A pH‐Dependence Implicit Formulation of Cation‐ and Anion‐exchange Capacities of Variable‐charge Soils

Cation‐ and anion‐exchange capacities (CEC and AEC) of variable‐charge soils are often expressed as a function of pH and the electrolyte concentration. A difficulty following this formulation is that changes in pH with time and space must be computed precisely if ion transport is to be predicted. In this paper, an alternative formulation of CEC and AEC is presented in which pH does not appear explicitly. The formulation is based on the notion that, unless H + or OH − is added, changes in the total cation adsorption, Q cat (= CEC), and the total anion adsorption, Q an (= AEC), in response to a change in the total electrolyte concentration, C , are nearly equivalent. This means that the net surface charge remains virtually constant and leads to an equation that relates d[H + ]/d C to partial derivatives of Q cat and Q an with respect to [H + ] and C . Using this relation, we show that, if the exchange capacities are expressed by Q cat = k cat [H + ] − a cat C b cat and Q an = k an [H + ] − a an C b an , the change in Q cat (or Q an ) with C in a soil saturated with monovalent ions is described by an ordinary differential equation which does not contain pH as a variable. The Q cat – C relations predicted by solving the equation closely agreed with those by the conventional method in which pH‐dependent adsorption, mass balance, and electroneutrality equations were solved simultaneously. The advantage of this approach is that once the adsorption parameters are known, the transport equation for H + need not be solved in predicting transport of electrolyte ions in soil.