HOMOGENEOUS IONIC EQUILIBRIA 219 



M^XX.-^^M.X, 



M 2 + X X 2 - = 



and the condition equations are: 



M x + MA + M X X 2 = C 

 M 2 + M 2 X 2 + MA = C 



where C and C 2 are the total concentrations of the base M or acid X 1? 

 which are necessarily equivalent, and the base M 2 or the acid X 2> which 

 are likewise equivalent. From these eight equations the concentrations 

 of the eight different molecular species may be determined for any con- 

 centrations Cj. and C 2 of the total acids and the total bases in solution. 

 In this case, interaction with the solvent is assumed not to take place. 

 In a mixture of two electrolytes with a common ion we have the reaction 

 equations : 



M! + X X- = K^U.X 



M 2 + X X- = # 2 M 2 X 



and the condition equations: 



M,X + M x = C x 

 M,X + M 2 = C 2 

 M X X + M 2 X + X = C x + C 2 . 



In this case the solution of the problem is comparatively simple. 



In a mixture of two electrolytes having an ion in common, assuming 

 the mass-artion law to hold, the ionization of the electrolytes in the mix- 

 ture will be the same as that in the original solutions before mixing, if 

 the concentrations of the qommon ion in these solutions, before mixing, 

 are equal. Such solutions are said to be isohydric. 1 This result is a 

 consequence of the law of mass-action. Let M + , M 2 + and X~ be the 

 concentrations of two solutions having in common the ion X~. It is 

 obvious that the concentration of the common ion in these two solutions 

 will be equal to M/ for the first solution and M 2 + for the second solution. 

 Let a volume V t liters of the first solution be mixed with a volume of V 2 

 liters of the second solution. If the concentrations of the ion X~ in the 

 two original solutions are equal, then we obviously have: 



M x + = M 2 + = X-. 



1 Arrheniua, Ann. d. Phj/s. S0 f 51 (1887) ; Ztachr. /. phys. Chem. 2,284 (1888) ; t&id., 

 5, 1 (1890). 



