THE DISTRIBUTION OF MOLECULES 93 



With lower concentrations of ethanol the fraction of the ethanol 

 molecules which are in contact with hydroxy! groups is proportional to 

 the concentration. Thus for these low concentrations we obtain for the 

 average energy correction 



X _ X. = 0.041 X lO-'M erg (47) 



which gives the same value as (46) when A = 0.117. 



For higher concentrations of ethanol than A = 0.117 there will usually 

 be more than one contact with hydroxyl. However, these will not in general 

 be adjacent but will be distributed nearly according to the laws of chance. 

 If they were distributed absolutely uniformly over the surface of the 

 ethanol molecules there would be no tendency to orient these molecules. 



According to the probability laws therefore the effective surface area, 

 Sjih, of contact with the hydroxyl groups should be proportional to the 

 square root of the number of contacts. Since, by (45) the energy varies 

 as h^ it is thus directly proportional to the number of contacts or is pro- 

 portional to the concentration A. Therefore Equation (47) gives the value 

 of X — Ai} for concentrations above A = 0.117, as well as for concentrations 

 below this value. 



In general we may thus assume that ^ — X/j is proportional to A as in 

 Equation (47) and may place 



l — l^ = MA (48) 



where M is the proportionality factor. 



Going back to the derivation of Equations (25) from (19), (22) and 

 (23) we may now correct the value of Xav in (19) by means of (48) ob- 

 taining 



h, =l,/ — S,q)^' + MA (49) 



Instead of (24) we then find 



It- (50) 



Pa = Ke 

 and (25) is replaced by 



S-*'P^'^ + MB 



In the example we are considering (ethanol-hexane) the term MB is 

 0.041 X io-^'*5 while S a^>^^ is 3.66 X IQ-^^P so the effect of orientation 

 of molecules is practically negligible. 



In the foregoing analysis we have considered the orientation of a given 



