92 PHENOMENA, ATOMS, AND MOLECULES 



vapor pressures of these mixtures. We now wish to determine what correc- 

 tions should be appHed to these results to take into account the orienting 

 effect of the ethanol molecules on each other. 



We see from Equation (20) that the energy needed to transfer an 

 ethanol molecule from pure ethanol to a mixture is 



where /5 is the surface fraction of hexane in the mixture. This expression 

 was substituted in the exponent of the Boltzmann equation to obtain 

 Equation (25a) which would give the uncorrected vapor pressure of 

 ethanol. To get the corrected vapor pressures we should add to yA, before 

 making this substitution, the correction given by Equation (44). We place 

 in Equation (33) Yad = Yftc = 34 and yah = ycd = o and obtain Yo = 68. 

 From the value of Sa and Sb we find = 0.359 and c = 0.641. Thus 

 Equation (44) becomes 



l-\,^2.72X 10-^^6^ erg (45) 



The choice of the value ^ is a matter which requires careful analysis. 

 Suppose the mixture is nearly pure hexane containing only a small amoimt 

 of ethanol. Most of the ethanol molecules will be surrounded only by 

 hexane molecules so that for these molecules & = o. There will be some 

 ethanol molecules, however, whose surface will be in contact with hydroxyl 

 groups of adjacent molecules. For these the value of h will be determined 

 by the area of contact between two hydroxyl groups. 



When molecules are arranged like close packed spheres each is in con- 

 tact with 12 others, so that the area of contact is S/12. We may suppose 

 that about 3 of these 12 regions of contact, for the hydroxyl radical in an 

 alcohol, are occupied by the union with the alkyl group. Thus the surface 

 of 30 A^, which we have taken as the effective surface of the hydroxyl, 

 represents 9 possible regions of contact, each contact having an area of 

 3.3 A^. Allowing for a probable deformation we may thus take the area 

 of contact between adjacent hydroxyl groups to be roughly 3.5A-, or 4.2 

 per cent of the whole svirface of an ethanol molecule. Since the surface 

 fraction of the hydroxyl in pure ethanol is 0.359 and the surface fraction 

 of each contact is 0.042, we see that there should be on the average 

 0.359/0.042 = 8.5 hydroxyl groups in contact with each ethanol molecule. 

 In a mixture of ethanol with hexane in which the mol fraction of ethanol 

 is A = o.iiy (i.e. 1/8.5) each ethanol molecule will be in contact, on 

 the average, with one hydroxyl group. For such a mixture we may there- 

 fore put b = 0.042. Equation (45) then gives 



l — l, = 0.0048 X 10-'* erg (46) 



