326 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



the system fulfills the condition pv = RT, in which case the only manner 

 in which the concentration is involved in the expression for the thermo- 

 dynamic potential is in the logarithmic term of the above equation. In 

 order to evaluate the term F(vT xyz. . ) it is necessary to know the equa- 

 tion of state of the system, since the value of M as given by the equation: 



,,02, = -. 



obviously involves the term f pdv , which cannot be evaluated without 



}v 



a knowledge of the equation of state. The equations of state for mix- 

 tures of ordinary liquids are comparatively complex, and a general solu- 

 tion of the problem has not been effected, even for liquids of simple type ; 

 while, in the case of mixtures of substances whose equations of state are 

 comparatively complex, even an approximate solution has been little more 

 than attempted. This subject has been treated in detail by van der 

 Waals. 6 



b. Jahn's Theory of Electrolytic Solutions. Nernst 7 and Jahn 8 

 attempted to solve the problem of solutions of strong electrolytes by 

 introducing various correction terms. Since the true equation of state 

 for mixtures containing electrolytes is not known, even approximately, 

 it is obvious that these theories necessarily involve assumptions of an 

 arbitrary nature. These assumptions must contain within them the 

 equivalent of an equation of state. In how far these assumptions are 

 allowable may be ascertained by comparing the consequences of these 

 theories with the experimental facts. Jahn set up the conditions for 

 equilibrium, employing as a criterion for equilibrium, the variation of 

 Planck's function: 



It is on the whole immaterial what function is employed as criterion for 

 equilibrium, provided, always, that it fulfills the conditions of a charac- 

 teristic function. 9 These functions involve the energy of the system and, 

 in order that the condition for equilibrium may be solved, it is necessary 

 to have an expression for the energy of the system in terms of its com- 

 position. In the case of ideal systems, Dalton's law may be assumed to 

 hold, in which case the energy of a mixture of substances is equal to the 

 sum of the energies of its constituents. Jahn assumed an equation for 



van der Waals-Kohnstamm, loc. cit. 

 'Nernst, Ztschr. f. phys. Chem. 38, 487 (1901). 

 Jahn, Ztschr. 1. phys. Chem. 41, 257 (1902). 

 Gibbs, Scientific Papers 1, pp. 85 et seq. (1906). 



