556 RICE 



ART. L 



to the surface. Hence Langmuir concluded that the molecules 

 lie flat in the surface, in the gaseous adsorbed films."* 



Equation (19) is an example of an adsorption law deducible 

 from statistical considerations. We shall bring these references 

 to such equations to a conclusion by adapting an argument to 

 be found in Rideal's Surface Chemistry, p. 71, which leads to 

 another example of them. Let there be Wi molecules of a solute m 

 the surface layer of thickness f and area s, and n^ molecules of 

 solute in a volume V of the solution. If the layer is of the uni- 

 molecular type, the evidence for which we shall discuss in the 

 next section, there is a free volume in it of amount sf — n-iV, 

 where v is the effective volume of one molecule. If we add some 

 more molecules to the solution there will be a division into two 

 groups; one whose number is bn^ will be found in the layer, one 

 whose number is bn^ will be found in the solution. The volume 

 concentration of the first group will be 5wi/(sf — Uiv), of the 

 second bUi/V, and these two concentrations will have the ratio 

 exp(— u/U) where u is the energy of adsorption; i.e., 



X' 



sf — iiiv V 

 X being written for exp{—u/kt). By integration we obtain 



log {si; — Hiv) = — —^ + constant 



= — \vc + constant , 



« 



where c is the bulk concentration. Hence 



s^ — HiV = Ce-^"". 

 Since Ui is zero when c vanishes, C = s^ and therefore 



niv = 5^(1 — 6"^"') 



* Quoted from page 128 of Adam's Physics and Chemistry of Sur- 

 faces. The reader must not interpret "gaseous adsorbed" as meaning 

 adsorbed from the superincumbent gas. It is a term applied to a special 

 type of film, of which we shall say more at a later stage. 



