80 PHENOMENA, ATOMS, AND MOLECULES 



The energy of transfer of molecules A and B between two pure liquids 

 A and B is thus proportional to the surface areas of these molecules. 



The Boltzmann equation may now be used to calculate the distribution 

 of molecules between the vapor phase and a binary mixture of liquids. If 

 we let pA be the partial pressure of the A--molecules in the vapor then by 

 the generalized Boltzmann equation (3) we have 



'-z =. Kc 

 A 



where Iay is given by Equation (19) and K is a constant into which are 



grouped as factors the a priori probabilities and the dimensional factors 



needed to allow us to express the concentrations in the liquid in terms of 



the mol-fraction A while that of the vapor phase is expressed as a 



pressure p. We are hereby making the tacit but reasonable assumption 



that the probability coefficients are independent of the concentrations of 



the components. The vapor pressure Pa of the pure liquid A is given by 



(22) if we place A = 1 and I-av = ^af' so that 



Dividing (23) by (24) and by combining with (19) ' 



p,=P^Ae''^ (25a) 



and in a similar way the partial pressure of component B is 



Sb<p , 



These equations for the vapor-pressures of binary mixtures reduce to the 

 well known Raoult's law when qp = o, that is, when the energy of mixing 

 is zero. 



Comparison with experimental data, particularly with the accurate data 

 of Zawidski (J. v. Zawidski, Zeit. phys. CJicm. 55, 129-203 (1900) ) shows 

 that even for liquids which depart considerably from Raoult's law these 

 equations, which involve only one adjustable constant cp, usually agree with 

 the data within the experimental error. In the case of mixtures in which S 

 and S differ considerably, the use of these factors and the use of the 

 surface fractions a and ^ instead of the mol fractions, are found to be 

 thoroughly justified. 



The rather meager experimental data available show that in changing 

 from one member of a homologous series of compounds to another, in a 

 given type of mixture, the values of q) change in general in the manner 

 indicated by (17). 



