Thermodynamic Properties Of Aqueous Species Research Articles

Optimized thermodynamic properties of REE aqueous species (REE3+ and REEOH2+) and experimental database for modeling the solubility of REE phosphate minerals (monazite, xenotime, and rhabdophane) from 25 to 300 °C

Rare earth elements (REE) are critical elements found in monazite, xenotime, and hydrated REE phosphates which typically form in hydrothermal mineral deposits. Accurate predictions of the solubility of these REE phosphates and the speciation of REE in aqueous fluids are both key to understanding the controls on the transport, fractionation, and deposition of REE in natural systems. Previous monazite and xenotime solubility experiments indicate the presence of large discrepancies between experimentally derived solubility constants versus calculated solubilities by combining different data sources for the thermodynamic properties of minerals and aqueous species at hydrothermal conditions. In this study, these discrepancies were resolved by using the program GEMSFITS to optimize the standard partial molal Gibbs energy of formation (ΔfG°298) of REE aqueous species (REE3+ and REE hydroxyl complexes) at 298.15 K and 1 bar while keeping the thermodynamic properties fixed for the REE phosphates. A comprehensive experimental database was compiled using solubility data available between 25 and 300 °C. The latter permits conducting thermodynamic parameter optimization of ΔfG°298 for REE aqueous species. Optimal matching of the rhabdophane solubility data between 25 and 100 °C requires modifying the ΔfG°298 values of REE3+ by 1–6 kJ/mol, whereas matching of the monazite solubility data between 100 and 300 °C requires modifying the ΔfG°298 values of both REE3+ and REEOH2+ by ~15–31 kJ/mol and ~ 2–10 kJ/mol, respectively. For xenotime, adjustments of ΔfG°298 values by 1–26 kJ/mol are only necessary for the REE3+ species. The optimizations indicate that the solubility of monazite in acidic solutions is controlled by the light (L)REE3+ species at <150 °C and the LREEOH2+ species at >150 °C, whereas the solubility of xenotime is controlled by the heavy (H)REE3+ species between 25 and 300 °C. Based on the optimization results, we conclude that the revised Helgeson-Kirkham-Flowers equation of state does not reliably predict the thermodynamic properties of REE3+, REEOH2+, and likely other REE hydroxyl species at hydrothermal conditions. We therefore provide an experimental database (ThermoExp_REE) as a basic framework for future updates, extensions with other ligands, and optimizations as new experimental REE data become available. The optimized thermodynamic properties of aqueous species and minerals are available open access to accurately predict the solubility of REE phosphates in fluid-rock systems.

PyGeochemCalc: A Python package for geochemical thermodynamic calculations from ambient to deep Earth conditions

Over the past half century, techniques for evaluating the thermodynamics of water-rock interactions from ambient to deep Earth conditions have advanced incredibly and in myriad directions. As these tools for analyzing the thermodynamic states of geochemical species as a function of temperature, pressure, and composition have multiplied, so too have the possibilities for tracing water-rock interaction from ambient to deep conditions on Earth and beyond. Yet, the aqueous geochemical community still lacks a centralized platform for incorporating this constantly updating thermodynamic data into aqueous geochemical models. Here, we introduce PyGeochemCalc (PyGCC), a community-driven, open-source Python package that meets this need by providing a consolidated set of functions for calculating the thermodynamic properties of gas, aqueous, and mineral (including solid solutions and variable-formula clays) species, as well as reactions amongst these species, over a broad range of temperature and pressure conditions. The PyGCC package utilizes the revised Helgeson-Kirkham-Flowers (HKF) equation of state, and newly proposed density-based extrapolations based upon it, to calculate the thermodynamic properties of aqueous species; a choice of equations of state and electrostatic models (including the Deep Earth Water (DEW) model) to calculate thermodynamic and dielectric properties of water; and heat capacity functions to calculate thermodynamic properties of minerals and gases. Additionally, PyGCC integrates these functions to generate thermodynamic databases for various geochemical programs, including the Geochemist's Workbench (GWB), EQ3/6, TOUGHREACT, and PFLOTRAN, with straightforward possibilities for extension to other simulators. The various functions in the package can also be modularly utilized, and introduced into other modeling tools, as desired. In this paper, we detail the capabilities of PyGCC and the equations it relies on for calculating thermodynamic properties of water, aqueous species, and gases. Although the fundamental thermodynamic data necessary for state-of-the-science PyGCC calculations will necessarily evolve as our collective geochemical knowledge base expands, PyGCC's open source, community-driven design will allow for users to keep pace via rapid implementation of these advancements in this modern geochemical tool.

Thermodynamic Properties of Aqueous Species Calculated Using the HKF Model: How Do Different Thermodynamic and Electrostatic Models for Solvent Water Affect Calculated Aqueous Properties?

Thermodynamic properties of aqueous species are essential for modeling of fluid-rock interaction processes. The Helgeson-Kirkham-Flowers (HKF) model is widely used for calculating standard state thermodynamic properties of ions and complexes over a wide range of temperatures and pressures. To do this, the HKF model requires thermodynamic and electrostatic models of water solvent. In this study, we investigate and quantify the impact of choosing different models for calculating water solvent volumetric and dielectric properties, on the properties of aqueous species calculated using the HKF model. We identify temperature and pressure conditions at which the choice of different models can have a considerable effect on the properties of aqueous species and on fluid mineral equilibrium calculations. The investigated temperature and pressure intervals are 25–1000°C and 1–5 kbar, representative of upper to middle crustal levels, and of interest for modeling ore-forming processes. The thermodynamic and electrostatic models for water solvent considered are: Haar, Gallagher and Kell (1984), Wagner and Pruß (2002), and Zhang and Duan (2005), to calculate water volumetric properties, and Johnson and Norton (1991), Fernandez and others (1997), and Sverjensky and others (2014), to calculate water dielectric properties. We observe only small discrepancies in the calculated standard partial molal properties of aqueous species resulting from using different water thermodynamic models. However, large differences in the properties of charged species can be observed at higher temperatures (above 500°C) as a result of using different electrostatic models. Depending on the aqueous speciation and the reactions that control the chemical composition, the observed differences can vary. The discrepancy between various electrostatic models is attributed to the scarcity of experimental data at high temperatures. These discrepancies restrict the reliability of the geochemical modeling of hydrothermal and ore formation processes, and the retrieval of thermodynamic parameters from experimental data at elevated temperatures and pressures.

A suite of programs, OptimA, OptimB, OptimC, and OptimS compatible with the Unitherm database, for deriving the thermodynamic properties of aqueous species from solubility, potentiometry and spectroscopy measurements

This paper describes four programs for Windows, designed to obtain the thermodynamic properties of aqueous species from experimental data and reporting them in the Unitherm database format (HCh software package). Programs OptimA and OptimS allow users to derive the standard Gibbs free energies of aqueous species from the results of chemical experiments (e.g., potentiometry or solubility) and from ultraviolet–visible (UV–Vis) absorption spectra, respectively; programs OptimB and OptimC enable optimization of the parameters of the revised Helgeson–Kirkham–Flowers equation of state and the modified Ryzhenko–Bryzgalin electrostatic model, respectively, for an aqueous species from its standard Gibbs free energy or stability constant as a function of temperature and pressure.

Thermodynamic description of Np(VI) solubility, hydrolysis, and redox behavior in dilute to concentrated alkaline NaCl solutions

The solubility of Np(VI) was investigated in carbonate-free NaCl solutions (0.1 M &amp;le; I &amp;le; 5.0 M) at T = 22 &amp;plusmn; 2 &amp;deg;C to derive thermodynamic properties of aqueous species and solid compounds formed under alkaline conditions. The experimentally derived solubility curves can be divided into four main regions: (I) ~7 &amp;le; pHm &amp;le; ~9, showing a steep decrease in Np solubility with a slope (log [Np] vs. pHm) of &amp;ndash;3 or &amp;ndash;2 (depending on NaCl concentration); (II) ~9 &amp;le; pHm &amp;le; ~10.5, with a nearly pH-independent [Np]; (III) ~10.5 &amp;le; pHm &amp;le; ~13.5, showing an increase in the solubility with a well-defined slope of +1. A region (IV) with a slope &amp;ge; +2 was only observed at I &amp;ge; 1.0 M NaCl and pHm &amp;ge; ~13.5. The solubility-controlling solid Np phases were characterized by X-ray diffraction (XRD), quantitative chemical analysis, thermogravimetric analysis and scanning electron microscopy-energy-dispersive spectrometry (SEM-EDS), confirming the presence of anhydrous Na2Np2O7(cr) in regions II and III. The same solid phase was identified in region I except for the system in 0.1 M NaCl, where a NpO2(OH)2&amp;middot;H2O(cr) phase predominates. XRD patterns of this solid phase show a very good agreement with that of metaschoepite (UO3&amp;middot;2H2O), highlighting the similarities between Np(VI) and U(VI) with respect to solid phase formation and structure. Based on the analysis of solubility data, solid phase characterization and chemical analogy with U(VI), the equilibrium reactions 0.5 Na2Np2O7(cr) + 1.5 H2O ⬄ Na+ + NpO2(OH)3 &amp;ndash; and 0.5 Na2Np2O7(cr) + 2.5 H2O ⬄ Na+ + NpO2(OH)4 2&amp;ndash; + H+ were identified as controlling Np(VI) solubility in regions II and III, respectively. The predominance of NpO2 + in the aqueous phase of region I (quantified by UV&amp;ndash;vis/NIR) indicates the reductive dissolution of Np(VI) [either as Na2Np2O7(cr) or NpO2(OH)2&amp;middot;H2O(cr)] to Np(V)aq. Oxidation to Np(VII) can explain the experimental observations in region IV, although it is not included in the chemical and thermodynamic models derived. The conditional equilibrium constants determined from the solubility experiments at different ionic strengths were evaluated with both the specific ion interaction theory (SIT) and Pitzer approaches. Thermodynamic data for aqueous Np(VI) species [NpO2(OH)3 &amp;ndash; and NpO2(OH)4 2&amp;ndash;] and solid compounds [Na2Np2O7(cr) and NpO2(OH)2&amp;middot;H2O(cr)] that are relevant under alkaline conditions were derived. These data are not currently included in the Nuclear Energy Agency-Thermochemical Database (NEA-TDB) compilation.

Chemical modeling of high temperature aqueous processes

Chemical modeling is a very powerful tool to predict and understand the behavior of complex aqueous processing systems. Equally powerful is the educational aspect associated with building such models. In recent years, chemical modeling has undergone tremendous development. The new capabilities of various software have changed the way engineers simulate aqueous solutions in hydrometallurgical processes. This paper presents new developments and strategies to model the chemistry of high temperature aqueous processing systems. The acid pressure leach of nickeliferous laterites is used as an example. In this work, calculation of standard thermodynamic properties of aqueous species was performed with the revised Helgeson-Kirkham-Flowers (HKF) model as well as with the Density model. Nonidealities, including weak ion-pair formations, were treated through the Bromley-Zemaitis ion interaction method. The above models were implemented through the OLI-Systems® commercial software. Monometallic sulphate solutions like Al 2(SO 4) 3–H 2SO 4, MgSO 4–H 2SO 4, NiSO 4–H 2SO 4, Fe 2O 3–H 2SO 4 were used to fit new thermodynamic parameters which were verified on progressively more complex solution mixtures. Finally, simulation results of laterite leach solutions were compared with available experimental data and very good agreement was found.

Thermodynamic properties of solutions in metastable systems under negative or positive pressures

Metastable systems are created when the interface between the atmosphere (in which P atm = 1 bar) and water forms a spherical meniscus either concave toward the air (water filling capillaries, wherein P water < P atm) or convex toward the air (fog water droplet, wherein P water > P atm). Soil water, undergoing negative pressure (“capillary potential”) remains bound to the solid matrix (instead of flowing downward) by the capillary meniscus, concave toward the undersaturated dry atmosphere. The positive counterpart of tensile water in soils is the pressurized water contained in fine droplets suspended in oversaturated humid air, as in clouds. All these systems are anisobaric domains the phases of which have different pressures. Geochemical consequences of such characteristics are assessed here by calculating the consequences of the positive or negative water potential on the equilibrium constants of reactions taking place in stretched or pressurized aqueous solutions. Thermodynamic properties of aqueous species are obtained by using the TH model, used explicitly for positive pressures but extrapolated to negative ones for soil solutions. It appears that soil water dissolves gases, offering an alternative explanation of the observed enrichment of atmospheric noble gases in groundwater and of carbonic gas in the unsaturated zone below the root zone. Water droplets obviously show the opposite behavior, that is, a decreasing dissolutive capability with decreasing droplet size (water pressure increases), inducing some climatic consequences. An application of this approach to the solid-solution equilibria is performed by comparing experimental solubility of amorphous silica in unsaturated media on the one hand, to theoretical calculations taking account of the negative water pressure on the other hand. This comparison outlines the potential complexity of anisobaric situations in nature and the necessity to develop a suitable approach for solid pressure.

Aqueous high-temperature solubility studies. II. The solubility of boehmite at 0.03 m ionic strength as a function of temperature and pH as determined by in situ measurements

The solubility of pure synthetic boehmite (γ-AlOOH) has been measured over a wide range of pH (2–10, depending on temperature), and temperature (100–290°C) at 0.03 mol · kg −1 ionic strength (NaCl) in a hydrogen-electrode concentration cell (HECC), which provided continuous in situ measurement of hydrogen ion molality (Palmer et al. 2001). A least-squares regression of the results obtained was used to determine the molal solubility quotients (Q s0 to Q s4) of boehmite. The solubility products (Q sn) were extrapolated to infinite dilution (K sn), permitting calculation of the thermodynamic properties of aqueous species of aluminum for comparison with previous works, such as Bourcier et al. (1993) and Castet et al. (1993). These results are generally consistent with the latter study conducted near infinite dilution, although some significant differences are apparent, particularly near the solubility minimum.

Dissolution of primary minerals of basalt in natural waters: I. Calculation of mineral solubilities from 0°C to 350°C

The solubilities of forsterite, fayalite, enstatite, ferrosilite, hedenbergite, diopside, anorthite, high-albite, magnetite, hematite, ulvöspinel, ilmenite, F-apatite and OH-apatite and olivine, plagioclase, orthopyroxene, clinopyroxene and Fe–Ti oxide solid solutions of fixed composition were calculated in the temperature range 0–350°C at saturated water vapour pressure. The thermodynamic database used for end-member minerals was that of Robie and Hemingway [Robie, R.A., Hemingway, B.S., 1995. Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressures and at higher temperatures. U.S. Geol. Surv. Bull. 2131, 461 pp.] except for plagioclases [Arnórsson, S., Stefánsson, A., 1999. Assessment of feldspar solubility constants in water in the range of 0° to 350°C at vapor saturation pressures. Am. J. Sci. 299, 173–209.] and that of Shock and Helgeson [Shock, E.L., Helgeson, H.C., 1988. Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: correlation algorithms for ionic species and equation-of-state predictions to 5 kb and 1000°C. Geochim. Cosmochim. Acta 53, 2009–2036.] and Shock et al. [Shock, E.L., Oelkers, E.H., Johnson, J.W., Sverjensky, D.A., Helgeson, H.C., 1992. 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. J. Chem. Soc., Faraday Trans. 88, 803–826.] for most aqueous species. For aqueous Fe(OH) 4 − and Al(OH) 4 −, the thermodynamic properties reported by Diakonov et al. and Pokrovskii and Helgeson [Pokrovskii, V.A., Helgeson, H.C., 1995. Thermodynamic properties of aqueous species and the solubilities of minerals at high pressures and temperatures: the system Al 2O 3–H 2O–NaCl. Am. J. Sci. 295, 1255–1342], respectively, were used. In the present study, the standard partial molal properties and the HKF equation-of-state parameters for aqueous H 4SiO 4 0 were revised to better describe the recent experimental results at low temperatures. For H 4SiO 4 0, the new parameters are also consistent with quartz solubility experiments up to 900°C and 5 kbar. Further, the HKF equation-of-state parameters for aqueous Ti(OH) 4 0 were estimated from rutile solubility [Ziemniak, S.E., Jones, M.E., Combs, K.E.S., 1993. Solubility behaviour of titanium (IV) oxide in alkaline media at elevated temperatures. J. Sol. Chem. 22, 601–623.], which enables the calculations of the solubility of Ti-bearing minerals at elevated temperatures and pressures. Much higher solubilities were found for the silicate minerals below 100°C than previously reported, which is related to higher quartz solubility at low temperature and correspondingly new data on the thermodynamic properties of H 4SiO 4 0. The present results are particularly important for the stabilities of primary basaltic minerals of natural composition under weathering conditions. They are also of importance for the study of equilibrium/dis-equilibrium conditions in active geothermal systems.

A new equation of state for correlation and prediction of standard molal thermodynamic properties of aqueous species at high temperatures and pressures

A new expression for partial molar volumes of aqueous solutes at infinite dilution has been developed in an empirical form based on Fluctuation Solution Theory for use over wide ranges of temperature and pressure. The solvent density and compressibility characterize the solvent properties, providing a much better description, especially in the critical region, than do models based on the solvent dielectric constant. The formulation has been integrated and differentiated to obtain analytic expressions for the Gibbs energy of hydration and Henry's constant, as well as the infinite dilution partial molar enthalpy and heat capacity of hydration at supercritical temperatures. For partial molar heat capacities at subcritical temperatures, an additional temperature-dependent function is used. Using newly established comprehensive databases of experimental V 2 0 and C 0 p,2 for nonelectrolytes and 1-1 electrolytes, supplemented with smaller databases for Δ hyd H 2 0 and Δ hyd G 2 0 for nonelectrolytes and κ 2 0 for electrolytes, it is shown that accurate correlations of all available data are obtained with the new model. For nonelectrolytes, the accuracy of predictions for all hydration and derivative properties at densities greater than 250 kg m −3 and at temperatures from ambient to over 700 K using only data at 298 K is almost as good as fitting the model's five parameters to all the data. For 1-1 electrolytes, predictions of C 0 p,2 near the critical temperature from V 2 0 near the critical temperature are satisfactory for NaCl(aq).

The solubility of zinc oxide in 0.03 m NaTr as a function of temperature, with in situ pH measurement

The solubility of zincite (ZnO) has been measured in noncomplexing solutions over a wide range of pH m (4–11), and temperature (75–200°C) at 0.03 mol · kg −1 ionic strength in NaTr media (sodium trifluoromethanesulfonate, a noncomplexing 1:1 electrolyte), in a hydrogen electrode concentration cell (HECC), which provided continuous in situ measurement of hydrogen ion molality. Total zinc content was analyzed by atomic absorption using graphite furnace, flame, and inductively coupled plasma (ICP) spectrometers. The direction of approach to the equilibrium saturation state was varied to demonstrate that the system was reversible thermodynamically. Separate experiments were performed in alkaline solutions (0.03 mol · kg −1 NaOH) at 25 and 50°C in polypropylene syringes, and between 50 and 290°C in a Teflon-lined pressure vessel. The aim of these experiments was to reach higher pH m (>8 depending on the temperature) to determine the thermodynamic properties of the negatively charged species, Zn(OH) 3 −. A least-squares regression of the results obtained at this ionic strength was used to determine the molal solubility products (Q sn) of zincite. The solubility products (Q sn) were extrapolated to infinite dilution (K sn), permitting calculation of the thermodynamic properties of aqueous species of zinc for comparison with previous work.

Experimental investigation of aluminum-silica aqueous complexing at 300°C

Equilibrium constants for aqueous Al–Si complexes at 300°C and saturated water vapour pressure (86 bar) were generated experimentally from the difference between the solubility of boehmite in silica-free and silica-bearing solutions. At strongly acidic (pH<2) and near-neutral to basic (pH>4.5) conditions aluminum silica aqueous complexes form according to Al 3++H 4SiO 4 0=AlH 3SiO 4 2++H + and Al(OH) 4 −+H 4SiO 4 0=Al(OH) 3H 3SiO 4 −+H 2O for which the logarithm of the equilibrium constants was found to be 3.23±0.25 and 2.32±0.20, respectively. No solubility increase following addition of aqueous silica was observed in the slightly acidic range (2.5<pH<4), indicating that Si complexation with Al(OH) 2+, Al(OH) 2 +, and Al(OH) 3 0, is negligible. The equilibrium constant obtained for AlH 3SiO 4 2+ formation at 300°C was combined with published values for this complex at 25 to 150°C [Pokrovski, G.S., Schott, J., Harrichoury, J.-C., Sergeyev, A.S., 1996. The stability of aluminum silicate complexes in acidic solutions from 25 to 150°C. Geochim. Cosmochim. Acta 60, 2495–2501.] to generate standard partial molal thermodynamic properties at 25°C and 1 bar and HKF (revised Helgeson–Kirkham–Flowers model; [Tanger, J.C., Helgeson, H.C., 1988. Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: revised equations of state for the standard partial molal properties of ions and electrolytes. Am. J. Sci., 288, 19–98; Shock, E.L., Helgeson, H.C., 1988. Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: correlations algorithms for ionic species and equation of state predictions to 5 kbar and 1000°C. Geochim. Cosmochim. Acta, 52, 2009–2036; Shock, E.L., Oelkers, E.H., Johnson, J.W., Sverjensky, D.A., Helgeson, H.C., 1992. Calculation of the thermodynamic properties of aqueous species at high pressures and temperatures. J. Chem. Faraday Trans. 88 (6), 803–826.] equation of state parameters for this complex. Calculations indicate that Al–Si complexing can increase Al solubility of up to 1/2 an order of magnitude at 500°C and 1 kbar. As a consequence, Al–Si complexes should be taken into account to accurately model chemical equilibria in hydrothermal and metamorphic fluids.

Thermodynamic properties of aqueous species and the solubilities of minerals at high pressures and temperatures: the system Al 2O 3H 2OKOH

Experimental solubilities of gibbsite and corundum in aqueous KOH solutions at elevated temperatures and pressures reported by Fricke and Jucaitis (1930), Wesolowski (1992), and Pascal and Anderson (1989) were used together with the Hückel (1925) and Setchénow (1892) equations for activity coefficients of aqueous species and the thermodynamic properties of the aluminate ion AlO 2 − to retrieve dissociation constants for the potassium aluminate ion pair KAlO 2 0. The calculations were carried out using values of the Hückel extended-term parameter for aqueous KOH and dissociation constants for KOH 0 generated in the present study. Supercritical solubilities of corundum reported in the literature were regressed with the aid of a speciation model which explicitly provides for the formation in solution of triple ion clusters (Oelkers and Helgeson, 1990). Values of the dissociation constant for KAlO 2 0 generated from these data were subsequently regressed with the revised Helgeson-Kirkham-Flowers (HKF) equations of state (Tanger and Helgeson, 1988; Shock et al., 1989) to obtain HKF equations of state coefficients and the standard partial molal thermodynamic properties at 25°C and 1 bar of KAlO 2 0, which can be used to calculate the standard partial molal thermodynamic properties of the species at temperatures to 1000°C and pressures to 5 kbar. Combining these parameters and properties with those for AlO 2 − (Pokrovskii and Helgeson, 1995) permits calculation to within 0.05 log units of the experimental solubilities of corundum in KOH solutions reported by Barns et al. (1963) and Anderson and Burnham (1967) at temperatures to 800°C and pressures to 5 kbar. Similar calculations carried out for temperatures from 80 to 300°C at P SAT ( P SAT refers to 1 bar at temperatures < 100°C and to the equilibrium pressure for coexisting liquid and vapor H 2O at higher temperatures) indicate that addition of KCl to dilute KOH solutions increases the solubilities of gibbsite, boehmite, and diaspore in response to increasing formation of KAlO 2 0 and the decrease in the activity coefficient of AlO 2 −. At temperatures ∼ ≤ 80°C, the two factors contribute comparably to the solubility of gibbsite in solutions with KCl concentrations up to 5 molal.

Thermodynamic properties of aqueous species and the solubilities of minerals at high pressures and temperatures; the system Al 2 O 3 -H 2 O-NaCl

Thermodynamic properties of aqueous species and the solubilities of minerals at high pressures and temperatures; the system Al 2 O 3 -H 2 O-NaCl

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.

Estimation of the dielectric constant of H 2O from experimental solubilities of quartz, and calculation of the thermodynamic properties of aqueous species to 900°C at 2 kb

Experimental quartz solubilities in H 2O ( Anderson and Burnham, 1965, 1967) were used together with equations of state for quartz and aqueous species ( Helgeson et al., 1978; Walther and Helgeson, 1977) to calculate the dielectric constant of H 2O ( ϵ H 2O ) at pressures and temperatures greater than those for which experimental measurements ( Heger, 1969; Lukashov et al., 1975) are available ( 0.001 ⩽ P ⩽ 5 kb and 0 ⩽ T ⩽ 600°C). Estimates of ϵ H 2O computed in this way for 2 kb (which are the most reliable) range from 9.6 at 600°C to 5.6 at 800°C. These values are 0.5 and 0.8 units greater, respectively, than corresponding values estimated by Quist and Marshall (1965), but they differ by <0.3 units from extrapolated values computed from Pitzer's (1983) adaptation of the Kirkwood (1939) equation. The estimates of ϵ H 2O generated from quartz solubilities at 2 kb were fit with a power function of temperature, which was then used together with equations and data given by Helgeson and Kirkham (1974a,b, 1976) Helgeson et al. (1981), and Helgeson (1982b, 1984) to calculate Born functions, Debye Hückel parameters, and the thermodynamic properties of Na +, K +, Mg ++, Ca ++, and other aqueous species of geologic interest at temperatures to 900°C.

Chemical interaction of aqueous solutions with epidote-feldspar mineral assemblages in geologic systems; 1, Thermodynamic analysis of phase relations in the system CaO-FeO-Fe 2 O 3 -Al 2 O 3 -SiO 2 -H 2 O-CO 2

Simultaneous consideration of Moessbauer and/or experimental phase equilibrium data for epidote, andradite, and hedenbergite together with the thermodynamic properties of aqueous species, CO/sub 2/-H/sub 2/O fluids, and coexisting minerals permits comprehensive analysis of mineral stabilities and the effects of preferential site occupancy and solid solubility on hydrothermal solution compositions in the system CaO-FeO-Fe/sub 2/O/sub 3/-Al/sub 2/O/sub 3/-SiO/sub 2/-H/sub 2/O-CO/sub 2/ at high pressures and temperatures. Assuming substitutional order/disorder in epidote solid solutions to be independent of composition together with random mixing and equal interaction of cations on energetically equivalent sites in garnet and epidote solid solutions permits calculation of the extent of Al/sup 3 +/ and Fe/sup 3 +/ partitioning between coexisting garnet and epidote. The results of these calculations agree closely with published compositions of garnet and epidote solid solutions in skarn deposits, low-grade metamorphic rocks, and geothermal systems.