THE DISTRIBUTION OF MOLECULES 87 



involving the solubility of the acid, is 16.9 ergs per cm.^ while B1/B2, from 

 the solubility of the water, gives very nearly the same value, viz. qp = 9.7. 

 These are to be compared with cp = 13.6 from Table V for butyric acid- 

 water mixtures at higher temperature from vapor pressure data. 



From the very rough data available on the solubilities of higher fatty 

 acids we obtain the values given in Table VI. 



The 5th column gives the surface fraction a corresponding to the 

 carboxyl group whose actual surface is taken to be 45A-. The 6th column 

 gives the value of f^obs obtained by Equations (26) from the observed 

 value of the solubility while the 7th column gives qp^n? which is calculated 

 by Equation (17) with the same values for the y's as those already used 

 for the calculations of Table V. 



It will be seen that the agreement is reasonable and indicates that the 

 marked decrease in solubility of the fatty acids in water as we pass to the 

 higher fatty acids is fully explained by our theory of independent surface 

 action. 



It is important to note that the solubility of wafer in the fatty acids 

 does not continue to decrease without limit as the length of chain increases. 

 As soon as the solubilities have become small Equations (27) are ap- 

 plicable. As the length of chain increases a approaches zero and q) ap- 

 proaches the limiting value 51.4 corresponding to y(R-H20) (see Table 

 V). We see, however, from {2'/) that Sa, the area of the molecule of acid, 

 continues to increase as the chain lengthens and thus A, the solubility of 

 the acid in water, decreases without limit. On the other hand, Sb, the area 

 of the water molecule, remains constant so that the solubility B, of water 

 in the acid, decreases only because of the increasing qp and thus approaches 

 a limiting value as the chain lengthens. 



ORIENTATION OF MOLECULES IN A LIQUID PHASE 



Thus far we have considered particularly the distribution of molecules 

 between different phases on the assumption that there is no mutual orienta- 

 tion of the molecules within the phases. Although the agreement of our 

 theory with experiment proves that in the case of many liquids this orient- 

 ing effect is negligible, it is believed that such orientation (and correspond- 

 ing segregation) is the main cause of deviations which occur with the more 

 polar substances. 



For example, the vapor pressures of mixtures of alcohols with water 

 give values of qp which are nearly constant or independent of the concen- 

 tration, except that the values obtained from the partial pressures of water 

 over the mixtures containing more than about 0.5 mol fraction of water 

 give values of (p which are much too low. Thus, although the partial vapor 

 pressures of methanol over the whole range agree with the value qp = 6.1, 



