Free energy of exchange

The introduction of unsaturated aromatic compounds also leads to better charge delocalization and enhanced ion exchange affinity. This is+ rerified by 1) the higher free energy of exchange versus in biprotonated histammonium (83) (AC ... 

For aqueous systems and large r, the terms of the second bracket of equation 5.37 dominate and the free energy of exchange is governed by differences in the free energies of hydration of the counter-ions. Conversely, for small r, the terms of the first bracket in equation 5.37... 

Figure 3.2. Dependence of f-values of adsorbed cations on the mole fraction of exchange sites occupied by Rb and Na in the NaV b and Li+/Na+ exchange reaction on smectite. Adapted from R. G. Cast. 1969. Standard free energies of exchange for alkali metal cations on Wyoming bentonite. Soil Sci. Soc. Am. Proc. 33 37-41 1972. Alkali metal cation exchange on Chambers montmorillonite. Soil Sci. Soc. Am. Proc. 36 14-19.)...

Gast, R. G, 1969. Standard free energies of exchange for alkali metal cations on Wyoming bentonite. Soil Sci. Soc. Am. Proc. 33 37-41. 

K represents the real equilibrium constant for an exchange between Z = 0 and Z = Zmax. The standard free energy of exchange is obtained as AG = — RT In K. The enthalpy of exchange is derived from the Vant Hoff equation, and the entropy change is calculated from the AG and AH values ... 

These values of AG are related to the free energy of exchange for a competition between two counterions the absolute value of dG is directly related to the difference of affinity of both counterions in competitions. 

During titration of a polyacid, the free energy of exchange dG(T) is given by the potentiometric area between both neutralization curves experimentally, these values are found to be independant of the polymer concentration. In fact, the pH values are... 

Fig. 10. Free energy of exchange AG obtained by potentiometry at 25 °C as a function of the charge density.

Figure 4 Free energy of exchange AG 2 at pH 1.60 and 6.5 as function of pH-pK for fidsorption from aqueous solutions on to graphite of I, trinitrophenol II, 2,4-dinitrobenzoic acid III, 2,5-dinitrophenol IV, 2,4-dinitrophenol V, 2,6-dinitrophenol VI, 2,4-dinitroaniline VII, m-dinitrobenzene (Calculated from data in Izv. Vyssh. Uchebn, Zaved., Khim., Khim. Tekhnoi, 1979, 22, 1246).

As can be seen, there is a simple and unambiguous correlation between the value of the total free energy of exchange and that of the equihbrium constant. It is also expressed by the... 

One way of probing the interactions between solvated ions is to study aqueous bulk electrolyte activity coefficients, y. For the most common choice of reference state, the mean activity coefficient is a measure of the excess free energy, fM = ksT In y, of transferring a solvated salt pair from an infinite dilution to a solution -with a finite salt concentration. In the present context, we are interested in the ion specijkity and therefore — for a fixed salt concentration — define a free energy of exchanging one counter ion -with another. For example,... 

A good example of this is the frequently studied Na/Ca-zeolite A system, which has received much attention because of its importance in detergency applications. Careful and detailed experimental studies over a period spanning some 20 years by different sets of workers [14-20] resulted in calculated values of the standard free energy of exchange (kj equiv ) which ranged from -0.59 [14] to -3.09 [17]. Plots of the corrected selectivity coefficient (defined below see... 

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