Amorphous silica solubilities V. Predictions of solubility behavior in aqueous mixed electrolyte solutions to 300°C

Solubilities of amorphous silica in several aqueous electrolyte solutions up to 300°C (Marshall, 1980a; Chen and Marshall, 1982) fitted the Setchénow equation, $\text{log(}\text{s}{}^0\text{s}\text{) = D·m}$ as described earlier (Marshall, 1980b) where s⁰ and s are molal solubilities of silica in pure water and salt solution, respectively, m is the molality of salt, and D is a proportionality constant related to the particular salt and temperature. It is now shown that, to a first approximation, the D parameters for various salts at the same temperature are additive. For instance, D(NaCl) ? D(KCl) = D(NaNO₃) ? D(KNO₃) or D(MgSO₄) = D(MgCl₂) + D(Na₂S0₄) ? 2D(NaCl). It also follows that $\text{(}\text{s}{}_0\text{s}\text{) =}\text{∑}\text{i}\text{(D}{}_{\mathrm{i}}\text{m}{}_{\mathrm{i}}\text{)}$.This additivity principle was used to estimate amorphous silica solubilities in mixed NaCl-Na₂SO₄, NaCl-MgCl₂, NaCl-MgSO₄, Na₂SO₄-MgCl₂, Na₂SO₄-MgSO₄, and MgCl₂-MgSO₄ aqueous solutions up to 300°C. The method produces results that agree reasonably well with experimental values and would be useful for predicting silica solubilities, for example, in seawater and its hydrothermal concentrates and in geothermal energy applications.     

Transfer and exchange equilibria in a portion of the pyroxene quadrilateral as deduced from natural and experimental data

Differences in the chemical composition of metamorphic and igneous pyroxene minerals may be attributed to a transfer reaction, which determines the Ca content of the minerals, and an exchange reaction, which determines the relative Mg:Fe²⁺ ratios. Natural data for associated Ca pyroxene (Cpx) and orthopyroxene (Opx) or pigeonite are combined with experimental data for Fe-free pyroxenes, to produce the following equations for the Cpx slope of the solvus surface: $\text{> 1080°C: T =}\text{1000}\text{(0.468 + 0.246X}{}^{\mathrm{Cpx}}\text{? 0.123 ln (1–2 [Ca]))}$$\text{< 1080°C: T =}\text{1000}\text{(0.054 + 0.608X}{}^{\mathrm{Cpx}}\text{? 0.304 ln (1–2 [Ca]))}$, and the following equation for the temperature-dependence of the Mg-Fe distribution coefficient: $\text{T =}\text{1130}\text{(}\text{ln}\text{K}{}_{\mathrm{p}}\text{+ 0.505)}$, where T is absolute temperature, X is $\text{Fe}{}^{\mathrm{2+}}\text{(Mg + Fe}{}^{\mathrm{2+}}\text{))}$, [Ca] is $\text{Ca}\text{(Ca + Mg + Fe}{}^{\mathrm{2+}}\text{)}$ in Cpx, and K_D is the distribution coefficient, defined as $\text{X}{}^{\mathrm{Opx}}\text{/(1 ? X}{}^{\mathrm{Opx}}\text{) ÷ X}{}_{\mathrm{Cpx}}\text{/(1 ?}{}^{\mathrm{Cpx}}\text{)}$.The transfer and exchange equations form useful temperature indicators, and when applied to 9 sets of well-studied rocks, yield pairs of temperatures that are in good agreement. For example, temperatures obtained for the Bushveld Complex are 1020°C (solvus equation) and 980°C (exchange equation), based on 7 specimens. The uncertainty in these numbers, due to precision and accuracy errors, is estimated to be ±60°.     

Fractionation of stable carbon isotopes by marine phytoplankton

Stable carbon isotope fractionation by seventeen species of marine phytoplankton, representing the classes of Bacillariophyceae, Chlorophyceae, Prasinophyceae, Chrysophyceae, Haptophyceae and Dinophyceae have been determined in laboratory culture experiments using bicarbonate enriched artificial sea water. The values (Δ_HCO3^? = δ¹³C of algae vs HCO₃^?) range from ?22.1 to ?35.5%. Nitzschia closterium shows the smallest fractionation of ? 22.1% and Isochrysis galbana, the greatest of ?35.5%,. Since these algae were cultured under identical laboratory conditions, the wide range of Δ_HCO3^? values is seemingly due to the presence of different metabolic pathways within these organisms.A temperature dependent fractionation of 0.36% per °C with decreasing temperatures was measured for Skeletonema costatum whereas, smaller temperature dependencies of ?0.13, +0.15 and ?0.07%. per °C were observed for Dunaliella sp., Monochrysis lutheri and Glenodinium foliaceum, respectively.The consistency of values of Skeletonema costatum, Dunaliella sp. and Monochrysis lutheri grown at salinities of 22, 26, 32 and 36% indicates that natural salinity variations have negligible effects on the isotopic composition of marine phytoplankton.     

Thio complexes of gold and the transport of gold in hydrothermal ore solutions

The solubility of gold in aqueous sulphide solutions has been determined from pH_20°C ≈ 4 to pH_20°C ≈ 9.5 in the presence of a pyrite-pyrrhotite redox buffer at temperatures from 160 to 300°C and 1000 bar pressure. Maximum solubilities were obtained in the neutral region of pH as, for example, with m_NaHS = 0.15 m, pH_20°C = 5.96, T = 309°C, P = 1000 bar where a gold solubility of 225 mg/kg was obtained. It was concluded that three thio gold complexes contributed to the solubility. The complex Au₂(HS)₂S^2? predominated in alkaline solution, the Au(HS)₂^? complex occurred in the neutral pH region, and in the acid pH region, it was concluded with less certainty that the Au(HS)° complex was present. Formation constants calculated forAu₂(HS)₂S^2? and Au (HS)₂^? emphasize their high stability. In the temperature range from 175 to 250°C, values of pβ for Au₂(HS)₂S^2? vary from ?53.0 to 47.9 (±1.6) and from ?23.1 to ?19.5 ( ± 1.5) for Au(HS)₂^?. Equilibrium constante for the dissolution reactions, $\text{Au° + H}{}_2\text{S + HS}{}^{\mathrm{?}}\text{? Au(HS)}{}_2{}^{\mathrm{?}}\text{+}\text{1}\text{2}\text{H}{}_2$ and 2Au° + H₂S + 2H8^? ? Au(HS)₂^? + H₂ vary from pK_m = +2.4 to +2.55 (±0.10) for Au₂(HS)₂S^2? and from pK_n = + 1.29 to + 1.19 (±0.10) for Au(HS)₂^? over the temperature range 175 to 250°C. Enthalpies of these dissolution reactions were calculated to be ΔH_m° = ?5.2 ±2.0 kcal/mol and ΔH_n° = +1.7 ±2.0 kcal/mol respectively. It was concluded that gold is probably transported in hydrothermal ore solutions as both thio and chloro complexes and may be deposited in response to changes in temperature, pressure, pH, oxidation potential of the system and total sulphur concentration.     

The thermodynamics of the carbonate system in seawater

The apparent constants (K'_i) for the ionization of carbonic acid in seawater at various salinities (S,%.) have been fit to equations of the form ln $\text{K'}{}_{\mathrm{i}}\text{= ln K}{}_{\mathrm{i}}\text{+ A}{}_{\mathrm{i}}\text{S}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+ B}{}_{\mathrm{i}}\text{S}$whereK_i is the thermodynamic ionization constant in water, A_i, and B_i are adjustable parameters. The temperature dependence (TK) of K_i, A_i and B_i were of the form, a₀ + a₁/T + a₃ ln T. Equations of similar forms have been used to analyze the ionization constants for water and boric acid and the solubility product of calcite in seawater. The effect of pressure on the apparent constants ($\text{K}{}^{\mathrm{p}}{}_{\mathrm{i}}\text{K}{}^{\mathrm{o}}{}_{\mathrm{i}}$) have been fit to equations of the form ln $\text{(}\text{K}{}^{\mathrm{p}}{}_{\mathrm{i}}\text{K}{}^{\mathrm{o}}{}_{\mathrm{i}}\text{) = ? (ΔVP + 0.5 ΔK P}{}^2\text{)/RT}$ where the volume (ΔV) and compressibility (ΔK) changes are polynomial functions of temperature. The equations generated for various açids in seawater have been used to examine the carbonate system in seawater. Equations relating the NBS and Tris pH scales have been derived as well as equations of pH as a function of temperature and pressure. The equations from Hansson (1972, Ph.D. Thesis, University of Göteborg, Sweden) and Mehrbachet al. (1973, Limnol. Oceanogr.18, 897–907) have been used to examine the components of the carbonate system. At a fixed total alkalinity and total carbon dioxide, differences of ±0.01 m-equiv kg^?1 in HCO^?₃ and CO^2?₃ were found; however, the [CO₂] and P_co2 are nearly the same. The contribution of borate ion, B(OH)^?₄ determined from the equations of Hansson (1972, Ph.D. Thesis, University of Göteborg, Sweden) and Lyman (1957, Ph.D. Thesis, University of California, Los Angeles) differ by ±0.01 m-equiv kg^?1 for waters with the same salinity and temperature.     

La sénégalite,Al2 (PO4) (OH)3 · H2O,un nouveau minéral

Senegalite is orthorhombic, mm2, a:b:c:=1.296:1:1.007; $\text{a}{}_0\text{=9.673,}\text{b}{}_0\text{=7.596,}\text{c}{}_0\text{=7.668}\text{A}\text{?}$, Z=4, G_calc=2551; space group Pna2. The strongest lines in the powder pattern are: 5.41(7); 4.089(9); 3.834(10); 3.610(8); 2.990(9); 2.348(8); 2.070(7) 1.929(7); 1.505(7) Å. The chemical analysis: Al₂O₃ ? 46.23; Fe₂O₃ ? 0.28; P₂O₅ ? 31.85 H₂O ? 21.00; sum 99.34, gives a formula Al₂(PO₄)(OH)₃ · H₂O. Colourless optically biaxial positive, n_S: α=1.562, β=1.566, γ=1.587, plane of optical axies (001), Z=a, Y=c; 2V=53°, weak dispersion r > v. Measured density 2.552. The DTA curve shows endothermic reactions at 250, 370 and 440°C corresponding to the dehydration of mineral. Infrared spectrum indicates the presence of OH and H₂O groups. Found in oxidation zone of Kouroudiako iron deposit, Senegal, associated with turquoise, augelite, wavellite and crandallite.     

Etude des inclusions fluides du système N2-CO2 de dolomites et de quartz de Tunisie septentrionale. Données de la microcryoscopie et de l'analyse à la microsonde à effet Raman

Optical and analytical studies were performed on 400 N₂ + CO₂ gas bearing inclusions in dolomites and quartz from Triassic outcrops in northern Tunisia. Other fluids present include brines (NaCl and KCl bearing inclusions) and rare liquid hydrocarbons. At the time of trapping, such fluids were heterogeneous gas + brine mixtures. In hydrocarbon free inclusions the $\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}$ mole ratio was determined using two different non-destructive and punctual techniques: Raman microprobe analysis, and optical estimation of the volume ratios of the different phases selected at low temperatures. In the observed range of compositions, the two methods agree reasonably well.The N₂ + CO₂ inclusions are divided into three classes of composition: (a) $\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}\text{> 0,57}$: Liquid nitrogen is always visible at very low temperature and homogenisation occurs in the range ?151°C to ? 147°C (nitrogen critical temperature) dry ice (solid CO₂) sublimates between ?75°C and ?60°C; (b) $\text{0,20 <}\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}\text{? 0,57}$: liquid nitrogen is visible at very low temperature but dry ice melts on heating; liquid and gas CO₂ homogenise to liquid phase between ?51°C to ?22°C; (c) $\text{N}{}_2\text{(N}{}_2\text{+ CO}{}_2\text{)}\text{? 0,20}$: liquid nitrogen is not visible even at very low temperature (?195°C) and liquid and gas CO₂ homogenise to liquid phase between ?22°C and ?15°C. The observed phases changes are used to propose a preliminary phase diagram for the system CO₂-N₂ at low temperatures.Assuming additivity of partial pressures, isochores for the CO₂-N₂ inclusions have been computed. The intersection of these isochores with those for brine inclusions in the same samples may give the P and T of trapping of the fluids.     

The solubility of noble gases in water and in NaCl brine

A direct-sampling, mass-spectrometric technique has been used to measure simultaneously the solubilities of He, Ne, Ar, Kr, and Xe in fresh water and NaCl brine (0 to 5.2 molar) from 0° to 65 °C, and at 1 atm total pressure of moist air. The argon solubility in the most concentrated brines is 4 to 7 times less than in fresh water at 65 °C and 0°C, respectively. The salt effect is parameterized using the Setschenow equation.

$\text{ln}\text{[}\text{β}{}^{\mathrm{i}}{}_{\mathrm{o}}\text{(T)}\text{β}{}^{\mathrm{i}}\text{(T)}\text{= MK}{}^{\mathrm{i}}{}_{\mathrm{M}}\text{(T)}$

where M is NaCl moiarity, βⁱ_o(T) and βⁱ(T) the Bunsen solubility coefficients for gas i in fresh water and brine, and Kⁱ_M(T) the empirical salting coefficient. Values of Kⁱ_M(T) are calculated using volumetric concentration units for noble gas and NaCl content and are independent of NaCl molarity. Below about 40°C, temperature coefficients of all Kⁱ_M are negative. The value of K^He_M is a minimum at 40°C. K^Ar_M decreases from about 0.40 at 0°C to 0.28 at 65 °C. The absolute magnitudes of the differences in salting coefficients (relative to K^Ar_M) decrease from 0° to 65°C. Over the range of conditions studied, all noble gases are salted out, and K^He_M ? K^Ne_M < K^Ar_M < K^Kr_M < K^Xe_M.From the solubility data, we calculated $\text{Δ}\text{G}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{H}{}^0{}_{\mathrm{tr}}$ and $\text{Δ}\text{C}{}^{\mathrm{O}}{}_{\mathrm{p,tr}}$ for the transfer of noble gases from fresh water to 1 molar NaCl solutions. At low temperatures $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, is positive, but decreases and becomes negative at temperatures ranging from about 25°C for He to 45°C for Xe. At low temperatures, the dissolved electrolyte apparently interferes with the formation of a cage of solvent molecules about the noble gas atom. At higher temperatures, the local environment of the gas atom in the brine appears to be slightly more ordered than in pure water, possibly reflecting the longer effective range of the ionic fields at higher temperature.The measured solubilities can be used to model noble gas partitioning in two-phase geothermal systems at low temperatures. The data can also be used to estimate the temperature and concentration dependence of the salt effect for other alkali halides. Extrapolation of the measured data is not possible due to the incompletely-characterized minima in the temperature dependence of the salting coefficients. The regularities in the data observed at low temperatures suggest relatively few high-temperature data will be required to model the behavior of noble gases in high-temperature geothermal brines.     

Evaluation of deep temperatures of hydrothermal systems by a new gas geothermometer

The chemical composition of gas mixtures emerging in thermal areas can be used to evaluate the deep thermal temperatures. Chemical analyses of the gas compositions for 34 thermal systems were considered and an empirical relationship developed between the relative concentrations of H₂S, H₂, CH₄ and CO₂ and the reservoir temperature. The evaluated temperatures can be expressed by: $\text{t°C =}\text{24775}\text{α + β + 36.05}\text{?273}$ where $\text{α = 2 log}\text{CH}{}_4\text{CO}{}_2\text{?log}\text{H}{}_2\text{CO}{}_2\text{?3 log}\text{H}{}_2\text{S}\text{CO}{}_2$ (concentrations in % by volume) and β = 7 logP_co2     

The use of the specific interaction model to estimate the partial molal volumes of electrolytes in seawater

The specific interaction model has been used to determine the partial molal volume of electrolytes in 0.725 m NaCl and 35‰ salinity seawater solutions at 25°C. The partial molal volumes of electrolytes (MX) were estimated at a given ionic strength (I) from

$\text{V}\text{(}\text{MX}\text{) =}\text{V}{}^0\text{(}\text{MX}\text{) +}\text{S}{}_{\mathrm{v}}\text{I}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1 + I}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}\text{+ v}{}_{\mathrm{M}}\text{∑}\text{X}\text{B}{}_{\mathrm{<mtext>MX</mtext>}}\text{[X] + v}{}_{\mathrm{X}}\text{∑}\text{M}\text{B}{}_{\mathrm{<mtext>MX</mtext>}}\text{[X]}$

, where S_V is the Debye-Hückel limiting law slope, v_i is the number of ions i formed when MX dissociated, [i] is the total molality of ion i and B_MX is a specific interaction parameter that varies slowly with ionic strength. The values of $\text{V}\text{(}\text{MX}\text{)}$ estimated by using this equation were found to agree very well with experimental values in NaCl and seawater providing there are not strong interactions between M and X. For electrolytes that form ion pairs (i.e. MX°) corrections must be made. Methods are discussed for making these corrections.     

Fission track studies of xenolithic chondrites: implications regarding brecciation and metamorphism

We have studied fission tracks in phosphates from one gas-poor chondrite and three gas-rich chondrites to determine their thermal history and brecciation time scales. More than 70 percent of the tracks in whitlockites in these meteorites are due to the decay of extinct Pu²⁴⁴.Whitlockites separated from Bhola, a gas-poor chondrite, have $\text{ρ}{}_{\mathrm{Pu}}\text{ρ}{}_{\mathrm{U}}\text{= 2.6–5.2}$ and a model fission track age of 4.0 Gyr for a $\text{(}\text{Pu}\text{U}\text{)}{}_{\mathrm{4.55Gyr}}\text{= 0.045}$. Brecciation of the Bhola meteorite must have occurred at ?4.3 Gyr to account for the metal data (Scott and Rajan, 1981). A minimum cooling rate of $\text{0.9}{}_{\mathrm{–0.2}}{}^{0.3}\text{K}\text{Myr}$ in the temperature interval 800 to 300 K obtained from the track data is a factor of seven higher than the metallographic cooling rate ($\text{0.1}\text{K}\text{Myr}$).For the gas-rich chondrites, the $\text{ρ}{}_{\mathrm{Pu}}\text{ρ}{}_{\mathrm{U}}$ in whitlockites are: Weston, 32–148; Fayetteville, 21–227; and St. Mesmin, 26–137. Whitlockites from all these meteorites give model fission track ages of 4.4 Gyr assuming a $\text{(}\text{Pu}\text{U}\text{)}{}_{\mathrm{4.55\; Gyr}}\text{= 0.045}$. The final brecciation event definitely did not reset the track clock in phosphates of St. Mesmin. Our data suggest that it is also true for Weston and Fayetteville. We conclude that our observed fission track ages date the end of metamorphic cooling in the meteorite parent bodies and support the planetesimal model for the formation of xenolithic chondrites.     

Karibibite,a new FeAs mineral from South West Africa

Karibibite (ideally, Fe₂As₄O₉) occurs in vugs in massive loellingite of the Karibib pegmatite area, South West Africa. It is brownish yellow and finely fibrous. The thickness of the soft, single fibers is less than 1 micron, unsuitable for single-crystal X-ray study. Electron diffraction and X-ray powder pattern indicate that the mineral is orthorhombic, with $\text{a}{}_0\text{= 27.91}\text{A}\text{?}\text{, b}{}_0\text{= 6.53}\text{A}\text{?}\text{and c}{}_0\text{(}\text{fiber axis}\text{) = 7.20}\text{A}\text{?}$. The space group cannot be given. The mineral is paramagnetic with yellow fluorescence and is pleochroic with γ > 2.10, α = 1.96, 2V_α large, d = 4.07. It is soluble in acids and alkali hydroxide. Decomposition starts around 320 °C. The infra-red absorption spectrum indicates absence of AsO₄ groups. The mineral is classified tentatively as an oxide or arsenite.     

Density calculations for silicate liquids. I. Revised method for aluminosilicate compositions

Equations are developed for calculating the density of aluminosilicate liquids as a function of composition and temperature. The mean molar volume at reference temperature T_r, is given by $\text{V}{}_{\mathrm{r}}\text{= ∑X}{}_{\mathrm{i}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{i}}\text{+ X}{}_{\mathrm{A}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$, where the summation is taken over all oxide components except A1₂O₃, X stands for mole fraction, terms are constants derived independently from an analysis of volume-composition relations in alumina-free silicate liquids, and $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is the composition-dependent apparent partial molar volume of Al₂O₃. The thermal expansion coefficient of aluminosilicate liquids is given by $\text{α = ∑X}{}_{\mathrm{i}}\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}\text{+ X}{}_{\mathrm{A}}\text{}\text{?}\text{ga}{}_{\mathrm{A}}{}^{\mathrm{o}}$, where $\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}$ terms are constants independent of temperature and composition, and $\text{}\text{?}\text{ga}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is a composition-dependent term representing the effect of Al₂O₃ on the thermal expansion. Parameters necessary to calculate the volume of silicate liquids at any temperature T according to V(T) = V_rexp[α(T-T_r)], where T_r = 1400°C have been evaluated by least-square analysis of selected density measurements in aluminosilicate melts. Mean molar volumes of aluminosilicate liquids calculated according to the model equation conform to experimentally measured volumes with a root mean square difference of 0.28 $\text{cc}\text{mole}$ and an average absolute difference of 0.90% for 248 experimental observations. The compositional dependence of $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is discussed in terms of several possible interpretations of the structural role of Al³⁺ in aluminosilicate melts.     

Thermochemistry of the high structural state plagioclases

The enthalpies of solution of a suite of 19 high-structural state synthetic plagioclases were measured in a Pb₂B₂O₅ melt at 970 K. The samples were crystallized from analyzed glasses at 1200°C and 20 kbar pressure in a piston-cylinder apparatus. A number of runs were also made on Amelia albite and Amelia albite synthetically disordered at 1050–1080°C and one bar for one month and at 1200°C and 20 kbar for 10 hr. The component oxides of anorthite, CaO, Al₂O₃ and SiO₂, were remeasured.The ΔH of disorder of albite inferred in the present study from albite crystallized from glass is 3.23 kcal, which agrees with the 3.4 found by Holm and Kleppa (1968). It is not certain whether this value includes the ΔH of a reversible displacive transition to monoclinic symmetry, as suggested by Helgesonet al. (1978) for the Holm-Kleppa results. The enthalpy of solution value for albite accepted for the solid solution series is based on the heat-treated Amelia albite and is 2.86 kcal less than for untreated Amelia albite.The enthalpy of formation from the oxides at 970 K of synthetic anorthite is ?24.06 ± 0.31 kcal, significantly higher than the ?23.16 kcal found by Charluet al. (1978), and in good agreement with the value of ?23.89 ± 0.82 given by Robieet al. (1979), based on acid calorimetry.The excess enthalpy of mixing in high plagioclase can be represented by the expression, valid at 970 K: ΔH^ex(±0.16 kcal) = 6.7461 X_abX²_An + 2.0247 X_AnX²_Ab where X_Ab and X_An are, respectively, the mole fractions of NaAlSi₃O₈ and CaAl₂Si₂O₈. This ΔH^ex, together with the mixing entropy of Kerrick and Darken's (1975) Al-avoidance model, reproduces almost perfectly the free energy of mixing found by Orville (1972) in aqueous cation-exchange experiments at 700°C. It is likely that Al-avoidance is the significant stabilizing factor in the high plagioclase series, at least for X_An≥ 0.3. At high temperatures the plagioclases have nearly the free energies of ideal one-site solid solutions. The Al-avoidance model leads to the following Gibbs energy of mixing for the high plagioclase series: $\text{ΔG}{}^{\mathrm{mix}}\text{= ΔH}{}^{\mathrm{ex}}\text{+ RT X}{}_{\mathrm{Ab}}\text{ln[X}{}^2{}_{\mathrm{Ab}}\text{(2 ? X}{}_{\mathrm{Ab}}\text{)]+ X}{}_{\mathrm{An}}\text{ln}\text{[X}{}_{\mathrm{An}}\text{(1+X}{}_{\mathrm{An}}\text{)}{}^2\text{]}\text{4}$. The entropy and enthalpy of mixing should be very nearly independent of temperature because of the unlikelihood of excess heat capacity in the albite-anorthite join.     

Oxygen and sulfur isotope equilibria in the BaSO4HSO4−H2O system from 110 to 350°C and applications

Oxygen isotope exchange between BaSO₄ and H₂O from 110 to 350°C was studied using 1 m H₂SO₄-1 m NaCl and 1 m NaCl solutions to recrystallize the barite. The slow exchange rate (only 7% exchange after 1 yr at 110°C and 91% exchange after 22 days at 350°C in 1 m NaCl solution) prompted the use of the partial equilibrium technique. However, runs at 300 and 350°C were checked by complete exchange experiments. The temperature calibration curve for the isotope exchange is calculated giving most weight to the high temperature runs where the partial equilibrium technique can be tested. Oxygen isotope fractionation factors (α) in 1 m NaCl solution (110–350°C), assuming a value of 1.0407 for α_CO2H2O at 25°C, are:

.These data, when corrected for ion hydration effects in solution (Truesdell, 1974), give the fractionation factors in pure water:

.In the 1 m H₂SO₄-1 m NaCl runs, sulfur isotope fractionation between HSO^?₄ and BaSO₄ is less than the detection limit of 0.4%. A barite-sulfide geothermometer is obtained by combining HSO^?₄H₂S and sulfide-H₂S calibration data.Barite in the Derbyshire ore field, U.K., appears to have precipitated in isotopic equilibrium with water and sulfur in the ore fluid at temperatures less than 150°C. At the Tui Mine, New Zealand, the barite-water geothermometer indicates temperatures of late stage mineralization in the range 100–200°C. A temperature of 350 ± 20°C is obtained from the barite-pyrite geothermometer at the Yauricocha copper deposit, Peru, and oxygen isotope analyses of the barite are consistent with a magmatic origin for the ore fluids.     

The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutralization of Na2SiO3

The partial molal volume of silicic acid ($\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$) in 0.725 M NaCl at 1°C was calculated from the measured volume change (Δ$\text{V}\text{?}{}_{\mathrm{n}}$) due to the neutralization of anhydrous sodium metasilicate with HCl and the $\text{V}\text{?}\text{(HCl)}$ and $\text{V}\text{?}\text{(NaCl)}$ obtained from the literature. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 59.0 cm}{}^3\text{mol}\text{? 1}$, determined under experimental conditions of pH = 2.2, compares favorably with $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 58.9 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ calculated from the measured volume change due to the hydrolysis of the meta-silicate salt at pH = 11 and from the partial molal volume due to electrostriction ($\text{V}\text{?}{}_{\mathrm{elect}}$) of water by charged Si species present in the solution at the high pH. This agreement lends support to a semiempirical model for calculating $\text{V}\text{?}{}_{\mathrm{elect}}$ in developed by Millero (1969). $\text{V}\text{?}\text{(NaOH) = ? 5.45 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ in 0.725 M NaCl needed for this calculation was also determined in this work. The rate of polymerization of Si(OH)₄ at 1°C was monitored to insure that the monomer Si(OH)₄ was the main Si species present during the determination of $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ by neutralization of the alkali silicate. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ determined in this study compares favorably with the value calculated from high pressure solubility measurements.     

Phase relations in the system NaCl-KCl-H2O II: Differential thermal analysis of the halite liquidus in the NaCl-H2O binary above 450°c

Thermal analysis of the halite liquidus in the system NaCl-H₂O has been conducted for NaCl mole fractions (X_NaCl) greater than 0.25 (i.e., > 50 wt. % NaCl) at pressures between 0.3 and 4.1 kb and temperatures greater than 450°C. The position of the liquidus was located by differential thermal analysis (DTA) of cooling scans only, as heating scans did not produce definitive DTA peaks. The dP/dT slope of the liquidus is positive and steep at high pressures, but at high X_NaCl, and pressures below 0.5 kb it appears to reverse slope and intersects the three-phase curve (liquid-halite-vapour) at a shallow angle. However, due to the complex nature of the DTA signal when P <- 0.5 kb, there is considerable doubt about exactly what event has been recorded in the experiments conducted at these low pressures.The solubility of halite can be expressed as a function of the mole-fractional-based activity of NaCl in the liquid phase (L) in temperature (T, °K) and pressure (P, bars) In $\text{α}{}_{\mathrm{NaCl(L.T.P)}}\text{=}\text{?19.884 ? 0.001275T ? 1388}\text{T + 3.2305 In (T) ? 0.07574PT}$ Our liquidus data (based on 10 compositions) above 500 bars for these brines were combined with this equation to generate activity coefficients of NaCl which were fit within their experimental uncertainties to the following one parameter Margules equation In $\text{γ}{}_{\mathrm{NaCl(L.T.P)}}\text{=}\text{(0.7268 ? 695.7}\text{T ? 0.1217PT)}\text{(1 ? X}{}_{\mathrm{NaCl}}\text{)}{}^2$. Concentrated solutions of NaCl show negative deviations from ideality which rapidly increase in magnitude with decreasing X_NaCl.