HETEROGENEOUS EQUILIBRIA 255 



it being assumed that the two electrolytes have a negatives ion X~ in 

 common. Here, S u is the concentration of the un-ionized fraction of the 



first electrolyte, which is assumed to be present in excess, so that there 

 exists an equilibrium between the solid salt M 1 X 1 and the solution. If 

 the laws of ideal solutions hold, the concentration S u of the un-ionized 



fraction of the first salt should remain constant. The total concentra- 

 tion S of the first salt is then given by the equation: 



(65) S = M+ + S U . 



If a second electrolyte with a common ion X 1 is added, then, in the mix- 

 ture, we have the equilibrium expressed by the equation: 



M 



(66) 



o i, 



S u 



where M^ + M 2 + is the concentration of the common ion X~, which we 

 may write 2C. It follows from Equation 66 that: 



(67) 



and substituting for this value in Equation 65, we have for the solubility 

 the expression: 



K^S U 



(68) s = S+-, 



An examination of this equation shows that the addition of an electrolyte 

 with a common ion reduces the solubility of the first electrolyte. If we 

 plot values of S as ordinates and those of 2C^ as abscissas, the resulting 



curve will be a rectangular hyperbola, whose axis is raised above the 

 origin by the distance S . As the concentration of the added electrolyte, 



and consequently the concentration of the common ion, is increased 

 indefinitely, the solubility approaches the value S u as a limit. The rep- 



resentation of solubility results is greatly simplified if the solubility is 

 plotted against the reciprocal of the common ion concentration, ia which 

 case a linear curve obviously results. This curve ends in a point 



