Vanselow convention

Here, meq is number of milliequivalents and CEC is the cation exchange capacity, expressed in milliequivalents per 100 g of sediment. According to the Vanselow convention, alternatively, the activity is expressed as the the fraction of the sites occupied by the ion,... 

Under the Vanselow convention, as previously mentioned, extra work is needed to figure this set of derivatives. Differentiating Equation 9.38 gives,... 

This expression is called the Gaines-Thomas convention (Gaines and Thomas 1953). If using the molar concentration instead, it is identical to the Vanselow convention (Vanselow 1932). Gapon (1933) proposed the following form ... 

It has been proved (Hogfeldt 1955) that the thermodynamic equilibrium constant can be expressed in terms of the Rothmund-Kornfeld approximation parameters. For the Vanselow convention, it is expressed as... 

Because the activities of species in the exchanger phase are not well defined in equation 2, a simplified model—that of an ideal mixture—is usually employed to calculate these activities according to the approach introduced bv Vanselow (20). Because of the approximate nature of this assumption and the fact that the mechanisms involved in ion exchange are influenced by factors (such as specific sorption) not represented by an ideal mixture, ion-exchange constants are strongly dependent on solution- and solid-phase characteristics. Thus, they are actually conditional equilibrium constants, more commonly referred to as selectivity coefficients. Both mole and equivalent fractions of cations have been used to represent the activities of species in the exchanger phase. Townsend (21) demonstrated that both the mole and equivalent fraction conventions are thermodynamically valid and that their use leads to solid-phase activity coefficients that differ but are entirely symmetrical and complementary. 

The mole fraction convention is employed in the Vanselow equation (20)... 

Adsorption of a dissolved ionic species is always part of an exchange reaction that involves a competing ionic species. The desorbing species creates the vacant site to be occupied by the adsorbing one. Soil scientists use a variety of ion exchange models (e.g., the Gaines-Thomas, Gapon, Vanselow, and Rothmund-Kornfeld models) in which different conventions are used to write the concentrations of dissolved and adsorbed species. These models are adequately described and compared elsewhere (cf. Bolt 1979 Sposito 1981, 1989 Appelo and Postma 1993). 

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