SURFACES OF DISCONTINUITY 553 



Szyszkowski's formula in the latter case. A further assumption 

 is that the adsorbed layer is one molecule thick and that no 

 further adsorption occurs in a second layer beyond this. This 

 assumption is also in keeping with what are nowadays believed 

 to be the conditions at the surface of a solution, a matter to 

 which we shall devote some attention later on, as it is one on 

 which Gibbs' equation brings important considerations to bear. 

 Let a fraction 6 of the surface be covered with adsorbed gas, and 

 the rate at which molecules evaporate from unit area of the 

 adsorbed layer be ad, a being a function of the temperature and 

 depending also on the attractive forces. The rate at which gas 

 molecules unpinge on unit area of the surface is proportional to 

 the density of the gas and the average molecular velocity, i.e., 

 to p0 (t is the absolute temperature). Since p = pt this rate is 

 therefore proportional to p/t^. Therefore the rate of condensa- 

 tion (which by the postulates we take to be comparable with 

 and proportional to the rate of impact) on unit area of the bare 

 surface can be written as ^pt~\ where j3 is a constant. We 

 suppose that no condensation occurs on the top of an adsorbed 

 layer. (That is the second postulate above and assumes that 

 the attractive forces of the solid do not extend appreciably 

 through the first layer, — a reasonable assumption on our present 

 knowledge.) Thus the rate of condensation on unit area of the 

 surface of the adsorbed layer will be 



^pt-Kl - 9) 

 since a fraction 1 — is bare. Hence in equilibrium 



/3prKl - d) = a9 , 

 from which we easily obtain 



P 



e = 



P + oi^ 



P 



p + a 

 where a is a constant depending on attractive forces and tem- 



