A fundamental equation for calcite dissolution kinetics

A fundamental rate equation for the dissolution of calcite in a pure 0.7 M KC1 solution has been determined. Between pH 8.0 and 10.1 the kinetics of the dissolution reaction can be expressed by the equation

$\text{d[Ca}{}^{\mathrm{2+}}\text{]/dt = kA(C-[Ca}{}^{\mathrm{2+}}\text{]}\text{1}\text{2}\text{[CO}{}_3{}^{\mathrm{2?}}\text{]}\text{1}\text{2}\text{)}$

, where d[Ca²⁺]/dt is the rate in mole cm^?3s^?1, k is the apparent rate constant in s^?1 cm^?2, A is the calcite surface area and C is the square root of the calcite solubility constant. The apparent rate constant at 20°C is 9.5 × 10^?6s^?1cm^?2. The apparent activation energy for the reaction between 5 and 50°C is 8.4 kcal mole^?1.The reaction rate is pH independent above pH = 7.5. At pH values less than 8, [CO₃^2?] becomes negligible, and the rate becomes fast and should be dependent on the calcite surface area alone, if there is no change in mechanism.The stirring coefficient between 2.8 and 11.1 rev s^?1 is 0.33. This, together with the relatively high activation energy, indicates that the reaction is mainly chemically controlled.Interpolation of the experimental results into seawater systems gives a computed rate several magnitudes greater than the observed rate, but considerably less than that calculated for a diffusion-controlled reaction.     

Experimental paleotemperature equation for planktonic foraminifera

Small live individuals of Globigerinoides sacculifer which were cultured in the laboratory reached maturity and produced garnets. Fifty to ninety percent of their skeleton weight was deposited under controlled water temperature (14° to 30°C) and water isotopic composition, and a correction was made to account for the isotopic composition of the original skeleton using control groups.Comparison of. the actual growth temperatures with the calculated temperature based on paleotemperature equations for inorganic CaCO₃ indicate that the foraminifera precipitate their CaCO₃ in isotopic equilibrium. Comparison with equations developed for biogenic calcite give a similarly good fit. Linear regression with Craig's (1965) equation yields: $\text{t = ?0.07 + 1.01}\text{t}\text{?}\text{(r= 0.95)}$ where t is the actual growth temperature and $\text{t}\text{?}$ Is the calculated paleotemperature. The intercept and the slope of this linear equation show that the familiar paleotemperature equation developed originally for mollusca carbonate, is equally applicable for the planktonic foraminifer G. sacculifer.Second order regression of the culture temperature and the delta difference (δ¹⁸Oc ? δ¹⁸Ow) yield a correlation coefficient of r = 0.95: $\text{t}\text{?}\text{= 17.0 ? 4.52(δ}{}^{18}\text{Oc ? δ}{}^{18}\text{Ow) + 0.03(δ}{}^{18}\text{Oc ? δ}{}^{18}\text{Ow)}{}^2$$\text{t}\text{?}\text{, δ}{}^{18}\text{Oc}$ and δ¹⁸Ow are the estimated temperature, the isotopic composition of the shell carbonate and the sea water respectively.A possible cause for nonequilibnum isotopic compositions reported earlier for living planktonic foraminifera is the improper combustion of the organic matter.     

Partial molal volume calculations for the dissolution of aged amorphous silica in salt water and seawater at 0–2°C

Measurement of solubility as a function of pressure allows calculation of $\text{3}\text{V}\text{?}{}_1$. Using this experimental approach, the best estimate of $\text{3}\text{V}\text{?}{}_1$ for the dissolution of aged amorphous silica in salt water or seawater at 0–2°C is ?9.9 cm³ mol^?1 (standard error = 0.4 cm³ mol^?1). This gives , which compares well with other published values of .     

Geochimie et teneurs isotopiques des systèmes saisonniers de dissolution de la calcite dans un sol sur craie

In a soil developed on the Cretaceous chalk of the Eastern Paris basin, calcite dissolution begins at the surface. The soil water is rapidly saturated in calcite. Calcite dissolution follows two different pathways according to seasonal pedoclimatic conditions.During winter: the soil is only partly saturated in water and the CO₂ partial pressure is low (Ca 10^?3 atm.). As a consequence total inorganic dissolved carbon (TIDC) is a hundred times the carbon content of the gaseous phase. Equilibrium is usually observed between the two phases. It is a closed system. The measured carbon 14 activity (87,5%) and ¹³C content ($\text{δ}{}_{\mathrm{tidc}}{}^{13}\text{C = ?12,2\%0}$) of the drainage water are very close to theoretical values calculated for an ideal mixing system between gaseous and mineral phases (respectively characterized by the following isotopic values: $\text{δ}{}_{\mathrm{G}}{}^{13}\text{C = ?21,5\%0}$; $\text{A}{}_{\mathrm{G}}{}^{14}\text{C = 118\%}$; $\text{δ}{}_{\mathrm{M}}{}^{13}\text{C = +2,9\%0}$; $\text{A}{}_{\mathrm{M}}{}^{14}\text{C = 28\%}$).During spring and summer: the soil moisture decreases, the input of biogenic CO₂ induces an increase of the soil CO₂ partial pressure (Ca from 3.10^?3 atm to 7.10^?3 atm). The carbon content of the gaseous phase is higher by an order of magnitude compared to winter conditions. Therefore the aqueous phase is undersaturated in CO₂ with respect to the latter. This disequilibrium occurs as a result of unbalanced rates of CO₂ dissolution and CO₂ effusion toward atmosphère. It is an open system. The carbon isotopic ratio of the aqueous phase is regulated by that of the gaseous phase, as demonstrated by the agreement between measured and calculated isotopic compositions (respectively δ_{L mes} = from ?9,4%0 to ?11,5%0, δ_{l calc} = from ?9,8%0 to ?13,9%0 A_{L mes} = 119%, A_{L calc} = from 119% to 125%).The solutions originating from both systems (open and closed) move downwards without significant mixing together. It has also been observed that no significant variation of the TIDC isotopic composition occurs during precipitation of secondary calcite.     

On the observation of 92Nb and 94Nb in nature

Radioactivity measurements have shown evidence for long-lived ⁹²Nb and $\text{2.03 × 10}{}^4\text{yr}{}^{94}\text{Nb}$ in natural niobium. The specific activity of ⁹⁴Nb was observed to be 0.32 ± 0.03 dis/min. kg Nb and that of ⁹²Nb to be 0.058 ± 0.035 dis/min. kg Nb. With $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ taken as ≈ 1.7 × 10⁸yr, the isotopic abundance of ⁹⁸Nb is 1.2 × 10^?10 per cent.     

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.     

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

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.     

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.     

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 geochemical evolution of the Pleistocene Lake Lisan-Dead Sea system

The geochemical history of Lake Lisan, the Pleistocene precursor of the Dead Sea, has been studied by geological, chemical and isotopic methods.Aragonite laminae from the Lisan Formation yielded (equivalent) Sr/Ca ratios in the range 0.5 × 10^?2?1 × 10^?2, Na/Ca ratios from 3.6 × 10^?3 to 9.2 × 10^?3, $\text{δ}{}^{18}\text{O}{}_{\mathrm{PDB}}$ values between 1.5 and 7%. and $\text{δ}{}^{13}\text{C}{}_{\mathrm{PDB}}$ from ?7.7 to 3.4%..The distribution coefficient of Na⁺ between aragonite and aqueous solutions, $\text{λ}{}^{\mathrm{A}}{}_{\mathrm{Na}}$, is experimentally shown to be very sensitive to salinity and nearly temperature independent. Thus, Na/Ca in aragonite serves as a paleosalinity indicator.Sr/Ca ratios and $\text{δ}{}^{18}\text{O}$ values in aragonite provide good long-term monitors of a lake's evolution. They show Lake Lisan to be well mixed, highly evaporated and saline. Except for a diluted surface layer, the salinity of the lake was half that of the present Dead Sea (15 vs 31%).Lake Lisan evolved from a small, yet deep, hypersaline Dead Sea-like, water body. This initial lake was rapidly filled-up to its highest stand by fresh waters and existed for about 40,000 yr before shrinking back to the present Dead Sea. The chemistry of Lake Lisan at its stable stand represented a material balance between a Jordan-like input, an original large mass of salts and a chemical removal of aragonite. The weighted average depth of Lake Lisan is calculated, on a geochemical basis, to have been at least 400, preferably 600 m.The oxygen isotopic composition of Lake Lisan water, which was higher by at least 3%. than that of the Dead Sea, was probably dictated by a higher rate of evaporation.Na/Ca ratios in aragonite, which correlate well with $\text{δ}{}^{13}\text{C}$ values, but change frequently in time, reflect the existence of a short lived upper water layer of varying salinity in Lake Lisan.     

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:

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

     

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.     

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.     

An evaluation of rate equations for calcite precipitation kinetics at pCO2 less than 0.01 atm and pH greater than 8

We used a reproducible seeded growth technique with a pH-stat to study the kinetics of calcite precipitation at 25°C. We performed different experiments at initial Ca²⁺ and HCO₃^? concentrations ranging from 0.7–2 and 4–7 mmol L^?1, pH values ranging from 8.25 to 8.70, $\text{pCO}{}_2$ values ranging from 0.0006 to 0.01 atm, and ionic strengths ranging from 0.015 to 0.10 mol L^?1. With this experimental data set, we used initial rate measurements and integral methods to test several precipitation rate equations. Rate equations that possess a disequilibrium functional dependence, such as the BURTON et al. (1951) dislocation model, forms of the Davies and Jones (1955) model, and the model used by Reddy and Nancollas (1973), did not adequately describe the kinetics of calcite precipitation at pH greater than 8 and $\text{pCO}{}_2$ less than 0.01 atm. Rate equations that describe independent dissolution and precipitation mechanisms with elementary reactions, such as the equation presented by Plummeret al. (1978), and nancollas and Reddy (1971) were more successful. However, Plummer's model did not adequately describe the rate of all experiments due to the presence of an OH^? surface term in the precipitation rate equation. The elementary reaction of the Nancollas and Reddy model is written in terms of bulk Ca²⁺ and CO₃^? concentrations, and appears to be the most successful model which describes calcite precipitation at pH > 8 and $\text{pCO}{}_2\text{< 0.01}$ atm. The Nancollas and Reddy model, altered to account for varying ionic strengths, adequately described the rate of all experiments and yielded a precipitation rate constant of $\text{118.2 ± 13.9}$ dm⁶ mol^?1 m^?2 s^?1, with an apparent Arrhenius activation energy of 48.1 kJ mol^?1.     

Liquidus relationships in the system CaCO3Ca(OH)2CaS and the solubility of sulfur in carbonatite magmas

CaCO₃Ca(OH)₂CaS serves as a model system for sulfide solubility in carbonatite magmas. Experiments at 1 kbar delineate fields for primary crystallization of CaCO₃, Ca(OH)₂ and CaS. The three fields meet at a ternary eutectic at 652°C with liquid composition (wt%): CaCO₃ = 46.1%, Ca(OH)₂ = 51.9%, CaS = 2.0%. Two crystallization sequences are possible for liquids that precipitate calcite, depending upon whether the liquid is on the low-CaS side, or the high-CaS side of the line connecting CaCO₃ to the eutectic liquid. Low-CaS liquids precipitate no sulfide until the eutectic temperature is reached leading to sulfide enrichment. The higher-CaS liquids precipitate some sulfide above the eutectic temperature, but the sulfide content of the melt is not greatly depleted as the eutectic temperature is approached. Theoretical considerations indicate that sulfide solubility in carbonate melts will be directly proportional to and inversely proportional to ; it also is likely to be directly proportional to melt basicity, defined here by . A strong similarity exists in the processes which control sulfide solubility in carbonate and in silicate melts. By analogy with silicates, ferrous iron, which was absent in our experiments, may also exert an important influence on sulfide solubility in natural carbonatite magmas.     

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.     

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

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

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

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

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.     

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.     

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.