Divalent exchange

Equations 3 and 6, and some closely related empirical variants, have been used to fit many isotherms for monovalent-divalent exchange (23). For example, a two-parameter fit to isotherm data can be obtained by using the Rothmund-Kornfeld equation... 

The Gapon equation is widely recognized as empirical in nature and thermodynamically dubious (e.g., see references 7 and 24) but has nonetheless often been used successfully to fit cation-exchange data. We will demonstrate later that the Gapon equation can indeed describe monovalent-divalent exchange under conditions in which sorption in the diffuse layer is minor in comparison with chemisorption. 

Figure 8. Predicted concentrations of major surface and solution species in monovalent-divalent exchange model fits of Figures 7 and 9. The diffuse-layer species represent the excess (K+, Na+, Ca2+) or deficit (Cl ) of ions relative to the bulk solution. Part a log C versus log TOTNa for fit of Na -CVf" exchange data (Figure 7) without consideration of surface complexation. Part b log C versus log TOTNa for fit of Na+-Ca2+ exchange data (Figure 7) with surface complexation of Na and Ca2+. Part c log C versus leg TOTKfor fit of K -C( + exchange data (Figure 9) with surface complexation of K+-Ca2+. Continued on next page.

Figure 8.19. Arrangement of H2O chains linking divalent exchange cations to the surfaces of the 15-A two-layer hydrate (a), and the 20-A hydrate (b). (Adapted from V.

Univalent-divalent exchange (za = 2, zb = 1) is an important application of ion-exchange technology. For this case, the selectivity coefficient is ... 

The variation of the equilibria in the system Dowex 50 resin-Ca-Mg-Na is shown in Figure 9. The two divalent-monovalent exchanges are concentration-dependent. The divalent-divalent exchange is not. 

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