Ion-exchange constant

The original ion-exchange treatment was developed for competition between reactive and inert monoanions, but Chaimovich, Quina and their coworkers have extended it to competition between mono and dianions (Cuccovia et al., 1982a Abuin el al., 1983a). The ion-exchange constant for exchange between thiosulfate dianion and bromide monoanion is not dimensionless as in (7) but depends on salt concentration, and the formalism was developed for analysing micellar effects upon reaction of dianionic nucleophiles, e.g. thiosulfate ion. 

The ion-exchange constants, K, in (7) should be related to the individual mass action constants, K land Ky, and this seems to be correct, based on limited evidence and some major approximations (Bunton et al., 1983a). A recent and more detailed data analysis shows that the value of the ion-exchange constant is consistent with values of the individual constants (Rodenas and Vera, 1985). 

CTAC1, CTABr, CTAOH + OH . k /ky, 0.01. Kinetic data analysed using either independent binding or ion exchange constants. IE and M A... 

The ion exchange method, (28, 80) which consists in determining the ion exchange constants of a complexed and uncomplexed transition metal cation versus a non-complex forming reference cation, leading to the determination of... 

A pseudophase ion exchange model has been applied to reactions in micellar systems with varying success (1-7). According to this model, the distribution of nucleophile is considered to depend on the ion-exchange equilibrium between the nucleophile and the surfactant counterion at the micelle surface. This leads to a dependence on the ion-exchange constant (K g) as well as on the degree of dissociation (a) of the surfactant counterion. The ion exchange (IE) model has recently been extended to oil in water microemulsions (8). 

The theory of glass membranes with two layers characterized by different ion exchange constants and different mobilities of the exchanged ions was developed by Conti and Eisenman [61]. Assuming a stationary state they obtained (3.4.1) or (3.4.4) expanded by an expression that is a function of the cation concentration at the boundary between the two membrane phases and their mobilities. This term can be considered constant. 

From (6.44), we see that in order to obtain a selective membrane, the value of the ion-exchange constant must be small and the sodium ion mobility in the hydrated layer relative to that of the hydrogen ion must also be small. The expansion of the selectivity coefficient to include selectivity to other ions involves inclusion of more complex ion-exchange equilibria, and the use of a more complex form of the Nernst-Planck equation. This rapidly leads to intractable algebra that requires numerical solution (Franceschetti et al 1991 Kucza et al 2006). Nevertheless, the concept of the physical origin of the selectivity coefficient remains the same. Electrochemical impedance spectroscopy has been successfully used in analysis of the ISE function (Gabrielli et al 2004). 

The significance of all the quantities are the same as in the previous equation, except for K and Ka which represent the stability constant of M(AcAc) and equilibrium ion exchange constant, respectively. 

In follows from equations (3.32) and (3.33) that the ion-exchange constant (Xex) for monovalent ions, A and B is given by (Poole and Poole, 1991) ... 

The ion-exchange constant also determines the elution order for a series of ionic solutes and it may be related to the capacity ratio of an analyte ion, A, in the presence of a counter ion, B. Equation (3.34) may be rearranged to give equation (3.35), which relates the capacity ratio of A to the ion exchange constant for that pair of ions and the concentrations of the counter ion, B, in the mobile phase and the stationary phase... 

The ion-exchange constant does vary from one pair of ions to another therefore selectivity can be controlled by appropriate choice of the counter ion. However, selectivity is more conveniently manipulated by controlling the pH of the mobile phase and taking advantage of differences in the values of the analytes to be separated. In contrast with reversed-phase liquid chromatography (see section 3.6.2.1) the retention of weak acids and weak bases will reach a maximum when the compounds are in their ionized forms. Zwitterionic compounds such as amino acids, peptides and proteins can be separated on anion exchangers or cation exchangers. 

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. 

Ion exchange constant for ions of like charge Mass action binding constant of ion X. 

The measured CEC is highly sample specific, so that use of generalized ion-exchange constants such as Kx for conditions involving various solids is of dubious validity. 

KXY Ion-exchange constant for ions Y and X, given by [YW][XM]/[YM][XW] mYs Mole ratio of micellar-bound Y to micellized surfactant cmc Critical micelle concentration... 

In practice computer simulation has generally been used to predict the variation of with concentration of reactant, surfactant, or added electrolyte in terms of various values of the parameters, k, and This simulation procedure has been used as an indirect method for the determination of the ion exchange constant K, and, for example, for the competition between various counterions for micelles, there is reasonable agreement between the values obtained kinetically and by other methods [25,72-79],... 

For both systems the data can be fitted with an ion exchange constant = 4, and the second order rate constant in the micellar pseudophase is about one-third of this in water, probably because the high ionic content of the Stern layer exerts a negative salt effect upon the reaction. 

Very similar results have been obtained by a number of workers for reactions involving hydrophilic anions in cationic micelles [72,73,76]. An important point is that the ion-exchange constants determined from rates or equilibria of hydroxide ion reactions in cationic micelles agree reasonably well with independent estimates from physical measurements on the relative affinities of various anions for cationic micelles [74,86]. 

In the second step, with the hydrolysis constants and the specific interaction parameter for ZrOH" and for Zr3(OH) fixed to the values optimised as detailed above, the equilibrium constants and interaction parameter for all other species in the overall hydrolysis model were obtained by a global fit of the potentiometric, solubility, solvent extraction and ion exchange data mentioned above. The fit was extended to the determination of equilibrium constants for heterogeneous reactions ion exchange constants, solubility constants and liquid/liquid distribution coefficients. The fit was based on a preselection of the stoichiometries of dominant species which included invariably the species Zr(OH)4(aq), Zr ) ), Zr (OH)Jj and Zr4(OH)i6(aq) and various other mono-, di-, tri- and tetravalent species to improve the fit. The potential formation of chloride complexes of Zr was considered for chloride containing solutions, using the stability constants determined in Section V-4. If all fitted results were found insensitive to the equilibrium constants of a given species, the respective species was removed from the list of species. 

To date the chemical trapping method has been used to estimate interfacial concentrations of water, alcohols, and counterions in cationic micelles and microemulsions [65,128] the affinity of cationic micelles toward Cl versus Br", expressed as an ion-exchange constant [Eq. (11)] [129], and interfacial alcohol/water molar ratios in microemulsions and distributions of 1-butanol and 1-hexanol between aggregate interfaces and bulk aqueous phases (O/W microemulsions) [130] and bulk oil phases (W/O microemulsions) over a range of alcohol and surfactant concentrations [131]. The focus here is on results in microemulsions. 

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