Activity coefficient exchanger component

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. 

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 rational activity coefficients cannot be evaluated in any simple manner. Following the model of Truesdell and Christ (16), a regular solution approach to the problem can lead to expressions for the rational activity coefficients. If the exchange sites have the same charge and approximately the same size, then a symmetrical solid solution will be formed where the rational activity coefficients for the two components are given by ... 

The task of calculating the composition of a soil exchanger phase in equilibrium with a soil solution has two distinct parts the thermodynamic exchange equilibrium constants must be determined and the activity coefficients of the components of the exchanger phase must be estimated. The first part of the problem, that of obtaining exchange equilibrium constants, is nog particularly difficult since a number of measurements of... 

The fact that the selective uptake of metal ion by the ion exchanger is associated with highly coordinated species undetectable in the solution, even vtiien ligand concentrations in the two phases have been kept similar, has to be attributed to either the immobilization of these species by their interaction with the organic component of the exchanger matrix or to sizable reduction of activity coefficients of ion species in the resin phase because of the lowering of the dielectric constant of the resin phase media. 

The abstract thermodynamic treatment outlined above resembles Kielland s approach to ion exchange equilibria on aluminosilicates, but unlike the latter case no simplifying assumptions are made concerning the relationship between the concentrations of the resin phase components and their activity coefficients. 

The brackets represent the thermodynamic activity. At low concentrations in water, the concentration value can be used for activity at higher concentrations or with other ions in solution, the concentration value must be multiplied by the activity coefficient. The activity of the ions on the ion-exchange medium is not readily available the mole fraction, defined as the moles of an individual component divided by the total moles of all components in the phase, has been used in its place (Rieman and Walton 1970). 

Even more advantageous is the fact that with the concentration of the feed mixture increasing, the distance between the fronts of the two components under separation noticeably increases. This corresponds to an increase in the separation selectivity, which further enhances the productivity of the process. An analogous phenomenon was first observed by Nelson and Kraus [116] in 1958 in the separation of concentrated solutions of LiCl from HCl on the anion-exchange resin Dowex-lxlO. The prolonged retention of HCl at increasing LiCl concentration was explained at that time by the authors as due to a drop of the activity coefficient of HCl in the resin phase (which, obviously, was not a correct explanation). 

Actually the selectivity coefficient includes into itself equilibrium constant and activities coefficients of competing ions of exchange capacity relative to the activities of the same components in the solution expressed in molar fractions. If activities coefficients in the solution are close to 1 then at equilibrium is valid the equality... 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

Fig. 11-4. Exchange of C02 between atmosphere and ocean in a two-box ocean model. Reservoir contents are shown in units of Pg C ( = 1012 kg C), exchange coefficients in yr l, and residence times in years. For comparison, the exchange of atmospheric carbon with the biosphere is shown in parallel. For simplicity the biosphere is represented by the two reservoirs of short-lived photosynthetic active components and the long-lived structural material. A more detailed breakdown of the biospheric reservoir is shown in Fig. 11-6.

All tubes contained the following components (in /nmoles unless stated otherwise) potassium phosphate, pH 6.5, 100 ascorbate, 6.0 fumarate, 50 tyramine-/3/3 -3H, 2.0, specific activity 1.15 X 10 CPM//nmole catalase, 300 units, dopamine /3-hydroxylase (4), Final volume, 0.68 ml. at 25°C. Octopamine determined by a minor modification of a published procedure (17). A 0.05 ml. sample of water was obtained by lyophilization and dissolved in 10 ml. of Bray s scintillation mixture. Radioactivity determined in a Packard liquid scintillation spectrometer total counts collected were sufficient to yield a 5% coefficient of variation. The expected tritium release was calculated from the octopamine formed, assuming that the amount of tritium was the same in both /3 positions of the tyramine. The results for the amount of tritium released have been corrected for the amount of exchangeable tritium initially present in the tyramine. 

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