THE DISTRIBUTION OF MOLECULES 



75 



the Boltzmann equation (4). The probabiHty coefficients pi and po may 

 be taken equal since the geometrical probabilities of the two orientations 

 are the same. Putting T = 293° we find kT = 4.0 X I0~^^ erg. Thus the 

 exponent is 5.5 or 1 1.5 according to the two values of y^. The correspond- 

 ing probability ratios P2/P1 are 300 and looooo respectively. 



Thus with the lower value of ys the probability of the orientation a in 

 Fig. I is 300 times greater than that of b while with the higher and more 

 reasonable value of ys the ratio is lOOOOO to i. 



A more complete justification of the use of the principle of independent 

 surface action is being published elsewhere.^ A brief summary of the 

 principal results will be given here and then further applications will be 

 made, chiefly dealing with adsorbed films at interfaces. 



Evaporation of Pure Substances. Consider a molecule AC (Fig. 2) 

 whose surface 5* is composite and let a represent the fraction of its surface 

 which is of one kind A (say a hydrocarbon chain) while c is the fraction 



Fig. 2. — Diagram of a molecule AC and of the same molecule in liquid AC. 



of the surface which is of the second kind C (say one or more hydroxyl 

 groups). Then 



a + c=i (6) 



If we are dealing with a pure liquid each molecule is surrounded by 

 others of the same kind. As a first approximation let us assume that the 

 molecules around a given molecule are neither orientated nor segregated 

 but are arranged in a purely random manner as if no surface energies, 1, 

 were acting. We shall consider later by means of the Boltzmann principle 

 what errors are made by this simplifying assumption. 



* A general discussion of the mechanism and the nature of the forces at the 

 surfaces of molecules and applications of the independent surface action to orientation 

 will be published in the book on Colloid Chemistry being edited by Jerome Alexander. 

 A paper giving a detailed mathematical treatment of vapor pressures of liquids and 

 their binary mixtures and of the mutual solubilities of liquids, together with a com- 

 parison with available experiment data, is being submitted to the Journal of Physical 

 Chemistry for publication. 



