same Molecular 

 Concentration. 

 The difference between the values per gramme-equivalent 



of any property for two simple solutions, 1 and 2, of the 



same concentration will be 



(Pi-P,)/n=* l ^^+ ((,.-*,)«!- ft.-* a )«i. • (11) 

 Now a in all cases diminishes as n increases. Provided, 

 therefore, the values of the (l — k)'s have the same sign, and 

 the rates of change of the a's with concentration are inversely 

 proportional, or approximately so, to the (I — k)'s of their 

 respective solutions, we shall have (P 1 — F 2 )/n exactly or 

 approximately constant, i.e. independent of the concentration. 

 This approximate constancy will of course hold in all cases at 

 extreme dilution. 



In the case of solutions of moderate strength this pheno- 

 menon has been observed by Valson and Bender * for the 

 density and refractive index, by Wagner f for viscosity con- 

 stants, and by Jahn J for the electromagnetic rotation of the 

 plane of polarization ; and a very close approximation to con- 

 stancy in the case of the densities of very dilute solutions is 

 clearly shown in the results of Kohlrausch and Hallwachs's § 

 observations. 



It is obvious, from the values of I and k determined above 

 for the density of sodium and potassium chlorides, that, as 

 Bender found, this approximate constancy must hold for the 

 densities of these salts. For l — k for NaCl has the value 

 + 0-01424, and for KC1 +0-01316; while a glance at the 

 first table shows that the ionization-coefficient of solutions of 

 the former salt falls off somewhat more rapidly with increasing 

 concentration than that of the latter. It is equally obvious 

 that as the value of l — k for the thermal expansion of NaCl 

 is *0 3 91, and for KC1 '0 2 13, the thermal expansions of these 

 salts will not exhibit this constancy. We accordingly find 

 from Bender's observations 



For n = 1. 1-5. 2. 2-5. 



(P 1 -P 2 )/w= -0 3 108 -0 4 85 -0 4 815 -0 4 78 



* Wied. Ann. xxxix. (1890) p. 89. 



t Zeitschr.fiirphys. Chemie, v. (1890) p. 31. 



% Wied. Ann. xliii. (1891) p. 280. 



§ Ibid. liii. (1894) p. 14. 



