Gaines-Thomas conventions

The activities fi may be calculated in different ways (e.g., Appelo and Postma, 1993) and, in collecting exchange constants from the literature, care must be taken to note the method used. By the Gaines-Thomas convention, the activity... 

Substituting, the mass action equation (Eqn. 9.34) becomes, for the Gaines-Thomas convention,... 

Since we are honoring the Gaines-Thomas convention, the activity of a sorbed ion in the calculation results is the fraction of the total equivalents of the sediment s exchange capacity the ion occupies. The resulting values are,... 

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 ... 

As an example, for the exchange of Na+ and Ca +, the number of exchangeable cations is used in the Gaines-Thomas (1953) convention. According to the Gaines-Thomas convention, Eqs. 3.10 and 3.11 are rewritten as... 

The cation exchange coefficients relative to Na" for various ions following the Gaines-Thomas convention (Eq. 3.24) are reported in Appelo and Postma (2007), based partly on a compilation by Bruggenwert and Kamphorst (1982). The given ranges represent many measurements from different soils and for different clay minerals. 

The previous calculations are based on the Gaines-Thomas convention. If they are calculated based on the law of mass action (Eq. 3.11), and the unit of meq/ mL is used, the exchangeable fractions become Pn = 0.25 and Po, = 0.75 Now these calculated exchangeable fractions from the law of mass action are significantly different from those from the Gaines-Thomas convention. 

No value for dmq/dmp is needed to evaluate the and Freundlich models. For the Langmuir model and the ion exchange model under the Gaines-Thomas and Gapon conventions,... 

Evangelou, V. P. and R. E. Phillips. 1989. Theoretical and experimental interrelationships of thermodynamic exchange parameters obtained by the Argersinger and Gaines and Thomas conventions. Soil Sci. 148 311-321. 

If the equivalent fraction convention for exchanger phase activities is adopted (i.e., the Gaines-Thomas approach), the molar concentrations are proportional to the equivalent fractions, and it can easily be shown that the half reaction constants and the binary-exchange constants (selectivity coefficients) are related by... 

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). 

Note that no individual sites are considered, just the surface taken as an exchanger. The activity convention is to use equivalent fractions, as in the Gaines-Thomas case thus, the corresponding selectivity coefficient is given by... 

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