Electrolyte Pitzer model

A model of electrolyte solutions which takes into account both electrostatic and specific interactions for individual solutions would be an improvement over the Bates-Guggenheim convention. It is hoped that the Pitzer model of electrolytes [10], which uses a virial... 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

At higher ionic strength values, an additional dependence on [i] is often required to fit the observed solubility data. Alternatively, the Pitzer model can be used with a high degree of accuracy to describe the short-range binary (neutral-neutral, neutral-cation, neutral-anion) and ternary (neutral-neutral-neutral, neutral-cation-anion) interactions between ions and neutral species in single and mixed electrolyte solutions. ... 

Following is a relatively simple calculation using the Pitzer model to compute the activity coefficient of HCOj in seawater. The exercise is based largely on Millero (1983). (See also Harvie et al. 1984 Pitzer 1987). The activity coefficient of a trace cation in NaCl electrolyte solution can be written... 

PABALAN PITZER Models for Aqueous Electrolyte Mixtures... 

The strongest interactions in an electrolyte solution occur between ions of opposite sign. Within the Pitzer model these are accounted for by the B a and Cca functions, which are known for most solutes. The mixing parameters By and /yk, while having relatively small effect in dilute solutions such as seawater, are important in the much more concentrated mixtures typical of the atmospheric aerosol. Further examples of the effects of individual ions on partial pressures can be seen in partial pressure measurements, e.g. (6.50L... 

This work and others (5, 51) have shown how the Pitzer model, together with appropriate Henry s law constants, can be used to calculate the solubility of volatile strong electrolytes in multicomponent solutions. The treatment of NH3 summarized above shows that Pitzer formalism can also be used to describe the solubility of weak and non-electrolytes. We have noted how, for low concentrations of NH3, the Pitzer equations reduce to a series of binary interaction terms similar in form to those of the well known Setchenow equations. However, the thermodynamically based approach constitutes a significant improvement over the use of purely empirical equations to predict individual thermodynamic properties because it is equally applicable to both electrolytes and uncharged species, and provides a unified description of a number of important solution properties. 

The Pitzer model adds a virial expansion to a simplified version of the D-H equation and begins by describing the total excess free energy of an electrolyte solution as... 

The other major contribution to the systematization of our knowledge of aqueous electrolyte solutions at elevated temperatures and pressures takes a completely different approach. This was presented in a series of four papers by H.C. Helgeson and co-workers between 1974 and 1981, with fairly extensive modifications added by Tanger and Helgeson (1988). We present here an outline of this model, with some explanation and comparison with the Pitzer model. We refer to it as the HKF or revised... 

Pitzer electrolytes allows modeling the composition of different water-salt systems in a wide range of temperature with sufficiently high accuracy. In Figure 1.7 calculation results of activities coefficients after Pitzer may be compared with the data of other methods. 

Pitzer developed a semi-empirical model to calculate ( ) (Pitzer, 1973). Using the original Pitzer model, ( ) of a single electrolyte can be calculated by the following equation (see Appendix A for the notation of parameters) ... 

In the following section we discuss the problems of activities of ionic species. Following that we discuss the conventions used to obtain numerical values for the state variables of individual ions, and we discuss the theory underlying the two major approaches to systematizing the data on electrolytes, the HKF and the Pitzer models. Because these are essentially equations of state, we introduced them in Chapter 13 ( 13.6.2 and 13.6.3). 

Nonelectrolyte G mcxlels only account for the short-range interaction among non-charged molecules (—One widely used G model is the Non-Random-Two-Liquid (NRTL) theory developed in 1968. To extend this to electrolyte solutions, it was combined with either the DH or the MSA theory to explicitly account for the Coulomb forces among the ions. Examples for electrolyte models are the electrolyte NRTL (eNRTL) [4] or the Pitzer model [5] which both include the Debye-Hiickel theory. Nasirzadeh et al. [6] used a MSA-NRTL model [7] (combination of NRTL with MSA) as well as an extended Pitzer model of Archer [8] which are excellent models for the description of activity coefficients in electrolyte solutions. Examples for electrolyte G models which were applied to solutions with more than one solvent or more than one solute are a modified Pitzer approach by Ye et al. [9] or the MSA-NRTL by Papaiconomou et al. [7]. However, both groups applied ternary mixture parameters to correlate activity coefficients. Salimi et al. [10] defined concentration-dependent and salt-dependent ion parameters which allows for correlations only but not for predictions or extrapolations. 

Archer DG, Phys J (1991) Modification of the Pitzer Model to Calculate the Mean Activity-Coefficients of Electrolytes In a Water-Alcohol Mixed-Solvent Solution. Thermodynamic properties of the NaBr -l-H20 system. Chem Ref Data 20 509-555... 

Figure 8.3 shows a decision tree to help in the choice for the thermodynamic property model. Besides the four factors mentioned earlier, this decision tree takes into account the polarity of the mixture. Another feature of the mixture considered is the existence of pseudocomponents and the possibility of some of the components being electrolyte. The most common electrolyte methods are the Pitzer model and the electrolyte NRTL. 

The Pitzer model, which successfully describes the volumetric properties of fully dissociated electrolytes over an... 

The Pitzer model includes a modified Debye-Hiickel-like contribution and a virial term to take short range interactions into account. Only two parameters having physical meaning must be adjusted. Accurate results have been obtained for the properties of electrolyte solutions attaining molalities up to 6 moles/kg of solvent. Activity coefficients have been calculated from this model for solutions containing different salts. They have been correctly predicted for solutions of NaCl, KCl and CaCl2 (from [DEM 91]). 

We consider Pitzer s model for the calculation of activity coefficients in aqueous electrolyte solutions (Pitzer, 1991). It is the most widely used thermodynamic model for electrolyte solutions. 

Rard also employed Pitzer s electrolyte activity coefficient model to correlate the data. It was found that the quality of the fit depended on the range of molalities that were used. In particular, the fit was very good when the molalities were less than 3 mol/kg. 

Estimate Pitzer s electrolyte activity coefficient model by minimizing the objective function given by Equation 15.1 and using the following osmotic coefficient data from Rard (1992) given in Table 15.5. First, use the data for molalities less than 3 mol/kg and then all the data together. Compare your estimated values with those reported by Rard (1992). Use a constant value for in Equation 15.1. 

Can the species activity coefficients be calculated accurately An activity coefficient relates each dissolved species concentration to its activity. Most commonly, a modeler uses an extended form of the Debye-Hiickel equation to estimate values for the coefficients. Helgeson (1969) correlated the activity coefficients to this equation for dominantly NaCl solutions having concentrations up to 3 molal. The resulting equations are probably reliable for electrolyte solutions of general composition (i.e., those dominated by salts other than NaCl) where ionic strength is less than about 1 molal (Wolery, 1983 see Chapter 8). Calculated activity coefficients are less reliable in more concentrated solutions. As an alternative to the Debye-Hiickel method, the modeler can use virial equations (the Pitzer equations ) designed to predict activity coefficients for electrolyte brines. These equations have their own limitations, however, as discussed in Chapter 8. 

A very fine example was provided by the extensive use of Professor Pitzer s electrolyte activity coefficient theory within several acid gas phase equilibrium models. 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

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. 

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