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DIVISION S-2—"PARTICLE INTERACTIONS IN COLLOIDAL SYSTEMS"

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

Water Quality and Solute Dynamics Group, National Institute for Agro-Environmental Sciences, Kannondai 3-1-3, Tsukuba, Ibaraki, 305-8604 Japan

* Corresponding author (katouh{at}niaes.affrc.go.jp)

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⁺]/dC 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⁺]^-acatC^bcat and Q_an = k_an[H⁺]^-aanC^ban, 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.

Abbreviations: AEC, anion-exchange capacities • C, total electrolyte concentration • CEC, cation-exchange capacity • Q_an (= AEC), total anion adsorption • Q_cat (= CEC), total cation adsorption