THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 325 



ever, the concentrations of the various constituents present in the solu- 

 tion are such that the laws of ideal systems are no longer applicable 

 within the limits of experimental error, a general solution of the problem 

 is, at the present time, not possible. In other words, the general solution 

 of the problem involves a knowledge of the equation of state of the 

 system. According to the equilibrium principle of Gibbs, a system will 

 be in stable equilibrium when the entropy is a maximum. For many 

 purposes it is more convenient to introduce derived functions such as the 

 Gibbsian functions \p and in place of the entropy. For a mixture of any 

 number of components in a system, not subject to reaction, the free energy 

 is given by the equation: 



[(\-x-y-z- ) log (1-x-y-z--) 



(98) v 



+ x log x + y log y + z log z + ]+ F(xyz . . T), 



where x, y, z, etc., represent the amounts of the various constituents pres- 

 ent per gram mol of the mixture. The term F (xyz . . T) is, in general, a 

 determinate function of temperature and a linear function of xyz . . . 

 The term ( pdv is a function of the concentrations xyz. ., and represents 



Jv 



the work done in bringing the system from a condition in which the laws 

 of an ideal system are obeyed to the condition in which the system obeys 

 any given equation of state. 4 It is obvious that the condition for equi- 

 librium, d\\> 0, may at once be applied if the equation of state is 

 known, while, if the equation of state is not known, the problem is neces- 

 sarily insoluble, since it is not possible to evaluate the integral in ques- 

 tion. When reaction takes place between various constituents present in 

 the mixture, the condition for equilibrium leads to the equation: 



(99) 2AT = 0, 

 where 



(100) .M 



Here ra is the molecular weight of the constituent and \i is the thermo- 

 dynamic potential defined according to Gibbs. 5 The molecular potential 

 M, of a constituent, is given by an equation of the form: 



(101) M = RTlogx + F(vT xyz..) 



where F(vT xyz..) is a function of the composition of the system, as 

 well as of volume and temperature, except when the equation of state of 



4 van der Waals-Kohnstamm, "Lehrbuch der Thermodvnamik " Vol 2 

 Gibbs, Scientific Papers, Vol. 1, pp. 92 et seq. (1912). 



