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Determination of Rate Coefficients for Potassium-Calcium Exchange on Vermiculite using a Stirred-Flow Chamber

Inst. of Soils and Water

Svetlana Fishman

Dep. of Statistics, Agricultural Research Organization, The Volcani Center, Bet Dagan, 50250, Israel

Matthew J. Eick and Donald L. Sparks

Dep. of Plant and Soil Sciences, Univ. of Delaware, Newark, DE 19717-1303

*Corresponding author (vwarie{at}volcani).

ABSTRACT

A stirred-flow technique has been widely used to study the rate of ion adsorption on clays and soils. However, no mathematical analysis of chemical kinetics combined with mass transport has been used to derive rate coefficients for ion exchange phenomena. Accordingly, the objectives of this study were to: (i) develop a mathematical model of the kinetics of an elementary cation-exchange reaction combined with transport processes in a stirred-flow chamber and (ii) determine rate coefficients based on this model for K-Ca exchange on a vermiculite. The kinetics of exchange were described by a second-order mechanistic rate law from which the equilibrium exchange equation was derived. The second-order mechanistic rate law combined with an equation of mass balance describing transport were solved numerically. The equilibrium K-Ca exchange data were described by the Gaines and Thomas approach with a thermodynamic exchange equilibrium constant K_ex = 754.6 L mol^–1. The values of the apparent adsorption rate coefficient (k_a) ranged from 84 to 185 L² mol^–2 min^–1, as influent rate increased from 0.3 to 2.0 mL min^–1. The calculated K-Ca exchange half-life (t_1/2) ranged from 0.5 to 1.5 min, in agreement with published data based on batch methods.

Contribution from the Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel, no. 1260-E, 1993 series, and the Univ. of Delaware.

Received for publication January 29, 1994.