Homovalent exchange

This complicated equation can be transformed further by invoking the constraint in Eq. 5.67, but its principal implication can be appreciated more simply by examining the example of homovalent exchange (a = b = 1) ... 

The generalization of Eqs. 4.96 and 5.24 to include the possibility of imbibed water in an exchanger (thus making it a three-component mixture) is described in Chap. 5 of G. Sposito, The Thermodynamics of Soil Solutions, Clarendon Press, Oxford, 1981. The presence of charge fractions in Eq. 5.25 instead of mole fractions, as in Eq. 4.11, derives from the possible inequality of the stoichiometric coefficients, a and b, in the cation exchange reaction (cf. Eqs. 4.6 and 5.9). For homovalent exchange reactions, only mole fractions appear in the expressions for the adsorbate species activity coefficients. 

The results in Problem 4 of Chapter 4 imply that a kinetics analysis of the ion exchange reaction in Eq. 5.6 for binary, homovalent exchange leads to the adsorption isotherm equation ... 

An important component of homovalent exchange is the magnitude of the exchange selectivity coefficient. Commonly, homovalent cation-exchange reactions in soils or soil minerals exhibit a selectivity coefficient somewhere around 1 (Table 4.2). This value signifies that the soil mineral surface does not show any particular adsorption preference for either of the two cations. However, for a mineral where the A Ca Mg is... 

The homovalent exchange reaction (K-Na exchange) is Na-soil + K K-soil + Na+. 

Carbonic acid, 31 Carboxylic acids, 137 Cation exchange, 102,103,140,149, 513 Homovalent exchange, 191 Heterovalent exchange, 196 Thermodynamics of exchange,... 

This equation is reciprocal to Equation 1.79, except that concentrations are used here instead of activities (y 1) (Vanselow [1932] equation for homovalent exchange), that is, cM<, = aMei and cMei = aMei are the concentration or the activities of the ions in the solution. 

Eqs. (5) and (7) show that for homovalent exchange, the separation factor ay and the selectivity coefficient Kij are equal. For our example, this translates as... 

It has been found that for binary exchange, a mass action expression in which the ratio of sorbed cation mole fractions is raised to the nth power (n 1), can fit a wider range of empirical sorption data than when n = 1. Thus, for the homovalent exchange reaction. 

Maes, A., and A. Cremers. 1978. Charge density effects in ion exchange. Part 2. Homovalent exchange equilibria. J.C.S. Faraday 174 1234—1241. 

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