Temperature Dependence of the Parameters in the Pitzer Equations (original) (raw)
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Modeling the heat capacities of aqueous 1-1 electrolyte solutions with Pitzer's equations
1996
Apparent molar heat capacities C p,$ for 71 rare earth chlorides, nitrates, and perchlorates, alkaline earth and transition metal chlorides, nitrates, and perchlorates, and alkali metal carbonates and sulfates have been fitted to the Pitzer equation for heat capacities. The apparent molar heat capacities at infinite dilution C o (equal to the standard partial molar heat capacity, C o , 2 ) were used to evaluate a set of "best" ionic heat capacities, from which improved values of C o ,o for the electrolytes were calculated. These were then used in the Pitzer equation to reevaluate the higher Pitzer coefficients. The Pitzer coefficients so evaluated can express, in most cases, the behavior of C p,o within experimental error from infinite dilution to the upper limit of the data. Ionic heat capacities have been correlated with the absolute entropies of the ions by statistically assigning the ionic heat capacities to obtain the best linear fit.
Industrial & Engineering Chemistry Research, 2002
We have correlated simultaneously experimental data for osmotic and activity coefficients of strong electrolyte solutions using the Pitzer equation and a modification of it. The optimal value for the Pitzer b parameter is different from the traditional value of 1.2 when using higher concentrations in its determination. An analysis of the equation shows that it is possible to reduce the model to a three-parameter form that represents the coefficients at molalities as high as 25 with better accuracy than the model as proposed by Pitzer.
Industrial & Engineering Chemistry Research, 2003
We have predicted the osmotic and activity coefficients of strong electrolyte solutions using a modification of the Pitzer equation. The modified equation can be used for multicomponent aqueous solutions by applying a mixing rule at the Debye-Hü ckel term. We have found that the modification of the Pitzer equation retains the accuracy of the original equation without using any characteristic parameters evaluated from the experimental data. The new equation is predictive and simpler than the original Pitzer equation.
Modeling heat capacities of high valence-type electrolyte solutions with Pitzer's equations
1999
Apparent molar heat capacities C p,$ for 71 rare earth chlorides, nitrates, and perchlorates, alkaline earth and transition metal chlorides, nitrates, and perchlorates, and alkali metal carbonates and sulfates have been fitted to the Pitzer equation for heat capacities. The apparent molar heat capacities at infinite dilution C o (equal to the standard partial molar heat capacity, C o , 2 ) were used to evaluate a set of "best" ionic heat capacities, from which improved values of C o ,o for the electrolytes were calculated. These were then used in the Pitzer equation to reevaluate the higher Pitzer coefficients. The Pitzer coefficients so evaluated can express, in most cases, the behavior of C p,o within experimental error from infinite dilution to the upper limit of the data. Ionic heat capacities have been correlated with the absolute entropies of the ions by statistically assigning the ionic heat capacities to obtain the best linear fit.
Computers & Geosciences, 2016
The thermal and volumetric properties of complex aqueous solutions are described according to the Pitzer equation, explicitly taking into account the speciation in the aqueous solutions. The thermal properties are the apparent relative molar enthalpy () and the apparent molar heat capacity (,). The volumetric property is the apparent molar volume (). Equations describing these properties are obtained from the temperature or pressure derivatives of the excess Gibbs energy and make it possible to calculate the dilution enthalpy (∆H), the heat capacity () and the density (ρ) of aqueous solutions up to high concentrations. Their implementation in PHREEQC V.3 (Parkhurst and Appelo, 2013) is described and has led to a new numerical tool, called PhreeSCALE. It was tested first, using a set of parameters (specific interaction parameters and standard properties) from the literature for two binary systems (Na 2 SO 4-H 2 O and MgSO 4-H 2 O), for the quaternary K-Na-Cl-SO 4 system (heat capacity only) and for the Na-K-Ca-Mg-Cl-SO 4-HCO 3 system (density only). The results obtained with PhreeSCALE are in agreement with the literature data when the same standard solution heat capacity (C 0) and volume (V 0) values are used. For further applications of this improved computation tool, these standard solution properties were calculated independently, using the Helgeson-Kirkham-Flowers (HKF) equations. By using this kind of approach, most of the Pitzer interaction parameters coming from literature become obsolete since they are not coherent with the standard properties calculated according to the HKF formalism. Consequently a new set of interaction parameters must be determined. This approach was successfully applied to the Na 2 SO 4-H 2 O and MgSO 4-H 2 O binary systems, providing a new set of optimized interaction parameters, consistent with the standard solution properties derived from the HKF equations.
Modification of the Pitzer equations for application to electrolyte + polar non-electrolyte mixtures
Journal of Electroanalytical Chemistry, 1994
The fitting of experimental osmotic and activity coefficient values to Pitzer equations requires the use of a large number of adjustable parameters when polar neutral species are present in the system. This is because the Pitzer equations consider the ~ion-neutral and Aneutral_neutra I as constant interaction parameters for the fitting. The modification of the original Pitzer equations, by considering the dependence of these binary interaction parameters concerning the polar neutral components, on both the ionic strength and the neutral species concentration in the system, leads to a considerable improvement in these fittings. To test the applicability of these modified Pitzer equations, they were used to fit several series of data from the literature, related to pure aqueous solutions of different amino acids, or urea, as well as aqueous mixtures of an electrolyte plus an amino acid, or urea.
Journal of Solution Chemistry, 2014
The Pitzer equations have been shown to be very useful in estimating the physical chemical properties of mixed electrolyte solutions like seawater. The equations account for all the ionic interactions occurring in a mixed electrolyte solution. In this paper, the Pitzer equations have been used to estimate the partial molar volumes of ions in 0.725 molÁkg -1 NaCl, which is a near equivalent for average seawater of absolute salinity S A = 35.165 gÁkg -1 . The calculated results at 25°C for a number of cations and anions are in good agreement with the measured values in 0.725 molÁkg -1 NaCl. The estimates in seawater are limited, due to the scarcity of volume data for metal sulfate and bicarbonate salts. The model can now be used to make reasonable estimates of the effect of pressure on equilibria in the oceans and other mixed electrolyte solutions over a wide range of composition, at 25°C, and for some of the major sea salts and the rare earth cations from 0 to 100°C.