HETEROGENEOUS EQUILIBRIA 277 



that of a ternary electrolyte in the presence of a common univalent ion 

 and in that of a common divalent ion. 



Harkins 34 has calculated solubility curves on the assumption that 



(74) S m (S + C) n = 1, 



where ra and n are the number of ions resulting from the dissociation, 

 while S is the solubility of the salt and C is the concentration of the 

 added salt. The curves calculated on these assumptions correspond 

 roughly with the observed curves. An exact correspondence is not to be 

 expected, since the assumptions made in calculating these curves are 

 obviously only roughly fulfilled. 



The equations given above obviously do not account for the form of 

 the curves at higher concentrations, particularly for the increase in the 

 solubility of a ternary salt on the addition of larger amounts of a salt 

 with a common divalent ion. According to Harkins this increase is due 

 to the formation of an intermediate ion MX* according to the reaction: 



M + X- = MX*. 



On this assumption the solubility on the addition of a salt with a com- 

 mon univalent ion is given by the equation: 



(75) S 



where K^ is the constant resulting from the reaction: 



MX* + X- = MX 2 . 



It is evident, from this equation, that, if intermediate ions MX* are 

 formed, then, on the addition of an electrolyte NX, the solubility depres- 

 sion will be smaller than in the case where no intermediate ions are 

 formed. From this equation, it follows, also, as may readily be seen 

 by differentiating with respect to the concentration of the common ion 

 X", that with increasing concentration the solubility must decrease irre- 

 spective of the values of the constants K and K. 



If a salt of the type MY 2 is added, the solubility is given by the 

 equation: 



(76) S = MX, + XM 



Here K 2 is the equilibrium constant resulting from the reaction: 



M+ + + X- = MX+. 



"Harkins, Joe. cit. 



