Thermodynamic properties activity coefficient

In 1979, the Department of Energy initiated support of a number of fundamental projects in the chemistry of flue gas desulfurization. Five chapters in this book report the initial results of this effort. The topics of fundamental work include thermodynamic properties, activity coefficients in aqueous solutions, sulfur and NOx chemistry, and sulfite oxidation kinetics. The results provide the foundation for quantitative understanding of the FGD processes. 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

The accurate determination of relative retention volumes and Kovats indices is of great utility to the analyst, for besides being tools of identification, they can also be related to thermodynamic properties of solutions (measurements of vapor pressure and heats of vaporization on nonpolar columns) and activity coefficients on polar columns by simple relationships (179). 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

In addition to deciding on the method of normalization of activity coefficients, it is necessary to undertake two additional tasks first, a method is required for estimating partial molar volumes in the liquid phase, and second, a model must be chosen for the liquid mixture in order to relate y to x. Partial molar volumes were discussed in Section IV. This section gives brief attention to two models which give the effect of composition on liquid-phase thermodynamic properties. 

The thermodynamic properties of real electrolyte solutions can be described by various parameters the solvent s activity Oq, the solute s activity the mean ion activities a+, as well as the corresponding activity coefficients. Two approaches exist for determining the activity of an electrolyte in solution (1) by measuring the solvent s activity and subsequently converting it to electrolyte activity via the thermodynamic Gibbs-Duhem equation, which for binary solutions can be written as... 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

Lewis and Randall stated that in dilute solutions the activity coefficient of a strong electrolyte is the same in all solutions of the same ionic strength this statement was confirmed in thermodynamic deductions of activity coefficients. The molality version of 7 can be applied in a fully analogous way and allows a more straightforward treatment of solution properties. [Conversion of molality into molarity requires the solution densities e.g., for a solute of molar mass M and a solution of density q we have... 

Helgeson, H. C. and D. H. Kirkham, 1974, Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures, II. Debye-Hiickel parameters for activity coefficients and relative partial molal properties. American Journal of Science 274, 1199-1261. 

This permits provisional calculation of the compositional dependence of the equilibrium constant and determination of provisional values of the solid phase activity coefficients (discussed below). The equilibrium constant and activity coefficients are termed provisional because it is not possible to determine if stoichiometric saturation has been established without independent knowledge of the compositional dependence of the equilibrium constant, such as would be provided from independent thermodynamic measurements. Using the provisional activity coefficient data we may compare the observed solid solution-aqueous solution compositions with those calculated at equilibrium. Agreement between the calculated and observed values confirms, within the experimental data uncertainties, the establishment of equilibrium. The true solid solution thermodynamic properties are then defined to be equal to the provisional values. 

By examining the compositional dependence of the equilibrium constant, the provisional thermodynamic properties of the solid solutions can be determined. Activity coefficients for solid phase components may be derived from an application of the Gibbs-Duhem equation to the measured compositional dependence of the equilibrium constant in binary solid solutions (10). 

By examining the compositional dependence of the equilibrium constant, the thermodynamic properties of the solid solution can be determined if the final solution is either at equilibrium or stoichiometric saturation. That is, the provisional activities and activity coefficients will be valid if either equilibrium or stoichiometric saturation is attained in the solubility data. 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

Besides the difference in the expressions for activity coefficients and other thermodynamic properties from those published and used by the hydrocarbon processing industries, it is more important to realize the need to describe the ionic and... 

The techniques used in the critical evaluation and correlation of thermodynamic properties of aqueous polyvalent electrolytes are described. The Electrolyte Data Center is engaged in the correlation of activity and osmotic coefficients, enthalpies of dilution and solution, heat capacities, and ionic equilibrium constants for aqueous salt solutions. 

The examples in section 3.1.2 of calculations using stability constants involve concentrations of M, L, and ML . Rigorously, a stability constant, as any thermodynamic equilibrium constant should be defined in terms of standard state conditions (see section 2.4). When the system has the properties of the standard state conditions, the concentrations of the different species are equal to their activities. However, the standard state conditions relate to the ideal states described in Chapter 2, which can almost never be realized experimentally for solutions of electrolytes, particularly with water as the solvent. For any conditions other than those of the standard state, the activities and concentrations are related by the activity coefficients as described in Chapter 2, and especially... 

The thermodynamic properties of snbsnrface aqneons solntions are expressed in terms of a single species solntion activity coefficient for each molecnlar constituent. Its composition, however, shonld be considered on the basis of molecnlar specia-tion in the aqueous solution, which in tnm is related to biological nptake exchange reactions and transport throngh the snbsnrface. 

Verevkin, S.R et al.. Thermodynamic properties of mixtures containing ionic liquids. Vapor pressures and activity coefficients of n-alcohols and benzene in binary mixtures with l-methyl-3-butyl-imidazolium bis(trifluoromethyl-sulfonyl)imide. Fluid Phase Equilib., 236, 222, 2005. 

---