COLLOID CHEMISTRY OF THE SOIL IN RELATION TO PLANT NUTRITION 729 



must be remembered that 1,364 calories per mole represents the free- 

 energy difference for a ten-fold change in the activity of a given ion.) 



Relationships involving ionic ratios 



From the fundamental condition that in an equilibrium system the 

 chemical potential of mobile molecular species must everywhere be 

 the same, the following relationships involving ratios of ionic activities 

 in a true solution ( S ) and in colloidal systems ( I and II ) in equilibrium 

 with the solution can be deduced. These relationships hold independ- 

 ently of the geometrical relationship of the cations to the colloidal 

 phases. 

 For homovalent pairs of ions such as Na and K, Ca and Mg: 



For monovalent-divalent pairs such as K and Ca: 



«K 



LV'CaJ 



Colloid I - 



LV'^aJ 



Solution =: 



LV"C"aJ 



Colloid II. 



These are general equilibrium relationships; two colloids initially not 

 in equilibrium with the same solution will undergo adjustment of the 

 ionic proportions until the above conditions are fulfilled. 



Thus, if roots may be treated purely as non-metabolizing ex- 

 changers at equilibrium in a colloidal substrate, and if the equilibrium 

 solution is sufficiently dilute, then the activity ratios for the two dis- 

 sociating colloids are the same, although the absolute activity will, in 

 general, be different. The appropriate ratios are easily determined by 

 analysis of the dilute solutions. If the absolute cation activity for one 

 cation on one colloidal phase is determined, then all others can be 

 calculated by use of the above ratios. This method was first used by 

 Schiiffelen and Loosjes in characterizing colloidal substrates for plant 

 growth. 



Some workers have preferred to avoid this last step and have used 

 small dilute exchanges against neutral salts, in order to determine the 

 above ratios (Schofield, 1955) and through them to calculate a poten- 

 tial or free-energy characteristic of the soil-water system (Woodruff, 

 1955a ) . For satisfactory validity, the composition of the exchange com- 

 plex must not be appreciably changed by the exchange reaction, and 



