SURFACES OF MOLECULES 237 



represents the total energy change per unit area. For all the pure hydro- 

 carbons, such as pentane and nonane, y is equal to about 48 ergs cni."^ 

 The fact that this value is practically independent of the length of the 

 hydrocarbon chain proves that the surface forces are very nearly uniform 

 over the whole of the hydrocarbon molecule. 



When a hydrocarbon, such as hexane, evaporates, molecules pass from 

 the interior of the liquid into the vapor. If we consider a drop of hexane 

 liquid to be removed from a large volume of the liquid into the free space 

 above it, the work that would be needed to form this drop would be equal 

 to ^Y where S is the surface area of the drop. Since we are regarding 

 molecules as having surfaces possessing certain properties, we may say that 

 the work necessary to remove a single molecule of hexane from the liquid, 

 which is the latent heat of evaporation per molecule, will also be equal to 

 Sy, where 6" is now the surface area of the molecule and y is the surface 

 energy of the molecule per unit area. 



The molecular surface S for the molecule of vapor may be calculated 

 from the molecular volumes (molecular weight divided by density), assum- 

 ing the surfaces to be the same as in the case of closely packed spheres. 

 This assumption would probably be quite accurate for large molecules, but 

 would be only a rough approximation in the short chain hydrocarbons. 

 From the known values of the latent heats of evaporation, the values of y 

 can then be calculated. Practically all of the normal hydrocarbons, with the 

 exception of methane, give the value y = 34 =i= i ergs cm."-. This value is 

 of the same order of magnitude as the value 48 found from measurements 

 of surface tension. The fact that y is found to be constant proves that the 

 work done in removing molecules from the liquid to the vapor phase is 

 strictly proportional to the molecular surface. In other words, the latent 

 heat of evaporation is proportional to the two-thirds power of the molecular 

 volume. 



This theory can readily be extended to cover the case of the heats of 

 evaporation of the various aliphatic alcohols. If 5^ is the total surface of the 

 molecule of vapor, then aS is the surface of the head of the molecule 

 (hydroxyl group) while cS is the area of the tail (hydrocarbon chain). 

 We may let Yo and Yc represent the surface energies per unit area of the 

 heads and tails respectively when the molecule is in the vapor phase. Thus 

 Say a is the total energy of the head and Scyc the total energy of the tail. 



If the molecules of alcohol in the liquid phase were arranged at random, 

 that is, if they did not orientate each other appreciably, and did not tend to 

 form clusters (segregation), then it may readily be shown that the total 

 inter facial surface energy in the liquid between the hydroxyl groups and 

 the hydrocarbon chains will be Sacyac, where Yac is the interfacial surface 



