EFFECTS OF MOLECULAR DISSYMMETRY 269 



If ^ were zero, thermal agitation would make the molecules assume the / 

 most varied shapes. It seems likely, however, that in most of these con- 

 figurations there will he a relatively large part of the surface of the hydro- 

 carbon chain exposed, so that p] will be larger than p^. But this difference 

 in probabilities will be a very moderate one, not at all able to compensate 

 for the very small value of the exponential factor in Equation (5) when 1 

 has the value 58. X 10"^^ erg. 



In these calculations we have used the total surface energy yo instead 

 of the free energy. The thermal agitation may tend to oppose the contrac- 

 tion of the surface of a single molecule, but probably to a much smaller 

 extent than in the case of a large surface of many molecules. However, the 

 conclusion that there is ample energy to bring about a nearly spherical form 

 would not be altered if A, were half as great as we found, so that for the 

 present we shall not attempt to draw a distinction between free energy and 

 total energy in applying Equation (5). 



If a palmitic acid molecule is surrounded by water, the hydroxyl group 

 is nearly completely surrounded by water molecules, while the hydrocarbon 

 chain will draw itself as nearly as possible into a sphere, since the interfacial 

 surface energy between water and hydrocarbon is about 59 ergs, which is 

 even more than the surface energy of a hydrocarbon f against vapor). 



Before proceeding with the properties of the palmitic acid molecule let 

 us consider the somewhat simpler problem of a hydrocarbon molecule. To 

 facilitate comparison we will assume that the hydrocarbon molecule has the 

 same volume (^gyA^) as the palmitic acid molecule. This corresponds 

 approximately to hexadecane C16H34. Let us now calculate the energy 

 needed to transfer such a molecule from a hydrocarbon liquid to — i, the 

 interior of a mass of water ; 2. a vapor phase, and 3. an adsorbed film on 

 the surface of the water. 



While the hydrocarbon molecule is in a liquid consisting of other (satu- 

 rated) hydrocarbons its surface energy may be taken to be zero, since there 

 are no interfaces, even if the surrounding hydrocarbon molecules are of 

 diflFerent molecular weight. When the molecule is transferred to the interior 

 of a large volume of water the surface energy is X = .^yo where s, the 

 surface of the molecule, is 304 A^ and the interfacial surface energy 

 Yo = 59 ergs per cm. Hence ^ = 179 X lo'^'* erg. For the formation of a 

 molecule of vapor we have the same value of s but yo = 50 so that 

 1=152X10-14. 



These energies correspond respectively to the heat of solution and the 

 heat of evaporation of the hydrocarbon molecule. Actually the heat of 

 evaporation is about 55 per cent of the value calculated in this way. The 

 agreement as to order of magnitude is satisfactory. The surface energy 50. 

 ergs per cm^ is that which is measured when a fraction (probably about J/3) 



