The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C

The mineral solubility model of Harvie and Weare (1980) is extended to the eight component system, Na-K-Mg-Ca-H-Cl-SO₄-OH-HCO₃-CO₃-CO₂-H₂O at 25°C to high concentrations. The model is based on the semi-empirical equations of Pitzer (1973) and co-workers for the thermodynamics of aqueous electrolyte solutions. The model is parameterized using many of the available isopiestic, electromotive force, and solubility data available for many of the subsystems. The predictive abilities of the model are demonstrated by comparison to experimental data in systems more complex than those used in parameterization. The essential features of a chemical model for aqueous electrolyte solutions and the relationship between pH and the equilibrium properties of a solution are discussed.     

The solubilities of calcite,aragonite and vaterite in CO2-H2O solutions between 0 and 90°C,and an evaluation of the aqueous model for the system CaCO3-CO2-H2O

Calculations based on approximately 350 new measurements (Ca_T-PCO₂) of the solubilities of calcite, aragonite and vaterite in CO₂-H₂O solutions between 0 and 90°C indicate the following values for the log of the equilibrium constants K_C, K_A, and K_V respectively, for the reaction CaCO₃(s) = Ca²⁺ + CO^2?₃: $\text{Log K}{}_{\mathrm{C}}\text{= ?171.9065 ? 0.077993T +}\text{2839.319}\text{T}\text{+ 71.595 log T}$$\text{Log K}{}_{\mathrm{A}}\text{= ?171.9773 ? 0.077993T +}\text{2903.293}\text{T}\text{+71.595 log T}$$\text{Log K}{}_{\mathrm{V}}\text{= ?172.1295 ? 0.077993T +}\text{3074.688}\text{T}\text{+ 71.595 log T}$ where T is in ^oK. At 25°C the logarithms of the equilibrium constants are ?8.480 ± 0.020, ?8.336 ± 0.020 and ?7.913 ± 0.020 for calcite, aragonite and vaterite, respectively.The equilibrium constants are internally consistent with an aqueous model that includes the CaHCO⁺₃ and CaCO⁰₃ ion pairs, revised analytical expressions for CO₂-H₂O equilibria, and extended Debye-Hückel individual ion activity coefficients. Using this aqueous model, the equilibrium constant of aragonite shows no PCO₂-dependence if the CaHCO⁺₃ association constant is between 0 and 90°C, corresponding to the value logK_Cahco⁺3 = 1.11 ± 0.07 at 25°C. The CaCO⁰₃ association constant was measured potentiometrically to be between 5 and 80°C, yielding logK_CaCO⁰3 = 3.22 ± 0.14 at 25°C.The CO₂-H₂O equilibria have been critically evaluated and new empirical expressions for the temperature dependence of K_H, K₁ and K₂ are $\text{log K}{}_{\mathrm{H}}\text{= 108.3865 + 0.01985076T ?}\text{6919.53}\text{T}\text{? 40.45154 log T +}\text{669365.}\text{T}{}^2$, $\text{log K}{}_1\text{= ?356.3094 ? 0.06091964T +}\text{21834.37}\text{T}\text{+ 126.8339 log T —}\text{1684915.}\text{T}{}^2$ and logK₂ = ?107.8871 ? 0.03252849T + 5151.79/T + 38.92561 logT ? 563713.9/T² which may be used to at least 250°C. These expressions hold for 1 atm. total pressure between 0 and 100°C and follow the vapor pressure curve of water at higher temperatures.Extensive measurements of the pH of Ca-HCO₃ solutions at 25°C and 0.956 atm PCO₂ using different compositions of the reference electrode filling solution show that measured differences in pH are closely approximated by differences in liquid-junction potential as calculated by the Henderson equation. Liquid-junction corrected pH measurements agree with the calculated pH within 0.003-0.011 pH.Earlier arguments suggesting that the CaHCO⁺₃ ion pair should not be included in the CaCO₃-CO₂-H₂O aqueous model were based on less accurate calcite solubility data. The CaHCO⁺₃ ion pair must be included in the aqueous model to account for the observed PCO₂-dependence of aragonite solubility between 317 ppm CO₂ and 100% CO₂.Previous literature on the solubility of CaCO₃ polymorphs have been critically evaluated using the aqueous model and the results are compared.     

CO2-H2O mixtures in the geological sequestration of CO2. I. Assessment and calculation of mutual solubilities from 12 to 100°C and up to 600 bar

Evaluating the feasibility of CO₂ geologic sequestration requires the use of pressure-temperature-composition (P-T-X) data for mixtures of CO₂ and H₂O at moderate pressures and temperatures (typically below 500 bar and below 100°C). For this purpose, published experimental P-T-X data in this temperature and pressure range are reviewed. These data cover the two-phase region where a CO₂-rich phase (generally gas) and an H₂O-rich liquid coexist and are reported as the mutual solubilities of H₂O and CO₂ in the two coexisting phases. For the most part, mutual solubilities reported from various sources are in good agreement. In this paper, a noniterative procedure is presented to calculate the composition of the compressed CO₂ and liquid H₂O phases at equilibrium, based on equating chemical potentials and using the Redlich-Kwong equation of state to express departure from ideal behavior. The procedure is an extension of that used by King et al. (1992), covering a broader range of temperatures and experimental data than those authors, and is readily expandable to a nonideal liquid phase. The calculation method and formulation are kept as simple as possible to avoid degrading the performance of numerical models of water-CO₂ flows for which they are intended. The method is implemented in a computer routine, and inverse modeling is used to determine, simultaneously, (1) new Redlich-Kwong parameters for the CO₂-H₂O mixture, and (2) aqueous solubility constants for gaseous and liquid CO₂ as a function of temperature. In doing so, mutual solubilities of H₂O from 15 to 100°C and CO₂ from 12 to 110°C and up to 600 bar are generally reproduced within a few percent of experimental values. Fugacity coefficients of pure CO₂ are reproduced mostly within one percent of published reference data.     

Solubility of metallic mercury in octane, dodecane and toluene at temperatures between 100°C and 200°C

The solubility of metallic mercury in dodecane, octane and toluene has been investigated experimentally at temperatures up to 200°C and pressures up to 6 bars (toluene). The equilibrium Hg concentrations are very similar in octane and dodecane, reaching values of 821 ppm and 647 ppm, respectively at 200°C, whereas they are significantly lower in toluene (e.g., 280 ppm at 200°C). The behavior of Hg in toluene is nevertheless similar to that in the alkanes. There is a strong prograde dependence of Hg concentration on temperature in both types of solvent, which can be described by the following experimentally determined relationships:

     

Thermodynamics of brine-salt equilibria—I. The systems NaCl-KCl-MgCl2-CaCl2-H2O and NaCl-MgSO4-H2O at 25°C

A thermodynamic model for concentrated brines has been developed which is capable of predicting the solubilities of many of the common evaporite minerals in chloro-sulfate brines at 25°C and 1 atm. The model assumes that the behaviour of the mean stoichiometric ionic activity coefficient in mixtures of aqueous electrolytes can be described by the Scatchard deviation function and Harned's Rule. In solutions consisting of one salt and H₂O, the activity coefficient is described by the expression where $\text{a}\text{?}$ and B? salt specific parameters obtained from data regression. In a mixture of n electrolytes and H₂O, B? for the ith component is given by $\text{B}{}^{\mathrm{<mtext>i</mtext><mtext>?</mtext>}}{}_{\mathrm{i}}\text{=B}\text{i}\text{?}{}_{\mathrm{i}}\text{+σ α}{}_{\mathrm{ij}}\text{y}{}_{\mathrm{j}}$ where α_ij is a (constant) mixing parameter characterizing the interaction of the i and j components and y_j is the ionic strength fraction of the jth component. The activity of H₂O is obtained from a Gibbs-Duhem integration and does not require any additional parameters or assumptions. In this study, parameters have been obtained for the systems NaCl-KCl-MgCl₂-CaCl₂-H₂O and NaCl-MgSO₄-H₂O at 25°C and 1 atm. Computed solubility curves and solution compositions predicted for invariant points in these systems agree well with the experimental data. The model is flexible and easily extended to other systems and to higher temperatures.     

Decomposition reactions of magnesium sulfate hydrates and phase equilibria in the MgSO4-H2O and Na-Mg-Cl-SO4-H2O systems with implications for Mars

We report new measurements of equilibrium relative humidities for stable and metastable hydration-dehydration equilibria involving several magnesium sulfates in the MgSO₄·nH₂O series. We also report a comprehensive thermodynamic treatment of the system including solution properties and experimental data from the published literature, i.e. solubilities, heat capacities and additional decomposition humidities. While for some magnesium sulfate hydrates solubility data in the binary system MgSO₄-H₂O are sparse, there is a reasonable database of solubility measurements of these hydrates in the ternary MgCl₂-MgSO₄-H₂O and the quaternary reciprocal Na⁺-Mg²⁺-Cl⁻-SO₄²⁻-H₂O systems. To make these data suitable for the determination of solubility products, we parameterized a Pitzer ion interaction model for the calculation of activity coefficients and water activities in mixed solutions of these systems and report the ion interaction parameters for the Na⁺-Mg²⁺-Cl⁻-SO₄²⁻-H₂O system. The model predicted solubilities in the reciprocal system are in very good agreement with experimental data. Using all available experimental data and the solution model an updated phase diagram of the MgSO₄-H₂O system covering the whole temperature range from about 170 to 473 K is established. This treatment includes MgSO₄·H₂O (kieserite), MgSO₄·4H₂O (starkeyite), MgSO₄·5H₂O (pentahydrite), MgSO₄·6H₂O (hexahydrite), MgSO₄·7H₂O (epsomite) and MgSO₄·11H₂O (meridianiite). It is shown that only kieserite, hexahydrite, epsomite and meridianiite show fields of stable existence while starkeyite and pentahydrite are always metastable. Due to sluggish kinetics of kieserite formation, however, there is a rather extended field of metastable existence of starkeyite which makes this solid a major product in dehydration reactions. The model predicted behavior of the magnesium sulfates is in excellent agreement with observations reported in the literature under terrestrial temperature and relative humidity conditions. We also discuss the implications of the new phase diagram for sulfates on Mars.     

Phase equilibria in the system CO2-H2O I: New equilibrium relations at low temperatures

Graphical analysis of free-energy relationships involving binary quadruple points and their associated univariant equilibria in the system CO₂-H₂O suggests the presence of at least 2 previously unrecognized quadruple points and a degenerate binary invariant point involving an azeotrope between CO₂-rich gas and liquid. Thermodynamic data extracted from the equilibrium involving clathrate (hydrate), gas, and ice (H = G+I) are employed along with published data to calculate the P-T range of the 3-ice equilibrium curve, S+I = H, where S is solid CO₂. This equilibrium curve intersects the H = G+I curve approximately where the latter curve intersects the S+H = G curve, thus confirming the existence of one of the inferred quadruple points involving the phases S, G, H, and I. Recognition of some binary equilibria probably have been hampered by extremely low mutual solubilities of CO₂ and H₂O in the fluids phases which, for example, render the S+H = G virtually indistinguishable from the CO₂-sublimation curve.To make the published portion of the L(liquid CO₂)-G-H equilibrium “connect” with the other new quadruple point involving S, L, G, and H, it is necessary to change the sense of the equilibrium from L = G+H at higher pressures to L+H = G at lower pressures by positing a L = G azeotrope at very low concentrations of H₂O. At the low-pressure origin of the azeotrope, which is only a few bars above the CO₂-triple point, the azeotrope curve intersects the 3-phase curve tangentially, creating a degenerate invariant point at which the 3-phase equilibrium changes from L+H = G at lower pressures to L = G+H at higher pressures. The azeotrope curve is offset at slightly lower temperature from the L = G+H curve until the 3-phase equilibrium terminates at the quadruple point involving G, L, H, and W (water). With further increase in pressure the azeotrope curve tracks the L = G+W equilibrium and apparently terminates at a critical end point in close proximity to critical endpoints for the CO₂-saturation curve and the L = G+W curve.Thermodynamic data for clathrate extracted from the slope of the H = G+I curve are consistent with a solid-state phase transformation in CO₂-clathrate between 235 and 255 K. Published work shows that the type-I clathrate phase, whose atomic structure is a framework of water molecules with CO₂ molecules situated in large “guest” sites within the framework, is variable in composition with ∼1 guest site vacancy per unit cell at the high-temperature limit of its stability; the number of water molecules, however, remains constant. The formula (CO₂)_8-y·46H₂O, where y is the number of vacancies per unit cell, is in keeping with the atomic structure, whereas the traditional formula, CO₂·nH₂O, where n (hydration number) = 5.75, is misleading.Ambient P-T conditions in the Antarctic and Greenland ice sheets are compatible with sequestering large amounts of carbon as liquid CO₂ and/or clathrate.     

Phase relations in the CH4-H2O-NaCl system at 2 kbar, 300 to 600°C as determined using synthetic fluid inclusions

Synthesis of fluid inclusions in the CH₄-H₂O-NaCl system was accomplished by subjecting fractured quartz or fluorite, along with known quantities of CH₄, H₂O, and NaCl, to a pressure of 2 kbar and temperatures of 300, 400, 500, or 600°C, in sealed Au capsules. Under the elevated P-T conditions, some of the fractures healed, trapping fluids as inclusions. Microthermometric measurements conducted on the fluid inclusions show that at 2 kbar and 400 to 600°C, there are very broad regions of fluid unmixing in the CH₄-H₂O-NaCl system. For those bulk fluid compositions that lie in the two-phase (i.e., immiscible fluids) field, the high-density phase is enriched in NaCl, whereas the low-density phase is enriched in CH₄. For any given bulk composition, the degree of NaCl enrichment in the high-density phase increases, whereas the degree of CH₄ enrichment in the low-density phase decreases, as temperature increases from 400 to 600°C. Our experimental constraints on the size of the two-phase field are generally consistent with results generated using the equation-of-state GEOFLUIDS (available at http://geotherm.ucsd.edu/geofluids/). However, when comparing the compositions of coexisting immiscible fluids, as determined experimentally vs. calculated using GEOFLUIDS, we find that some relatively small but probably significant differences exist between our experiments and this equation of state.     

CO2-H2O mixtures in the geological sequestration of CO2. II. Partitioning in chloride brines at 12-100°C and up to 600 bar

Correlations presented by Spycher et al. (2003) to compute the mutual solubilities of CO₂ and H₂O are extended to include the effect of chloride salts in the aqueous phase. This is accomplished by including, in the original formulation, activity coefficients for aqueous CO₂ derived from several literature sources, primarily for NaCl solutions. Best results are obtained when combining the solubility correlations of Spycher et al. (2003) with the activity coefficient formulation of Rumpf et al. (1994) and Duan and Sun (2003), which can be extended to chloride solutions other than NaCl. This approach allows computing mutual solubilities in a noniterative manner with an accuracy typically within experimental uncertainty for solutions up to 6 molal NaCl and 4 molal CaCl₂.     

Solubility of KFe(CrO4)2·2H2O at 4–75°C

The solubility of KFe(CrO₄)₂·2H₂O, a precipitate recently identified in a Cr(VI)-contaminated soil, was studied in dissolution and precipitation experiments. Ten dissolution experiments were conducted at 4–75°C and initial pH values between 0.8 and 1.2 using synthetic KFe(CrO₄)₂·2H₂O. Four precipitation experiments were conducted at 25°C with final pH values between 0.16 and 1.39. The log K_SP for the reaction

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Isopiestic measurement of the osmotic and activity coefficients for the NaOH-NaAl(OH)4-H2O system at 313.2 K

By using a specially designed and constructed isopiestic apparatus, we measured the osmotic coefficients at 313.2 K for the NaOH-NaAl(OH)₄-H₂O system with the total alkali molality, m_NaOHT (m_NaOH + m_NaAl[OH]4), from 0.05 mol/kg H₂O to 12 mol/kg H₂O and α_K (m_NaOHT/m_NaAl(OH)4) from 1.64 to 5.53. The mean standard deviation of the measurements is 0.0038. Several sets of the Pitzer model parameters for NaOH-NaAl(OH)₄-H₂O system were then obtained by regressing the measured osmotic coefficients with the Pitzer model and the Pitzer model parameters for NaOH(aq). One set of the results is as follows: β⁽⁰⁾_NaOH: 0.08669, β⁽¹⁾_NaOH: 0.31446, β⁽²⁾_NaOH: −0.00007367, C^Φ_NaOH: 0.003180, β⁽⁰⁾_NaAl(OH)4: 0.03507, β⁽¹⁾_NaAl(OH)4: 0.02401, C^Φ_NaAl(OH)4: −0.001066, θ_{OH⁻Al(OH)4⁻}: 0.08177, Ψ_Na⁺OH⁻_Al(OH)4⁻: −0.01162. The mean standard difference between the calculated and the measured osmotic coefficients is 0.0088. With the obtained Pitzer model parameters, we calculated the values of K = (γ_{NaAl(OH)4,cal²} · m_{Al(OH)4⁻,exp})/(γ_NaOH,cal² · m_OH⁻,exp) for the gibbsite solubility. The results show that the obtained Pitzer model parameters are reliable, and the relative error of the calculated activity coefficients should be < 2.1%. We also compared the calculated gibbsite solubility data among several activity coefficients models over a range of m_NaOHT at various temperatures. The comparison indicates that our activity coefficients model may be approximately applied in the ranges of temperature from 298.2 to 323.2 K and m_NaOHT from 0 to 8 mol/kg H₂O. We also calculated the stoichiometric activity coefficients of NaOH and NaAl(OH)₄ and the activity of H₂O for the NaOH-NaAl(OH)₄-H₂O system, and these calculations establish their variations with m_NaOHT and α_K. These variations imply that the strengths of the repulsive interactions among various anions are in the following sequence: Al(OH)₄⁻-Al(OH)₄⁻ < Al(OH)₄⁻-OH⁻ < OH⁻-OH⁻, and the attractive interaction between Al(OH)₄⁻ and H₂O is weaker than that between OH⁻ and H₂O.     

An experimental study of the solubility of molybdenum in H2O and KCl-H2O solutions from 500 °C to 800 °C, and 150 to 300 MPa

The solubility of molybdenum (Mo) was determined at temperatures from 500 °C to 800 °C and 150 to 300 MPa in KCl-H₂O and pure H₂O solutions in cold-seal experiments. The solutions were trapped as synthetic fluid inclusions in quartz at experimental conditions, and analyzed by laser ablation inductively coupled plasma mass spectrometry (LA ICPMS).Mo solubilities of 1.6 wt% in the case of KCl-bearing aqueous solutions and up to 0.8 wt% in pure H₂O were found. Mo solubility is temperature dependent, but not pressure dependent over the investigated range, and correlates positively with salinity (KCl concentration). Molar ratios of ∼1 for Mo/Cl and Mo/K are derived based on our data. In combination with results of synchrotron X-ray absorption spectroscopy of individual fluid inclusions, it is suggested that Mo-oxo-chloride complexes are present at high salinity (>20 wt% KCl) and ion pairs at moderate to low salinity (<11 wt% KCl) in KCl-H₂O aqueous solutions. Similarly, in the pure H₂O experiments molybdic acid is the dominant species in aqueous solution. The results of these hydrothermal Mo experiments fit with earlier studies conducted at lower temperatures and indicate that high Mo concentrations can be transported in aqueous solutions. Therefore, the Mo concentration in aqueous fluids seems not to be the limiting factor for ore formation, whereas precipitation processes and the availability of sulfur appear to be the main controlling factors in the formation of molybdenite (MoS₂).     

Crystallization of sodium sulfate phases in porous materials: The phase diagram Na2SO4-H2O and the generation of stress

Mechanical disintegration by crystal growth of salts in pores is generally considered as an important mechanism of rock breakdown both on Earth and on Mars. Crystal growth is also a major cause of damage in porous building materials. Sodium sulfate is the most widely used salt in accelerated weathering tests of natural rocks and building materials. This paper provides an updated phase diagram of the Na₂SO₄-H₂O system based on a careful review of the available thermodynamic data of aqueous sodium sulfate and the crystalline phases. The phase diagram includes both the stable phases thenardite, Na₂SO₄(V), and mirabilite, Na₂SO₄·10H₂O, and, the metastable phases Na₂SO₄(III) and Na₂SO₄·7H₂O. The phase diagram is used to discuss the crystallization pathways and the crystallization pressures generated by these solids in common laboratory weathering experiments and under field conditions. New crystallization experiments carried out at different temperatures are presented. A dilatometric technique is used to study the mechanical response of sandstone samples in typical wetting-drying experiments as in the standard salt crystallization test. Additional experiments with continuous immersion and evaporation were carried out with the same type of sandstone. Both, the theoretical treatment and the results of the crystallization experiments confirm that the crystallization of mirabilite from highly supersaturated solutions is the most important cause of damage of sodium sulfate in porous materials.     

Thermodynamic modeling of binary CH4-H2O fluid inclusions

This work reports the application of thermodynamic models, including equations of state, to binary (salt-free) CH₄-H₂O fluid inclusions. A general method is presented to calculate the compositions of CH₄-H₂O inclusions using the phase volume fractions and dissolution temperatures of CH₄ hydrate. To calculate the homogenization pressures and isolines of the CH₄-H₂O inclusions, an improved activity-fugacity model is developed to predict the vapor-liquid phase equilibrium. The phase equilibrium model can predict methane solubility in the liquid phase and water content in the vapor phase from 273 to 623 K and from 1 to 1000 bar (up to 2000 bar for the liquid phase), within or close to experimental uncertainties. Compared to reliable experimental phase equilibrium data, the average deviation of the water content in the vapor phase and methane solubility in the liquid phase is 4.29% and 3.63%, respectively. In the near-critical region, the predicted composition deviations increase to over 10%. The vapor-liquid phase equilibrium model together with the updated volumetric model of homogenous (single-phase) CH₄-H₂O fluid mixtures (Mao S., Duan Z., Hu J. and Zhang D. (2010) A model for single-phase PVTx properties of CO₂-CH₄-C₂H₆-N₂-H₂O-NaCl fluid mixtures from 273 to 1273 K and from 1 to 5000 bar. Chem. Geol.275, 148-160), is applied to calculate the isolines, homogenization pressures, homogenization volumes, and isochores at specified homogenization temperatures and compositions. Online calculation is on the website: http://www.geochem-model.org/.     

Application of the Pitzer ion interaction model to isopiestic data for the Fe2(SO4)3-H2SO4-H2O system at 298.15 and 323.15 K

Recent isopiestic studies of the Fe₂(SO₄)₃-H₂SO₄-H₂O system at 298.15 K are represented with an extended version of Pitzer’s ion interaction model. The model represents osmotic coefficients for aqueous {(1 − y)Fe₂(SO₄)₃ + yH₂SO₄} mixtures from 0.45 to 3.0 m at 298.15 K and 0.0435 ? y ? 0.9370. In addition, a slightly less accurate representation of a more extended molality range to 5.47 m extends over the same y values, translating to a maximum ionic strength of 45 m. Recent isopiestic data for the system at 323.15 K are represented with the extended Pitzer model over a limited range in molality and solute fraction. These datasets are also represented with the usual “3-parameter” version of Pitzer’s model so that it may be incorporated in geochemical modeling software, but is a slightly less accurate representation of thermodynamic properties for this system. Comparisons made between our ion interaction model and available solubility data display partial agreement for rhomboclase and significant discrepancy for ferricopiapite. The comparisons highlight uncertainty remaining for solubility predictions in this system as well as the need for additional solubility measurements for Fe³⁺-bearing sulfate minerals. The resulting Pitzer ion interaction models provide an important step toward an accurate and comprehensive representation of thermodynamic properties in this geochemically important system.     

The effect of sulfate on aluminum concentrations in natural waters: some stability relations in the system Al2O3-SO3-H2O at 298 K

While gibbsite and kaolinite solubilities usually regulate aluminum concentrations in natural waters, the presence of sulfate can dramatically alter these solubilities under acidic conditions, where other, less soluble minerals can control the aqueous geochemistry of aluminum. The likely candidates include alunogen, Al₂(SO₄)₃ · 17H₂O, alunite, KAl₃(SO₄)₂(OH)₆, jurbanite, Al(SO₄)(OH) · 5H₂O, and basaluminite, Al₄(SO₄)(OH)₁₀ · 5H₂O. An examination of literature values shows that the log $\text{K}{}_{\mathrm{sp}}\text{= ?85.4}$ for alunite and log $\text{K}{}_{\mathrm{sp}}\text{= ?117.7}$ for basaluminite. In this report the log $\text{K}{}_{\mathrm{sp}}\text{= ?7.0}$ is estimated for alunogen and log $\text{K}{}_{\mathrm{sp}}\text{= ?17.8}$ is estimated for jurbanite. The solubility and stability relations among these four minerals and gibbsite are plotted as a function of pH and sulfate activity at 298 K. Alunogen is stable only at pH values too low for any natural waters (<0) and probably only forms as efflorescences from capillary films. Jurbanite is stable from $\text{pH < 0}$ up to the range of 3–5 depending on sulfate activity. Alunite is stable at higher pH values than jurbanite, up to 4–7 depending on sulfate activity. Above these pH limits gibbsite is the most stable phase. Basaluminite, although kinetically favored to precipitate, is metastable for all values of pH and sulfate activity. These equilibrium calculations predict that both sulfate and aluminum can be immobilized in acid waters by the precipitation of aluminum hydroxysulfate minerals.Considerable evidence supports the conclusion that the formation of insoluble aluminum hydroxy-sulfate minerals may be the cause of sulfate retention in soils and sediments, as suggested by Adams and Rawajfih (1977), instead of adsorption.     

Solid-liquid equilibria of Mg(OH)2(cr) and Mg2(OH)3Cl·4H2O(cr) in the system Mg-Na-H-OH-Cl-H2O at 25°C

The solubility of crystalline Mg(OH)₂(cr) was determined by measuring the equilibrium H⁺ concentration in water, 0.01-2.7 m MgCl₂, 0.1-5.6 m NaCl, and in mixtures of 0.5 and 5.0 m NaCl containing 0.01-0.05 m MgCl₂. In MgCl₂ solutions above 2 molal, magnesium hydroxide converted into hydrated magnesium oxychloride. The solid-liquid equilibrium of Mg₂(OH)₃Cl·4H₂O(cr) was studied in 2.1-5.2 m MgCl₂. Using known ion interaction Pitzer coefficients for the system Mg-Na-H-OH-Cl-H₂O (25°C), the following equilibrium constants at I = 0 are calculated:

     

Complex formation in the ternary system Mg(II)-CO2-H2O

The carbonato and hydrogencarbonato complexes of Mg²⁺ were investigated at 25 and 50° in solutions of the constant ClO₄^? molality (3 M) consisting preponderantly of NaClO₄. The experimental data could be explained assuming the following equilibria: Mg²⁺ + CO_2B + H₂O ag MgHCO⁺₃ + H⁺, $\text{log}{}^1\text{β}{}_1\text{= ?7.64}{}_4\text{± 0.01}{}_7\text{(25°), ?7.46}{}_2\text{± 0.01}{}_1\text{(50°)}$, Mg²⁺ + 2 CO_2g + 2 H₂Oag Mg(HCO₃)⁰₂ ± 2 H⁺, $\text{log}{}^1\text{β}{}_2\text{= ?15.00 ± 0.14 (25°)}$, ?15.37 ± 0.39 (50°), Mg²⁺ + CO_2g + H₂Oag MgCO⁰₃ + 2 H⁺, $\text{log}{}^1\text{k}{}_1\text{= ?15.64 ± 0.06 (25°)}$,?15.23 ± 0.02 (50°), with the assumption γ_MgCO3⁰ = γ_Mg(HCO3)⁰2, ΔG⁰(I = 0) for the reaction MgCO⁰₃ + CO_2g + H₂O = Mg(HCO₃)⁰₂ was estimated to be ?3.9₁ ± 0.8₆ and 0.6 ± 2.4 kJ/mol at 25 and 50°C, respectively. The abundance of carbonate linked Mg(II) species in fresh water systems is discussed.     

Mineral solution equilibria—II. An experimental study of mineral solubilities and the thermodynamic properties of aqueous CaCl2 in the system CaO-SiO2-H2O-HCl

Speciation of aqueous calcium chloride and the solubility of wollastonite represented by the reaction wollastonite + 2HCl° → CaCl₂° + quartz + H₂O were experimentally investigated at 1 and 2 kbar in the range 425–600°C using rapid-quench hydrothermal techniques and a modified Ag + AgCl buffer technique (Frantz and Popp, 1979). Variation in the measured concentration in HCl° as a function of total dissolved calcium was used to identify associated aqueous CaCl₂° as the predominant calcium species in the fluid at temperatures above 500°C at 2 kbar. The data were used to calculate the equilibrium constant for the above reaction as a function of temperature and pressure, from which the difference in Gibbs free energy of formation between CaCl₂° and HCl° at 1 and 2 kbar, 450°–600°C was calculated. Solubility constants for minerals in the system MgO-CaO-SiO₂-H₂O-HCl-CO₂ were calculated using the data from this study and from Frantz and Popp (1979). Calculated mineral solubilities were used to calculate the solution compositions and solid alteration products resulting from interactions of a Ca-Mg silicate mineral (diopside) with hydrothermal solutions containing a range of different total chloride concentrations. High total chloride (2.0 m) in the solution results in Si-Mg enrichment in the solids and Ca enrichment in the fluid, whereas low total chloride (0.008 m) results in Mg enrichment in the solids and Ca-Si enrichment in the fluid.     

Mineral equilibria in a six-component seawater system,Na-K-Mg-Ca-SO4-Cl-H2O,at 25°C

Phase relations in the 6-component system Na-K-Mg-Ca-SO₄-Cl-H₂O have been calculated for halite saturation, 25°C and 1 atm pressure. Using a Jänecke projection with the apices Ca-Mg-K₂-SO₄, 27 stable invariant points have been located which are connected by 69 univariant curves. Polyhalite is the only quaternary solid, but anhydrite occupies the bulk of the interior tetrahedral space. Consequently, 24 of the invariant points lie very close to the Ca-free base, Mg-K₂-SO₄. The remaining three points involve tachyhydrite and/or antarcticite. All points but two (20,27) represent peritectic conditions. Metastable equilibria have been calculated for the Ca-free system and yield relations corresponding to the solar diagram.Seawater lies in the subspace anhydrite-halite-carnallite-kieserite-bischofite (point 20) and its evaporation has been discussed for conditions of equilibrium and fractional crystallization. After gypsum is converted to anhydrite, halite precipitates. The next phase, under equilibrium conditions, is glauberite, crystallizing at the expense of anhydrite. Continued evaporation leads to glauberite resorption and eventual replacement by polyhalite. Then follow the magnesium sulfates epsomite, hexahydrite and kieserite, which are joined by carnallite. Polyhalite is replaced by anhydrite and bischoflte is added at the final invariant condition. Kainite does not appear as a primary phase under equilibrium conditions, but it is an important phase during fractional crystallization, where Ca-phases are not allowed to back-react with the brine.Up to the appearance of glauberite, thickness ratios of halite: anhydrite couplets (equilibrium or fractionation) can vary from 0 to 7, the relative amount of halite increasing with more intense evaporation. During evaporation, the activity of H₂O decreases from 0.98 (seawater) to 0.34 (final invariant brine). The data provided can be used to evaluate the effects of mineral precipitation, evaporation and brine mixing for a wide variety of natural brines.