554 RICE 



ART. L 



perature. If n is the number of molecules actually adsorbed 

 per unit area at any moment, and Um the maximum number 

 which could possibly be adsorbed if the unit area were entirely 

 covered with a monomolecular layer, 6 is n/n,n, and so Langmuir's 

 result can be written 



V 

 n = Um — I (20) 



The result is of considerable theoretical importance in connec- 

 tion with the so-called "poisoning" of solid catalysts. The 

 formal similarity of (19) and (20) is obvious, the pressure of the 

 gas being the analogue of solution concentration in (19). As 

 stated above, Langmuir's analysis could easily be adapted to 

 prove (19) and so by the aid of Gibbs' equation to derive 

 Szyszkowski's relation. Frenkel in the Zeit.f. Physik, 26, 117, 

 (1924) derives a special functional form for the constant a in 

 (20). On certain assumptions he shows that the mean length 

 of time during which a molecule adheres to the surface is equal 

 to T exp iii/kt), where r is the period of thermal oscillation, at 

 right angles to the surface, of an adsorbed molecule, u the energy 

 of desorption, i.e., the energy required to tear an adsorbed 

 molecule away, and k the gas constant per molecule. Thus the 

 rate of evaporation from unit area is n/[T exp {u/kt)\ and so the 

 constant a is equal to r~i exp { — u/kt). Also it can be shown 

 from the kinetic theory of gases that jS = (2Trmk)~^, where m is 

 the mass of a molecule. Hence Frenkel's form of Langmuir's 

 result can be written 



P 



n = n„ 



, (27rm/c)i -I 

 p + -^ e ^« 



For further information on these and similar equations the 

 reader can consult Chapter V of Rideal's Surface Chemistry 

 and Chapter VIII of Adam's Physics and Chemistry of Sur- 

 faces (1930). 



SI. Energy of Adsorption 

 Returning to adsorption at the surfaces of solutions, it has 



