71 PHENOMENA, ATOMS, AND MOLECULES 



Here p\ and pi are defined as the a priori probabilities of the molecules 

 in the two regions or two states under consideration. These probabilities 

 are frequently dependent upon geometrical factors, but often involve a 

 knowledge of the quantum phenomena accompanying the change in state. 

 Fortunately the factors pi and p2 vary little if any with temperature and, 

 in the case of related phenomena, the values of pi/p2 are often nearly alike, 

 or at any rate their variations produce an effect which is usually small 

 compared to that caused by the exponential factor. Thus the generalized 

 Boltzmann equation becomes of great practical value even when we do 

 not possess sufficient theoretical knowledge to determine the value of the 

 probability coefficients. 



The ratio of the concentrations 7Ji/w2 is also equal to the ratio P1/P2 

 of the actual probabilities per unit volume for the existence of molecules 

 in the two states, so that 



Pi_^ ^/ (4) 



P2~ P2 



This equation may be applied for example to study the probability of 

 any particular orientation of a molecule in a liquid, with respect to neigh- 

 boring molecules or to deal with the orientation of molecules in adsorbed 

 films at interfaces between phases. Equation C^) on the other hand may 

 be used in studying the distribution of molecules between phases and inter- 

 faces and also in considering the segregation of certain molecules in the 

 neighborhood of others, due to the local fields of force. Debye and Hiickel 

 (Phys. Zeitschr. 24, 185, 305 (1923)) for example have recently used 

 the Boltzmann equation to determine the segregation of negative ions 

 around positive ions (and vice versa) and have thus evolved a new theory 

 nf electrolytic solutions. 



Before we can use Equations (3) and (4) in the way suggested, it is 

 necessary to have definite knowledge of the energy change "k involved in 

 the change of state. 



In the case of the molecules of organic substances of non-polar type 

 the so-called physical properties are usually roughly additive. For example, 

 the addition of each CH2 to a hydrocarbon chain in most compounds 

 containing such chains increases the volume, raises the boiling point, and 

 alters the solubilities in approximately the same way. It is reasonable to 

 assume, therefore, that the field of force about any particular group or 

 radical in a large organic molecule is characteristic of that group and, as 

 a first approximation, is independent of the nature of the rest of the 

 molecule. For convenience we shall refer to this as the principle of inde- 

 pendent surface action. 



