Activity coefficients of aqueous species

Let us now assume that, at first approximation, all activity coefficients of aqueous species are 1. Equation 8.91 becomes... 

The EQ3/6 software package consists of several principal components. These are the EQ3NR and EQ6 codes, the EQLIB library, and the thermodynamic ta base. The EQLIB library and the thermodynamic data base support both of the main modeling codes. EQLIB contains math routines, routines that perform various computer system functions, and routines that evaluate scientific submodels, such as for activity coefficients of aqueous species, that are common to both EQ3NR and EQ6. The data base covers a wide range of chemical elements and nominally allows calculations in the temperature range 0-3(X)°C at a constant pressure of 1.013 bar from 0-l()0°C and the steam-liquid water equilibrium pressure from 1(X)-3(X)°C. 

Activity Coefficients of Aqueous Species. The original version of EQ3/6 followed Helgeson et al. (1) in using the "B-dot" equation to describe the activity coefficients of aqueous solutes and a recommended approximation for the activity of water. The "B-dot" equation represents a simple extension of the Debye-Huckel equation and is only useful in relatively dilute solutions (deviations from precise measurements can be seen at ionic strengths below 0.1 molal, and become severe above 1.0 m). Beginning with version 3245, EQ3/6 offers two alternatives, the Davies (40) equation and Pitzer s equations (21,24,20,29). 

In the 3245 version of EQ3/6, the Newton-Raphson algorithm was modified to treat activity coefficients of aqueous species as known constants during a Newton-Raphson step. The... 

One new feature added to SOLMINEQ.88 is the Pitzer method of calculating the activity coefficients of aqueous species as discussed by Kharaka et al. (1987), and detailed in Kharaka et al. 

Ionic strength and thermochemical properties of solid solutions are necessary to be obtained to estimate activity coefficients of aqueous species and components in solid solutions. 

Model a is the constant-capacitance model, which may be used in analogy to the constant ionic medium approach in aqueous chemistry Restriction to one value of high ionic strength (in terms of composition and concentration of the electrolyte) assures constancy of activity coefficients of aqueous species and a model of the sohd-hquid interface, which is sufficiently described by a compact layer. It is assumed that the drop in potential in the inner part of the electric double layer at the high electrolyte concentrations is quite extensive so that the difluse part can be completely neglected. 

Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (2), Pitzer and co-workers (4, ,j5), and" Cruz and Renon (7j, presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. 

Figure 8,12 Salting-out phenomenon for aqueous CO2. Activity coefficient of neutral species increases with increasing salinity, determining decreased solubility of aqueous CO2 in water, T and P conditions being equal. Reprinted from Garrels and Christ (1965), with kind permission from Jones and Bartlett Publishers Inc., copyright 1990.

In the computer program REDEQL2 (and GEOCHEM), the activity coefficients for aqueous species are calculated from the Davies equation. Generally, this equation is used for the computation of activity coefficients of ions in aqueous solutions up to an ionic strength of 0.5 M, even though Dyrssen et al. (21) indicate that this equation can be used for ionic strength up to 1.0 M. 

Equation (5.14) describes the relationship between real (thermodynamic) equilibrium constant and concentrations of the reagents. Equations for activity coefficients of aqueous ionic species as the function of concentrations of all ionic species in solution (at least at ionic strengths up to 0.1 mol dm are well known and generally accepted. It should be emphasized that these equations apply only to the solution species. When E Vy log 7, - log 7, in Eq. (5.14) is constant for each i over the entire data set, one can simply use Eqs. (5.7) and (5,9) to calculate AT, and then calculate using the following relationship... 

Here, mg refers to molality of aqueous species, and moles of solid per kg water for any precipitated minerals. The activity coefficients of all species are computed at each step these are used to check whether any solid phases have become supersaturated by comparing ion activity products with solubility products (as in 19.90). When a phase precipitates, the set of equations is adjusted accordingly, incorporating the new product or reactant. 

We can safely assume that the activity coefficients of the species in the organic phase are constant as they are uncharged and have concentrations that are not changing significantly. Hence only the activity coefficients of the aqueous species are expected to vary with the change in composition of the aqueous phase. The activity coefficients ... 

The user can select different models (Pitzer, Davies, and SIT) for calculating the activity coefficients of aqueous solutions. All of the input data are user-defined. The code can be used just as a calculational tool where all of the inputs are defined and solution equilibria calculated, or as a tool to optimise values of chemical potentials for different species and/or ion-interaction parameters, based on best fits to given experimental data. Multiple data sets of a specific chemical system (e.g., solubility of a sohd phase) in different media can be evaluated simultaneously. 

Theoretical relationships for activity coefficients. The Setschenow equation is used to calculate the activity coefficients of aqueous molecular species in salt solutions. The Pitzer based methods may be used for binary or multicomponent solution activity coefflcient calculations for all species in the solution. 

Eor simplicity, it will be assumed that the ratio of the activity coefficients of the species in the organic phase keeps constant, whereas in the aqueous phases the values of the activity coefficients of the metal ions and hydrogen ions will be calculated using the Debye-Hiickel equation. Therefore, Eqnations (6.2) and (6.3) can be expressed as follows ... 

Figure 1.1 shows chemical equilibrium model of the natural system. Variables which determine the thermochemical feature of this system include temperature, total pressure, activities of dissolved species in aqueous solution (ions, ion pairs, complexes etc.), gaseous fugacity, activities of components in solid phases and dissolved species in aqueous solution where activity of i species, is equal to Yi mj (mi is molality of i species in aqueous solution and mole fractiOTi of i component in solid solution and yi is activity coefficient of i species in aqueous solution and of each component in solid phase). 

Assuming chemical equilibrium between aqueous solution and solid phase at constant temperature and pressure, concentration of dissolved species could be estimated. In order to estimate the concentration the values of other variables (concentration and activity coefficient of each component in solid phase and activity coefficient of dissolved species in aqueous solution) have to be estimated. 

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