The Power Exchange Function: A General Model for Metal Adsorption onto Geological Materials

Abstract

The empirical data on adsorption of metal cations by naturally occurring soil materials can be systematized in terms of power exchange functions. For example, given the reaction PbX + Ca²⁺ = CaX + Pb²⁺, the exchange function is: K_ex = ([Pb²⁺]/[Ca²⁺]) (CaX/PbX)ⁿ where K_ex and n are constants, the brackets denote activities of the ions, and CaX and PbX are their mole fractions on sorbent X. This approach is mathematically equivalent to regular solution exchange when the mole fractions of two competing cations sorbed lie between 0.25 and 0.75, and to Freundlich isotherm-type behavior when the mole fraction of the minor cation is < 0.05. Combined literature review and laboratory study show that the exchange behavior of H⁺, Na⁺, K⁺, Ca²⁺, Mg²⁺, Cd²⁺, Co²⁺, Ni²⁺, Pb²⁺, UO ²⁺₂ and Zn²⁺ and their hydroxy-complexes on a variety of adsorbents (montmorillonites, beidellite, illite, ferric oxyhydroxides, zeolites, soils and humic materials) can be accurately described for a wide range of competing sorbate concentrations and ratios using from one to three power exchange expressions. The adsorption of the alkali metal and alkaline earth cations on pure clays at about 10⁻² to 10⁻⁴ M often follows the power exchange function with n = 1, corresponding to simple ion exchange. Adsorption of heavy metals (between 10⁻³ and 10⁻⁷ M) is usually more complex, and fits power exchange functions with n = 0.8 to 2.0. Log-linearization of power exchange expressions yields lines with correlation coefficients usually in the range from 0.98 to 1.00. The power exchange model is a potentially useful predictor of heavy metal levels in the subsurface controlled by adsorption processes.