chapter Six 



THE DISTRIBUTION AND ORIENTATION 



OF MOLECULES 



When thermal equilibrium prevails the distribution of molecules 

 between two regions in which the potential energies of the molecules are 

 different is given in general by the Boltzmann equation 



A 



rii _ kt (i) 



Here tii and no are the numbers of molecules per unit volume in Regions 

 I and II and X is the potential energy which must be expended to move 

 a molecule from Region I to Region II, while T is the absolute tempera- 

 ture and k is the Boltzmann constant^ 1.372X10"^^ erg per degree. 

 This equation is closely related to the well known Nernst equation for 

 the electromotive force of a concentration cell. 



Equation (i) cannot usually be directly applied to the distribution of 

 molecules between separate phases. For example, if we consider the 

 equilibrium between a liquid and its vapor and let W2 be the concentration 

 in the vapor and n^ that in the liquid phase we find that (i) must be 

 replaced by 



Ml ^ kt (2) 



— = Ae 



The factor A corresponds to the integration constant of the Clapeyron 

 equation for vapor pressures, and its theoretical value must be determined 

 in accordance with the third law of thermodynamics. 



A generalized form of the Boltzmann equation has been much used 

 in recent years : 



A 



'^ = t.e^^ - (3) 



* The Boltzmann constant is merely the gas constant R expressed per molecule 

 instead of per gram molecule. 



71 



