Equivalent fraction convention, exchanger

Because the activities of species in the exchanger phase are not well defined in equation 2, a simplified model—that of an ideal mixture—is usually employed to calculate these activities according to the approach introduced bv Vanselow (20). Because of the approximate nature of this assumption and the fact that the mechanisms involved in ion exchange are influenced by factors (such as specific sorption) not represented by an ideal mixture, ion-exchange constants are strongly dependent on solution- and solid-phase characteristics. Thus, they are actually conditional equilibrium constants, more commonly referred to as selectivity coefficients. Both mole and equivalent fractions of cations have been used to represent the activities of species in the exchanger phase. Townsend (21) demonstrated that both the mole and equivalent fraction conventions are thermodynamically valid and that their use leads to solid-phase activity coefficients that differ but are entirely symmetrical and complementary. 

If the equivalent fraction convention for exchanger phase activities is adopted (i.e., the Gaines-Thomas approach), the molar concentrations are proportional to the equivalent fractions, and it can easily be shown that the half reaction constants and the binary-exchange constants (selectivity coefficients) are related by... 

Note that no individual sites are considered, just the surface taken as an exchanger. The activity convention is to use equivalent fractions, as in the Gaines-Thomas case thus, the corresponding selectivity coefficient is given by... 

Since we are honoring the Gaines-Thomas convention, the activity of a sorbed ion in the calculation results is the fraction of the total equivalents of the sediment s exchange capacity the ion occupies. The resulting values are,... 

Equations 3.21 and 3.22 are the Gapon (1933) convention. In this case, the molar and equivalent exchangeable fractions are the same because both are based on a single exchange site with the subscript of X, i, in Eq. 3.17 equal to 1. 

In Eq. 3.27, the fact that the molar and equivalent exchangeable fractions are the same if the Gapon convention is used. In other words, [lyi-X] = Pi, and [Na-X] = Pnj. For a homo valent exchange, i = 1, the preceding equation results... 

For horseradish peroxidase (HRP), it was long thought that only a small fraction of the free-radical content was ESR detectable conventional ESR spectra show a narrow component equivalent to about 0.01 spins/heme. However, recent work has demonstrated that much of the free-radical spectrum is extremely broad due to interaction of the radical with ferryl ion, probably through an anisotropic exchange interaction [109]. When these broad components are taken into account, the number of free... 

The heat exchange process within the fractionating column should, ideally, bring about complete separation of the substances in the mixture, but the degree of success that actually is achieved depends on a number of factors. Before discussing the factors that contribute to the effective functioning of a column, the terms number of theoretical plates and height equivalent to a theoretical plate (HETP) which are conventionally used to convey information on the efficiency of a column, need to be defined. 

One of conventional ways to describe ion exchange reactions is to use equivalent scale instead of molar scale. This is the reason for use of fractional coefficients. 

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