Constant Ionic Medium Reference State

All equilibrium constants in the present discussion are based on the concentration (not activity) scale. This is a perfectly acceptable thermodynamic scale, provided the ionic strength of the solvent medium is kept fked at a reference level (therefore, sufficiently higher than the concentration of the species assayed). This is known as the constant ionic medium thermodynamic state. Most modern results are determined at 25 °C in a 0.15 M KCl solution. If the ionic strength is changed, the ionization constant may be affected. For example, at 25 °C and 0.0 M ionic strength, the pXj of acetic acid is 4.76, but at ionic strength 0.15 M, the value is 4.55 [24]. 

The intrinsic equilibrium constants are postulated to be independent of the composition of the solid phase They remain conditional in the sense of the constant ionic medium reference state if interacting ions such as H+ are expressed as concentrations. 

The constant-capacitance model (Goldberg, 1992) assigns all adsorbed ions to inner-sphere surface complexes. Since this model also employs the constant ionic medium reference state for activity coefficients, the background electrolyte is not considered and, therefore, no diffuse-ion swarm appears in the model structure. Activity coefficients of surface species are assumed to sub-divide, as in the triplelayer model, but the charge-dependent part is a function of the overall valence of the surface complex (Zk in Table 9.8) and an inner potential at the colloid surface exp(Z F l,s// 7). Physical closure in the model is achieved with the surface charge-potential relation ... 

Electrodes sensitive to one of the ion-pair partners in the so-called constant ionic strength cell [95] proved to be valuable to measure the free ion concentration and to determine the stoichiometric equilibrium constant. The latter has a clear thermodynamic meaning if the ionic strength of the medium is indicated, since in this approach, the reference standard state is not the usual infinite dilution of all species dissolved in the solvent (y-> 1, as c -> 0), but is the infinite dilution of the reacting species in the constant ionic medium (7—> 1, as c 0 at 1 = constant) [7]. Even if the constant ionic strength attenuates the variation of liquid junction potentials, the lower the association constant, the lower the consistency of the obtained constant. 

Because we cannot define absolute values for the chemical potential, we restrict ourselves to give changes in chemical potential (resulting from a change in a chemical composition or a change in pressure or temperature). By choosing a suitable reference state, we are able to define the chemical potential (usually at r = 298.2 K and P = 1 atm). In equations 23-26, we define the reference state either as infinite dilution or as constant ionic medium. 

Acidity scales are used commonly to assess the chemical and biological state of seawater. The international operational scale of pH fulfills the primary, requirement of repro ducibility and leads to useful equilbrium data. Nevertheless, these pH numbers do not have a well defined meaning in respect to all marine processes. Seawater of 35%o salinity behaves as a constant ionic medium, effectively stabilizing both the activity coefficients and the liquid junction potential. It may be possible, therefore, to determine hydrogen ion concentrations in seawater experimentally. One method is based on cells without a liquid junction and is used to establish standard values of hydrogen ion concentration (expressed as moles of H /kg of seawater) for reference buffer solutions. 

The constant ionic medium reference state determines the activity coefficients of the aqueous species. 

The Constant Ionic Medium Reference State is compared with the more common Infinite Dilution Reference State in Chap. 2 of G. Sposito, op. cit. ... 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

Determining solubility constants in aqueous solutions generally involves analytical work to determine concentrations [ ] or potentiometric measurements to obtain activities. The ratio of activity and concentration—i.e., the activity coefficient and its change with concentration— depends on the choice of the standard state. If pure water is chosen as a standard state, the activity coefficients approach unity only in dilute solutions. It is therefore necessary to express the so-called thermodynamic constants TK (48) in terms of activities. If, on the other hand, one chooses as reference an aqueous solution of comparatively high and constant ionic strength, the activity coefficients remain close to unity even at rather high concentrations of the reacting species. In this case, we may use stoichiometric constants K (48), expressed in molarities, M, and related to a particular ionic medium. 

F (jE°(/=o.2) — J5°(/=o)) (1) This cycle holds for every medium. Equation 1 connects the four basic quantities T Ks0, Ks0, E°(j=o>, and E° 1) without any nonthermo-dynamic assumptions. This enables us to evaluate solubility constants for every appropriate ionic medium using data which have been determined with reference to the usual aqueous standard state. The conversion of Ks into TKs and vice-versa may also be performed using the Debye-Hiickel equation and its extensions as shown in Equation 2. 

In this expression is the rate constant for the reaction at absolute temperature T and zero ionic strength in a medium of dielectric constant Sr and is the rate constant in a standard reference state of... 

Table 21.2 Hydrolysis of tetravalent actinide ions. Constants pfi i listed refer to formation of the first mononuclear complex in solutions of various ionic strengths / in tight and heavy water, at 25°C. Medium (Na,HYZlO, if not otherwise stated.

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