542 RICE ART. L 



18. The Exponential Adsorption Isotherm 



Historically, the oldest equation is one usually referred to as 

 the "exponential adsorption isotherm." We have already 

 mentioned that Gibbs does not use the term "adsorption," 

 and the word itseh has been used somewhat loosely to cover 

 effects complex in origin and due to the operation of more than 

 one cause. It has been suggested that a rough criterion of 

 adsorption proper is that it takes place very rapidly, whilst in 

 many cases the effects produced by the presence of a porous 

 substance such as charcoal immersed in a gas or gas-mixture or 

 in a solution require considerable time to reach completion, 

 McBain has suggested that the whole phenomenon should be 

 called "sorption", and that portion of it which occurs rapidly 

 should be termed adsorption proper. Rapidity of occurrence, 

 however, can only be a rough guide at best. It is only in terms 

 of the effect which Gibbs calls the "excess" (or defect in the 

 case of negative adsorption or "desorption") of a component 

 at a surface that a precise definition can be given. Actually 

 adsorption is to some extent a phenomenon which recalls absorp- 

 tion, i.e., the dissolution of a gas or solute throughout the entire 

 space occupied by a phase. Adsorption, however, differs from 

 absorption in certain fundamental respects. As is well known, 

 absorption equilibrium in a heterogeneous system is governed 

 thermodynamically by a relation which demands (in the 

 simplest case) that the ratio of the concentrations (or more 

 exactly the activities) of a gas or solute in the different phases 

 present shall be independent of the absolute quantity of gas or 

 solute in the system. However, no such constancy obtains in a 

 system consisting of an aqueous solution in which finely divided 

 material such as charcoal is immersed; the concentration term 

 of the solute in the aqueous phase has to be raised to a power less 

 than unity in order to obtain a relation which is capable of 

 fitting with sufficient accuracy the observed values of the 

 adsorption. It is this relation which is called the "exponential" 

 adsorption equation and is written in the form 



re = A;c" , 



