Heterovalent exchange

Both approaches lead to identical standard thermodynamic values of exchange (9-10). Such a difference in the choice of the surface concentration scale is of course only important for heterovalent exchange equilibria. For the heterovalent case the numerical value for both selectivity coefficients, Kg (Gaines Thomas) and (Vanselov) differ and, consequently, their variation with surface composition also differs. 

Rather small selectivity differences are observed for homovalent-and heterovalent exchanges involving alkali, alkaline earth, bivalent transition metal ions, aluminium and rare earth cations, as is amply evidenced from the extensive compilation by Bruggenwert and Kamphorst (16). This compilation includes various clay minerals illite, montmorillonite, vermiculite and kaolinlte. 

Heterovalent exchange. Although double layer theory predicts increasing AG of mono-bivalent exchange with charge density increase, such a relationship was not always obvious (20,48). 

Standard free energy changes of heterovalent exchange equilibria among complexes increase with charge density agreemen +with double layer expectations as shown for the Ag(en) ... 

Na - K - Co exchange in Y zeolite. Heterovalent exchange reactions in zeolites generally show an even more pronounced dependency on loading (116-118). Rees (116) observed variations of the selectivity coefficient by a factor 1000 for the Na-Ca and Na-llg exchange in zeolite A at 25 °C. An+exajnple of e treipe variations is shown in fig. 9 for the K -Co and Na -Co selectivities in zeolite Y at 45 °C (117). The exchange... 

Selectivity Coefficient Homovalent Exchange0 Heterovalent Exchange ... 

The heterovalent exchange reaction (K-Ca exchange) is Ca-soil + 2K <=> 2K-soiI + Ca2+, except for the Gapon convention where it would be Ca1/2-soil + K4 o K-soil + 1/2 Ca2+. 

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

When heterovalent exchange (e.g., exchange involving both mono- and bivalent ions) takes place, which is frequently seen in soil-solution systems, the quantitative treatment runs into further difficulties. In this case, the determination of mole fractions also becomes problematic. The Vanselow equation assumes that the monovalent and bivalent ions are equivalent when calculating mole fractions. Other empirical equations, however, simply introduce some factors for the ions with different valencies. For example, according to Krishnamoorthy and Overstreet (1949), this factor is 1 for monovalent ions, 1.5 for divalent ions, and 2 for trivalent ions, which is not in agreement in stoichiometry. Another model... 

Figure 4 Computerized V3 (solid lines) and C (dashed lines) concentration distributions during IE kinetic process for heterovalent exchange (unlike ions) ...

In the case of heterovalent exchange the value of the selectivity coefficient depends upon the choice of the concentration units, and is related to the separation factor according to the following equation ... 

The exchange of ions at the solid-water interface is usually described by reactions in which equivalents of counterion charge are conserved. As an example of heterovalent exchange, the replacement of Na+ by Ca2+ as the counterion adjacent to a negatively charged surface may be represented by... 

Eriksson applied Donnan equilibrium calculations to heterovalent exchange, reasoning that clays in a salt solution could be thought of as an ion species restricted from free diffusion. His equation was... 

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. 

Because here we have univalent cations, equivalent and molar fractions are the same, but for heterovalent exchange, both fraction types can be found (see below). Of course both plots are mirror images around the diagonal, because = 1. The... 

Before advancing further, we will show an example of heterovalent exchange, between Ca " and Na+ in a Brucedale soil sample homoionized with Ca " ... 

Occasionally, isotherms of binary and multicomponent exchanges are described using various empirical adsorption equations. These cannot be used for the prediction of multicomponent equilibria [88]. In fact, a closer inspection of these equations reveals that they have no in-built facility for true prediction (i.e. for the calculation of equilibria over ranges of different total solution concentrations for heterovalent exchanges). Thus these equations are useful in describing the observed isotherm in a mathematical form but the only pre-... 

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