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

Y Bottinga  D Weill  P Richet 《Geochimica et cosmochimica acta》1982,46(6):909-919

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.  相似文献   

The thermodynamics of the carbonate system in seawater     

Frank J Millero 《Geochimica et cosmochimica acta》1979,43(10):1651-1661

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.  相似文献   

The system pargasite-H₂O-CO₂: a model for melting of a hydrous mineral with a mixed-volatile fluid—I. Experimental results to 8 kbar     

J.R Holloway 《Geochimica et cosmochimica acta》1973,37(3):651-666

The stability of the amphibole pargasite [NaCa₂Mg₄Al(Al₂Si₆))O₂₂(OH)₂] in the melting range has been determined at total pressures (P) of 1.2 to 8 kbar. The activity of H₂O was controlled independently of P by using mixtures of H₂O + CO₂ in the fluid phase. The mole fraction of H₂O in the fluid ($\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$) ranged from 1.0 to 0.2.At P < 4 kbar the stability temperature (T) of pargasite decreases with decreasing $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ at constant P. Above P ? 4 kbar stability T increases as $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ is decreased below one, passes through a T maximum and then decreases with a further decrease in $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$. This behavior is due to a decrease in the H₂O content of the silicate liquid as $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ decreases. The magnitude of the T maximum increases from about 10°C (relative to the stability T for $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{= 1}$) at P = 5 kbar to about 30°C at P = 8 kbar, and the position of the maximum shifts from $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{? 0.6}$ at P = 5 kbar to $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}\text{? 0.4}$ at P = 8 kbar.The H₂O content of liquid coexisting with pargasite has been estimated as a function of at 5 and 8 kbar P, and can be used to estimate the H₂O content of magmas. Because pargasite is stable at low values of $\text{X}{}_{\mathrm{H}}{}_2\text{O}{}^{\mathrm{1fl}}$ at high P and T, hornblende can be an important phase in igneous processes even at relatively low H₂O fugacities.  相似文献   

Total individual ion activity coefficients of calcium and carbonate in seawater at 25°C and 35%. salinity,and implications to the agreement between apparent and thermodynamic constants of calcite and aragonite     

L.Niel Plummer  Eric T. Sundquist 《Geochimica et cosmochimica acta》1982,46(2):247-258

We have calculated the total individual ion activity coefficients of carbonate and calcium, and , in seawater. Using the ratios of stoichiometric and thermodynamic constants of carbonic acid dissociation and total mean activity coefficient data measured in seawater, we have obtained values which differ significantly from those widely accepted in the literature. In seawater at 25°C and 35%. salinity the (molal) values of and are $\text{0.038 ± 0.002}$ and $\text{0.173 ± 0.010}$, respectively. These values of and are independent of liquid junction errors and internally consistent with the value . By defining and on a common scale (), the product is independent of the assigned value of and may be determined directly from thermodynamic measurements in seawater. Using the value and new thermodynamic equilibrium constants for calcite and aragonite, we show that the apparent constants of calcite and aragonite are consistent with the thermodynamic equilibrium constants at 25°C and 35%. salinity. The demonstrated consistency between thermodynamic and apparent constants of calcite and aragonite does not support a hypothesis of stable Mg-calcite coatings on calcite or aragonite surfaces in seawater, and suggests that the calcite critical carbonate ion curve of Broecker and Takahashi (1978, Deep-Sea Research25, 65–95) defines the calcite equilibrium boundary in the oceans, within the uncertainty of the data.  相似文献   

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

Frank J Millero 《Geochimica et cosmochimica acta》1977,41(2):215-223

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 , 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.  相似文献   

Diffusion of ions in sea water and in deep-sea sediments   总被引：3，自引：0，他引：3  

Sandra Gregory 《Geochimica et cosmochimica acta》1974,38(5):703-714

The tracer-diffusion coefficient of ions in water, D_j⁰, and in sea water, $\text{D}{}_{\mathrm{j}}{}^1$, differ by no more than zero to 8 per cent. When sea water diffuses into a dilute solution of water, in order to maintain the electro-neutrality, the average diffusion coefficients of major cations become greater but of major anions smaller than their respective $\text{D}{}_{\mathrm{j}}{}^1$ or D_j⁰ values. The tracer diffusion coefficients of ions in deep-sea sediments, D_j,sed., can be related to $\text{D}{}_{\mathrm{j}}{}^1$ by $\text{D}{}_{\mathrm{j,sed.}}\text{= D}{}_{\mathrm{j}}{}^1\text{·}\text{α}\text{θ}{}^2$, where θ is the tortuosity of the bulk sediment and a a constant close to one.  相似文献   

The ionization of acids in estuarine waters     

Frank J Millero 《Geochimica et cosmochimica acta》1981,45(11):2085-2089

The stoichiometric, $\text{K}{}_{\mathrm{HA}}{}^1$, and apparent, K'_HA, constants for the ionization of a number of weak acids (NH₄⁺, HSO₄^?, HF, H₂O, B(OH)₃, H₂CO₃, HCO₃^?, H₃PO₄, H₂PO₄^?, HPO₄², H₃AsO₄ H₂AsO₄^? and HAsO₄^2?) in seawater at 25°C diluted with water have been fitted to equations of the form (Millero, 1979). In $\text{K}{}_{\mathrm{HA}}{}^1\text{= In K}{}_{\mathrm{HA}}\text{+ AS}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+ BS}$ where In K_HA is the thermodynamic constant in water, S is the salinity, A and B are adjustable parameters. The validity of this equation in estuarine waters has been examined by using an ion pairing model (Millero and Schreiber, 1981). The calculated values of $\text{K}{}_{\mathrm{HA}}{}^1$ and K'_HA at S = 35%. are in good agreement with the measured values for all the systems examined. The equation used to extrapolate the measured values to pure water K_HA predicted values that agreed with those determined by using the ion pairing model. The exception was the ionization of HPO₄^2? due to the strong interactions of Ca²⁺ and Mg²⁺ with PO₄^3?. The differences in the predicted values of $\text{K}{}_{\mathrm{HA}}{}^1$ in seawater diluted with pure water and average river water were very small for all the acids except HPO₄^2? (the maximum ΔpK = 0.96 in average river water). The larger difference in the $\text{K}{}_{\mathrm{HA}}{}^1$ for HPO₄^2? in river waters is due to the strong interactions of Ca²⁺ and PO₄^3?.  相似文献   

Theoretical prediction of phase relations among aqueous solutions and minerals: Salton Sea geothermal system     

Dennis K. Bird  Denis L. Norton 《Geochimica et cosmochimica acta》1981,45(9):1479-1494

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

James R. Wood 《Geochimica et cosmochimica acta》1975,39(8):1147-1163

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.  相似文献   

The solubility of noble gases in water and in NaCl brine     

S.P. Smith  B.M. Kennedy 《Geochimica et cosmochimica acta》1983,47(3):503-515

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. 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.  相似文献   

Trace element partitioning and melt structure: An experimental study at 1 atm pressure     

Bjørn O. Mysen  David Virgo 《Geochimica et cosmochimica acta》1980,44(12):1917-1930

Diopside-melt and forsterite-melt rare earth (REE) and Ni partition coefficients have been determined as a function of bulk compositions of the melt. Available Raman spectroscopic data have been used to determine the structures of the melts coexisting with diopside and forsterite. The compositional dependence of the partition coefficients is then related to the structural changes of the melt.The melts in all experiments have a ratio of nonbridging oxygens to tetrahedral cations ($\text{NBO}\text{T}$) between 1 and 0. The quenched melts consist of structural units that have, on the average, 2 (chain), 1 (sheet) and 0 (three-dimensional network) nonbridging oxygens per tetrahedral cation. The proportions of these structural units in the melts, as well as the overall $\text{NBO}\text{T}$, change as a function of the bulk composition of the melt.It has been found that Ce, Sm, Tm and Ni crystal-liquid partition coefficients ($\text{K}{}^{\mathrm{crystal?liq}}{}_{\mathrm{i}}\text{=}\text{C}{}^{\mathrm{crystal}}{}_{\mathrm{i}}\text{C}{}^{\mathrm{liq}}{}_{\mathrm{i}}$) decrease linearly with increasing $\text{NBO}\text{T}$. The values of the individual REE crystal-liquid trace element partition coefficients have different functional relations to $\text{NBO}\text{T}$, so that the degree of light REE enrichment of the melts would depend on their $\text{NBO}\text{T}$.The solution mechanisms of minor oxides such as CO₂, H₂O, TiO₂, P₂O₅ and Fe₂O₃ in silicate melts are known. These data have been recast as changes of $\text{NBO}\text{T}$ of the melts with regard to the type of oxide and its concentration in the melt. From such data the dependence of crystal-liquid partition coefficients on concentration and type of minor oxide in melt solution has been calculated.  相似文献   

Light hydrocarbons in Red Sea brines and sediments     

Roger A. Burke  James M. Brooks  William M. Sackett 《Geochimica et cosmochimica acta》1981,45(5):627-634

Light hydrocarbon (C₁-C₃) concentrations in the water from four Red Sea brine basins (Atlantis II, Suakin, Nereus and Valdivia Deeps) and in sediment pore waters from two of these areas (Atlantis II and Suakin Deeps) are reported. The hydrocarbon gases in the Suakin Deep brine (T = ~ 25°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 85‰}$, $\text{CH}{}_4\text{=}\text{~ 71}\text{1}$) are apparently of biogenic origin as evidenced by $\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3$) ratios of ~ 1000. Methane concentrations (6–8 μl/l) in Suakin Deep sediments are nearly equal to those in the brine, suggesting sedimentary interstitial waters may be the source of the brine and associated methane.The Atlantis II Deep has two brine layers with significantly different light hydrocarbon concentrations indicating separate sources. The upper brine (T = ~ 50°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 73‰}$, CH₄ = ~ 155 μl/l) gas seems to be of biogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~1100}$], whereas the lower brine (T = ~ 61°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 155‰}$, CH₄ = ~ 120μl/l) gas is apparently of thermogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~ 50}$]. The thermogenic gas resulting from thermal cracking of organic matter in the sedimentary column apparently migrates into the basin with the brine, whereas the biogenic gas is produced in situ or at the seawater-brine interface. Methane concentrations in Atlantis II interstitial waters underlying the lower brine are about one half brine concentrations; this difference possibly reflects the known temporal variations of hydrothermal activity in the basin.  相似文献   

On calculating activity coefficients and other excess functions from the intracrystalline exchange properties of a double-site phase     

John Geover 《Geochimica et cosmochimica acta》1974,38(10):1527-1548

For a phase at equilibrium in which two cation species are partitioned ideally between two sub-lattice sites, the excess functions of mixing (free energy, enthalpy and entropy) are directly related to the bulk composition of the phase and ΔG_E°(T, P), the standard-state intra- crystalline exchange free energy. If the phase is not at equilibrium internally, an additional ordering parameter is necessary to fix the excess free energy of mixing, G_mix^EX, unambiguously. Conversely, for any fixed G_mix^EX there exists an infinity of possible intracrystalline cation dis- tributions, only one of which is the equilibrium distribution for the specified temperature and pressure. As ideal intraphase cation ordering becomes more pronounced, G_mix^EX decreases. In response, the total free energy of mixing for the phase decreases progressively for non-end member compositions, approaching, at the limits of ordering, values appropriate for stabilizing compounds of intermediate composition.The model-dependent activity coefficient for component A in the phase, γ_A^T, can be calculated for any bulk composition, X_A^T, either from G_mix^EX directly or from more basic equations involving the interrelation of chemical potentials at equilibrium. A general form for γ_A^T is ln $\text{γ}{}_{\mathrm{A}}{}^{\mathrm{T}}\text{= 1n[}\text{2(X}{}_{\mathrm{A}}{}^{\mathrm{\alpha }}\text{X}{}_{\mathrm{A}}{}^{\mathrm{\beta }}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/}\text{(X}{}_{\mathrm{A}}{}^{\mathrm{\alpha }}\text{+X}{}_{\mathrm{A}}{}^{\mathrm{\beta }}\text{)}\text{]+Y}$, where Xj^κ denotes the mole fraction of species j in site κ. The first term on the right-hand side of this equation is the contribution to γ_A^T from ideal intracrystalline partitioning, and is common to the several theories lately presented to model intraphase cation partitioning. It can be shown rigorously that this term contributes to a negative deviation from ideality for the bulk phase. The second term is the contribution to the macroscopic activity coefficient from non-ideal intraphase partitioning, and is related to an enthalpy of mixing, H_mix^N in excess of that resulting from ideal inter-site cation ordering. While the expression represented by Y can take several functional forms, the additional enthalpy can be evaluated explicitly for specific non-ideal partitioning models from the relation $\text{H}{}_{\mathrm{mix}}{}^{\mathrm{N}}\text{= 2RT(1? X}{}_{\mathrm{A}}{}^{\mathrm{T}}\text{) ∝}\text{Y}\text{(1 ? X}{}_{\mathrm{A}}{}^{\mathrm{T}}\text{)}{}^2\text{dX}{}_{\mathrm{A}}{}^{\mathrm{T}}$.In those cases, G_mix^EX can also be determined exactly.  相似文献   

Sedimentary iron monosulfides: Kinetics and mechanism of formation     

Albert J Pyzik  Sheldon E Sommer 《Geochimica et cosmochimica acta》1981,45(5):687-698

The reaction between hydrous iron oxides and aqueous sulfide species was studied at estuarine conditions of pH, total sulfide, and ionic strength to determine the kinetics and formation mechanism of the initial iron sulfide. Total, dissolved and acid extractable sulfide, thiosulfate, sulfate, and elemental sulfur were determined by spectrophotometric methods. Polysulfides, S₄^2? and S₅^2?, were determined from ultraviolet absorbance measurements and equilibrium calculations, while product hydroxyl ion was determined from pH measurements and solution buffer capacity.Elemental sulfur, as free and polysulfide sulfur, was 86% of the sulfide oxidation products; the remainder was thiosulfate. Rate expressions for the reduction and precipitation reactions were determined from analysis of electron balance and acid extractable iron monosulfide vs time, respectively, by the initial rate method. The rate of iron reduction in moles/liter/minute was given by $\text{d(}\text{reduction}\text{Fe)}\text{dt}\text{= kS}{}_{\mathrm{t}}{}^{0.5}\text{(J}{}^{\mathrm{+}}\text{)}{}^{0.5}\text{A}{}_{\mathrm{FeOOH}}{}^1$ where S_t was the total dissolved sulfide concentration, (H⁺) the hydrogen ion activity, both in moles/ liter; and A_FeOOH the goethite specific surface area in square meters/liter. The rate constant, k, was 0.017 ± 0.002m^?2 min^?1. The rate of reduction was apparently determined by the rate of dissolution of the surface layer of ferrous hydroxide. The rate expression for the precipitation reaction was $\text{d(FeS)}\text{dt}\text{= kS}{}_{\mathrm{t}}{}^1\text{(H}{}^{\mathrm{+}}\text{)}{}^1\text{A}{}_{\mathrm{FeOOH}}{}^1$ where $\text{d(FeS)}\text{dt}$ was the rate of precipitation of acid extractable iron monosulfide in moles/liter/minute, and k = 82 ± 18 mol^?1l²m^?2 min^?1.A model is proposed with the following steps: protonation of goethite surface layer; exchange of bisulfide for hydroxide in the mobile layer; reduction of surface ferric ions of goethite by dissolved bisulfide species which produces ferrous hydroxide surface layer elemental sulfur and thiosulfate; dissolution of surface layer of ferrous hydroxide; and precipitation of dissolved ferrous specie and aqueous bisulfide ion.  相似文献   

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

Ralph Kretz 《Geochimica et cosmochimica acta》1982,46(3):411-421

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°.  相似文献   

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

Walter Riesen  Heinz Gamsjäger  Paul W. Schindler 《Geochimica et cosmochimica acta》1977,41(9):1193-1200

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.  相似文献   

The effect of pressure on the solubility of minerals in water and seawater     

Frank J Millero 《Geochimica et cosmochimica acta》1982,46(1):11-22

The effect of presure on the solubility of minerals in water and seawater can be estimated from In where the volume (ΔV) and compressibility (ΔK) changes at atmospheric pressure (P = 0) are given by Values of the partial molal volume ($\text{V}\text{?}$) and compressibilty ($\text{K}\text{?}$) in water and seawater have been tabulated for some ions from 0 to 50°C. The compressibility change is quite large (~10 × 10^?3 cm³ bar^?1 mol^?1) for the solubility of most minerals. This large compressibility change accounts for the large differences observed between values of ΔV obtained from linear plots of In K_sp versus P and molal volume data (Macdonald and North, 1974; North, 1974). Calculated values of $\text{K}{}^{\mathrm{P}}{}_{\mathrm{sp}}\text{K}{}^{\mathrm{o}}{}_{\mathrm{sp}}$ for the solubility of CaCO₃, SrSO₄ and CaF₂ in water were found to be in good agreement with direct measurements (Macdonald and North, 1974). Similar calculations for the solubility of minerals in seawater are also in good agreement with direct measurements (Ingle, 1975) providing that the surface of the solid phase is not appreciably altered.  相似文献   

Prediction of Gibbs free energies of calcite-type carbonates and the equilibrium distribution of trace elements between carbonates and aqueous solutions     

Dimitri A Sverjensky 《Geochimica et cosmochimica acta》1984,48(5):1127-1134

A linear correlation exists between the standard Gibbs free energies of formation of calcite-type carbonates (MCO3) and the corresponding conventional standard Gibbs free energies of formation of the aqueous divalent cations (M2+) at 25 °C and 1 bar ΔGMCO30 = m(ΔGf,M2+0) ? 141,200 cal · mole?1 where m is equal to 0.9715. This relationship enables prediction of the standard free energies of formation of numerous hypothetical carbonates with the calcite structure. Associated uncertainties typically range from about ± 250 to 600 cal · mole?1. An important consequence of the above correlation is that the thermodynamic equilibrium constant for the distribution of two trace elements M and N between carbonate mineral and aqueous solution at 25 °C and 1 bar is proportional to the free energy difference between the corresponding two aqueous ions: In Combination of predicted standard free energies, entropies and volumes of carbonate minerals at 25°C and 1 bar with standard free energies of aqueous ions and the equation of state in Helgesonet al. (1981) enables prediction of the thermodynamic equilibrium constant for trace element distribution between carbonates and aqueous solutions at elevated temperatures and pressures. Interpretation of the thermodynamic equilibrium constant in terms of concentration ratios in the aqueous phase is considerably simplified if pairs of divalent trace elements are considered that have very similar ionic radii (e.g., $\text{Sr}{}^{\mathrm{2+}}\text{Pb}{}^{\mathrm{2+}}$, $\text{Mg}{}^{\mathrm{2+}}\text{Zn}{}^{\mathrm{2+}}$). In combination with data for the stabilities of complex ions in aqueous solutions, the above calculations enable useful limits to be placed on the concentrations of trace elements in hydrothermal solutions.  相似文献   

Revised values for the Gibbs free energy of formation of [Al(OH)_{4 aq}⁻], diaspore,boehmite and bayerite at 298.15 K and 1 bar,the thermodynamic properties of kaolinite to 800 K and 1 bar,and the heats of solution of several gibbsite samples     

Bruce S. Hemingway  Richard A. Robie  James A. Kittrick 《Geochimica et cosmochimica acta》1978,42(10):1533-1543

Solution calorimetric measurements compared with solubility determinations from the literature for the same samples of gibbsite have provided a direct thermochemical cycle through which the Gibbs free energy of formation of [Al(OH)_{4 aq}^?] can be determined. The Gibbs free energy of formation of [Al(OH)_{4 aq}^?] at 298.15 K is ?1305 ± 1 kJ/mol. These heat-of-solution results show no significant difference in the thermodynamic properties of gibbsite particles in the range from 50 to 0.05 μm.The Gibbs free energies of formation at 298.15 K and 1 bar pressure of diaspore, boehmite and bayerite are ?9210 ± 5.0, ?918.4 ± 2.1 and ?1153 ± 2 kJ/mol based upon the Gibbs free energy of [A1(OH)_{4 aq}^?] calculated in this paper and the acceptance of ?1582.2 ± 1.3 and ?1154.9 ± 1.2 kJ/mol for the Gibbs free energy of formation of corundum and gibbsite, respectively.Values for the Gibbs free energy formation of [Al(OH)_{2 aq}⁺] and [AlO_{2 aq}^?] were also calculated as ?914.2 ± 2.1 and ?830.9 ± 2.1 kJ/mol, respectively. The use of [AlC_{2 aq}^?] as a chemical species is discouraged.A revised Gibbs free energy of formation for [H₄SiO_4aq⁰] was recalculated from calorimetric data yielding a value of ?1307.5 ± 1.7 kJ/mol which is in good agreement with the results obtained from several solubility studies.Smoothed values for the thermodynamic functions C_P⁰, ($\text{H}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, $\text{(}\text{G}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, S_T⁰ - S₀⁰, $\text{ΔH}{}_{\mathrm{?,298}}{}^0$ kaolinite are listed at integral temperatures between 298.15 and 800 K. The heat capacity of kaolinite at temperatures between 250 and 800 K may be calculated from the following equation: C_P⁰ = 1430.26 ? 0.78850 T + 3.0340 × 10^?4T² ?1.85158 × 10^?4T²$\text{1}\text{2}\text{+ 8.3341 × 10}{}^6\text{T}{}^{\mathrm{?2}}$.The thermodynamic properties of most of the geologically important Al-bearing phases have been referenced to the same reference state for Al, namely gibbsite.  相似文献   

Constantes de formation des complexes hydroxydés de l'aluminium en solution aqueuse de 20 a 70°C     

Yves Couturier  Gil Michard  Gérard Sarazin 《Geochimica et cosmochimica acta》1984,48(4):649-659

Stability constants of hydroxocomplexes of Al(III):Al(OH)²⁺ and A1(OH)₄^? have been measured in the 20–70°C temperature range by reactions involving only dissolved species. The stability constant ${}^1\text{K}{}_1$ of the first complex ion is studied by measuring pH of solutions of aluminium salts at several concentrations. ${}^1\text{β}{}_4$ of aluminate ion is deduced from equilibrium constants of the reaction between the trioxalato aluminium (III) complex ion and Al³⁺ in acid medium, and between the same complex ion and A1(OH)₄^? in alkaline medium. The K values and the associated ΔH are ${}^1\text{K}{}_1\text{= 10}{}^{\mathrm{?5.00}}$ and ΔH₁ = 11.8 Kcal; ${}^1\text{β}{}_4\text{= 10}{}^{\mathrm{?22.20}}$ and ΔH₄ = 42.45 Kcal. These last results are not in agreement with the values of recent tables for $\text{ΔG}{}^0\text{?}$ and $\text{ΔH}{}^0\text{?}$ of Al³⁺ and Al(OH)₄^?. We suggest a consistent set of data for dissolved and solid Al species and for some aluminosilicates.  相似文献