Thermodynamics of ion exchange

The thermodynamic equilibrium constant for an equilibrium ion-exchange process, described by Equation 7.1, can be expressed as follows [14] 

In addition to the representation of concentration with the help of the equivalent ionic fraction (Equations 7.2a and b), there are other forms of expressing the concentration in ion- exchange experiments such as the cationic mole fraction defined as [33] 

Using the above definitions, it is possible to express the activities as follows [33]  

Nevertheless, the thermodynamic formulation normally used for zeolites is the one developed by Gaines and Thomas [34], who expressed the equilibrium constant (Equation 7.5) as follows. 

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This point was raised by K. L. Babcock, L. E. Davis, and R. Overstreet, Ionic activities in ion-exchange systems, Soil Sci. 72 253 (1951). The problem of the Reference State for ion exchangers is reviewed by L. W. Holm, On the thermodynamics of ion exchange equilibria. I. The thermodynamical equilibrium in relation to the reference states and components, Aark. Kem. 10 151 (1956). 

Several workers have reported thermochemical data for ion exchange in resins but a relatively recent extensive study has been given by Boyd, some of whose results are presented in Tables 5.3a-d. These and similar studies offer a means of attempting to unify the thermodynamics of ion exchange with the exchange mechanism as postulated by various molecular theories. 

The dynamic character of polymers such as Nafion in terms of solvent swelling can have a marked influence on the thermodynamics of ion exchange processes. 

In conclusion the attention of the reader is drawn to the elegant and detailed examination of the thermodynamics of ion exchange in clinoptilolite from Death Valley Junction, California, carried out by Pabalan [71], and by Pabalan and Bertelti [72]. 

Ion adsorption to mineral surfaces is an important phenomenon in many industrial applications as well as in the study of the natural environment. Ion exchange on constant charge minerals was initially the ion adsorption process that was studied most intensively both experimentally and theoretically. The success in this field was due to a combination of efforts. Mineralogists andcrystallographers unravelled the detailed structure of the minerals after 1930, theoretical chemists developed the well known double layer theories around 1910-1925, and the thermodynamics of ion exchange was formulated around 1950. Colloid and soil chemists in the mean time developed the various applications of this work and it became widely used by practitioners. 

Selectivity of sorption of organic ions by crosslinked polyelectrolytes in competition with small ions, in particular with metal ions, should be considered on the basis of the analysis of thermodynamic relationships of ion exchange. 

The selectivity of ion exchange Ks can easily be determined experimentally for the simplest systems of exchange between monovalent ions. The value of Ks may be used for analysis of thermodynamic functions AG°, AH0 and AS0, of sorption selectivity... 

The thermodynamic analysis of the selectivity of ion exchange with the participation of ions of quaternary ammonium bases [56--58] has shown that an increase in bonding selectivity, when metal ions are replaced by organic ions, which is usually accompanied by an increase in entropy of the system (Table 5). It follows from Table 5 that a drastic increase in bonding selectivity upon passing to a triethylbenzylammonium counterion (the most complex ion) is due to a considerable increase in the entropy of the system. 

Vansant EF, Uytterhoeven JB (1972) Thermodynamics of the exchange on n-alkylammonium ions on Na-montmorillonite. Clays Clay Mineral 20 47-54... 

However, if the valences of the exchanging cations are equal, the selectivity coefficient or pseudo-equilibrium constant is not affected by concentration. As already mentioned, one isotherm corresponds to a specific temperature in the case of adsorption or ion exchange of equal valence ions, whereas additionally, the same normality is required for the existence of only one isotherm in the case of ion exchange of different valence ions, due to the concentration-valence effect (Helfferich, 1962). The determination of the true equilibrium constant should be based on the thermodynamic activities (activity coefficients) of the species rather than concentrations. It is clear that the difficulties in the determination of activity coefficients also complicate the determination of the true equilibrium constant (Culfaz and Yagiz, 2004). 

Secondly, selectivity is not always achievable. For example, permselectivity of ion-exchanging polymer films fails at high electrolyte concentration. We have shown that even if permselectivity is not thermodynamically found, measurements on appropriate time scales in transient experiments can lead to kinetic permselectivity. To rationalise this behaviour we recall that the thermodynamic restraint, electrochemical potential, can be split into two components the electrical and chemical terms. These conditions may be satisfied on different time scales. Dependent on the relative transfer rates of ions and net neutral species, transient responses may be under electroneutrality or activity control. 

Grant, S. A., and P. Fletcher, Chemical thermodynamics of cation exchange reactions, Ion Exchange and Solvent Extraction 11 1 (1993). A useful survey of the chemical modeling of multicomponent cation exchange systems. 

Goulding, K. W. T. 1983. Adsorbed ion activities and other thermodynamic parameters of ion exchange defined by mole or equivalent fractions. J. Soil Sci. 34 69-74. 

Treatment of Ion Exchange by the Law of Mass Action As mentioned earlier, there are models describing the equilibrium of the exchange reactions that use the law of mass action. In strict thermodynamic sense, the law of mass action is valid only for homogeneous systems. In order to be able to use it in solid-liquid systems, the layer containing the ions belonging to the solid is... 

On the basis of those discussed here, we can say that the thermodynamic parameters of ion exchange determined by linear isotherm equations are not correct. We determine the mechanism of sorption (ion exchange and/or adsorption) and then choose the isotherm equation. When simultaneous interfacial processes take place, the dominant process, if any, has to be selected or experimentally separated, or Equation 1.119 should be used. 

Table 3 Thermodynamic Functions of Ion Exchange of Amino Acid Cations on Strong-Acid Cation-Exchange Resin in Hydrogen Form...

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