HOMOGENEOUS IONIC EQUILIBRIA 221 



a similar condition holds. If, for example, solutions of sodium chloride 

 and potassium chloride have the same ion concentration, then, on mixing, 

 the concentration of the ions in the mixture will be the same as that in 

 the original solutions. Apparently, then, the isphydric principle holds, 

 even in the case of electrolytes which do not obey the law of mass-action. 

 This principle has been employed very extensively for the purpose of 

 calculating the concentrations in mixtures of strong electrolytes. If the 

 electrolytes in a given mixture do not obey the law of mass-action, then 

 it is obviously impossible to calculate the equilibrium in the mixture 

 unless we know the law governing this equilibrium. The isohydric prin- 

 ciple is an empirical relation which has been assumed to govern the 

 equilibrium in mixtures. In order to test the correctness of this prin- 

 ciple, it is obviously necessary to determine the concentrations of the 

 ions in the mixture by some independent means. 



The law of equilibrium for a given electrolyte in a mixture must 

 reduce in the limit to that of a solution of the electrolyte in the pure 

 solvent. It has been shown that, for a strong electrolyte, Equation 11 

 holds very nearly. According to this equation, the ratio of the product 

 of the concentrations of the ions divided by the concentration of the 

 un-ionized fraction varies as an exponential function of the ion concen- 

 tration. It is clear that this relation conforms to the principle of iso- 

 hydric solutions. In a mixture of electrolytes, the equation might take 

 the form: 



u 



where P^ is the value of the ion product, C u is the concentration of the 

 un-ionized fraction, and C^ is the total concentration of the positive or 



negative ions in the mixture. Indeed, it is apparent that an equation 

 of the form: 



(51) ? ?-=F(ZC) 



L u 



will conform to the isohydric principle, 1 where F(2C^) is any explicit 

 function of the total ion concentration of the mixture. For, on mixing 

 two solutions whose ion concentrations are C* and C^", the equilibrium 

 will be unaffected by the relative volumes of the solutions mixed, pro- 



>Arrhenius, Ztschr. f. phys. Chem. 31, 218 (1899). 



