﻿Kinetic Theory of Adsorption. 703 



But 0=X/X',and 



cr = cr ll 



M1 -X. 



X' 



Bui X is identical with Gibbs's " surface excess," T, and 

 a is numerically identical with the surface tension ; by 

 Gibbs's equation, for small concentrations, 



Y _ c da _ c a Q — d l dX. 

 x ~ ~ ST ' dc~ ~ RT ' ~T~ ' ~dc ' 



which on integration gives 



i v RTX ' 1 1 , 



InX =— — .In rt + ln L 



a -a l 



where In k is an integration constant. 



L ., RTX' 1 



Li we write = - , 



a — a x n 



l 

 this becomes X = he n , 



which is the " exponential formula." 



The same argument applies to adsorption from a dilute 

 solution, where a is taken as the free surface energy of the 

 surface in contact with pure solvent, and the apparent ad- 

 sorption (to which Gibbs's relation applies) is taken equal to 

 the true adsorption, which is permissible in dilute solution. 



The exponent 



1 __ osmotic work in adsorption of X' gm.mol. 

 n ~ total work in adsorption of X' gm.mol. 



RTX' RT 



RTX' + WX'-RT + W 



where W is the non-osmotic work in the adsorption of 1 gm. 

 mol. ; this is probably accounted for by the work done in 

 the orientation of the surface molecules, and is not likely to 



vary much with temperature. It follows that - is a quantity 



always less than unity, which tends towards unity with rise 

 of temperature. This is in accord with experience. 



W 



Again, n-l=^, 



so that, at a given temperature, the greater the orientational 



