Ion exchange equations

Taking into account the interdependence between chemical potentials and component activity jij = p + RT In a, Eqs. (3.1) and (3.2) yield a well known ion exchange equation... 

In systems with two oxo moieties, electrophilic attack occurs at the nitrogen of the cyclic amide. As an illustration, triazidiridine dione 32 was converted in good yield to the salt 16 upon treatment with Mel and followed by ion exchange (Equation 4) <2005H(65)1629>. Similar reactivity was observed with substrate 33, but in this case a 3/1 mixture of O-acylated and iV-acylated products 34 and 35 was obtained (Equation 5) <1997J(P1)2223>. 

Extension of the equilibrium model to column or field conditions requires coupling the ion-exchange equations with the transport equations for the 5 aqueous species (Eq. 1). To accomplish this coupling, we have adopted the split-operator approach (e.g., Miller and Rabideau, 1993), which provides considerable flexibility in adjusting the sorption submodel. In addition to the above conceptual model, we are pursuing more complex formulations that couple cation exchange with pore diffusion, surface diffusion, or combined pore/surface diffusion (e.g., Robinson et al., 1994 DePaoli and Perona, 1996 Ma et al., 1996). However, the currently available data are inadequate to parameterize such models, and the need for a kinetic formulation for the low-flow conditions expected for sorbing barriers has not been established. These issues will be addressed in a future publication. 

The equations of heterogeneous isotope exchange are simpler than ion-exchange equations because the two ions are chemically the same. In the treatment by the law of mass action, it means that the equilibrium constant is equal to 1. The selectivity coefficients at X = 0 and X = 1 can be determined by measuring heterogeneous isotope exchange in which the concentration of the radioactive isotopes is very low and approaches zero (carrier-free radioactive isotope). 

A review of some leading semiempirical models precedes examination of physicochemical modeling of ion exchange. Such models will likely be used for the foreseeable future to describe ion-exchange phenomena in complex svstems. Thus, they represent the reference point for development of improved models. Methods of incorporating the semiempirical ion-exchange equations in general chemical equilibrium models are also described. 

The ion-exchange equation written for the current system takes the form... 

In summary, then, either the gas or the solid ideal solution model applied to a mixture of exchange cations would convert equation 3.6 to an ion exchange equation of the form... 

This form of exchange equation, which equates the active mass of adsorbed cations to the mole fraction of these cations on the exchange sites, is often referred to in the soil chemistry literature as the Vanselow equation. Ion exchange equations of this form are the mathematical expression of the important hypothesis of ion exchange, that ... 

The concentration-cha-ge effect can be derived from ion exchange equation 3.23. The equation is first simplified by the principle that electrolyte activities can be expressed in terms of products of the activities of the constituent ions. Thus, (ACl) = (A) (Q) and BO ) = (B) (0) The solution activity ratio, (AQ)V(B02), is then equated to (A)V(B), and equation 3.23 can be rewritten without the explicit inclusion of the solution anion ... 

It appears, therefore, that all of these studies, carried out by several different techniques, are in reasonable agreement on the equilibrium quotients for Na(I)/Ca(II) exchange on samples of montmorillonite from several different sources. Ion-exchange equations give a good correlation of the adsorption behavior on montmorillonite, in agreement with prior studies (see, e.g.. References... 

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