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.     

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.     

Origin of granitic magma by crustal remobilisation: Rb-Sr and Pb/Pb geochronology and isotope geochemistry of the late Archaean Qôrqut Granite Complex of southern West Greenland

Rb-Sr and Pb/Pb whole rock isochrons on the Qôrqut Granite Complex yield ages of $\text{2530 ± 30}\text{Myr}\text{(}\text{initial}{}^{87}\text{Sr}{}^{86}\text{Sr}\text{= 0.7081 ± 0.0008)}$ and 2580 ± 80 Myr respectively. A model relating initial Sr and Pb isotopic compositions of the Qôrqut granites to the Sr and Pb isotopic compositions of the Amîtsoq gneisses (ca. 3700 Myr) and Nûk gneisses (ca. 2900 Myr) at 2550 Myr ago, as well as Sr and Pb contents of the gneiss units, suggests that between 40 and 50% of the Qôrqut granite magma was generated by partial melting of Amîtsoq gneisses, and the remainder by partial melting of Nûk gneisses.     

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.     

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

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.     

Light hydrocarbons in Red Sea brines and sediments

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.     

Complexing of silica by iron(III) in natural waters

Determination of amorphous silica solubility in acidified ferric nitrate solutions confirms the presence of ferric silicate complexing. A dissociation constant for the reaction:

$\text{FeH}{}_3\text{SiO}{}_4{}^{\mathrm{2+}}\text{→}\text{Fe}{}^{\mathrm{3+}}\text{+}\text{H}{}_3\text{SiO}{}_4{}^{\mathrm{?}}$

of 10^?9.8 ± 0.3 pK units at room temperature (22 ± 3°C) is obtained, in close agreement with reported values at 25°C corrected to zero ionic strength of 10^?9.9 by Weber and Stumm and 10^?9.5 by Olson and O'Melia. Iron-silicate complexing may be of significance to the mobilization of silica in acid waters associated with oxidizing sulphide deposits and coal strip mining and the precipitation of secondary silicate mineral phases.     

Stability of ethylxanthate ion in neutral and weakly acidic media. Part 1: Influence of pH

Xanthates are used in the flotation of sulfide ores although their aqueous solutions are not stable under certain conditions. Their stability in acidic and weakly acidic aqueous solutions was therefore investigated, as these media are required for some processes.The peak absorbances of ethylxanthate ion and carbon disulfide were first determined in aqueous solution. The decomposition of ethylxanthate ion was analyzed by measuring variations in absorbance (at 301 nm) and pH with respect to time. A pH regulation system was then used while measuring variations in absorbance and productions of protons caused by xanthate decomposition.The results concerning xanthate half-lives show good agreement with the literature, but the kinetic results deviate substantially. The following relation was obtained for half-life:

$\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{=9.67×10}{}^{\mathrm{?6}}\text{(pH)}{}^{11}\text{;4?7;T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{in seconds}$

We established that ethylxanthate decomposition at pH 4 is a first order reaction with respect to ethylxanthate concentration, and postulating this order to the other pH values, the following kinetic relation was found:

$\text{v= ?(1.22×10}{}^4\text{[H}{}^{\mathrm{+}}\text{]?1.36×10}{}^{\mathrm{?2}}\text{)([}\text{EtX}{}^{\mathrm{?}}\text{]}{}_{\mathrm{\infty }}\text{) (4?pH?7)}$

where v is the rate of decomposition (mol l^?1 min^?1), and [EtX^?]_∞ is the ethylxanthate concentration when the decomposition equilibria are reached (mol l^?1). The better concentration was found to obey the law:

$\text{[}\text{EtX}{}^{\mathrm{?}}\text{]}{}_{\mathrm{\infty }}\text{=3.142×10}{}^{\mathrm{?5}}\text{pH ? 1.255 × 10}{}^{\mathrm{?4}}\text{(4?pH?6)}$

     

A study of strontium in core 119K,Discovery deep,Red Sea

The isotopic composition of strontium of pore water and of authigenic minerals leached from the sediment of core 119K with hot aqua regia is similar to that of the brine in the Discovery deep and differs from that of normal seawater. The average ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratio of strontium removed by acid leaching is 0.7077 ± 0.0007 (1σ) compared to a value of 0.70904 for the Red Sea. The detrital silicate fraction exhibits an approximate inverse correlation between ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratios and strontium concentrations which provides tentative support for a model in which the detrital silicate fraction of deep-sea sediment is considered to be a mixture of terrigenous dust of sialic composition enriched in radiogenic ⁸⁷Sr and of volcanogenic material of basaltic composition and low ⁸⁷Sr abundance. The ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratios of the shells of foraminifers and pteropods, expressed as δ ⁸⁷Sr‰ relative to 0.70904 for seawater, decrease from $\text{?0.23 ± 0.17‰}$ at 90 cm to $\text{?0.82 ± 0.17‰}$ at 273 cm and remain constant at this value to a depth of 450 cm. The lowering of the δ ⁸⁷Sr values is attributed both to the presence of aragonite overgrowths on pteropod shells and to possible isotope exchange with strontium in the connate fluid.     

Delivery of transuranic elements by rain to the Mediterranean Sea

The concentrations of ²³⁸Pu, ^{239 + 240}Pu, ²⁴¹Am and ¹³⁷Cs were determined in rain samples collected at Monaco in the course of 1978–1979. Based on these data, the annual deliveries of these radionuclides to the Mediterranean by rain are computed to be 0.18 ± 0.01 pCim^?2 for ²³⁸Pu, 8.1 ± 0.1 pCim^?2 for ^{239 + 240}Pu, 0.58 ± 0.02 pCim^?2 for ²⁴¹Am and 351 ± 4 pCim^?2 for ¹³⁷Cs.Comparing the delivery data with the mixed layer inventories of ^{239 + 240}Pu and ²⁴¹Am in the Mediterranean, the upper limits of the mean residence time of these radionuclides in the mixed layer were estimated to be 12.3 yr for ^{239 + 240}pu and 2.9 yr for ²⁴¹Am. These values are consistent with the conclusion deduced from the vertical distribution pattern of these transuranic elements in the Mediterranean.Based on delivery values, the annual activity ratios for ${}^{238}\text{pu}{}^{\mathrm{239\; +\; 240}}\text{Pu}$, ${}^{241}\text{Am}{}^{\mathrm{239\; +\; 240}}\text{Pu}$ and ${}^{\mathrm{239\; +\; 240}}\text{pu}{}^{137}\text{Cs}$ are found to be 0,022, 0.072 and 0.023 respectively. The ${}^{238}\text{pu}{}^{\mathrm{239\; +\; 240}}\text{pu}$ and ${}^{\mathrm{239\; +\; 240}}\text{Pu}{}^{137}\text{Cs}$ activity ratios vary within relatively narrow ranges with time, while a much wider variation was observed for the ${}^{241}\text{Am}{}^{\mathrm{239\; +\; 240}}\text{Pu}$ activity ratio. The cause of the wider variation of the ${}^{241}\text{Am}{}^{\mathrm{239\; +\; 240}}\text{Pu}$ ratio may be related to the difference in the mean age of fallout brought down in different seasons.     

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.     

Diffusivity of oxygen in jadeite and diopside melts at high pressures

The diffusivity of oxygen was determined in melts of Jadeite (NaAlSi₂O₆) and diopside (CaMgSi₂O₆) compositions using diffusion couples with ¹⁸O as a tracer. In the Jadeite melt, the diffusivity of oxygen increases from $\text{6.87}{}_{\mathrm{?0.25}}{}^{\mathrm{+0.28}}\text{× 10}{}^{\mathrm{?10}}\text{cm}{}^2\text{/}\text{sec}$ at 5 Kb to $\text{1.32 ± 0.08 × 10}{}^{\mathrm{?9}}\text{cm}{}^2\text{/}\text{sec}$ at 20 Kb at constant temperature (1400°C), whereas in the diopside melt at 1650°C, the diffusivity decreases from $\text{7.30}{}_{\mathrm{?0.18}}{}^{0.29}\text{× 10}{}^{\mathrm{?7}}\text{cm}{}^2\text{/}\text{sec}$ at 10 Kb to $\text{5.28}{}_{\mathrm{?0.55}}{}^{\mathrm{+0.60}}\text{× 10}{}^{\mathrm{?7}}\text{cm}{}^2\text{/}\text{sec}$ at 17 Kb. These results demonstrate that the diffusivity is inversely correlated with the viscosity of the melt. For the jadeite melt, in particular, the inverse correlation is very well approximated by the Eyring equation using the diameter of oxygen ions as a unit distance of translation, suggesting that the viscous flow is rate-limited by the diffusion of individual oxygen ions. In the diopside melt, the activation volume is slightly greater than the molar volume of oxygen ion, indicating that the individual oxygen ion is the diffusion unit. The negative activation volume obtained for the jadeite melt is interpreted as the volume decrease associated with a diffusive jump of an oxygen ion due to local collapse of the network structure.     

Investigations of an intrusive contact,northwest Nelson,New Zealand—II. Diffusion of radiogenic and excess 40Ar in hornblende revealed by 40Ar39Ar age spectrum analysis

The Rameka Gabbro, emplaced 367 Ma ago, experienced a well documented reheating on intrusion of the Separation Point Batholith 114 Ma ago. ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analyses of hornblende from the Rameka Gabbro show diffusion gradients which provide information on the ⁴⁰Ar boundary concentration during reheating.Three samples of hornblende exhibit age spectra that conform to a model of ⁴⁰Ar loss by diffusion, implying a zero ⁴⁰Ar boundary concentration during heating. The calculated ⁴⁰Ar loss from these samples, together with a model of heat flow in the aureole, provide estimates of diffusion coefficients of ⁴⁰Ar in Mg-rich hornblende which correspond to an activation energy, E, of ~60 kcal-mol^?1 and a frequency factor. D₀, of ~ 10^?3 cm²-sec^?1. When combined with laboratory diffusion results, these data yield a well defined diffusion law (E = 63.3 ± 1.7 kcal-mol^?1, $\text{D}{}_0\text{= 0.022}{}^{\mathrm{+0.048}}{}_{\mathrm{?0.010}}\text{cm}{}^2\text{-}\text{sec}{}^{\mathrm{?1}}$).The age spectra of the eight other samples record steep gradients of excess ⁴⁰Ar over the first few percent of gas release. Although this effect causes high apparent conventional K-Ar ages, the plateau segments of many sampes still record the crystallization age of 367 ± 5 Ma. These measurements show that the excess ⁴⁰Ar phase developed locally in the intergranular regions of the gabbro, following intrusion of the batholith. on time scales that varied from 10⁴ to 10⁶years. The minimum average ${}^{40}\text{Ar}{}^{36}\text{Ar}$ ratio of this component was found to be 1300 ± 400. The partial pressure of Ar was at least 10^?2 bars in some places.A single ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analysis of plagioclase reveals a ‘saddle-shaped” release pattern with a minimum at 140 Ma.In conjunction with theoretical diffusion models and a diffusion law, ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age spectrum analysis of hornblende that has experienced a post-crystallization heating can provide close estimates of the maximum temperature of the thermal event as well as both age of crystallization and reheating.     

Carbonate equilibria in hydrothermal systems: First ionization of carbonic acid in NaCl media to 300°C

The ionization quotients of aqueous carbon dioxide (carbonic acid) have been precisely determined in NaCl media to 5 m and from 50° to 300°C using potentiometric apparatus previously developed at Oak Ridge National Laboratory. The pressure coefficient was also determined to 250°C in the same media. These results have been combined with selected information in the literature and modeled in two ways to arrive at the best fits and to derive the thermodynamic parameters for the ionization reaction, including the equilibrium constant, activity coefficient quotients, and pressure coefficients. The variation with temperature of the two fundamental quantities $\text{Δ}\text{V}\text{?}{}^{\mathrm{o}}$ and $\text{Δ}\text{C}\text{?}{}^{\mathrm{o}}{}_{\mathrm{p}}$ were examined along the saturation vapor pressure curve and at constant density. The results demonstrated again that for reactions with minimal electrostriction changes the magnitudes and variations of $\text{Δ}\text{C}\text{?}{}^{\mathrm{o}}{}_{\mathrm{p}}$ and $\text{Δ}\text{V}\text{?}{}^{\mathrm{o}}$ with temperature are small and, in addition, $\text{Δ}\text{C}\text{?}{}_{\mathrm{p}}$ and $\text{Δ}\text{V}\text{?}$ are approximately independent of salt concentration.The results have also been applied to an examination of the solubility of calcite as a function of pH (in a given NaCl medium) for the neutral to acidic region both for systems with fixed CO₂ pressure and systems where the calcium ion concentration equals the concentration of carbon. The pH of saturated solutions of calcite with P_CO2 of 12 bars increases from 5.1 to 5.5 between 100° and 300°C.     

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.     

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.     

Sodium and potassium coprecipitation in aragonite

The coprecipitation of Na and K was experimentally investigated in aragonite. The distribution functions were determined at pH 6.8 and 8.8 over aqueous Na and K concentrations of between 5 × 10^?4and 2.0 M and temperatures of between 25 and 75°C.The mole fractions of Na and K in aragonite are related to the aqueous ratios of Na and Ca by a function of the form

$\text{log}\text{X}{}_{\mathrm{Na}}{}_2\text{CO}{}_3\text{,K}{}_2\text{CO}{}_3\text{= C}{}_0\text{+ C}{}_1\text{log}\text{a}{}^2{}_{\mathrm{Na}}\text{? ,K}{}^{\mathrm{?}}\text{a}{}_{\mathrm{Ca}}{}^{\mathrm{2+}}$

where C₀ and C₁ are constants at a given temperature. This equation was derived by a statistical model assuming a heterogeneous energy distribution for the sites of incorporation. The independence of the coprecipitation process from aqueous anion activities suggests that carbonate is the only anionic species in the solid solution.     

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.     

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.