122 BUTLER art. d 



A perfect gas mixture is one in which there is no interaction 

 between the components, so that the energy is the sum of the 

 energies which each component would possess if present in the 

 same volume (and at the same temperature) by itself, and the 

 entropy and pressure the sum of the entropies and pressures of 

 the components separately under the same conditions.* In 

 such a perfect gas mixture it is evident that the potential of each 

 component is not affected by the presence of the other com- 

 ponents and may also be represented by (127). 



When a liquid and a gaseous mass are coexistent, the poten- 

 tials of those components which are common to the two phases 

 must have the same values in each. Thus, if *S2 is an actual 

 component of coexistent liquid and vapor phases and its 

 concentration in the vapor is nii''^^ /v'^°\ its potential in the gas 

 phase, provided that the latter has the properties of a perfect 

 gas mixture, is given by the equation 



^ , ^t m^ (129) 



M2 = ^2 + M^iO) log ^(o) , 



and this is also the value of its potential in the liquid. 



As an example of the determination of the potentials in a 

 liquid by means of a coexistent vapor phase, we may consider 

 a solution with two volatile components Si and Si. If the 

 partial pressures of the components in the vapor are pi and 

 P2, their potentials in the vapor by (128) are 



At 

 /*! = /^(^) + ]^) log Vu (130) 



At 



M2 = fiit) -\- ^^^ log P2, (131) 



where Mi^"\ Mi^'^'' are the molecular weights in the vapor. 

 These equations also give the values of the potentials in the 

 coexistent liquid phase. At constant temperature and total 

 applied pressure, applying (56) to the liquid phase, we have 



mi dfii + Mi djXi = 0, 



* A proof of this proposition is given by Gibbs (I, 155). 



