Pitzer Formalism Research Articles

Solution thermodynamics of first-row transition elements. 1. Apparent molal volumes of aqueous nickel dichloride nickel diperchlorate cupric chloride and cupric perchlorate from 15 to 55.degree.C

The authors have used a flow densimeter to measure the densities of aqueous solutions of NiCl/sub 2/, Ni(ClO/sub /)/sub 2/, CuCl/sub 2/, and Cu(ClO/sub 4/)/sub 2/ at 10/sup 0/C intervals from 15 to 55/sup 0/C. Infinite dilution apparent molal volumes are determined at each temperature by using the Redlich-Meyer equation. These values are fitted to the polynomial Phi/sub upsilon/ = a + bt + ct/sup 2/. The Pitzer formalism has been used to fit the volume data over the entire concentration range (0-3.5 m).

Modelling chemical equilibria of acid mine-drainage: The FeSO 4-H 2SO 4-H 2O system

Chemical equilibria in the FeSO 4-H 2SO 4-H 2O system have been modelled using the Pitzer formulation for the determination of activity coefficients over the temperature range from 10 to 60°C. The available experimental activity coefficient, enthalpy, heat capacity and mineral solubility data have been analysed to determine the temperature dependencies of the various ion interaction parameters necessary to describe chemical equilibria in this system. In this analysis, the previously published ion interaction parameters in the H 2SO 4-H 2O system have been reevaluated incorporating the higher-order electrostatic terms in the Pitzer formulation to account for asymmetric mixing of ions of dissimilar valence. The combined set of interaction parameters yield an accurate description of equilibria in the FeSO 4-H 2O system over the temperature range of 10 to 90°C and concentration conditions up to the solubility limit of ferrous sulphate hydrate. From an appraisal of solubility data for ferrous sulphate hydrates in water using these parameter expressions, the following relations for the temperature dependence of the solubility products for the heptahydrate (melanterite) and the monohydrate (szomolnokite) phases have been derived: log K sp = 1.447 − 0.004153T − 214949 T 2 Melanterite(FeSO 4·7H 2O) log K sp = 250211 − 0.063405T − 641220 T 2 Szomolnokite(FeSO 4·7H 2O) A comprehensive evaluation of ferrous sulphate hydrate solubility data in sulphuric acid solutions enabled the determination of the various additional parameters needed to describe the mixed system, FeSO 4-H 2SO 4-H 2O. The final model yields an excellent representation of all available mineral solubility data for the combined FeSO 4-H 2SO 4-H 2O system over a temperature range from 10 to 60°C, sulphuric acid concentrations from 0 to 6 molal and for iron sulphate concentrations up to the solubility limit.

Thermodynamics of concentrated electrolyte mixtures. Activity coefficients in aqueous sodium bromide-calcium bromide mixtures at 25.degree.C

The activity coefficients of NaBr and CaBr/sub 2/ in NaBr-CaBr/sub 2/ aqueous mixtures have been measured at 25/sup 0/C over the ranges of ionic strengths 0.1 to 7.5 m. The measurements were made with a dual electrometer amplifier using Na and Ca ion selective electrodes against a Br ion selective electrode. The data were fitted to Harned's equation of the form log ..gamma../sub i/ = log ..gamma../sub i//sup 0/ - ..cap alpha../sub AB/y/sub B/ - ..beta../sub AB/y/sub B//sup 2/ to compute the trace activity coefficients and were also analyzed by using the Pitzer formation. Deviations from the Pitzer formalism were observed for the experimental activity coefficients in this mixture.

Activity coefficients for (hydrogen bromide + calcium bromide + water) at various temperatures. Application of Pitzer's equations

Activity coefficients for HBr in (hydrogen bromide + calcium bromide + water) have been measured at constant total ionic strengths of 0.25, 0.5, 1.0, 2.5, 3.5, 4.0, and 5.0 mol·kg −1. The temperatures covered in this study were 278.15, 283.15, 298.15, 308.15, and 318.15 K. The e.m.f. method using a cell of the type: Pt/H 2(g, p = 101.325 kPa)/HBr( m 1), CaBr 2( m 2)/AgBr(s)/Ag(s) was used. The thermodynamic properties of this asymmetrical mixture including the activity coefficients of calcium bromide in the mixture have been calculated and interpreted in terms of Pitzer's formalism. The Pitzer mixing parameters: Θ H, Ca S and Ψ H, Ca, Br (including higher-order electrostatic effects), and Θ H, Ca and Ψ H, Ca, Br (excluding higher-order effects) as well as the temperature derivatives of the mixing coefficients: ∂Θ H, Ca S ∂T and ∂Ψ H, Ca, Br ∂T , have been estimated. The temperature derivatives of the Pitzer pure-electrolyte parameters for CaBr 2 are also included.

The ionization of boric acid in NaCl, NaCaCl and NaMgCl solutions at 25°C

The stoichiometric pK ★ for the ionization of boric acid has been determined from emf measurements in pure NaCl solution and in NaCl solution with small amounts of added CaCl 2 and MgCl 2 from I = 0.5 to 6.0 molal at 25°C. Our results in NaCl media at low concentrations are in good agreement (±0.01 pK units) with the results of Owen and King (1943). From the values of the pK★ we have determined the Pitzer parameters β 0 , β 1 and C ø for the interactions of Ca 2+ and Mg 2+ with B(OH) 4 −. Ion pairing constants for the interaction of borate ion with Ca 2+ and Mg 2+ were also determined from I = 0.5 to 6 m and values were extrapolated to pure water. These interactions are weak and the pK's in water and in NaCl solution are in reasonable agreement with values of other workers. Pitzer terms (β [MA]Cl 0) for the interaction of [MA] ion pairs with Cl − were also determined. The pK HA ★ data can be fitted within experimental error with one less parameter using the combined ion pairing/Pitzer approach than when using the Pitzer formalism alone. We, thus, favor the combined approach for calculating the ionic interactions in these solutions.

Densities and apparent molar volumes of aqueous NaCl–KBr mixtures at 298.15 K

Experimental differences in densities Δd of aqueous NaCl–KBr mixtures at I = 1, 2, 3, and 4 mol kg−1 and at 298.15 K are reported from pure NaCl to pure KBr solutions. Mean apparent molar volumes [Formula: see text] are calculated and excess volumes of mixing [Formula: see text] are correlated by Friedman equation, Δd and [Formula: see text] are analysed in terms of recently developed the Pitzer formalism without and with mixing terms. Pitzer equations can estimate the densities of such mixtures with uncommon cations and anions within ±0.02% at the high ionic strength of 4 mol kg−1.

Thermodynamics of concentrated electrolyte mixtures. I. Activity coefficients in aqueous NaCl−CaCl2 at 25°C

The activity coefficients of NaCl and CaCl2 in NaCl−CaCl2 aqueous mixtures have been measured at 25°C in the ionic strength range I=0.1–20. Where NaCl solubility permitted, both activity coefficients were measured over the whole range of compositions from pure NaCl to pure CaCl2 at constant I. The measurements were made using Na and Ca ion-selective electrodes vs. a Cl ion-selective electrode. The data are fitted to Harned equations of the form $$log \gamma _A = log \gamma _A^0 - \alpha _{AB} y_B - \beta _{AB} y_B^2$$ and were also analyzed using the Pitzer formalism. Excess free energies of mixing are calculated and presented in the I=0.1–5.0 range and the Friedman parameters calculated.