November 4, 1904.] 



SCIENCE. 



583 



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 ivere 

 equal to the sum of the equivalent concen- 

 trations of all the positive or negative ions 

 present in the mixture. 



This somewhat complicated statement 

 may be illustrated by the following ex- 

 ample : Suppose that a mixed solution is 

 0.1 normal with respect to sodium chloride 

 and 0.2 normal with respect to sodium sul- 

 phate, and that it is 0.18 normal with ref- 

 erence 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 prjnciple in regard to the conduc- 

 tivity of mixtures, which has been definitely 

 stated by Arrhenius, is shown by the exist- 

 ing 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 1/2 normal. Experiments confirming 

 this principle have been made upon eight 

 pairs of uni-univalent salts by Arrhenius, 

 Manson and Barmwater. In addition, the 

 principle has been shown by several Cana- 

 dian investigators, Archibald, McKay and 

 Barnes, to hold true for mixtures of po- 

 tassium 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 i;ni- 



uni, uni-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 mi- 

 gration-velocities of the ions. 



Of special interest is the relation of this 

 principle to the validity of the mass action 

 law. Almost all investigators of the con- 

 ductivity of mixtures have concluded from 

 the fact that upon mixing solutions 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 concentrations of both ions produced 

 by dilution. And in reality this con- 

 clusion, if regarded as a general expression 

 of the facts, is entirely unwarranted. It 

 is true that for certain typical combina- 

 tions of salts— those for which from one 

 molecule of each salt results by ionization 

 not more than one ion of the kind not com- 

 mon to the salts— the principle here stated 

 does coincide with the requirements of the 

 mass-action law. But for combinatiom 

 not so characterized the mass-action lav>' 

 predicts, as is readily seen upon formulat- 

 ing the equations, a conductivity of the 

 mixture widely divergent from that ac- 

 tually found, and, therefore, from that 

 expressed by the principle under consid- 

 eration. This last statement applies, for 

 example, to the mixtures before referred 

 to of potassium sulphate with sodium sul- 

 phate, and of potassium sulphate with 

 copper or magnesium sulphate, the first of 

 which have been studied with respect both 

 to their conductivity and freezing point. 



