Thermodynamics exchange constants

An experimentally variable Kv with respect to exchangeable Na+ load (Eq. 4.53) can be transformed to the thermodynamic exchange constant (Keq) as follows ... 

The equation employed to calculate the thermodynamic exchange constant (K ) from the Kv of Na+-Ca2+ exchange (see Reaction 4.38 for stoichiometry), for example, is as follows ... 

Selectivity coefficients are not generally constant over the whole exchange isotherm since their definition incorporates concentrations rather than activities. The relation between the thermodynamic exchange constant (/Cth) the mass action constant on a particular concentration scale is obtained by introducing activity coefficients into the expression for the selectivity coefficient, thus ... 

When the standard and reference states for the exchanger and external solution phases are defined according to the conventional theory of electrolyte solutions, the thermodynamic exchange constant is by definition equal to unity. Therefore from equation 5.23 the observed selectivity in dilute solutions arises from the activity coefficient ratio in the exchanger phase thus ... 

Rapid exchange between Xi and Xi is reported in reference (3). This means that the forward and reverse reaction rates of this step are mnch faster than all others, and hence this particnlar step can be treated as a qnasi-eqnihbrium. The two intermediates in that step are present at all times in concentrations related to one another by a thermodynamic eqnihbrium constant and can be Inmped into one pseudo-intermediate [Xs]. This approach is very useM in reducing the number of terms in the denominator of the rate equation, which is equal to the square of the number of intermediates in the cycle (7). 

If the metals bound in complexes exchange with biological ligands, the dissociation kinetics of these complexes, the ligand-exchange kinetics and the association kinetics with the biological ligands must be considered. Simple dissociation kinetics of complexes are related to their thermodynamic stability constants by the relationship ... 

We can now make sensible guesses as to the order of rate constant for water replacement from coordination complexes of the metals tabulated. (With the formation of fused rings these relationships may no longer apply. Consider, for example, the slow reactions of metal ions with porphyrine derivatives (20) or with tetrasulfonated phthalocyanine, where the rate determining step in the incorporation of metal ion is the dissociation of the pyrrole N-H bond (164).) The reason for many earlier (mostly qualitative) observations on the behavior of complex ions can now be understood. The relative reaction rates of cations with the anion of thenoyltrifluoroacetone (113) and metal-aqua water exchange data from NMR studies (69) are much as expected. The rapid exchange of CN " with Hg(CN)4 2 or Zn(CN)4-2 or the very slow Hg(CN)+, Hg+2 isotopic exchange can be understood, when the dissociative rate constants are estimated. Reactions of the type M+a + L b = ML+(a "b) can be justifiably assumed rapid in the proposed mechanisms for the redox reactions of iron(III) with iodide (47) or thiosulfate (93) ions or when copper(II) reacts with cyanide ions (9). Finally relations between kinetic and thermodynamic parameters are shown by a variety of complex ions since the dissociation rate constant dominates the thermodynamic stability constant of the complex (127). A recently observed linear relation between the rate constant for dissociation of nickel complexes with a variety of pyridine bases and the acidity constant of the base arises from the constancy of the formation rate constant for these complexes (87). 

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

The isomerization reactions of Pt-nucleobase adducts are expected to be difficult owing to the inertness and thermodynamic stability of the Pt-N bond [30]. For example, a half-life of about 23 years has been estimated for the direct NH3 exchange in [Pt(NH3)4]2+ in aqueous NH3 solution at 25 °C [31], Unfortunately, data on thermodynamic stability constants for Pt-N complexes is very limited because of their inertness (vide infra). Nevertheless, a few studies have reported Pt11 isomerization reactions in nucleobase complexes. 

EXCHANGE MASTER SPECIES defines the interrelation between the name of an exchanger and its master species. Based on this, EXCHANGE SPECIES describes a half-reaction and requires a selectivity coefficient for each exchanger species. In contrast to stability constants or dissociation constants, these selectivity coefficients are dependent on the respective solid phase with the specific features of their inner and outer surfaces (see also chapter 1.1.4.2). Therefore, within thermodynamically data collections they are only to be seen as placeholders that have to be changed according to site specific exchange constants. 

TABLE 4.2. Thermodynamic Equilibrium Constants of Exchange (ATCJ and Standard Enthalpy of Exchange (AH°e ) Values for Binary Exchange Processes on... 

Levy, R. and D. Hillel. 1968. Thermodynamic equilibrium constants of sodium-calcium exchange in some Israel soils. Soil Sci. 106 393-398. 

The advantage of the application of the law of mass action is that the equilibrium exchange constant allows the calculation of other thermodynamic parameters, namely, the Gibbs free energy (Equation 1.84) ... 

Stability constants are not always the best predictive tool for measuring the ease and the extent of chemical reactions involving complexes nor their stability with time, because their kinetic behavior can often be even more crucial. For example, when ligand exchange reactions of ML (e.g., [FeEDTA]) with other metal ions (e.g., Zn2+ or Ca2+) are ki-netically slow, they do not significantly influence ligand speciation. Another typical example of the thermodynamics vs kinetics competition is the fact that the degradability of some metal complexes (e.g., metal-NTA) is related to their kinetic lability, rather than to their thermodynamic stability constants. Kinetic rather than thermodynamic data are then used to classify metal complexes as labile, quasi-labile, slowly labile, and inert (or stable). See Section 3.2.6. 

Exchange constants for low-dimensional magnets are most commonly obtained via comparison of experimental data to the predicted behavior of a thermodynamic property for a given model, usually the magnetic susceptibility. Johnston et al. showed that the molar susceptibility xm of the uniform chain can be expressed as a ratio of polynomials in powers ofthe reduced temperature t t = hgT/ 2J ). The coefficients N and D are listed in Table 1. 

The titration data were used to determine the thermodynamic equilibrium exchange constants for the reactions involved. To... 

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 thermodynamic equilibrium constant can be evaluated by using the simplified form of the Gaines-Thomas equation [201], assuming that the change in water content in the exchanger is negligible. The equation, with defined as the corrected selectivity coefficient by Eq. (4), follows-. 

If the standard and reference states for the exchanger phase are defined differently, whilst maintaining the conventional states for the solution phase, a thermodynamic selectivity scale can be set up for various ions where the value of the exchange constant indicates the degree of selectivity, as first demonstrated by Bonner, Argensinger, Hogfeldt, and others. 

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. 

In Eqs. (3) and (4), overbars denote the ion-exchanger phase. For a cation-exchange reaction as shown here, the exchangeable ions (Na" " and H+) are termed counterions and the negatively charged ions in solution are called colons. K is the thermodynamic equilibrium constant, and denotes ionic activity. For convenience of measurement, concentrations are used in practice in place of activities. In this case, in Eq. (4), based on concentration, the selectivity... 

---