Homovalent

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. 

In this section we outiine, in a very simplified way, the main differences in spin coupling mechanisms between homovalent and mixed valence compounds. 

Figure 6. Illustration of exchange interactions in homovalent system consisting of two metal sites A and B. The system contains two electrons. The six distinct microstates are indicated on Ae left. The antiferromagnetic contribution results from mixing an excited state ionic configuration wiA Ae ground state singlet.

What determines the structural trends amongst the homovalent sp valent molecules with up to six atoms that are displayed in Fig. 1.14 In particular, why amongst the many possible structural variants does Na3 take a bent configuration, Na4 a rhombus, Na5 a two-dimensional... 

Fig. 1.14 The most stable structures of the homovalent 3s-, -valent molecules that are predicted by ab initio calculations. Distortions may occur from the idealized structure types drawn. Data compiled by H. S. Lim.

That is, our analysis henceforth will apply to steady states in solutions containing only monovalent ions, (e.g. Tl+, H+, NOJ, CH3COO-, etc.) or only divalent ions (e.g. Cd2+, Mg2+, Ca2+, SC>4, etc.), but not mixtures of univalent and divalent ions. The advantage of this so-called homovalent restriction is that it provides a simple proportionality... 

Fig. 24. Steady-state concentration profiles for the three kinds of homovalent ions in solution. The graph was drawn for cb = 1 and cb/2 = 1.75.

The distribution of potential in the solution when a homovalent steady state exists is of considerable interest. Obtained by integration of eqn. (91), it is... 

Fig. 25. Potential profile for a homovalent steady state, drawn for 7 = 1/3.

We are now in a position to examine, in quantitative detail, the effect of the supporting electrolyte, at least for steady-state homovalent transport in finite planar geometry. The amount of supporting electrolyte present, relative to electroactive electrolyte, is characterized by the support ratio that was defined as... 

ION EXCHANGE SELECTIVITY AS A SURROGATE INDICATOR OF RELATIVE PERMEABILITY OF HOMOVALENT IONS IN REVERSE OSMOSIS PROCESSES Parna Mukherjee and Arup K. SenGupta... 

For homovalent cation exchange, a = b and Eq. 5.14 reduces to the simple expression... 

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 ... 

Follow the approach in Section 4.2 to derive a rate law for a homovalent cation exchange reaction described by Eq. 5.6 under the assumption that the kinetics are surface controlled. Compare your result with the Bunzl rate law in Eq. 5.54. (Hint Show that Eq. 4.26 generalizes to the rate law ... 

Cation exchange in soils or clay minerals involves replacement of a given cation on a given mineral surface by another cation. Exchange equations are commonly used to evaluate ion availability to plant roots and/or release of metals to soil water (e.g., heavy metals to groundwater or surface water). There are two major types of cation-exchange reactions in soil systems—homovalent and heterovalent cation exchange. 

Homovalent cation exchange refers to exchanging cations with similar valence. For example, with Ca2+-Mg2+ exchange, the reaction can be expressed as follows ... 

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 limits of Equations B and C at zero and infinity imply that a plot of Equation B in terms of CRCa versus ExCa (with ExCa being the dependent variable) at constant CEC and ACa Mg will give a curvilinear line approaching the CEC asymptotically (Fig. 4A). A plot of CRCa versus ExCa/CEC would also produce a curvilinear line asymptotically approaching 1. The pathway from ExCa/CEC = 0 to ExCa/CEC = 1 depends only on Ca Mgor (Fig 4B). Similar conclusions apply to all other homovalent cation-exchange reactions (e.g., K+ - NH4 and K+ - Na+). 

TABLE 4.3. Cation Exchange Selectivity Coefficients for Homovalent (K-Na) and Heterovalent(K-Ca) Exchange... 

Selectivity Coefficient Homovalent Exchange0 Heterovalent Exchange ... 

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