338 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



where C is the molal concentration and x is a constant characteristic of 

 the salt. Combining this empirical equation with the differential thermo- 

 dynamic equations and integrating, he obtains the equation: 



( 121 ) log C + C~ = 2nC j 1 / 3 + Const., 



where C is the total salt concentration of the saturated solution. In 

 the case of salts without a common ion, Bronsted assumes: 



where C s is the total concentration of the saturating salt. This leads to 

 the equation: 



(122) log^ = x((y/-C 8 >/). 



V 



For the solubility of a salt in a mixture containing a salt with a common 

 ion, Bronsted assumes: 



C" = C and C" = C ,, 



O d 



where C" and C" are the concentrations of the uncommon and the com- 

 mon ion respectively. This leads to the equation: 



c s c t 



(123) log jf+f = 2* (C ( v - C 8 W) . 



s o 



These equations express the solubility of the saturating salt in terms of 

 the total concentration of all the salts in solution. The value of the 

 constant K depends upon the type of salt. For uni-univalent salts, 

 x = approximately 1/3 ; for bi-bivalent salts, 4/3 ; and for tri-trivalent 

 salts, 3. Bronsted shows, in the first place, that the form of the curve is 

 determined by the values of the constants C g and x. In the presence of 



salts without a common ion, the solubility of the saturating salt is in- 

 creased due to addition of the second electrolyte; and this increase is the 

 greater, the greater the value of the constant >t. Moreover, the relative 

 increase of the solubility is the greater, the smaller the value of C . In 



6 



the presence of salts with a common ion, the form of the solubility curve 

 depends upon the number of charges on the ions and the number of ions 

 resulting from the different salts. Bronsted shows that solubility curves 

 will, in general, exhibit a minimum. In the case of uni-univalent salts, 

 this minimum will lie at very high jconcentrations ; for bi-bivalent salts, 

 assuming x = 4/3, the minimum concentration is 0.12m; and for tri- 



