ADSORPTION 175 



taken up by an adsorbent. Thus, if meerschaum, a hard, porous 

 gel, is put in a chamber with ammonia gas, the gel will take up a 

 definite amount of gas per gram of adsorbent (meerschaum), 

 depending on the adsorption constant and a number of other 

 factors including temperature and the pressure of the gas. 



To characterize a substance by its adsorption constant is 

 tacit admission that the adsorption reaction is nonstoichiometric. 

 Van Bemmelen and others pointed out that the adsorption of 

 substances was not stoichiometric but followed the empirical 

 formula 



1 



a = ac- 

 n 



where a is the amount adsorbed per gram of the adsorbent; c, 

 the concentration of the solution in equilibrium; and a and n, 

 constants (« is the adsorption constant) , This formula was used 

 by Freundlich, who applied it extensively and showed that it 

 holds in a great number of systems; it is, therefore, known by 

 his name. 



A definite quantity of charcoal takes up a definite quantity 

 of gas at a given temperature and pressure, but the quantity 

 adsorbed does not vary proportionally to pressure; that is to say, 

 it is not stoichiometric. The equation of Freundlich expresses 

 this nonstoichiometric relationship. The curves obtained are 

 known as adsorption isotherms, because they depict the adsorption 

 behavior — the variation of adsorption with pressure — at con- 

 stant temperature. Freundlich's contribution lies chiefly in 

 the fact that he showed the adsorption equilibrium formula to 

 be widely applicable, but it is purely empirical and holds only 

 within a certain concentration range. 



Of more theoretical significance, yet holding less often in 

 practice, is the adsorption formula of Langmuir. It is based on 

 the theory that solid crystals are of a lattice structure (Fig. 143), 

 with surface atoms having free valences each of which is available 

 for attaching only one molecule from the surrounding gas or solu- 

 tion; in other words, it assumes adsorption to be stoichiometric. 

 The rate of adsorption depends upon the number of molecules 

 striking the surface (calculated from the kinetic theory of gases), 

 the fraction of molecules that adhere, and the area not covered 

 by adsorbed molecules. 



