THE DISTRIBUTION OF MOLECULES 



85 



are in reasonable agreement with others of similar nature already found. 

 These data are, however, probably only rough. The known existence of 

 double molecules in the vapors of the lower fatty acids should cause 

 deviations from our theory, but the effect is probably not sufficient to 

 prevent the theory from serving as a useful approximation over a wide 

 range of concentrations. 



TABLE V 

 The Mixture Energies (p of Fatty AaD-WATER Mixtures 



Mutual Solubilities of Liquids. When two immiscible liquids, A and 

 B, are in equilibrium, each has dissolved some of the other, and the partial 

 vapor pressure pA from one liquid must be the same as the pA from the 

 other. Thus, from Equations (25) we obtain the following two equations 

 which express the solubilities of the liquids in one another 



and (26) 



El 



kT 



(a.' — a,') 



The subscripts i and 2 refer to the two phases. 

 If each liquid is only very slightly soluble in the other, the equations 

 take the simple form 



kT • kT (^^\ 



A. = e and B^ = e ^^^ ' 



If Sa — Sb then {x = A and ^ = B and the two Equations (26) can 

 readily be combined to one of the convenient form 



1 + A 



1 — A 



kT 



e 



(28) 



where A = /^i — .^2 = ^2 — -^i- 



