74 



PHENOMENA, ATOMS, AND MOLECULES 



be materially altered if we should assume any other reasonable shape for 

 the molecule. We may take half the surface to consist of the hydroxy! 

 group while the CH3 radical occupies the other half, these areas being 

 each 32.5 A^. 



Imagine a molecule of methanol half immersed in a Hquid consisting of 

 other methanol molecules as illustrated diagrammatically in Fig. i. We use^ 

 R to denote a hydrocarbon radical and X to denote an active group such 

 as hydroxyl. Let us for the present disregard the structure of the liquid 

 and the orientation of the neighboring molecules and consider roughly 

 that half the liquid in contact with the given molecule consists of CH^ 

 while the other half is OH, as suggested in the diagram. Let us now cal- 

 culate the surface energy corresponding to the two orientations indicated. 

 If 6" is the surface of the molecule, yn the surface energy of CH3 and yR^ 

 the interfacial energy between CH3 and OH radicals then the total surface 

 energy of the molecule in position a is J^ Sys -f- 34 Sysx while in position 

 b it is ^ vSyj -|- Syn-'i. Thus the difference in energy between the two posi- 

 tions which is available for causing the orientation is 



l = iS (y.v— Ya) 



(5) 



/? 



X 

 R 



R 



X 



R 



X 



Position a. Position b. 



Fig. I. — Two conceivable orientations of a molecule in the surface of Methanol. 



Measurements of the surface energy of hydrocarbons give yn = 50 

 ergs per cm.^ The surface energy of water at 20° is 117, but since the 

 water molecules are decidedly polar they will undoubtedly be oriented in 

 the surface so that this value represents the energy of the least active part 

 of the molecule. We shall see from data on the heat of evaporation of 

 water and alcohol that a more reasonable value for yx is 190 ergs per cm^. 

 Placing 5^ = 6^.A^ in Equation (5) we find A, = 22. X io~^^ or 46 X io~^* 

 erg according as we take 117 or 190 as the value of yj. 



The degree of orientation of the molecules can now be calculated from 



