Dimitri A. Sverjensky

INORGANIC SPECIES IN GEOLOGIC FLUIDS : CORRELATIONS AMONG STANDARD MOLAL THERMODYNAMIC PROPERTIES OF AQUEOUS IONS AND HYDROXIDE COMPLEXES

Correlations among experimentally determined standard partial molal thermodynamic properties of inorganic aqueous species at 25 degrees C and 1 bar allow estimates of these properties for numerous monatomic cations and anions, polyatomic anions, oxyanions, acid oxyanions, neutral oxy-acid species, dissolved gases, and hydroxide complexes of metal cations. Combined with correlations among parameters in the revised Helgeson-Kirkham-Flowers (HKF) equation of state (Shock et al., 1992), these estimates permit predictions of standard partial molal volumes, heat capacities, and entropies, as well as apparent standard partial molal enthalpies and Gibbs free energies of formation to 1000 degrees C and 5 kb for hundreds of inorganic aqueous species of interest in geochemistry. Data and parameters for more than 300 inorganic aqueous species are presented. Close agreement between calculated and experimentally determined equilibrium constants for acid dissociation reactions and cation hydrolysis reactions supports the generality and validity of these predictive methods. These data facilitate the calculation of the speciation of major, minor, and trace elements in hydrothermal and metamorphic fluids throughout most of the crust of the Earth.

Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Standard partial molal properties of inorganic neutral species

The standard partial moial properties of organic aqueous species at high pressures and temperatures can be predicted using an adaptation of a revised equation of state for inorganic aqueous ions and electrolytes ( TANGER and HELGESON, 1988), together with correlations among equation of state parameters (SHOCK and HELGESON, 1988). These correlations include a charge-dependent relation between Born coefficients and the standard partial molal entropies of aqueous species at 25 “C and 1 bar (SHOCK et al., 1989). Thermodynamic calculations indicate that in the liquid phase the standard partial molal volumes ( 8’), heat capacities (C?“,), and entropies (SO), as well as the apparent standard partial molal enthalpies of formation (4A”) of aqueous electrolytes with organic anions maximize with increasing temperature at PSAT* and approach -co at the critical point of H20. In contrast, the corresponding properties of neutral organic aqueous species in the liquid phase minimize with increasing temperature PSAT and approach co at the critical point of H20. Predicted equilibrium constants for alkane solubilities and carboxylic acid dissociation reactions at elevated pressures and temperatures are in close agreement with experimental data reported in the literature, which supports the validity and generality of the equations of state as well as the predictive algorithms used in the calculations. As a consequence, high temperature/ pressure standard partial molal properties, as well as equilibrium constants and other reaction properties, can be predicted for reactions involving a wide variety of organic aqueous species for which little or no experimental data are available at temperatures > 25°C. Present capabilities permit such predictions to be made for hvdrothermal and magmatic conditions at pressures and temperatures as high as 5 kb and 1000°C. d

Prediction of the thermodynamic properties of aqueous metal complexes to 1000°C and 5 kb

A large number of aqueous metal complexes contribute significantly to hydrothermal, metamorphic, and magmatic processes in the crust of the Earth. Nevertheless, relatively few thermodynamic data other than dissociation constants (K) for a few dozen of these complexes have been determined experimentally at elevated temperatures and pressures. The calculations summarized below are intended to supplement these experimental data by providing interim predictions of the thermodynamic properties of supercritical aqueous metal complexes using the revised HKF (Helgeson et al., 1981) equations of state for aqueous species (Tanger and Helgeson, 1988; Shock et al., 1992) and correlations among equations of state parameters and standard partial molal properties at 25°C and 1 bar (Shock and Helgeson, 1988, 1990; Shock et al., 1989). These equations and correlations permit retrieval of the conventional standard partial molal entropies (S0), volumes (V0), and heat capacities (CP0) of aqueous metal complexes at 25°C and 1 bar from published values of log K in the supercritical region and the limited number of experimental dissociation constants available in the literature over relatively short ranges of elevated temperature at PSAT (PSAT and SAT are used in the present communication to refer to pressures corresponding to liquid-vapor equilibrium for the system H2O, except at temperatures <100°C, where they refer to the reference pressure of 1 bar). The standard partial molal properties computed in this way can then be used to generate corresponding values of ΔS0, ΔV0, and ΔCP0 of association, which for similar complexes correlate linearly with S0, V0 and CP0, respectively, of the constituent cations and ligands at 25°C and 1 bar. Generalizing these correlations and combining them with the equations of state permits prediction of the temperature and pressure dependence of log K and other thermodynamic properties of a large number of aqueous metal complexes. As a consequence, it is possible to retrieve values of log K at 25°C and 1 bar from the results of hydrothermal experiments at higher temperatures and pressures or to predict values of log K at hydrothermal conditions when no experimental data are available at temperatures and pressures above 25°C and l bar. Such predictions can be made for temperatures and pressures from 0°C and 1 bar to 1000°C and 5000 bars.

Calculation of the thermodynamic properties of aqueous species at high pressures and temperatures. Effective electrostatic radii, dissociation constants and standard partial molal properties to 1000 °C and 5 kbar

Within the framework of the revised HKF (H. C. Helgeson, D. H. Kirkham and G. C. Flowers, Am. J. Sci., 1981, 281, 1249) equations of state (J. C. Tanger IV and H. C. Helgeson, Am. J. Sci., 1988, 288, 19), prediction of the standard partial molal thermodynamic properties of aqueous ions and electrolytes at high pressures and temperatures requires values of the effective electrostatic radii of the ions (re), as well as provision for the temperature and pressure dependence of the relative permittivity of the solvent, H2O. Values of the relative permittivity of H2O, together with the Born functions needed to compute the standard partial molal Gibbs free energy, enthalpy, entropy, heat capacity and volume of solvation were calculated as a function of temperature and density from a modified version of the Uematsu–Franck equation (M. Uematsu and E. U. Franck, J. Phys. Chem. Ref. Data, 1980, 9, 1291). The temperature/pressure dependence of re is described in terms of a solvent function designated by g, which was evaluated in the present study at temperatures and pressures to 1000 °C and 5 kbar by regressing experimental standard partial molal heat capacities and volumes of NaCl reported in the literature together with published dissociation constants for NaClo at supercritical temperatures and pressures using the revised HKF equations of state for aqueous species. The calculated values of re decrease substantially with increasing temperature at constant pressure ⩽2 kbar, and with decreasing pressure at constant temperature 400 °C. The equations and parameters summarized below permit calculation of the standard partial molal properties of aqueous species from the revised HKF equations of state over a much more extensive range of temperature than was previously possible.

Partitioning of F-Cl-OH between minerals and hydrothermal fluids

Abstract A thermodynamic analysis of F-Cl-OH partitioning between minerals and hydrothermal fluids has resulted in the retrieval of standard-state Gibbs free energies for fluormuscovite, fluorphlogopite, fluorannite, fluortremolite, fluortalc, hydroxyapatite, fluorapatite, chlorapatite, and chlorannite from hydrothermal experimental studies. Standard-state entropies, heat capacities, and volumes are either derived from experimental studies or estimated following Helgeson et al. (1978). The derived thermodynamic properties are internally consistent and consistent with the thermodynamic properties of minerals and aqueous species from Berman (1988, 1990), Sverjensky et al. (1991a), Shock and Helgeson (1988), and Shock et al. (1989), and therefore can be extrapolated over a wide range of temperatures and pressures for application to geochemistry, igneous and metamorphic petrology, and ore deposits. The derived standard-state thermodynamic properties for F and Cl endmember phases provide a basis for predicting the fluoride and chloride concentrations of former aqueous fluids from the measured F and Cl concentrations in minerals. Speciation and solubility calculations simulating F and Cl partitioning between minerals and hydrothermal fluids in the systems Na 2 O-K 2 OAl 2 O 3 -SiO 2 -HF-H 2 O and Na 2 O-K 2 O-Al 2 O 3 -SiO 2 -HCl-H 2 O, and systems containing apatites, show that the partitioning is a strong function of temperature, pressure, and fluid composition. Increase of temperature favors partitioning of F into fluids with respect to minerals, while it favors partitioning of Cl into annite. The decrease of both pressure and pH of fluids favors partitioning of Cl into annite with respect to fluids. In addition to predicting fluoride and chloride concentrations in hydrothermal fluids, the results of this study enable mass transfer calculations including both F-C1-OH partitioning and metal complexing of halides during water-rock interactions in a variety of geological systems.

Zero-point-of-charge prediction from crystal chemistry and solvation theory

Abstract The pristine point of zero charge (pHPPZC) is a property of each solid in water that is widely used in the interpretation of adsorption processes and dissolution rates. Considerable effort has gone into attempting to calculate the pHPPZC values of oxides and silicates based on crystal chemistry and electrostatic models of the interaction between protons and OH surface groups. However, substantial discrepancies remain between calculated and measured values of the pHPPZC even for simple oxides such as quartz. This implies that the widespread use of real and fictive components (e.g., SiIVO2 and Al2IVO3) to interpret the surface characteristics of silicates is unwarranted. In the present paper, I show that by adding electrostatic solvation theory to crystal chemical and electrostatic models, the differences between pHPPZC values of crystalline solids can be accurately quantified. The new model sums free energy contributions associated with proton solvation, electrostatic repulsion of protons by cations underlying the surface, and electrostatic attraction of protons by oxygen anions near the surface. It results in a theoretical dependence of the pHPPZC on the dielectric constant of the kth solid (ϵk) and the ratio of the Pauling electrostatic bond strength to the cation-hydroxyl bond length ( s r M-OH ), according to the equation pH PPZC = − 0.5( ΔΩ r 2.303RT )( 1 ϵ k ) − B( s r M-OH ) + log K H + ″ , in which ΔΩ r , B, and KH+″ are constants. This relationship describes the pHPPZC values of oxides and silicates to better than ±0.5 and enables prediction of surface protonation reactions from the properties of the underlying crystal structure alone. These results suggest that the bonding of protons at the crystal-water interface is more analogous to the bonding in the bulk crystal structure than to the bonding in analogous aqueous complexes emphasized in other studies.

Thermodynamic assessment of hydrothermal alkali feldspar-mica-aluminosilicate equilibria

The thermodynamic properties of minerals retrieved from consideration of solid-solid and dehydration equilibria with calorimetric reference values, and those of aqueous species derived from studies of electrolytes, are not consistent with experimentally measured high-temperature solubilities in the systems K2O- and Na2O-Al2O3-SiO2-H2O-HCl (e.g., K-fs — Ms — Qtz — K+ — H+). This introduces major inaccuracies into the computation of ionic activity ratios and the acidities of diagenetic, metamorphic, and magmatic hydrothermal fluids buffered by alkali silicate-bearing assemblages. We report a thermodynamic analysis of revised solubility equilibria in these systems that integrates the thermodynamic properties of minerals obtained from phase equilibria studies (Berman, 1988) with the properties of aqueous species calculated from a calibrated equation of state (Shock and Helgeson, 1988). This was achieved in two separate steps. First, new values of the free energies and enthalpies of formation at 25°C and 1 bar for the alkali silicates muscovite and albite were retrieved from the experimental solubility equilibria at 300°C and Psat. Because the latter have stoichiometric reaction coefficients different from those for solid-solid and dehydration equilibria, our procedure preserves exactly the relative thermodynamic properties of the alkali-bearing silicates (Berman, 1988). Only simple arithmetic adjustments of −1,600 and −1,626 (±500) cal/mol to all the K- and Na-bearing silicates, respectively, in Berman (1988) are required. In all cases, the revised values are within ±0.2% of calorimetric values. Similar adjustments were derived for the properties of minerals from Helgeson et al. (1978). Second, new values of the dissociation constant of HCl were retrieved from the solubility equilibria at temperatures and pressures from 300–600°C and 0.5–2.0 kbars using a simple model for aqueous speciation. The results agree well with the conductance-derived dissociation constants from Franck (1956a,b) for temperatures from 300–550°C. Compared to the conductance-derived results of Frantz and Marshall (1984), our dissociation constants agree well at the highest densities, but are greater at lower densities. At the lowest density, at 600°C and 1 kbar, the discrepancy of 0.9 log units is within the overall uncertainties associated with our experimental results and those associated with deriving dissociation constants from conductance measurements in highly associated solutions (Oelkers and Helgeson, 1988). Finally, we also report an equation of state fit to the standard thermodynamic properties of the aqueous HCl molecule that is consistent with a wide array of independently determined dissociation constants of HCl and permits interpolation and extrapolation of the dissociation constant of HCl to 1000°C and 5.0 kbars.

Evaluation of internally consistent parameters for the triple-layer model by the systematic analysis of oxide surface titration data

Systematic analysis of surface titration data from the literature has been performed for ten oxides (anatase, hematite, goethite, rutile, amorphous silica, quartz, magnetite, δ-MnO2, corundum, and γ-alumina) in ten electrolytes (LiNo3, NaNO3, KNO3, CsNO3, LiCl, NaCl, KCl, CsCl, NaI, and NaClO4) over a wide range of ionic strengths (0.001 M–2.9 M) to establish adsorption equilibrium constants and capacitances consistent with the triple-layer model of surface complexation. Experimental data for the same mineral in different electrolytes and data for a given mineral/ electrolyte system from various investigators have been compared. In this analysis, the surface protonation constants (K,, and Ks,2) were calculated by combining predicted values of ΔpK(log Ks,2 − log Ks,1) (Sverjensky and Sahai, 1996) with experimental points of zero charge; site-densities were obtained from tritium-exchange experiments reported in the literature, and the outer-layer capacitance (C2) was set at 0.2 F·m−2. This scheme permitted us to retrieve consistent sets of values for the inner layer capacitance (C1), and for the electrolyte adsorption constants (Ks,L− and Ks,M+) corresponding, respectively, to the equilibria >SOH2+ + Laq− = >SOH2+ − L− and >SO− + Maq+ = >SO− − M+ Aqueous activity coefficients were calculated using the extended Debye-Huckel equation (Helgeson et al., 1981), which is valid to high ionic strengths (>0.5 M). Systematic analysis of the data reveals important trends and differences between triple-layer model predictions and experimental data and between data for the same mineral/ electrolyte from different investigators. Furthermore, the analysis yields an internally consistent set of triple-layer parameters which will be used in developing a predictive model for electrolyte adsorption based on Born solvation and electrostatic theory (Sahai and Sverjensky, 1997a).

F-Cl-OH partitioning between biotite and apatite

Abstract An assessment of F-C1-OH partitioning between natural apatite and biotite in a variety of rocks was used to evaluate reciprocal (Mg, Fe2+, AlVI) (F, Cl, OH) mixing properties for biotite according to the reciprocal salt solution model of Wood and Nicholls (1978). Ideal mixing of F-C1-OH and Fe-Mg-Al VI in the hydroxyl and octahedral sites is assumed for biotites with dilute Cl concentrations. The reciprocal interaction parameters, in terms of Gibbs free energies, for the reactions KMg3[AlSi3O10](OH)2 + KFe3[AlSi3O10](F)2 = KMg3[AlSi3O10](F)2 + KFe3[AlSi3O10](OH)2 Phl Fann Fphl Ann and KMg3[AlSi3O10](Cl)2 + KFe3[AlSi3O10](OH)2 = KMg3[AlSi3O10](OH)2 + KFe3[AlSi3O10] (Cl)2 Clphl Ann Phl Clann are about −10 kcal/mol and −4.5 kcal/mol, respectively. These mixing properties are consistent with standard state thermodynamic properties for F and Cl endmember phases from Zhu and Sverjensky (1991). The approach of studying F-C1-OH partitioning between biotite and apatite permits distinguishing the reciprocal effects from the effects of temperature, pressure, and fluid composition. The resultant mixing properties are consistent with observations both in hydrothermal experiments and in natural mineral assemblages. The mixing properties presented in this study enable us now to predict F and Cl concentrations of hydrothermal fluids from the measured F and Cl concentrations in biotite with variable Fe-Mg-AlVI proportions. A case study of the Santa Rita porphyry copper deposits, New Mexico, shows that hydrothermal fluids responsible for the phyllic alteration had a salinity about 3 molal Cl−, in agreement with fluid inclusion studies. Our internally consistent standard thermodynamic properties and solid solution models also lead to recalibration of the apatite-biotite geothermometer. The revised geothermometer predicts temperatures that agree with those estimated from other independent geothermometers. The large reciprocal effects in biotite also point out the need to revise other geothermometers using biotite and to revise the ideal mixing model for biotite in petrologic studies.

Solvation and electrostatic model for specific electrolyte adsorption

A solvation and electrostatic model has been developed for estimating electrolyte adsorption from physical and chemical properties of the system, consistent with the triple-layer model. The model is calibrated on experimental surface titration data for ten oxides and hydroxides in ten electrolytes over a range of ionic strengths from 0.001 M-2.9 M (Sahai and Sverjensky, 1997a). The model assumes the presence of a single type of surface site, >SOH. It is proposed that for a 1:1 electrolyte of the type M+L−, the logarithms of the adsorption constants (Ks,M+and Ks,L−) representing the equilibria >SO− + Maq+ = >SO− − M+and>SOH2+ + Laq− = >SOH2+ − L− contain contributions from an ion-intrinsic component and a solvation component. According to Born solvation theory, log Ks,M+ and log Ks, L− can be linearly correlated with inverse dielectric constant of the k-th mineral (1ϵk) resulting in the equations log Ks,M+ = − δωM+2.303RT1ϵk + log Kii,M+″and log Ks,L− = − δωL−2.303RT1ϵk + log Kii,L+″ The ion-intrinsic part (log Kii″) is a linear function of the inverse electrostatic radius (1re,j) of the j-th aqueous ion, where, in general, j = M+ or L−. The interfacial solvation coefficient (Δ, Ωj) associated with the solvation component is linearly related to the inverse effective radius (1Re,j) of the adsorbed ion and to the charge (Zj) on the ion. The model is consistent with surface protonation constants (Ks,1and Ks,2) calculated from experimental points of zero charge and values of ΔpK predicted from the Pauling bond-strength per unit bond-length (sr>S−OH) of the bulk mineral (Sahai and Sverjensky, 1997a), site-densities (Ns) from isotopic-exchange data, and outer-layer capacitance (C2) equal to 0.2 F m−2. As a first approximation, we also find an empirical trend between capacitance (C1) of the inner-layer and 1(re,ML·ωML) where re,ML is the electrostatic radius and ωML is the solvation coefficient of the aqueous electrolyte. Taken together, these correlations enable the calculation of surface protonation and electrolyte adsorption at equilibrium from the properties of the mineral/ solution system.