Models Pitzer

One of the most widely used activity coefficient models has been proposed by Pitzer in 1973 [6-10]. In principle, it is a series expansion of the Gibbs energy, analogous to the virial equation of state however, unlike to that, it is not directly justified by statistical mechanics. The expression is 

The first term Jll) represents a modified Debye-Hiickel term for the long-range interactions  

The second and the third terms take into account the short-range interactions, where binary and ternary parameters have to be adjusted as a function of the ionic strength. The Gibbs energy refers to the mass of the solvent. 

For the particular functions, several options have been discussed [6, 7). In the finally favored form for practical applications, the ternary interactions are neglected. The activity coefficients are expressed as 

The adjustable parameters are /slj and C. For the other parameters, the standard values are set to 

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Equilibrium constants calculated from the composition of saturated solutions are dependent on the accuracy of the thermodynamic model for the aqueous solution. The thermodynamics of single salt solutions of KC1 or KBr are very well known and have been modeled using the virial approach of Pitzer (13-15). The thermodynamics of aqueous mixtures of KC1 and KBr have also been well studied (16-17) and may be reliably modeled using the Pitzer equations. The Pitzer equations used here to calculate the solid phase equilibrium constants from the compositions of saturated aqueous solutions are given elsewhere (13-15, 18, 19). The Pitzer model parameters applicable to KCl-KBr-l O solutions are summarized in Table II. 

The species concentrations are formulated in activities using the Pitzer model (207) for the aqueous phase and the Hildebrand-Scott solubility parameter (208) for the organic phase. 

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 Pitzer model can be used to obtain activity coefficients for solutes in low (<0.1 mol L ), intermediate (0.1-3.5 mol L ) and high (>3.5 mol L ) ionic strength solutions. The Pitzer equations include terms for binary and ternary interactions between solute species as well as a modified DH expression. The general formula is... 

Although naturally occurring brines and some high ionic strength contaminated waters may require the more complicated expressions developed in the Davies, SIT, or Pitzer models, the use of Equations (3.3)-(3.5) is justified for the ionic strengths of many freshwaters. 

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. ... 

The An(V) model was developed using Np(V) but was not used for other actinides, because none are expected to be present in the +V oxidation state. Although U(VI) may be present, there were insufficient experimental data to develop an An(VI) model for the WIPP, and solubilities for this oxidation state were estimated from literature data rather than using a Pitzer model. 

The Pitzer model requires so-called interaction parameters involving the aqueous species of interest and major species in the water. Such parameters have been measured for major ions, but are often unavailable for trace species, including strong complexes. Sometimes the missing parameters can be reasonably assumed to be equal to those for similar species, however (cf. Langmuir and Melchior 1985). 

Weare (1987) (see also Millero 1983) suggested the following conceptual equation to describe the activity coefficient of an individual ion in the Pitzer model approach... 

Truesdell-Jones model SIT model Pitzer model... 

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... 

At ionic strengths between about 2 and 3.5 mol/kg the high salt concentrations lead to further interaction between anion and cation pairs, but also to important interaction between pairs of ions of the same charge and simultaneously between three ions where two have the same charge. The Pitzer model can accurately account for such effects with a complex series of interaction terms added to a... 

Pitzer model (charge, average size, binary and ternary interactions, ions of opposite and same sign)... 

DH-type, low ionic-strength term. Because the DH-type term lacks an ion size parameter, the Pitzer model is also less accurate than the extended DH equation in dilute solutions. However, a.ssuming the necessary interaction parameters (virial coefficients) have been measured in concentrated salt solutions, the model can accurately model ion activity coefficients and thus mineral solubilities in the most concentrated of brines. 

The Pitzer model could successfully reproduce the solubility in the ternary system Li2Se04-NiSe04-H20. 

PABALAN PITZER Models for Aqueous Electrolyte Mixtures... 

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