An XRD study of the crystal structure of gearksutite and its stability during heating to 300°C

The crystal structure of gearksutite, Ca and Al hydrofluoride CaAlF₄(OH) · H₂O, was refined using the Rietveld method with power diffraction data. The thermal stability of its crystal structure was studied for the first time using high-temperature XRD. Thermal XRD study of the mineral in the temperature range from 25 to 300°C revealed its stability to temperatures of 300-310°C. The mineral began to decay at temperatures greater than 300°C. The increase in the unit-cell parameters was established and the coefficients of thermal expansion were calculated.     

The effect of experiment geometry on the mechanism and rate of dissolution of quartz in basanite at 0.5 GPa and 1350 °C

Mineral dissolution is an important factor in many magmatic processes such as melting, assimilation and magma mixing. Since it is not possible to determine dissolution rates or mechanisms from natural samples, experimental measurements are very useful. However, the geometry of the crystal–melt system can have a large effect on the measured rate, depending on whether the contaminated melt formed during dissolution is gravitationally stable or unstable. This study examines the effects of the crystal–melt geometry on the dissolution rate and mechanism. The experiments were performed using basanite melt and cylinders and spheres prepared from a single crystal of natural quartz. All of the experiments were performed in the piston cylinder apparatus at 0.5 GPa and 1350 °C. Four crystal–melt geometries were used: (1) quartz cylinders on top of a column of melt; (2) quartz cylinders beneath a column of basanite melt; (3) quartz cylinders in the middle of column of melt; (4) quartz spheres on top of a column of basanite melt. These geometries allow an examination of non-convective, convective and mixed non-convective/convective dissolution. Sphere experiments were included, as this has been the most commonly used geometry in previous experimental studies. In all of the experiments quartz dissolves directly into the basanite without formation of cristobalite or tridymite. Quartz on top of a column of melt dissolves at a rate almost proportional to the square root of time and forms a silica-rich compositional boundary layer that is gravitationally stable. All of the samples show well-defined compositional gradients in the boundary layer; however, the melt at the interface varies in composition with time and plots of concentration as a function of distance normalized to time show that the diffusion rate of SiO₂ increases with time. These data suggest that the rate-controlling step during quartz dissolution is interface reaction rather than cation diffusion. Quartz on the bottom of a column of basanite dissolves much more quickly than in the quartz-on-top experiments and the dissolution rate is linear, due to the periodic gravitational instability and resultant convection of the boundary layer. Even though interface kinetics are the rate-controlling step in quartz dissolution, convection causes an increase in dissolution rate because it replenishes the boundary layer with new, silica-undersaturated melt, which dissolves the quartz more quickly than the contaminated melt. These data suggest that the interface reaction rate is controlled by the degree of undersaturation of the solvent melt in the dissolving component. Both quartz-in-middle and quartz sphere experiments dissolve at a rate intermediate between the two extremes and both show a power law rate. Both dissolve by a combination of convective and non-convective dissolution but the sphere experiments are affected by an additional factor. During the experiment the sphere can sink through the capsule causing forced convection which adds another complication to the interpretation of the dissolution rate data. The results of this study indicate that the choice of experiment geometry plays a major role in determining the observed dissolution rate. Mineral spheres, which have been widely used in the past, are not ideal for dissolution studies. Instead, dissolution rates and mechanisms are best determined in the absence of convection. These experiments have an additional advantage in that for diffusion-controlled dissolution, they allow determination of cation diffusivity. Received: 2 March 2000 / Accepted: 11 April 2000     

Low melt fraction connectivity of granitic and tonalitic melts in a mafic crustal rock at 800 °C and 1 GPa

In the absence of an externally applied stress, the segregation of small amounts of granitic or tonalitic melts from their residual mafic crystals is possible only if the melt forms an interconnected network phase. Accordingly, this research focuses on melt connectivity at low melt fraction (<4 wt% or 5 vol.%). Connectivity of granitic and tonalitic melts in amphibole-rich rock was assessed by performing two types of piston-cylinder experiments at 1 GPa and 800 °C. The first involved annealing samples that consisted of either alternating layers or homogeneous mixtures of calcic amphibole and metaluminous obsidian powder. The second type of experiment involved creating diffusion couples. Here, an upper cylinder of amphibole-saturated granitic or tonalitic melt was placed against a lower cylinder consisting of an amphibole-rich rock containing zero or a small melt (granitic or tonalitic) fraction. The upper part of the diffusion couple was doped with β emitter (¹⁵¹Sm or ¹⁴C) and functioned as an infinite melt reservoir. The lower part of the diffusion couple was considered to be the host rock. The experiments approached textural equilibrium which allowed us to characterize the wetting behaviour of the calcic amphibole by the hydrous silicic melt (granitic or tonalitic). These particular experiments also provided information concerning diffusive transport, because the β emitter could diffuse through the connected melt (liquid) in the amphibole-rich rock. The dihedral angle measurements show that melt connectivity was achieved. This conclusion is based on the fact that the dihedral angles, θ, consistently yielded median apparent values of 53°<θ<58° for an amphibole-rich rock/granitic melt system, and 46°<θ<48° for an amphibole-rich rock/tonalitic melt system. However, the frequency distribution of θ angles is found to be relatively broad. The results of the diffusion-couple experiments, assessed using the β radiographic technique, complement the dihedral (wetting) angle measurements by showing that melt connectivity is achieved at a melt fraction less than 4wt% (5 vol.%). Received: 15 April 1997 / Accepted: 23 September 1998     

Thermodynamics of ice polymorphs and ‘ice-like’ water in hydrates and hydroxides

Thermodynamic properties of water, in various families of hydroxides, oxihydroxides and hydrates (chlorides, chlorates, sulfates and sulfites …), have been calculated by using a large number of data available in the literature. A phase diagram of water has been used to find the first complete set of thermodynamic properties at 298 K, 1 bar of 8 ice polymorphs, from Ih (hexagonal ice, the common polymorph) to IX (very low temperature and high pressure polymorph). These results are used to illustrate the concept of ‘ice-like water’ available for a very large number of hydrated phases (noted X.H₂O) in which water is attached to the corresponding anhydrous substrate (noted X) within a large spectrum of different enthalpies (Δ_fH°) or Gibbs free energies (Δ_fG°), but within a relatively small range of others properties. Heat capacity (Cp°), entropy (S°), and volume (V°) of hydration water (X.H₂O−X=H₂O) appeared to be very close to those characterizing ice polymorphs such as ice II or ice VIII. This concept allows the authors to propose a classification of minerals in terms of affinity for water and to predict the relative stability of hydrated and dehydrated phases under climatic variations.     

Effects of water on strength and failure mode of coarse-grained granites at 300°C

Summary Deformation experiments have been performed in a triaxial compression cell at a temperature of 300°C and confining pressures up to 65 MPa using samples of homogeneous, fresh two-mica-granite (RM) and monzogranite (CM). The cylindrical specimens (d=70 mm, h=140 mm, V=540 cm³) were tested undrained under dry (105°C), as received, and water saturated conditions at deformation rates between and . The mechanical behaviour of the two types of coarse-grained, crystalloblastic granites is critically influenced by mineralogical composition, porosity, and the amount of intergranular water present in the samples. The failure stress of the CM granite is at about 65% of that of the RM granite; in both rocks strength decreases with increasing porosity and water content.The presence of interstitial water causes a failure mode of non-localized, homogeneously distributed microcracking in the central parts of the samples, whereas, in runs with dry granites, strain localization along a single shear fracture was observed. When aqueous fluids are present, the macroscopic style of deformation of granites appears to be ductile even at lowP andT conditions. Strength and angle of internal friction are reduced to very low values. The style of deformation, as well as the reduction of strength of the water-saturated rock samples, is due to mechanical and chemical effects of intergranular water at elevated temperatures.The maximum differential stresses measured for these coarse-grained granites are much lower than the strength commonly reported for other granites, e. g. Westerly and Charcoal granites. Our data suggest that the strength of the granitic crust under differential stress is lower than currently deduced from laboratory experiments.     

Experimental studies of Ta2O5 and columbite–tantalite solubility in fluoride solutions from 300 to 550°C and 50 to 100 MPa

It is well established that the fractionation of Li–F granitic magmas at depth leads to the accumulation of flux elements such as F and Li, and metal cations such as Ta and Nb in residual melts. However, it remains to be determined whether magmatic fractionation is sufficient to concentrate Nb and Ta into economically significant quantities, and what role hydrothermal–metasomatic processes play in the formation of such ore deposits. In the literature, reliable data about the solubility of Ta and Nb in hydrothermal solutions is missing or incomplete. This study provides a quantitative experimental estimation of the possible contribution from hydrothermal processes in Ta enrichment in cupolas of albitized and greisenized Li–F granite. Experimental studies of Ta₂O₅ and columbite–tantalite (Mn,Fe)(Nb,Ta)₂O₆ solubility were carried out in fluoride solutions consisting of HF, NaF, KF, and LiF. At low fluoride concentrations (0.01 and 0.1 m), Ta₂O₅ solubility at 550°C and 100 MPa under Co–CoO oxidizing conditions is low (near 10^?5–10^?4 m) in all fluoride solutions (HF, NaF, KF, LiF). At high fluoride concentrations (1 and 2 m) the highest Ta₂O₅ concentrations (10^?1 m) were detected in HF solutions. In KF, NaF, and LiF solutions, the Ta₂O₅ solubility is also high (10^?3–10^?2 m). The dependence of columbite–tantalite (Nb₂O₅-59 wt. %, Ta₂O₅-18 wt. %) solubility as a function of solution composition, T, and P has also been investigated. Tantalum and Nb concentrations have the highest values in HF solutions at reduced conditions (up to 10^?3 to 10^?2 m Ta in 1 m HF). In 1 m NaF solutions, the concentrations of Nb and Ta are, respectively, 2.5 and 3 orders of magnitude less than those in the 1 m HF solutions. Solubility of Ta and Nb in KF solutions has intermediate values. It is established that in NaF and KF solutions the dependence of solubility on pressure is distinctly negative. The Nb and Ta contents increase with increasing concentrations of HF and KF in solution, however, they do not change with increasing NaF concentration. In NaHCO₃, Na₂CO₃, and HCl solutions columbite–tantalite solubility is low. Even in 1 m chloride solutions the content is within the limits of 10^?5 m for Nb and 10^?6 to 10^?8 m for Ta. We conclude that hydrothermal transport of Ta and Nb is possible only in concentrated fluoride solutions.     

Toward an Understanding of Biogenic-silica Dissolution in Seawater – An Initial Rate Approach Applied between 40 and 90 °C

Summary The kinetics of phytoplankton frustule dissolution has generally been studied as the appearance of silicic acid in a batch reactor. Unfortunately, this approach, though often illuminating, has not so far been successful because of the difficulty of parameterising the full reaction curve. This current study shows how the initial rate approach to chemical kinetics offers a way around this bottleneck, thereby allowing much chemical kinetics information about frustule dissolution to be collected. The technique is shown to be flexible and suited to short reaction times which facilitate detailed quantitative kinetics investigation, indeed, as would be expected in a solution phase, kinetics study. The technique is exemplified by a dissolution study of uncleaned frustules of Cyclotella crypticaat 40 °C and above. The frustules were found to yield the same dissolution rate after 5 weeks dark storage, at 4 °C. Meanwhile, log dissolution rate was found to vary linearly with pH, with gradient 0.38 ± 0.01 (r ²=0.990). Linearity was upheld even at pHs as high as 14. Finally, a robust Arrhenius plot was established between 40 and 90 °C yielding an activation energy for dissolution of 84 ± 3 kJ mol ⁻¹. Follow through with the Eyring equation yielded an activation enthalpy, ΔH ^‡, and an activation entropy, ΔS ^‡, of 81 and 85 J mol ⁻¹ K ⁻¹, respectively. The discussion brings salient aspects of existing knowledge about diatom frustule dissolution kinetics into the wider context of silicate mineral dissolution.     

Thermodynamics of arsenates, selenites, and sulfates in the oxidation zone of sulfide ores: VI. Solubility of synthetic analogs of ahlfeldite and cobaltomenite at 25°C

The understanding of the mechanisms of the selenium behavior under near-surface conditions is an urgent problem of modern mineralogy and geochemistry, and is very important for solving environmental problems. The objective of this study is to synthesize analogs of ahlfeldite and cobaltomenite and to estimate their solubility in water. These analogs have been synthesized by mixing aqueous solutions of cobalt and nickel nitrates, respectively, and sodium selenite acidified with a solution of nitric acid. The obtained samples have been identified by X-ray diffraction and IR spectroscopy. The solubility has been determined by the isothermal saturation method in ampoules at 25°C, while the solubility products have been calculated using the Geochemist’s Workbench (GMB 7.0) software package. The solubility products of ahlfeldite and cobaltomenite are 10^?9.20 and 10^?9.44, respectively. The Eh-pH diagrams were calculated and plotted with the GMB 7.0 software package. The Eh-pH diagrams of the Ni-Se-H₂O and Co-Se-H₂O systems have been calculated for the average contents of these elements in underground water and their contents in acidic water of the oxidation zone of sulfide deposits. The formation of ahlfeldite and cobaltomenite under near-surface conditions is discussed.     

Thermodynamics of arsenates, selenites, and sulfates in the oxidation zone of sulfide Ores: Part VII. Solubility of synthetic analogs of erythrite and annabergite at 25°C

Understanding the mechanisms of arsenic’s behavior under near-surface conditions is one of the actual problems of contemporary mineralogy and geochemistry and is important for solving environmental problems. The aim of this study is to synthesize analogs of erythrite and annabergite and to investigate their solubility in water. These phases have been synthesized by the boiling-dry of aqueous solutions of cobalt and nickel nitrates mixed with sodium hydroarsenate alkalized with NaOH. The samples obtained have been identified with electron microprobe, X-ray diffraction, and IR spectroscopy. Solubility has been determined by the isothermal saturation method in ampoules at 25°C. The solubility has been calculated using the Geochemist’s Workbench (GMB 7.0) software package. The measured solubilities of erythrite and annabergite are 10^?35.76 and 10^?36.43, respectively. Eh-pH diagrams were calculated and plotted using the GMB 7.0 software package. The database comprises the thermodynamic parameters of 46 elements, 47 main particles, 48 redox pairs, 552 particles in solution, 624 solid phases, and 10 gases. The Eh-pH diagrams of the Ni-As-H₂O and Co-As-H₂O systems were plotted for the average contents of these elements in the acidic waters in the oxidation zones of sulfide deposits. The formation of erythrite and annabergite under near-surface conditions is discussed.     

Thermodynamics of Сlassical Schwarzschild Black Holes

Astronomy Reports - This paper assesses the thermodynamic properties of classical Schwarzschild Black Holes. We review the thermodynamic cycle in the Geroch gedanken experiment in its relation to...     

A thermodynamic model for the solubility of barite and celestite in electrolyte solutions and seawater to 200°C and to 1 kbar

This paper describes a model for barite and celestite solubilities in the Na–K–Ca–Mg–Ba–Sr–Cl–SO₄–H₂O system to 200°C and to 1 kbar. It is based on Pitzer's ion interaction model for the thermodynamic properties of the aqueous phase and on values of the solubility products of the solids revised in this work. It is shown how barite and celestite solubilities in electrolyte solutions can be accurately predicted as a function of temperature and pressure from previously determined Pitzer's parameters. The equilibrium constant for the BaSO₄(aq) ion pair dissociation reaction is calculated from recently reported barite solubility in Na₂SO₄ solutions from 0 to 80°C. Pressure corrections are evaluated through partial molal volume calculations and are partially validated by comparing model predictions to measured barite and celestite solubilities in pure water to 1 kbar and in NaCl solutions to 500 bars. The model is then used to investigate the tendency of ion pairing of Ca, Sr and Ba with sulfate in seawater. Finally, the activity coefficient of aqueous barium sulfate in seawater is calculated for temperature, pressure and salinity values found in the ocean and compared to published values.     

Hydration of periclase at 350 ∘C to 620 ∘C and 200 MPa: experimental calibration of reaction rate

The hydration of periclase to brucite was investigated experimentally. Single crystals of periclase machined to millimeter sized cubes with (100) surfaces were reacted with distilled water at temperatures of 350 to 620 ^°C and a pressure of 200 MPa for run durations of 5 to 40 minutes. Hydration produced a layer of brucite covering the surface of periclase. While the shrinking periclase largely retained its cube shape a surface roughness developed on the μm scale and eventually outward pointing spikes bounded by (111) faces emerged on the retreating faces of the periclase due to kinetic selection of less reactive (111) and (110) surfaces. The periclase to brucite conversion followed a linear rate law, where the reaction rate increased from 350 to 530 ^°C and then decreased towards higher temperature and finally vanished at about 630 ^°C, where periclase, brucite, and water are in equilibrium at 200 MPa. The overall kinetics of the hydration reaction is conveniently described in terms of a phenomenological interface mobility. Measuring the velocity of the hydration front relative to the lattice of the reactant periclase, the temperature dependence of its mobility is described by an Arrhenius relation with pre-exponential factor 1.7.10^?12 m ⁴/s.J and activation energy of E_A=55 kJ/mol.     

Partitioning of Fe and Mn between ilmenite and olivine at 1100 °C: constraints on the thermodynamic mixing properties of (Fe, Mn)TiO3 ilmenite solid solutions

The partitioning of Fe²⁺ and Mn²⁺ between (Fe, Mn)TiO₃ and (Fe, Mn)₂SiO₄ solid solutions in the system FeO-MnO-TiO₂-SiO₂ has been experimentally investigated at 1100 ^∘C and pressures of 1 bar and 25 kbar, over a wide range of Fe/Mn ratios, using electron microprobe analysis of quenched run products. The ilmenite solid solution in this system is within analytical uncertainty a simple binary between FeTiO₃ and MnTiO₃, but the olivine solid solution appears to contain up to 2.5 wt% TiO₂. The Fe-Mn partitioning results constrain precisely the difference in the thermodynamic mixing properties of the two solid solutions. If the mixing properties of (Fe, Mn)₂SiO₄ solid solutions are assumed to be ideal, as experimentally determined by Schwerdtfeger and Muan (1966), then the ilmenite is a regular, symmetric solution with W ^ilm _Fe-Mn=1.8±0.1 kJ mol⁻¹. The quoted uncertainty does not include the contribution from the uncertainty in the mixing properties of the olivine solution, which is estimated to be ±1.8 kJ mol⁻¹, and which therefore dominates the uncertainty in the present results. Nevertheless, this result is in good agreement with the previous experimental study of O'Neill et al. (1989), who obtained W ^ilm _Fe-Mn=2.2±0.3 kJ mol⁻¹ from an independent method. The results provide another item of empirical evidence supporting the proposition that solid solutions between isostructural end-members, in which order-disorder effects are not important, generally have simple thermodynamic mixing properties, with little asymmetry, modest excess entropies, and excess enthalpies approximately proportional to the difference in the molar volumes of the end-members. Received: 11 February 1998 / Accepted: 29 June 1998     

The thermoelastic behavior of clintonite up to 10?GPa and 1,000°C

The thermoelastic behavior of a natural clintonite-1M [with composition: Ca_1.01(Mg_2.29Al_0.59Fe_0.12)_Σ3.00(Si_1.20Al_2.80)_Σ4.00O₁₀(OH)₂] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 457.1(2) ?³, K _T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K _T0(a) = 0.0023(1) GPa⁻¹; β(b) = 1/3K _T0(b) = 0.0018(1) GPa⁻¹; β(c) = 1/K _T0(c) = 0.0072(3) GPa⁻¹]. The β-angle increases in response to the applied P, with: β_P = β₀ + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K _T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α₀ + α₁ T ^−1/2. The refined parameters for clintonite are as follows: α₀ = 2.78(4) 10⁻⁵°C⁻¹ and α₁ = −4.4(6) 10⁻⁵°C^1/2 for the unit-cell volume; α₀(a) = 1.01(2) 10⁻⁵°C⁻¹ and α₁(a) = −1.8(3) 10⁻⁵°C^1/2 for the a-axis; α₀(b) = 1.07(1) 10⁻⁵°C⁻¹ and α₁(b) = −2.3(2) 10⁻⁵°C^1/2 for the b-axis; and α₀(c) = 0.64(2) 10⁻⁵°C⁻¹ and α₁(c) = −7.3(30) 10⁻⁶°C^1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.     

Electrical conductivity of NaCl-bearing aqueous fluids to 600 °C and 1 GPa

The electrical conductivity of aqueous fluids containing 0.01, 0.1, and 1 M NaCl was measured in an externally heated diamond cell to 600 °C and 1 GPa. These measurements therefore more than double the pressure range of previous data and extend it to higher NaCl concentrations relevant for crustal and mantle fluids. Electrical conductivity was generally found to increase with pressure and fluid salinity. The conductivity increase observed upon variation of NaCl concentration from 0.1 to 1 M was smaller than from 0.01 to 0.1 M, which reflects the reduced degree of dissociation at high NaCl concentration. Measured conductivities can be reproduced (R ² = 0.96) by a numerical model with log \(\sigma\) = ?1.7060– 93.78/T + 0.8075 log c + 3.0781 log \(\rho\) + log \(\varLambda\) ₀(T, \(\rho\)), where \(\sigma\) is the conductivity in S m^?1, T is temperature in K, c is NaCl concentration in wt%, \(\rho\) is the density of pure water (in g/cm³) at given pressure and temperature, and \(\varLambda\) ₀ (T, \(\rho\)) is the molar conductivity of NaCl in water at infinite dilution (in S cm² mol^?1), \(\varLambda\) ₀ = 1573–1212 \(\rho\) + 537 062/T–208 122 721/T ². This model allows accurate predictions of the conductivity of saline fluids throughout most of the crust and upper mantle; it should not be used at temperatures below 100 °C. In general, the data show that already a very small fraction of NaCl-bearing aqueous fluid in the deep crust is sufficient to enhance bulk conductivities to values that would be expected for a high degree of partial melting. Accordingly, aqueous fluids may be distinguished from hydrous melts by comparing magnetotelluric and seismic data. H₂O–NaCl fluids may enhance electrical conductivities in the deep crust with little disturbance of v _p or v _p/v _s ratios. However, at the high temperatures in the mantle wedge above subduction zones, the conductivity of hydrous basaltic melts and saline aqueous fluids is rather similar, so that distinguishing these two phases from conductivity data alone is difficult. Observed conductivities in forearc regions, where temperatures are too low to allow melting, may be accounted for by not more than 1 wt% of an aqueous fluid with 5 wt% NaCl, if this fluid forms a continuous film or fills interconnected tubes.     

The ion-pair constant and other thermodynamic properties of HCl up to 350°C

Solubilities of silver chloride in aqueous hydrochloric acid solutions have been determined from 100 up to 350°C. From these measurements, the ionisation constant of HC1 has been evaluated up to 225°C. Evidence is presented to show that a protonated silver species, HAgCl₂⁰, exists at 275°C and above. Available experimental data up to 200°C have been firted to Pitzer's equation to generate an algorithm to calculate stoichiometric activity and osmotic coefficients of HCl up to 350°C and concentrations up to at least 3.0 m. Using the present results and those of Wrightet al. (1961), Pearsonet al. (1963) and Lukashowet al. (1976), the dissociation constant (K_d) of HCl as a function of temperature is described by the equation log₁₀K = 2136.898 + 1.020349T−4.5045 × 10⁻⁴T²−50396.40/T−901.770 10g₁₀T (Tin °K) which is valid in the range 25–350°C. Calculated enthalpy (ΔH⁰), entropy (ΔS⁰) and heat capacity change (ΔC_p⁰) functions for HCl dissociation have been rationalized in terms of changing solute and solvent characteristics as temperature is raised.     

Calculation of the standard partial molal thermodynamic properties and dissociation constants of aqueous HCl0 and HBr0 at temperatures to 1000°C and pressures to 5 kbar

Dissociation constants of aqueous ion pairs HCl⁰ and HBr⁰ derived in the literature from vapor pressure and supercritical conductance measurements Quist and Marshall 1968b, Frantz and Marshall 1984 were used to calculate the standard partial molal thermodynamic properties of the species at 25°C and 1 bar. Regression of the data with the aid of revised Helgeson-Kirkham-Flowers equations of state Helgeson et al 1981, Tanger 1988, Shock et al 1989 resulted in a set of equations-of-state parameters that permits accurate calculation of the thermodynamic properties of the species at high temperatures and pressures. These properties and parameters reproduce generally within 0.1 log unit (with observed maximum deviation of 0.23 log unit) the log K values for HBr⁰ and HCl⁰ given by Quist and Marshall (1968b) and Frantz and Marshall (1984), respectively, at temperatures to 800°C and pressures to 5 kbar.