Selectivity coefficient Vanselow

From the If constant, estimated graphically from the Vanselow exchange selectivity coefficient, a number of thermodynamic parameters can be estimated. For example,... 

In the quantitative treatment of ion-exchange processes, several authors used the law of mass action. The main difference among these approaches is how the activities and surface concentration of the ions are treated. The first such approach was the Kerr equation, which uses the concentration of the ions on the solid and liquid as well but totally neglected the activity coefficients (Kerr 1928). The Vanselow (1932) equation applied activities in the solution and expressed the concentration of the ions on the solid phase in mole fraction, and in this way, it defined the selectivity coefficient (Equation 1.79). 

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. 

With an arbitrary definition of KNaX as equal to unity, thus establishing a reference half reaction, the equilibrium constant for any other half reaction can be determined from measured selectivity coefficients. The Gapon equation can be readily implemented in this manner. Implementation of the Vanselow equation, however, requires modification of the general equilibrium models to account for the more complex dependence of mole fractions on the molar concentrations. An example ion-exchange calculation using the half reaction approach to represent the Gapon equation is presented in Appendix 2. 

In the Vanselow approach, the selectivity coefficient (conditional constant) given by Equation 5.18 is used, which effectively assumes ideality in the exchanger phase, in an attempt to overcome the lack of ability to obtain the corresponding activity coefficients. However, Vanselow selectivity coefficients show a dependence on the composition, especially for heterovalent exchange (i.e., exchange between ions of different charge, such as Na+-Ca +). Other forms of selectivity coefficients have been proposed, as detailed in the following discussion. Table 5.1 summarizes these coefficients. 

Evangelou, V. R, and R. E. Phillips. 1988. Comparison between the Gapon and Vanselow exchange selectivity coefficients. Soil Science Society of America Journal 52, no. 2 379-382. 

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