318 PHYSICAL CHEMISTRY 



by dilution, it is of interest to determine the effect of changing the 

 concentration of either ion separately. A study of the conductivity 

 and the freezing-point of mixtures of two salts having one ion in 

 common throws much light upon this question, for the following 

 simple principle has been found to represent this phenomenon : The 

 conductivity and the freezing-point lowering of a mixture of salts having 

 one ion in common are those calculated under the assumption that the 

 degree of ionization of each salt is that which it would have if present 

 alone at such an equivalent concentration that the concentration of either 

 of its ions were equal to the sum of the equivalent concentrations of all 

 the positive or negative ions present in the mixture. 



This somewhat complicated statement may be illustrated by the 

 following example : Suppose that a mixed solution is 0. 1 normal with 

 respect to sodium chloride and 0.2 normal with respect to sodium 

 sulphate, and that it is 0.18 normal with reference to the positive or 

 negative ions of these salts. The principle then requires that the 

 ionization of either of these salts in the mixture be the same as it is 

 in water alone when its ion-concentration is 0.18 normal. 



This principle in regard to the conductivity of mixtures, which has 

 been definitely stated by Arrhenius, is shown by the existing data to 

 hold true, almost, if not quite, within the small experimental error of 

 the determinations both for mixtures of salts of the same type and 

 for those of salts of different types up to a concentration of at least 

 normal. Experiments confirming this principle have been made upon 

 eight pairs of uni-univalent salts by Arrhenius, Manson, and Barm- 

 water. In addition, the principle has been shown by several Canadian 

 investigators, Archibald, McKay, and Barnes, to hold true for mix- 

 tures of potassium and sodium sulphates, potassium and copper or 

 magnesium sulphates (up to 0.1 normal), potassium sulphate and 

 chloride, barium and sodium chlorides, and zinc and copper sulphates 

 thus for almost every possible typical combination of uni-uni-, 

 imi-bi-, and bi-bivalent salts. That the same principle is true of the 

 freezing-point lowering is shown by the measurements of Archibald 

 with mixtures of potassium and sodium sulphate. This proves that 

 the phenomenon really has reference to the degree of ionization and 

 that it does not arise from a possible variation in the migration- veloc- 

 ities of the ions. 



Of especial interest is the relation of this principle to the validity 

 of the Mass-Action Law. Almost all investigators of the conductiv- 

 ity of mixtures have concluded, from the fact that upon mixing solu- 

 tions of equal ion-concentration there is no change in ionization, that 

 the results do conform to this law. Yet it is scarcely conceivable that 

 this law can apply to mixtures of salts in which the concentration of 

 one ion is varied while maintaining that of the other constant, in view 

 of the fact that it is known not to hold true for the variations of the 



