2l8 ELECTROLYTES IN BIOLOGICAL SYSTEMS 



and [K+]e on the ordinate, one finds a correlation between the two variables 

 which can be well expressed by straight lines. For these, one would write 



log ||^ = - a log [K+]e + b. (/) 



Hence, the dependence of [K+]i on [K+]e can be expressed as 



[K+]i = lo*^ X [K+]i'-'\ (2) 



It will be recalled that the widely used Freundlich's adsorption isotherm for a 

 variety of physico-chemical systems reads as follows (7): 



a = a X c^'" (3) 



in which a is the total amount adsorbed per unit of adsorbent and c, the equilib- 

 rium concentration in the solution after adsorption, a is called the 'adsorption 

 value' and i/n, the 'adsorption exponent'. The relationship of the constants, 

 b and a, in equations i and 2 to Freundlich's constants, a and i/n, is simply 



b = log a and a = 



n 



Values for a and b could easily be obtained graphically from figure 8. It was 

 thus possible to solve equation 2 numerically and plot the function (fig. 9). It 

 seems that in frog skin the relationship between intracellular and extracellular 

 K+ can, upon a first but good approximation, be expressed as a 'K+ isotherm'. 

 The question must now be asked, what is gained by the concept of adsorbed 

 K+ in frog skin? 



Aside from problems which arise with respect to the nature of the surfaces 

 involved, it would seem that an interpretation of the data on potassium in skin, 

 from the standpoint of chemical reactions, would be more profitable. 



Several isotherm equationsfor chemisorptionhave been theoretically derived. 

 One of the first and most important is Langmuir's isotherm, which can be 

 arrived at by considering adsorption as a bimolecular chemical reaction. The 

 data presented above on potassium in frog skin do not fit Langmuir's isotherm. 

 This, however, may not be surprising, since this isotherm applies only for the 

 ideal case of adsorption on homogeneous surfaces with no interactions of the 

 adsorbed atoms or molecules. One can hardly assume to have such conditions 

 for potassium in frog skin. Langmuir, and others after him, have made various 

 attempts to modify the original isotherm equation in order to explain quantita- 

 tive deviations of experimental results from the theory. It is well recognized 

 now that the sites of adsorption are often of varying activity and, furthermore, 

 that repulsive interactions between the adsorbed atoms or molecules occur. A 

 partial solution of the more difficult cases of adsorption has been achieved by 



