Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems

The rates of chemical reactions between aqueous sulfates and sulfides are essentially identical to sulfur isotopic exchange rates between them, because both the chemical and isotopic reactions involve simultaneous oxidation of sulfide-sulfur atoms and reduction of sulfate-sulfur. The rate of reaction can be expressed as a second order rate law: R = k ·[∑ SO 4 2− ]·[∑ S 2− ], where R is the overall rate, k is the rate constant and [∑SO 4 2− ] and [∑S 2− ] are molal concentrations. We have computed the rate constants from the available experimental data on the partial exchange of sulfur isotopes between aqueous sulfates and sulfides using the rate law established by us: ln( α e − α α e − α 0 ) = − kt([∑SO 4 2− ] + [∑S 2− ]) , where t is time and α 0 , α, and α e are, respectively, the fractionation factors at t = 0 (the initial condition), at the end of experiment, and at equilibrium. The equilibrium fractionation factor can be expressed as: 1000 ln α e = 6.463 × 10 6 T 2 + 0.56 (±.5) ( T in Kelvin). The rate constants are strongly dependent on T and pH, but not in as simple a manner as suggested by Igumnov (1976). Our rate constants in Na-bearing hydrothermal solutions decrease by 1 order of magnitude with an increase in pH by 1 unit at pH's less than ~3, remain constant in the pH range of ~4 to ~7, and again decrease at pH >7. The activation energy for the reaction also depends on pH: 18.4 ± 1 kcal/mole at pH = 2, 29.6 ± 1 kcal/mole at pH = 4 to 7, and between 40 and 47 kcal/mole at pH around 9. The observed pH dependence of the rate constant and of the activation energy can be best explained by a model involving thiosulfate molecules as reaction intermediates, in which the intramolecular exchange of sulfur atoms in thiosulfates becomes the rate determining step. The rate constants obtained in this study were used to compute the changes in the isotopic fractionation factors between aqueous sulfates and sulfides during cooling of fluids. Comparisons with data of coexisting sulfate-sulfide minerals in hydrothermal deposits, suggest that simple cooling was not a likely mechanism for coprecipitation of sulfate and sulfide minerals at temperatures below 350°C. Mixing of sulfide-rich solutions with sulfate-rich solutions at or near the depositional sites is a more reasonable process for explaining the observed fractionation. The degree of attainment of chemical equilibrium between aqueous sulfates and sulfides in a hydrothermal system, and the applicability of a O 2 - pH type diagrams to mineral deposits, depends on the ∑S content and the thermal history of the fluid, which in turn is controlled by the flow rate and the thermal gradient in the system. The rates of sulfate reduction by non-bacterial processes involving a variety of reductants are also dependent on T , pH, [∑SO 4 2− ], and [∑S 2− ], and appear to be fast enough to become geochemically important at temperatures above about 200°C.