SURFACES OF DISCONTINUITY 557 



or 



rii f 



(1 — €-'>''") 

 s V 



= g(l - e— ) , ^ 



(21) 



where g and a are constants. 



We see that this adsorption isotherm has the same feature as 

 (19), viz., that tii/s the surface concentration of the solute 

 approaches a hmiting value g as c increases. In fact, since g is 

 ^/v, we see by the definitions of f and v that g is the surface 

 concentration when the assumed unimolecular layer is quite 

 full. By measurements of the surface and bulk concentrations 

 at different states of dilution where the equation is valid we can 

 eliminate g and measure the constant a. By repeating these 

 measurements at another temperature we can determine the 

 value of a at this other temperature, say a' at temperature t'. 

 This gives us the ratio X'/X which is of course equal to a'/a. 

 But X = exp(—u/kt); hence we obtain 



and knowing k, t and t' we can obtain u the energy of adsorption. 



VIII. Experimental Investigations to Test the Validity of 

 Gibbs' Adsorption Equation 



S2. The Earlier Experiments to Test Gibbs' Equation 



The simplest conditions from a theoretical point of view for 

 testing the Gibbs equation exist at the boundary separating a 

 vapor from a liquid; however, this is not the easiest case to 

 test by experiment, and measurements carried out at air-liquid 

 or liquid-liquid interfaces make up the majority of the attempts 

 in this direction. When we have a binary mixture, the equa- 

 tion becomes (at constant temperature) 



da = —Tidjii — T2dijL2. 



As we have seen, this is only strictly valid for the surface of 



