276 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



tion of the common ion X~. In order to determine the concentration of 

 the common ion in the mixture, it is obviously necessary to know the 

 ionization functions for the various electrolytes concerned. While these 

 functions are not known, a fair approximation could probably be obtained 

 by assuming one of the functions given in Chapter IX. This would 

 necessarily involve the further assumption that intermediate ions are not 

 present. 



On the addition of a common divalent ion, the solubility is given by 

 the equation: 



(7*\ 



I' 2 ) 2 M++ > 



while, on the addition of a salt without a common ion, 



M~Y- 

 " -- ~' ' 



where K f is the constant of the reaction 



MY 2 = M" + 2Y-. 



Since different electrolytes of the same type are ionized to practically 

 the same extent in water, it follows that, in the mixture containing a 

 salt without a common ion, the equivalent concentrations X~ and M ++ 

 will not differ greatly from each other. The first two terms of Equation 

 73, therefore, will remain constant on the addition of a salt without a 

 common ion. The last term of this equation, however, will obviously 

 increase as the concentration of the ion Y~, due to the addition of a salt 

 NY, increases. It is evident, therefore, that according to this equation 

 the solubility of a ternary salt should be increased upon the addition of a 

 salt without a common ion. On the other hand, comparing Equations 71 

 and 72, it is evident that the addition of a common univalent ion will 

 cause a much greater solubility depression than will the addition of a 

 common divalent ion, since the concentration of the univalent ion appears 

 in the denominator with the exponent 2, while that of the divalent ion 

 appears in the denominator with the exponent %. Roughly, this is in 

 agreement with observations. As may be seen by reference to Figure 53, 

 the addition of a salt with a common univalent ion causes a much greater 

 depression than does the addition of a salt with a common divalent ion. 



As we have already seen, the solubility of a binary salt decreases as 

 the reciprocal of the concentration. of the common ion. The solubility 

 curve of a binary electrolyte, therefore, should lie intermediate between 



