A chemical model for the major electrolyte component of seawater based on the Brønsted-Guggenheim hypothesis

The Brønsted-Guggenheim hypothesis of specific ionic interaction is used to develop a chemical model for the major electrolyte components in seawater (Na⁺---K⁺---Mg²⁺---Ca²⁺---Cl⁻---SO₄²⁻ at 25°C and 1 atm total pressure. The model is shown to be in essential agreement with models based on the Bjerrum ion-association hypothesis (e.g., Garrels and Thompson, 1962), with calculations based on the ionic hydration and cluster expansion theories of electrolyte solutions, and with available experimental evidence.The Brønsted-Guggenheim model is computationally simpler than the currently accepted Bjerrum model and results directly in the conventional total single-ion activity coefficients that are most commonly required for calculations in seawater equilibria. The simple form of the equations should enable the model to be extended quite readily to cover a wide range of temperature, pressure and solution composition. However, applications are at present restricted by the availability of the appropriate interaction coefficients.     

Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. II. Formation constants for the monosilicate ions SiO(OH)3 and SiO2(OH)2. A precision study at 25°C in a simplified seawater medium

The hydrolysis of silicic acid, Si(OH)₄, was studied in a simplified seawater medium (0.6 M Na(Cl)) at 25°C. The measurements were performed as potentiometric titrations (hydrogen electrode) in which OH⁻ was generated coulometrically. The total concentration of Si(OH)₄, B, and log[H⁺] were varied within the limits 0.00075 B 0.008 M and 2.5 -log[H⁺] 11.7, respectively. Within these ranges the formation of SiO(OH)₃⁻ and SiO₂(OH)₂²⁻ with formation constants log β₋₁₁(Si(OH)₄ SiO(OH)₃⁻ + H⁺) = −9.472 ±0.002 and log β₋₂₁(Si(OH)₄ SiO₂(OH)₂²⁻ + 2H⁺) = −22.07 ± 0.01 was established. With B > 0.003 M polysilicate complexes are formed, however, with -log[H⁺] 10.7 their formation does not significantly affect the evaluated formation constants. Data were analyzed with the least squares computer program LETAGROPVRID.     

Theoretical considerations about the reactions of calcification in sea water

We examine the concentration variations of the different parameters X of the carbonate system in seawater when calcium carbonate precipitation occurs. Variations are expressed as ∂[X]/∂[Ca²⁺]. Four different cases are considered: spontaneous chemical precipitation; calcification combined with photosynthetic activity under a constant ΔCT/Δ[Ca²⁺] ratio; precipitation under constant p_CO2 and precipitation under constant [Ca²⁺]·[CO₃²⁻] ionic concentration product. The last condition should be maintained by an ecosystem which, thanks to the regulation of its calcifying and photosynthetic activity, would absorb 1 mol of carbon for organic tissue each time 1 mol of CaCO₃ is formed. This stoichiometric ratio would allow the activity of these biological communities to go on in practically closed systems during periods compatible with their growth or development cycles.     

The effect of ionic interaction on the rates of oxidation in natural waters

The effect of ionic interactions on the kinetics of disproportionation of HO₂, and the oxidation of Fe(II) and Cu(I) has been examined. The interactions of O₂ with Mg²⁺ and Ca²⁺ ions in seawater increases the lifetime by 3–5 times compared to water. The effect of OH⁻ on the oxidation of Fe(II) in water and seawater shows a second degree dependence from 5 to 45°C. The effect of salinity on the oxidation of Fe(II) was found to be independent of temperature, while the effect of temperature was found to be independent of salinity. The energy of activation for the overall rate constant was found to be 7 ± 0.5 kcal mol⁻¹.The effect of pH, temperature, salinity and ionic composition on the oxidation of Cu(I) has also been examined. In NaCl solutions from 0.5 to 6 M, the log k for the oxidation was a linear function of pH (6–8) with a slope of 0.2 ± 0.05. The reaction was strongly dependent on the Cl⁻ concentration with variation of from 0.3 to 340 min from 0.5 to 6 M Cl⁻. The rates of oxidation of Cu⁺ and CuCl⁰ responsible for these effects are dependent upon ionic strength. The energy of activation for the reaction was 8.5–9.9 kcal mol⁻¹ from 0.5 to 6 M. Studies of the oxidation in various NaX salts (X = I⁻, Br⁻ and Cl⁻) give rates in the order Cl⁻ > Br⁻ > I⁻ as expected, due to complex formation of Cu⁺ with X⁻.     

Characterization of vertical mixing at a tidal-front on Georges Bank

Studies of mixing were done at the northern flank of Georges Bank in the summer and autumn of 1988. Two time-series of the evolution and intensity of microstructure were examined over a tidal period in the context of tidal forcing and the evolution of the density and velocity field at the site. From the CTD, ADCP and microstructure observations (EPSONDE) on Georges Bank, several interesting features of the mixing processes were found. High dissipation and diffusivity regions appear near the bottom of the Bank. Turbulence near the bottom is highest in intensity and reaches farthest from the bottom at peak tidal flow and diminishes in intensity and vertical extent as the flow decreases. The thickness of the bottom turbulent layer has its maximum value when the flow is strongest and the stratification is weakest. Characterization of the dissipation rate and turbulent diffusivities in respect to buoyancy frequency N, current shear S, Richardson Number R_i and ε/νN² was done. Dissipation and χ_T showed little dependence on shear or N² but decreased at larger R_i. χ_t was found to be higher in regions of higher N² and increased as ε/νN² increased. K_T, K and K_ν, were all highest near the bottom in excess of 10⁻²m²s⁻¹ and decreased towards the surface. There was little suggestion of a dependence of mixing efficiency on S², R_i or ε/νN², but some indication that Γ decreases with decreasing N².     

The thermodynamics and kinetics of the hydrogen sulfide system in natural waters

The thermodynamics and kinetics of the H₂S system in natural waters have been critically reviewed. Equations have been derived for the solubility and ionization of H₂S in water and seawater as a function of salinity, temperature and pressure. Pitzer parameters for the interaction of the major cations (Na⁺, Mg²⁺ and Ca²⁺) with HS⁻ have been determined to allow one to calculate values of pK₁^* in various ionic media. The limited data available for the interaction of trace metals for HS⁻ are summarized and future work is suggested.The kinetics of oxidation of H₂S have also been examined as a function of pH, temperature, and salinity. The discrepancies in the available data are largely due to the different [O₂]/[HS−] ratios used in various studies. Over a limited pH range (6–8) the pseudo first order rate constant for the oxidation is shown to be directly proportional to the activity of HS⁻. Further studies are suggested to examine the effect of ionic media and temperature on the rate of oxidation.     

Carbon and nitrogen isotope composition of particulate organic matter in relation to mucilage formation in the northern Adriatic Sea

Carbon and nitrogen stable isotope ratios of particulate organic matter (POM) were studied approximately weekly during spring and summer 2003 and 2004 in the Gulf of Trieste (northern Adriatic Sea) in order to track the temporal variations and differences between two years. In parallel, particulate organic carbon (POC) and particulate nitrogen (PN), phytoplankton biomass (chlorophyll a), and N and P nutrients were monitored. All studied parameters, especially N and P nutrients and chlorophyll a, showed higher concentrations and larger variability in spring 2004. As a consequence the macroaggregates were produced in late spring 2004. The C and N isotope composition of POM was not directly linked to phytoplankton biomass dynamics. The δ¹³C_POC values covaried with temperature. In 2004, δ¹³C_POC variations followed the δ¹⁵N_PN values as well as the δ¹³C_DIC values which were probably more dependent on the photosynthetic use of ¹²C. Variations in δ¹⁵N_POM values were most probably the consequence of variations in N nutrient sources used in phytoplankton assimilation. The significant correlation between δ¹⁵N_PN values and nitrate concentrations in 2004 implies intense nitrate assimilation in the presence of higher nitrate concentration. This suggests nitrate as the key nutrient in the »new primary production«, later producing macroaggregates with a mean δ¹³C and δ¹⁵N values of − 19‰ and 5‰, respectively. A low fractionation factor ε, < 1‰, lower than that reported in other marine and lacustrine systems, was found probably to be a consequence of distinct phytoplankton species, i.e. several classes of autotrophic nanoflagellates, and specific growth conditions present in the Gulf of Trieste. The tentative use of C isotope composition of POM revealed a higher contribution of allochthonous organic matter in 2004 compared to 2003 due to higher riverine inflow.     

Aggregation of riverine colloidal iron in estuaries: A new kinetic study using stopped-flow mixing

The kinetics of aggregation of riverine colloidal iron have been examined using a stopped-flow technique which probes the first few seconds of mixing between river and sea water end members. A significant fraction, up to 80%, of the colloidal iron is aggregated during the first 1–2 s of mixing, indicating that the aggregation process is much faster than previously thought. Most of the aggregation induced by seawater results from the divalent cations Mg²⁺ and Ca²⁺, with the overall ionic strength having little influence. At equal concentrations of 27 mM, the rate of aggregation by alkaline earth cations increased with ionic size Mg²⁺ < Ca²⁺ < Sr²⁺ < Ba²⁺. The aggregation rates were indifferent to the anion (Cl⁻ or SO₄²⁻) present. Very high aggregation rates were also induced by the common water treatment coagulant Al₂(SO₄)₃ at concentrations in the range 20–30 µM Al(III), several orders of magnitude lower that those used for the seawater cations. Our results support the view that specific chemical interactions between the cations and the colloid particle surface, rather than simple electrical effects, control the colloid stability.     

Isotopic fractionation of dissolved nitrate during denitrification in the eastern tropical north pacific ocean

The isotopic composition (δ¹⁵N) of dissolved nitrate was measured at five stations within the oxygen-deficient region of the eastern tropical North Pacific Ocean (ETNP) and at one station 900 km northeast of Hawaii, which was considered to be representative of all major water masses of the Pacific. At this last station, the δ¹⁵N composition of dissolved nitrate decreased systematically from about +6‰ at 400 m to approximately +5‰ at 5,000 m; these results are consistent with other estimates from the western Pacific.In contrast, vertical profiles of δ¹⁵N of dissolved nitrate from the ETNP showed marked departure from the above observed trend and correlated with losses of nitrate arising from denitrification. Instantaneous fractionation factors (α) were estimated, using the one dimensional vertical diffusion-advection model. These results suggest that ¹⁴NO₃⁻ is consumed 3–4% faster than ¹⁵NO₃⁻, significantly larger than fractionations (2%) observed under laboratory conditions.Maximum rates of denitrification at 100 m were also evaluated and ranged from 0.6 to 8 μg-at 1⁻¹ yr⁻¹ for the stations investigated. The above upper limit is probably excessive, but the average maximum for the four stations analyzed is estimated to be 3.5 μg-at NO₃⁻ 1⁻¹ yr⁻¹. These results compare favorably with suitably corrected oxygen utilization rates derived from electron transport activity measurements.     

Singe-ion activities in aqueous solutions analogous to seawater

The method developed earlier, based on hydration numbers for individual ionic species, has been extended to aqueous systems of four electrolytes, MX, M₂Y, NX₂, and PX₂, with an unhydrated anion (X⁻). The procedure is used to calculate γ_Na, γ_Mg, γ_Ca, γ_Cl and γ_SO4 in a mixed electrolyte solution closely resembling seawater. Values of γ_K and γ_F in sea-water have also been estimated.     

The speciation of Fe(II) and Fe(III) in natural waters

The interactions of Fe(II) and Fe(III) with the inorganic anions of natural waters have been examined using the specific interaction and ion pairing models. The specific interaction model as formulated by Pitzer is used to examine the interactions of the major components (Na⁺, Mg²⁺, Ca²⁺, K⁺, Sr²⁺, Cl⁻, SO₄⁻, HCO₃⁻, Br⁻, CO₃²⁻, B(OH)₄⁻, B(OH)₃ and CO₂) of seawater and the ion pairing model is used to account for the strong interaction of Fe(II) and Fe(III) with major and minor ligands (Cl⁻, SO₄²⁻, OH⁻, HCO₃⁻, CO₃²⁻ and HS⁻) in the waters. The model can be used to estimate the activity and speciation of iron in natural waters as a function of composition (major sea salts) and ionic strength (0 to 3 M). The measured stability constants (K_FeX^*) of Fe(II) and Fe(III) have been used to estimate the thermodynamic constants (K_FeX) and the activity coefficient of iron complexes (γ_FeX) with a number of inorganic ligands in NaClO₄ medium at various ionic strengths: In(K_FeX/γ_Feγ_X) = InK_FeX − In(γ_FeX) The activity coefficients for free ions (γ_Fe, γ_x) needed for this extrapolation have been estimated from the Pitzer equations. The activity coefficients of the ion pairs have been used to determine Pitzer parameters (B_FeX, B_FeX⁰, C_FeX^φ) for the iron complexes. These results make it possible to estimate the stability constants for the formation of Fe(II) and Fe(III) complexes over a wide range of ionic strengths and in different media. The model has been used to determine the solubility of Fe(III) in seawater as a function of pH. The results are in good agreement with the measurements of Byrne and Kester and Kuma et al. When the formation of Fe organic complexes is considered, the solubility of Fe(III) in seawater is increased by about 25%.     

Diffusion of seawater ions. Part II. The role of activity coefficients and ion pairing

A theoretical evaluation of basic thermodynamic relationships reveals that variation of activity coefficients, ion pairing and electrical interactions must be considered when modelling ionic diffusion in seawater. The contributions of ion-pair formation and change in activity coefficient along the diffusion path were studied experimentally by conducting diffusion experiments in which solutions of KCl, NaCl, MgCl₂, Li₂SO₄, K₂SO₄, Na₂SO₄ and MgSO₄, at an ionic strength of 0.7, were allowed to diffuse into distilled water. The study reveals that the thermodynamic factor, required to correct for changes in the activity coefficient along the diffusion path, is significant for all the salts studied. Agreement between a simple diffusion model, which does not include ion pairing, and observed data was good for completely dissociated salts, but poor for salts which are known to form ion pairs at the concentration levels studied. The diffusion of MgSO₄, 0.425 of which is associated at I = 0.7, was successfully modelled by assuming that the diffusion coefficient of the MgSO₄⁰ ion pair is different from the diffusion coefficient of the dissociated salt. The diffusion coefficient of this ion pair is estimated to be 1.9 × 10⁻⁵ cm² s⁻¹ at 30°C, as compared to 0.49 × 10⁻⁵ cm² s⁻¹ for the dissociated salt. It is suggested that the high mobility of this ion pair could cause magnesium enrichment in pore water of sulfate depleted sediments.     

An improved model for the calculation of CO2 solubility in aqueous solutions containing Na, K, Ca, Mg, Cl, and SO4

An improved model is presented for the calculation of the solubility of carbon dioxide in aqueous solutions containing Na⁺, K⁺, Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ in a wide temperature–pressure–ionic strength range (from 273 to 533 K, from 0 to 2000 bar, and from 0 to 4.5 molality of salts) with experimental accuracy. The improvements over the previous model [Duan, Z. and Sun, R., 2003. An improved model calculating CO₂ solubility in pure water and aqueous NaCl solutions from 273 to 533K and from 0 to 2000 bar. Chemical Geology, 193: 257–271] include: (1) By developing a non-iterative equation to replace the original equation of state in the calculation of CO₂ fugacity coefficients, the new model is at least twenty times computationally faster and can be easily adapted to numerical reaction-flow simulator for such applications as CO₂ sequestration and (2) By fitting to the new solubility data, the new model improved the accuracy below 288 K from 6% to about 3% of uncertainty but still retains the high accuracy of the original model above 288 K. We comprehensively evaluate all experimental CO₂ solubility data. Compared with these data, this model not only reproduces all the reliable data used for the parameterization but also predicts the data that were not used in the parameterization. In order to facilitate the application to CO₂ sequestration, we also predicted CO₂ solubility in seawater at two-phase coexistence (vapor–liquid or liquid–liquid) and at three-phase coexistence (CO₂ hydrate–liquid water–vapor CO₂ [or liquid CO₂]). The improved model is programmed and can be downloaded from the website http://www.geochem-model.org/programs.htm.     

Sediment–water interactions of natural oestrogens under estuarine conditions

The natural human female hormones oestrone and 17β-oestradiol have been implicated in the disruption of endocrine systems in some wildlife adjacent to sewage effluents. The sorption behaviour of these two compounds under estuarine conditions was studied by spiking either 2.55 μg of oestrone or 2.65 μg of 17β-oestradiol in kinetic experiments. In equilibrium experiments, 3 ng of oestrone or 3.2 ng of 17β-oestradiol was added in each of the centrifuge tubes. Sorption onto sediment particles was relatively slow, with sorption equilibrium being reached in about 70 and 170 h for oestrone and 17β-oestradiol, respectively. The effects of a variety of environmental parameters on sorption were studied including salinity, sediment concentration (SC), the presence of a third phase, particle size and, also, surfactant concentrations. Results show that although salinity did not induce any statistically significant effect on the sorption of 17β-oestradiol, it did statistically enhance the sorption of oestrone, and a salting constant of 0.3 l mol⁻¹ was derived. The partition coefficient for both compounds decreased with increasing sediment concentration, a phenomenon that has been widely reported and attributed to the presence of colloids (which could enhance dissolved concentrations). In this paper, the true partition coefficients for sediment particles (K_p^true) and colloidal particles (K_c^true) have been calculated, and a K_p^true value of 141 and 102 ml g⁻¹ was obtained for oestrone and 17β-oestradiol, respectively. In addition, K_c^true values for oestrone (222×10² ml g⁻¹) and 17β-oestradiol (135×10² ml g⁻¹) were two orders of magnitude higher than their respective K_p^true values, suggesting that the colloidal particles are significantly stronger sorbents for natural oestrogens than sediment particles. Particles of different sizes were found to have different partition coefficients due to the strong relationships between partition coefficients for the two compounds and particulate organic carbon (POC) contents and specific surface areas (SSAs). The presence of a surfactant was shown to reduce the partition coefficients for the two compounds, although its concentrations being used were higher than those normally found in the natural environment.     

Diffusion coefficients of major ions in seawater

Self-diffusion coefficients of five major ions have been determined by a radioactive tracer method (capillary tube method) in seawater of salinity 34.86 at 25°C. Data are presented for Na⁺, Ca²⁺, Cl⁻, SO₄², and HCO₃⁻, which constitute about 95% by weight of sea salt. The influence of temperature and salinity on these coefficients has been studied for Na⁺ and Cl⁻ which are the major components of sea salt: self-diffusion coefficients of these two ions have been measured in seawater, at different temperatures for a salinity of 34.86 and at different salinities for a temperature of 25°C. Diffusion coefficients of the same ions have been determined at 25°C by using another radioactive tracer method (quasi-steady cell method). In this experiment, seawater ions were allowed to diffuse from natural seawater into dilute seawater. Data have been obtained at 25°C for Na⁺, Ca ²⁺, Cl⁻, SO₄²⁻ and HCO₃⁻, corresponding to different salinity gradients.     

Sorption of yttrium and rare earth elements by amorphous ferric hydroxide: Influence of pH and ionic strength

The sorption of yttrium and the rare earth elements (YREEs) by amorphous ferric hydroxide at low ionic strength (0.01 M ≤ I ≤ 0.09 M) was investigated over a wide range of pH (3.9 ≤ pH ≤ 7.1). YREE distribution coefficients, defined as _iK_Fe = [MS_i]_T / (M_T[Fe³⁺]_S), where [MS_i]_T is the concentration of YREE sorbed by the precipitate, M_T is the total YREE concentration in solution, and [Fe³⁺]_S is the concentration of precipitated iron, are weakly dependent on ionic strength but strongly dependent on pH. For each YREE, the pH dependence of log _iK_Fe is highly linear over the investigated pH range. The slopes of log _iK_Fe versus pH regressions range between 1.43 ± 0.04 for La and 1.55 ± 0.03 for Lu. Distribution coefficients are well described by an equation of the form _iK_Fe = (_Sβ₁[H⁺]^− 1 + _Sβ₂[H⁺]^− 2) / (_SK₁[H⁺] + 1), where _Sβ_n are stability constants for YREE sorption by surface hydroxyl groups and _SK₁ is a ferric hydroxide surface protonation constant. Best-fit estimates of _Sβ_n for each YREE were obtained with log _SK₁ = 4.76. Distribution coefficient predictions, using this two-site surface complexation model, accurately describe the log _iK_Fe patterns obtained in the present study, as well as distribution coefficient patterns obtained in previous studies at near-neutral pH. Modeled log _iK_Fe results were used to predict YREE sorption patterns appropriate to the open ocean by accounting for YREE solution complexation with the major inorganic YREE ligands in seawater. The predicted log _iK_Fe′ pattern for seawater, while distinctly different from log _iK_Fe observations in synthetic solutions at low ionic strength, is in good agreement with results for natural seawater obtained by others.     

Carbon cycling within the upper methanogenic zone of continental rise sediments; An example from the methane-rich sediments overlying the Blake Ridge gas hydrate deposits

Data from piston cores collected from Carolina Rise and Blake Ridge, and from many DSDP/ODP sites indicate that extreme ¹³C-depletion of methane and ΣCO₂ occurs within the uppermost methanogenic zone of continental rise sediments. We infer that ¹³C-depleted methane is generated near the top of the methanogenic zone when carbon of ¹³C-depleted ΣCO₂, produced by microbially-mediated anaerobic methane oxidation, is recycled back to methane through CO₂ reduction. Interstitial water and gas samples were collected in 27 piston cores, 16 of which penetrated through the sulfate reduction zone into methane-bearing sediments of the Carolina Rise and Blake Ridge. Isotopic measurements (δ¹³C_CH4, δ¹³C_CO2, δD_CH4, and δD_H2O) indicate that this methane is microbial in origin, produced by microbially-mediated CO₂ reduction. Methane samples form two distinct isotopic pools. (1) Methane from a seafloor seep site shows a mean δ¹³C_CH4 value of − 69 ± 2%., mirroring values found at ≥ 160 mbsf from a nearby DSDP site. (2) Twenty, areally-separated sites (sample depth, 10 to 25 mbsf) have δ¹³C_CH4 values ranging from −85 to −103%., and δ¹³C_CO2 as negative as −48%.. The very low δ¹³C values from the methane and CO₂ pools highlight the importance of carbon cycling within continental rise sediments at and near the sulfate-methane boundary.     

Stable carbon isotope distribution of particulate organic matter in the ocean: a model study

The stable carbon isotopic composition of particulate organic matter in the ocean, δ¹³C_POC, shows characteristic spatial variations with high values in low latitudes and low values in high latitudes. The lowest δ¹³C_POC values (−32‰ to −35‰) have been reported in the Southern Ocean, whereas in arctic and subarctic regions δ¹³C_POC values do not drop below −27‰. This interhemispheric asymmetry is still unexplained. Global gradients in δ¹³C_POC are much greater than in δ¹³C_DIC, suggesting that variations in isotopic fractionation during organic matter production are primarily responsible for the observed range in δ¹³C_POC. Understanding the factors that control isotope variability is a prerequisite when applying δ¹³C_POC to the study of marine carbon biogeochemistry. The present model study attempts to reproduce the δ¹³C_POC distribution pattern in the ocean. The three-dimensional (3D) Hamburg Model of the Oceanic Carbon Cycle version 3.1 (HAMOCC3.1) was combined with two different parametrizations of the biological fractionation of stable carbon isotopes. In the first parametrization, it is assumed that the isotopic fractionation between CO₂ in seawater and the organic material produced by algae, _P, is a function of the ambient CO₂ concentration. The two parameters of this function are derived from observations and are not based on an assumption of any specific mechanism. Thus, this parametrization is purely empirical. The second parametrization is based on fractionation models for microalgae. It is supported by several laboratory experiments. Here the fractionation, _P, depends on the CO₂ concentration in seawater and on the (instantaneous) growth rates, μ_i, of the phytoplankton. In the Atlantic Ocean, where most field data are available, both parametrizations reproduce the latitudinal variability of the mean δ¹³C_POC distribution. The interhemispheric asymmetry of δ¹³C_POC can mostly be attributed to the interhemispheric asymmetry of CO₂ concentration in the water. However, the strong seasonal variations of δ¹³C_POC as reported by several authors, can only be explained by a growth rate-dependent fractionation, which reflects variations in the cellular carbon demand.     

Chromium(VI) reduction by sulphur(IV) in aqueous solutions

The rates of the reduction of Cr(VI) with S(IV) were measured in deaerated NaCl solution as a function of pH, temperature and ionic strength. The rates of the reaction were found to be first order with respect to Cr(VI) and second order with respect to S(IV), in agreement with previous results obtained at concentrations two order higher than the present study. The reaction also showed a first-order dependence of the rates on the concentration of the proton and a small influence of temperature with an apparent energy of activation ΔH_app of 22.8 ± 3.4 kJ/mol. The rates were independent of ionic strength from 0.01 to 1 M. The rate of Cr(VI) reduction is described by the general expression

−d[Cr(VI)]/dt=k[Cr(VI)][S(IV)]²