238 PHENOMENA, ATOMS, AND MOLECULES 



energy per unit area. We should therefore be able to calculate the latent 

 heat of evaporation, X, from the difference between the energies in the 

 vapor and liquid phases. 



I = S(aya — acyac + He) 



If we take y^ = 193, Yc = 34, and Yoc =34, we get excellent agreement 

 between the observed latent heats of evaporation and the structures of most 

 monobasic alcohols. We have already seen that Yc is equal to 34 as the 

 value found for the evaporation of pure hydrocarbons. The value Yac = 34 

 was found as a result of experiments on the vapor pressures of mixtures 

 of alcohol and water. The interfacial energy between water and a hydro- 

 carbon is about 59, so that the value 34 is of the right order of magnitude. 

 The surface energy of water is 117, but this naturally represents the 

 surface energy of the least active part of the water molecule, whereas the 

 energy Yo equal to 193 corresponds to the most active part of the hydroxyl 

 group so that this value also appears reasonable. 



In the case of the alcohols having very long hydrocarbon chains another 

 effect can be clearly seen from the experimental results. In the molecule 

 of vapor the hydroxyl group is able to bury itself at least partially among 

 the coils of the hydrocarbon tail, so that the surface energy of the vapor 

 molecule decreases considerably, beginning- with chains of five or six 

 carbon atoms in length. With shorter chains than this, the hydroxyl group 

 is probably fully exposed. Particularly interesting results which are in good 

 agreement with the principle of independent surface action are found in 

 the case of dibasic and tribasic alcohols. The heat of evaporation depends 

 to a great extent on whether the separate hydroxyl groups are able to come 

 into contact with each other in the molecule of vapor and thereby decrease 

 the surface energy. 



The theory can readily be extended to calculate the partial vapor 

 pressures of binary solutions. The complete theory, taking into account 

 orientation and segregation of molecules within the liquid, would be very 

 complicated, but in many cases where the forces between molecules are not 

 too strong, these effects can be neglected in a first approximation. Assum- 

 ing then a random orientation and distribution of the molecules, the total 

 surface energy per molecule in a solution of any given concentration in 

 terms of interfacial surface energies, such as Yac, and surface fractions, 

 such as a and c, the work done in transferring a molecule from a liquid 

 to a vapor phase can then be calculated, and thus by applying the Boltz- 

 mann equation, it is possible to calculate the deviations from Raoult's law. 

 Thus, the partial pressure of any liquid in a binary mixture is given by 



Pj, = AP^ exp (cpSA^ykT) 



