THE DISTRIBUTION OF MOLECULES 79 



collapse, consists of the areas : Saq."^, SAab, S^^b and SA^d of the four 

 kinds of surfaces A, B, C and D. Considering that each of these sur- 

 faces forms contact with the others in proportion to their respective areas 

 and remembering that it takes two faces to make an interface, we find that 

 the energy A4 is 



'k^ = SAoracyac + ^'hdyM + u{i[^abyab + adya.i + ^cyt,c + cd{cd)] (15I 



The energy Iav that must be expended in transferring an A-molecule from 

 the liquid phase to the vapor is then 



"kiv = K2 ~\~ ^i — ^^l> 



the energy A3 dropping out. Substituting into this the values from Equa- 

 tions (13), (14) and (15) and replacing a by its value i — ^ we thus find 



(3^cb— U^ + or>ijo — ^kv)-S = '"'Y (16) 



where cp is independent of the concentrations of the components and is a 

 function of the y's: 



(p =z abyab -f adyad + bcybc + cdy^ — acyao — bdyM (17) 



In the case of the evaporation of a pure liquid A we place /5 = O in (16) 

 and find for the energy of evaporation 



X'av =Sj(aya — acyac + eye) (18) 



so that Equation (16) simplifies to 



i_,,. = y.,,—SM' (19) 



If we have two binary mixtures (i and 2) having the same components 

 but in different concentrations, the energy required to transfer an A- 

 molecule from i to 2 is, according to (19) 



l,=SM^2' — ^i') (20) 



and in a similar way it may be shown that the energy of transfer of a B 

 molecule from i to 2 is 



(.jn — ,--n)dy's= "X (21) 



As the first application of these equations let us make a comparison 

 jof the energy X4' for the transfer of a molecule A from a pure liquid A 

 to a pure liquid B, with the energy Ib for the transfer of a B molecule 

 from B to A. In liquid A, a = i and /5 = o while in B, a = o and /5 = i 

 and Equations (20) and (21) reduce to 



^A = Sa^> and V = Sji^ (22) 



