Binary Ion Exchange Equilibria

The ion exchange reactions in Eqs. 5.1 and 5.2 involve pairs of cations or anions, respectively, but this choice of the number of reacting ionic species is not unique, nor does it imply that the exchange has only two ions in the adsorbate. As the form of the general adsorption-desorption reaction in Eq. 4.3 makes apparent, ion exchange reactions can exhibit several ionic species, and it is only by analogy with complexation reactions that two reacting species are 

A large body of experimental research exists concerning two-component ion exchangers, whose behavior is described by Eq. 5.1 or 5.2.5 These systems thus exhibit binary ion exchange equilibria. The central problem in applying chemical thermodynamics to them is to derive equations that permit the calculation of and the activity coefficients of the two adsorbate species.6 Several approaches have been taken to solve this problem, each of which reflects a particular notion of how exchanger composition data can be utilized most effectively to calculate thermodynamic quantities. 

One conceptually simple approach is to express all binary ion exchange reactions as combinations of the special case of Eq. 4.3, in which the species Q is deleted and SR = SR, with the possibility that more than 1 mol of SR may combine with adsorptive ions to form the adsorbate species. This approach portrays ion adsorption formally as a complexation reaction and builds ion exchange reactions as combinations of these reactions.7 Since the adsorbate species may be formed from both cations and anions (cf. Eq. 4.3), ion exchange reactions involving charged complexes [e.g., CaCT(aq) as well as monatomic ions [e.g., Na (aq)J can be described. If the further simplification is made that adsorbate species activity coefficients do not depend on exchanger composition, then equilibrium spccialion calculations can be performed exactly as described 

Note that imposition of Eq. 4.9b requires that the first-order terms vanish that there be differing coefficients for the second order terms and that there be equal but opposite coefficients for llu third order terms. Moreover, if the infinite 

Since the Margules expansions represent a convergent power series in the mole fractions,8 they can be summed selectively to yield closed-form model equations for the adsorbate species activity coefficients. A variety of two-parameter models can be constructed in this way by imposing a constraint on the empirical coefficients in addition to the Gibbs-Duhem equation. For example, a simple interpolation equation that connects the two limiting values of f (f°° at infinite dilution and f = 1.0 in the Reference State) can be derived after imposing the scaling constraint 

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It has been emphasised already that accurate and reliable data are essential in the construction of adequate ion exchange models for the industrial applications of zeolite and other ion exchangers. In this section we will discuss ion exchange experimentation and its utility for industrial appHcations. We also discuss major pitfalls that may lead to unreliable results. Although industrial appHcations always involve more than two exchanging ions, seeing trends in the overaU equilibria under these circumstances may be difficult. Therefore, in this section, only binary ion exchange equilibria are considered in order to keep the major issues in focus. 

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