THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 337 



TABLE CXXXII. 



ACTIVITY COEFFICIENTS OF THALLOUS CHLORIDE IN MIXTURES AT 25. 

 C m InKN0 3 InKCl InHCl InTlNO 3 



Tfl 



0.001 0.970 0.970 0.970 0.970 



0.002 0.962 0.962 0.962 0.962 



0.005 0.950 0.950 0.950 0.950 



0.01 0.909 0.909 0.909 0.909 



0.02 0.872 0.871 0.871 0.869 



0.05 0.809 0.797 0.798 0.784 



0.1 0.742 0.715 0.718 0.686 



0.2 0.676 0.613 0.630 0.546 



As may be seen from the figure, the curves, connecting the reciprocal of 

 the mean reduced concentration -^- with the ionic strength, diverge 



c r 



largely at higher concentrations. With electrolytes of the same type, 

 such as potassium chloride and hydrochloric acid, the divergence is not 

 large. With potassium nitrate, however, the divergence at higher con- 

 centration is marked, as is also that for the ternary electrolytes, barium 

 chloride, thallous sulphate, and potassium sulphate. In view of the fact 

 that these curves necessarily pass through a point corresponding to a 

 saturated solution of pure thallous chloride, the conclusion of Lewis and 

 Randall that the curves become coincident at lower concentrations is 

 open to doubt, for it is conceivable that, since the curves exhibit a 

 marked curvature at higher concentration, such curvature may be main- 

 tained in mixtures at lower concentration. 



Lewis and Randall have also examined the solubility curves of higher 

 types of salts, and have shown that, for limited concentration intervals, 

 their principle of mixtures is able to account for the observed phenomena 

 quite closely. 



Solubility Relations According to Bronsted. Bronsted 16 has also 

 treated the solubility relations of mixtures of electrolytes. 16 * He assumes 

 that the van't Hoff factor i may be expressed as a function of the con- 

 centration by means of the equation: 16b 



(120) 2 i 



"Bronsted, loc. cit. 



16 Bronsted's theory of the solubility effects in mixtures of electrolytes is simply 

 interpreted in terms of Bjerrum's theory of electrolytic solutions. Bjerrum assumes that 

 electrolytes are completely ionized and that the observed effects are due to interaction 

 between the ions. So far as the experimental foundation of Bjerrum's theory is concerned, 

 however, it is based chiefly upon observations in mixtures of electrolytes. Naturally, 

 Bjerrum's theory, in the case of a solution of a pure electrolyte, is in harmony with that 

 of Milner. See Bjerrum: D. Kgl. Danske Vidensk. Selsk. Skrifter (7), 4, 1 (1906) ; Proc. 

 7th Intern. Congr. Appd. Chem., Sect. X (1909) ; Ztschr. f. Electroch. 17, 392 (1911) ; 'ibid., 

 2Jf } 321 (1918). 



16b Noyes and Falk, J. Am. Chem. Soc. 32, 1011 (1910). 



