Sedimentary iron monosulfides: Kinetics and mechanism of formation

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.     

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

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.     

Kinetic and thermodynamic factors controlling the distribution of SO32− and Na+ in calcites and selected aragonites

Significant amounts of SO₄^2?, Na⁺, and OH^? are incorporated in marine biogenic calcites. Biogenic high Mg-calcites average about 1 mole percent SO₄^2?. Aragonites and most biogenic low Mg-calcites contain significant amounts of Na⁺, but very low concentrations of SO₄^2?. The SO₄^2? content of non-biogenic calcites and aragonites investigated was below 100 ppm. The presence of Na⁺ and SO₄^2? increases the unit cell size of calcites. The solid-solutions show a solubility minimum at about 0.5 mole percent SO₄^2? beyond which the solubility rapidly increases. The solubility product of calcites containing 3 mole percent SO₄^2? is the same as that of aragonite. Na⁺ appears to have very little effect on the solubility product of calcites. The amounts of Na⁺ and SO₄^2? incorporated in calcites vary as a function of the rate of crystal growth. The variation of the distribution coefficient ($\text{D}$) of SO₄^2? in calcite at 25.0°C and 0.50 molal NaCl is described by the equation $\text{D = k}{}_0\text{+ k}{}_1\text{R}$ where $\text{k}{}_0$ and $\text{k}{}_1$ are constants equal to $\text{6.16 × 10}{}^{\mathrm{?6}}$ and $\text{3.941 × 10}{}^{\mathrm{?6}}$, respectively, and $\text{R}$ is the rate of crystal growth of calcite in mg·min^?1·g^?1 of seed. The data on Na⁺ are consistent with the hypothesis that a significant amount of Na⁺ occupies interstitial positions in the calcite structure. The distribution of Na⁺ follows a Freundlich isotherm and not the Berthelot-Nernst distribution law. The numerical value of the Na⁺ distribution coefficient in calcite is probably dependent on the number of defects in the calcite structure. The Na⁺ contents of calcites are not very accurate indicators of environmental salinities.     

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

The effect of presure on the solubility of minerals in water and seawater can be estimated from In

$\text{(}\text{K}{}^{\mathrm{P}}{}_{\mathrm{sp}}\text{K}{}^0{}_{\mathrm{sp}}\text{) +}\text{(?ΔVP + 0.5ΔKP}{}^2\text{)}\text{RT}$

where the volume (ΔV) and compressibility (ΔK) changes at atmospheric pressure (P = 0) are given by

$\text{ΔV =}\text{V}\text{?}\text{(M}{}^{\mathrm{+}}\text{, X}{}^{\mathrm{?}}\text{) ?}\text{V}\text{?}\text{[MX(s)]ΔK =}\text{K}\text{?}\text{(M}{}^{\mathrm{+}}\text{, X}{}^{\mathrm{?}}\text{) ?}\text{K}\text{?}\text{[MX(s)]}$

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.     

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.     

Concentration of Mn and separation from Fe in sediments—I. Kinetics and stoichiometry of the reaction between birnessite and dissolved Fe(II) at 10°C

Redox reactions between Fe²⁺ in solution and Mn-oxides are proposed as a mechanism for concentration of Mn in sediments both during weathering and diagenesis in marine sediments, e.g. the formation of Mn-nodules.If such a mechanism is to be effective, then reaction rates between Fe²⁺ and Mn-oxides should be fast. The kinetics and stoichiometry of the reaction between dissolved Fe²⁺ and synthetically prepared birnessite (Mn₇O₁₃·5H₂O) were studied experimentally in the pH range 3–6.Results show a stoichiometry which at pH < 4 conforms to a simple reaction between Fe²⁺ and birnessite, releasing Mn²⁺ and Fe³⁺ to the solution. At pH > 4 FeOOH is precipitated and excess Fe²⁺ consumption compared to the theoretical stoichiometry is observed. The excess Fe²⁺ consumption is not due to a formation of a quantitative MnOOH layer but rather to adsorption.Reaction kinetics are very fast at pH < 4 and change at pH 4 to a slower mechanism. At pH > 4 the reaction is fast initially until 17% of the bimessite has dissolved and changes then to a slower stage. The later stage can be described by the equation: $\text{J = km}{}_0\text{(H}{}^{\mathrm{+}}\text{)}{}^{\mathrm{?0.45}}\text{[Fe}{}^{\mathrm{2+}}\text{]}{}^{\mathrm{\gamma }}\text{(}\text{m}\text{m}{}_0\text{)}{}^{\mathrm{\beta }}$ where J is the overall rate of Mn²⁺ release, m₀ and m the mass of birnessite at time t = 0 and t > 0, β = 6.76?0.94 pH and γ has values of 0.76 at pH 5 and 0.39 at pH 6. The rate constant k is 7.2·10^?7 moles s^?1 g^?1 (moles/1)^?0.31 at pH 5 and 9.6·10^?8 moles s^?1 g^?1 (moles/1)^0.06 at pH 6.Diffusion calculations show that the rate is controlled by surface reaction and it is tentatively proposed that the availability of vacancies in octahedral [MnO₆]sheets of the birnessite surface could be rate controlling. It is concluded that reactions between Fe(II) and birnessite, and probably other Mn-oxides, are fast enough to be important in natural environments at the earth surface.     

Speciation of boron with Cu2+, Zn2+, Cd2+ and Pb2+ in 0.7 M KNO3 and in sea-water

The stability constants, $\text{K}{}^1{}_{\mathrm{MB}}$, for borate complexes with the ions of Cu, Pb, Cd and Zn are determined in this work by DPASV in 0.7 M KNO₃ at metal concentrations of 10^?7 M. The acidity constants of the Cu²⁺ ion are determined by DPASV in the same conditions. The following values for log $\text{K}{}^1{}_{\mathrm{MB}}$ () have been obtained: CuB: 3.48, CuB₂: 6.13, PbB: 2.20, PbB₂: 4.41, ZnB: 0.9, ZnB₂: 3.32, CdB: 1.42, and CdB₂: 2.7, while the values for the acidity constants of Cu are $\text{pK}{}^1{}_{\mathrm{CuOH}}\text{= 7.66}$ and . At the low concentration of boron in 35%. S sea-water complexes with borate represent only about 0.2% Cu, 0.03% Pb, 0.02% Zn and 0.003% Cd.     

Aqueous oxidation-reduction kinetics associated with coupled electron-cation transfer from iron-containing silicates at 25°C

Mechanisms and kinetics of aqueous $\text{Fe}{}^{\mathrm{+2}}\text{Fe}{}^{\mathrm{+3}}$ oxidation-reduction and dissolved O₂ interaction in the presence of augite, biotite and hornblende were studied in oxic and anoxic solutions at pH 1–9 at 25°C. Oxidation of surface iron on the minerals coincided with both surface release of Fe⁺² and by reduction of Fe⁺³ in solution. Reaction with iron silicates consumed dissolved oxygen at a rate that increased with decreasing pH. Both Fe⁺³ and O₂ consumption were shown to be controlled by coupled electron-cation transfer reactions of the form;

$\text{[}\text{Fe}{}^{\mathrm{+2}}\text{,}\text{1}\text{zM}{}^{\mathrm{+z}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{Fe}{}^{\mathrm{+3}}\text{→ [}\text{Fe}{}^{\mathrm{+3}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{Fe}{}^{\mathrm{+2}}\text{+}\text{1}\text{zM}{}^{\mathrm{+z}}$

and

$\text{[}\text{Fe}{}^{\mathrm{+2}}\text{,}\text{1}\text{zM}{}^{\mathrm{+z}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{H}{}^{\mathrm{+}}\text{+}\text{1}\text{4}\text{O}{}_2\text{→ [}\text{Fe}{}^{\mathrm{+3}}\text{]}{}_{\mathrm{silicate}}\text{+}\text{1}\text{zM}{}^{\mathrm{+z}}\text{+}\text{1}\text{2}\text{H}{}_2\text{O}$

where M is a cation of charge +z. The spontaneous reduction of aqueous Fe⁺³in the presence of precipitated Fe(OH)₃bracketed the surface oxidation standard half cell between +0.33 and +0.52 volts. Concurrent hydrolysis reactions involving cation release from the iron silicates were suppressed by the above reactions. Calculated oxidation depths in the minerals varied between 12 and 80Å and were apparently controlled by rates of solid-state cation diffusion.     

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.     

Rates of reaction of pyrite and marcasite with ferric iron at pH 2

The relative reactivities of pulverized samples (100–200 mesh) of 3 marcasite and 7 pyrite specimens from various sources were determined at 25°C and pH 2.0 in ferric chloride solutions with initial ferric iron concentrations of 10^?3 molal. The rate of the reaction:

$\text{FeS}{}_2\text{+ 14}\text{Fe}{}^{\mathrm{3+}}\text{+ 8}\text{H}{}_2\text{O}\text{= 15}\text{Fe}{}^{\mathrm{2+}}\text{+ 2}\text{SO}{}^{\mathrm{2?}}{}_4\text{+ 16}\text{H}{}^{\mathrm{+}}$

was determined by calculating the rate of reduction of aqueous ferric ion from measured oxidation-reduction potentials. The reaction follows the rate law:

where m_Fe³⁺ is the molal concentration of uncomplexed ferric iron, k is the rate constant and $\text{A}\text{M}$ is the surface area of reacting solid to mass of solution ratio. The measured rate constants, k, range from 1.0 × 10^?4 to 2.7 × 10^?4 sec^?1 ± 5%, with lower-temperature/early diagenetic pyrite having the smallest rate constants, marcasite intermediate, and pyrite of higher-temperature hydrothermal and metamorphic origin having the greatest rate constants. Geologically, these small relative differences between the rate constants are not significant, so the fundamental reactivities of marcasite and pyrite are not appreciably different.The activation energy of the reaction for a hydrothermal pyrite in the temperature interval of 25 to 50°C is 92 kJ mol^?1. This relatively high activation energy indicates that a surface reaction controls the rate over this temperature range. The BET-measured specific surface area for lower-temperature/early diagenetic pyrite is an order of magnitude greater than that for pyrite of higher-temperature origin. Consequently, since the lower-temperature types have a much greater $\text{A}\text{M}$ ratio, they appear to be more reactive per unit mass than the higher temperature types.     

Gibbsite solubility and thermodynamic properties of hydroxy-aluminum ions in aqueous solution at 25°C

Solubility curves were determined for a synthetic gibbsite and a natural gibbsite (Minas Gerais, Brazil) from pH 4 to 9, in 0.2% gibbsite suspensions in 0.01 M NaNO₃ that were buffered by low concentrations of non-complexing buffer agents. Equilibrium solubility was approached from oversaturation (in suspensions spiked with Al(NO₃)₃ solution), and also from undersaturation in some synthetic gibbsite suspensions. Mononuclear Al ion concentrations and pH values were periodically determined. Within 1 month or less, data from over-and undersaturated suspensions of synthetic gibbsite converged to describe an equilibrium solubility curve. A downward shift of the solubility curve, beginning at pH 6.7, indicates that a phase more stable than gibbsite controls Al solubility in alkaline systems. Extrapolation of the initial portion of the high-pH side of the synthetic gibbsite solubility curve provides the first unified equilibrium experimental model of Al ion speciation in waters from pH 4 to 9.The significant mononuclear ion species at equilibrium with gibbsite are Al³⁺, AlOH²⁺, Al(OH)⁺₂ and Al(OH)^?₄, and their ion activity products are $\text{1K}{}_{50}\text{= 1.29 × 10}{}^8$, $\text{1K}{}_{\mathrm{s1}}\text{= 1.33 × 10}{}^3$, $\text{1K}{}_{\mathrm{s2}}\text{= 9.49 × 10}{}^{\mathrm{?3}}$ and $\text{1K}{}_{\mathrm{s4}}\text{= 8.94 × 10}{}^{\mathrm{?15}}$. The calculated standard Gibbs free energies of formation (ΔG°_f) for the synthetic gibbsite and the A1OH²⁺, Al(OH)⁺₂ and Al(OH)^?₄ ions are ?276.0, ?166.9, ?216.5 and ?313.5 kcal mol^?1, respectively. These ΔG°_f values are based on the recently revised ΔG°_f value for Al³⁺ (?117.0 ± 0.3 kcal mol_?1) and carry the same uncertainty. The ΔG°_f of the natural gibbsite is ?275.1 ± 0.4 kcal mol^?, which suggests that a range of ΔG°_f values can exist even for relatively simple natural minerals.     

The ionization of acids in estuarine waters

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?.     

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

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.     

The kinetics of silica-water reactions

A differential rate equation for silica-water reactions from 0–300°C has been derived based on stoichiometry and activities of the reactants in the reaction SiO₂(s) + 2H₂O(l) = H₄SiO₄(aq)

where ($\text{A}\text{M}$) = (the relative interfacial area between the solid and aqueous phases/the relative mass of water in the system), and k₊ and k_? are the rate constants for, respectively, dissolution and precipitation. The rate constant for precipitation of all silica phases is $\text{log k}{}_{\mathrm{?}}\text{= ? 0.707 ?}\text{2598}\text{T}\text{(T, K)}$ and E_act for this reaction is 49.8 kJ mol^?1. Corresponding equilibrium constants for this reaction with quartz, cristobalite, or amorphous silica were expressed as $\text{log K = a + bT +}\text{c}\text{T}$. Using $\text{K =}\text{k}{}_{\mathrm{+}}\text{k}{}_{\mathrm{?}}$, k was expressed as $\text{log k}{}_{\mathrm{+}}\text{= a + bT +}\text{c}\text{T}$ and a corresponding activation energy calculated:

     

16.

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.     

17.

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.     

18.

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.     

19.

Dissociation constants for alkali earth and sodium borate ion pairs from 10 to 50°C     

E.J. Reardon 《Chemical Geology》1976,18(4):309-325

Potentiometric measurements in dilute sodium borate solutions with added alkali earth chlordie salts yield the following expressions for the dissociation constants of alkali earth borate ion pairs from 10 to 50°C:

$\text{p}\text{K(}\text{MgH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.266+0.001204 T}$

$\text{p}\text{K(}\text{CaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.154+0.002170 T}$

$\text{p}\text{K(}\text{SrH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.033+0.001738 T}$

$\text{p}\text{K(}\text{BaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.942+0.001850 T}$

where T is in °K. Enthalpies for the dissociation reactions at 25°C are less than 1 kcal./mole for all the alkali earth borate ion pairs.Values for pK(NaH₂BO₃°) from 5 to 55°C computed from the experimental data of Owen and King are in good agreement with those determined potentiometrically. The average value from both methods is 0.22 ± 0.1 at 25°C.Application to seawater of computed pK's for MgH₂BO₃⁺, CaH₂BO₃⁺ and NaH₂BO₃⁰ yields an apparent dissociation constant for boric acid of 8.73 vs. 8.70 measured by Lyman, 8.68 by Buch and 8.73 by Byrne and Kester.     

20.

Thermodynamic stability studies of the basic copper carbonate mineral,malachite     

James L Symes  Dana R Kester 《Geochimica et cosmochimica acta》1984,48(11):2219-2229

Natural malachite is a well defined solid demonstrating reproducible solubility behavior over a wide range of pH. The following equilibrium constants associated with the malachite dissolution equilibrium at 25°C, 1 atm were determined:

(infinite dilution)

$\text{K}{}^1{}_{\mathrm{sp}}\text{=}\text{[Cu}{}^{\mathrm{2+}}\text{]}{}^2\text{[CO}{}^{\mathrm{2?}}{}_3\text{]K}{}^2{}_{\mathrm{w}}\text{a}{}^2{}_{\mathrm{H+}}\text{= 10. ± 0.2 × 10}{}^{\mathrm{?32}}$

(0.72 ionic strength)

(36.9‰ salinity seawater). The temperature dependence of a “mixed” equilibrium constant, K_sp⁺, of the form:

has been measured at I = 0.72, yielding the relationship:

$\text{log K}{}^2{}_{\mathrm{sp}}\text{= (? 9.8 ± 0.03) × 10}{}^4\text{(}\text{1}\text{T°K}\text{) + (1.52 ± 0.09)}$

within a 5–25°C temperature range. The effect of pressure on the solubility of malachite in water and seawater was estimated from partial molar volume and compressibility data. For 25 °C at infinite dilution $\text{K'}{}_{\mathrm{sp}}\text{(1000 bar)}\text{K'}{}_{\mathrm{sp}}\text{(0)}\text{= 240}$ and in seawater $\text{K′}{}_{\mathrm{sp}}\text{(1000)}\text{K'}{}_{\mathrm{sp}}\text{(0)}\text{= 44}$.Comparison of stoichiometric and apparent malachite equilibrium constants has been used to estimate the extent of copper(II) ion interaction at the ionic strength of seawater. In dilute carbonate medium (total alkalinity, TA = 2.4 meq/kg H₂O, pH 8.3), 2.9% of total dissolved copper exists as the free copper(II) ion and in seawater (S = 36.9%., TA = 2.3 meq/kg H₂O, pH = 8.1), $\text{[Cu}{}^{\mathrm{2+}}\text{]}\text{T(Cu)}$ is 3.1%.Total dissolved copper levels of approximately 450–750 nMol/Kg are necessary to attain malachite saturation conditions in the open ocean. Observations of malachite particles suspended in seawater must be explained by precipitation or solid phase substitution reactions from localized environments rather than by direct precipitation from bulk seawater.     

	a	b	c	Eact(kJ mol -1)
Quarts	1.174	-2.028 x 103	-4158	67.4–76.6
α-Cristobalite	-0.739	0	-3586	68.7
β-Cristobalite	-0.936	0	-3392	65.0
Amorphous silica	-0.369	-7.890 x 10-4	3438	60.9–64.9

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

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.     

Diffusion of ions in sea water and in deep-sea sediments

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.     

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.     

Dissociation constants for alkali earth and sodium borate ion pairs from 10 to 50°C

Potentiometric measurements in dilute sodium borate solutions with added alkali earth chlordie salts yield the following expressions for the dissociation constants of alkali earth borate ion pairs from 10 to 50°C:

$\text{p}\text{K(}\text{MgH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.266+0.001204 T}$

$\text{p}\text{K(}\text{CaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.154+0.002170 T}$

$\text{p}\text{K(}\text{SrH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.033+0.001738 T}$

$\text{p}\text{K(}\text{BaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.942+0.001850 T}$

where T is in °K. Enthalpies for the dissociation reactions at 25°C are less than 1 kcal./mole for all the alkali earth borate ion pairs.Values for pK(NaH₂BO₃°) from 5 to 55°C computed from the experimental data of Owen and King are in good agreement with those determined potentiometrically. The average value from both methods is 0.22 ± 0.1 at 25°C.Application to seawater of computed pK's for MgH₂BO₃⁺, CaH₂BO₃⁺ and NaH₂BO₃⁰ yields an apparent dissociation constant for boric acid of 8.73 vs. 8.70 measured by Lyman, 8.68 by Buch and 8.73 by Byrne and Kester.     

Thermodynamic stability studies of the basic copper carbonate mineral,malachite

Natural malachite is a well defined solid demonstrating reproducible solubility behavior over a wide range of pH. The following equilibrium constants associated with the malachite dissolution equilibrium at 25°C, 1 atm were determined:

(infinite dilution)

$\text{K}{}^1{}_{\mathrm{sp}}\text{=}\text{[Cu}{}^{\mathrm{2+}}\text{]}{}^2\text{[CO}{}^{\mathrm{2?}}{}_3\text{]K}{}^2{}_{\mathrm{w}}\text{a}{}^2{}_{\mathrm{H+}}\text{= 10. ± 0.2 × 10}{}^{\mathrm{?32}}$

(0.72 ionic strength)

(36.9‰ salinity seawater). The temperature dependence of a “mixed” equilibrium constant, K_sp⁺, of the form:

has been measured at I = 0.72, yielding the relationship:

$\text{log K}{}^2{}_{\mathrm{sp}}\text{= (? 9.8 ± 0.03) × 10}{}^4\text{(}\text{1}\text{T°K}\text{) + (1.52 ± 0.09)}$

within a 5–25°C temperature range. The effect of pressure on the solubility of malachite in water and seawater was estimated from partial molar volume and compressibility data. For 25 °C at infinite dilution $\text{K'}{}_{\mathrm{sp}}\text{(1000 bar)}\text{K'}{}_{\mathrm{sp}}\text{(0)}\text{= 240}$ and in seawater $\text{K′}{}_{\mathrm{sp}}\text{(1000)}\text{K'}{}_{\mathrm{sp}}\text{(0)}\text{= 44}$.Comparison of stoichiometric and apparent malachite equilibrium constants has been used to estimate the extent of copper(II) ion interaction at the ionic strength of seawater. In dilute carbonate medium (total alkalinity, TA = 2.4 meq/kg H₂O, pH 8.3), 2.9% of total dissolved copper exists as the free copper(II) ion and in seawater (S = 36.9%., TA = 2.3 meq/kg H₂O, pH = 8.1), $\text{[Cu}{}^{\mathrm{2+}}\text{]}\text{T(Cu)}$ is 3.1%.Total dissolved copper levels of approximately 450–750 nMol/Kg are necessary to attain malachite saturation conditions in the open ocean. Observations of malachite particles suspended in seawater must be explained by precipitation or solid phase substitution reactions from localized environments rather than by direct precipitation from bulk seawater.