Supplementary Material and Data for: Experimental kinetic rate laws for aqueous pyrite reduction at underground hydrogen storage conditions (60-150 °C, up to 150 bar H2)

Journal: Geochimica et Cosmochimica Acta Title: Experimental kinetic rate laws for aqueous pyrite reduction at underground hydrogen storage conditions (60-150 °C, up to 150 bar H2) Authors: Hintzen, R., Hellmann, R., Roddatis, V.V., van Winden, J., Truche, L. Supplementary Material S.1 Characterization of the pyrite starting material: S.1-1 XRD pattern of the unaltered pyrite S.1-2 SEM imaging of the unaltered pyrite S.2 Native S: Removal from pyrite & impact on sulfide release kinetics: S.2-1 Thermal treatment S.2-2 Sulfide release kinetics as a function of native S abundance S.3 Pyrite titration models S.3-1 PY12 S.3-8 PY19 S.3-2 PY13 S.3-9 PY20 S.3-3 PY14 S.3-10 PY22 S.3-4 PY15 S.3-11 PY23 S.3-5 PY16 S.3-12 PY25 S.3-6 PY17 S.3-13 PY27 S.3-7 PY18 S.4 Uncertainty calculations S.5 Reductive dissolution experiments of pyrite: S.5-1 PY12 S.5-8 PY19 S.5-2 PY13 S.5-9 PY20 S.5-3 PY14 S.5-10 PY21 S.5-4 PY15 S.5-11 PY22 S.5-5 PY16 S.5-12 PY23 S.5-6 PY17 S.5-13 PY25 S.5-7 PY18 S.5-14 PY27 S.6 Alternative rate equation S.7 Performance of the kinetic rate laws S.7-1 1st kinetic rate law: U-shaped pH dependence S.7-2 2nd kinetic rate law: V-shaped pH dependence S.8 Gibbs free energy dependency S.8-1 PY12 S.8-6 PY18 S.8-2 PY13 S.8-7 PY23 S.8-3 PY14 S.8-8 PY25 S.8-4 PY15 S.8-9 PY27 S.8-5 PY17 S.1 Pyrite starting material: S.1-1 XRD pattern of the unaltered pyrite: The crushed and sieved pyrite powder (50-100 µm) was characterized and had a purity of 98.8 %. Impurities included 0.5 wt.% quartz (SiO2) and 0.7 wt.% native sulfur (S8) (Fig. S.1-1). A close-up of the diffraction pattern in the range 14-40 ° 2ϴ is given in Fig. S.2-1b. Fig. S.1-1: XRD diffractogram of the pyrite starting material (50-100 µm grain size fraction) showing trace impurities of quartz (SiO2) and native S (S8). S.1-2 SEM images of the unaltered pyrite Back-scattered electron images are given in Fig. S.1-2 to illustrate the surfaces of the unaltered pyrite starting material. The images were obtained from the cleaned (after removal of surface fines) and purified (after removal of native sulfur) 50-100 µm grain size fraction. The vast majority of grains show clean, inclusion-free surfaces (Fig. S.1-2 A, B). A few grains are partly overgrown by an O-enriched Fe, S-phase (Fig. S.1-2 B close-up). This overgrowth is inherited from the natural alteration history of the pyrite specimen prior to our experiments. Fig. S.1-2: Back-scattered electron images of the cleaned and purified pyrite (FeS2) starting material. S.2 Native S: Removal from pyrite & impact on sulfide release kinetics: The presence of native sulfur in the pyrite starting material was considered a critical impurity. It was suspected and confirmed to react with dissolved H2 to produce sulfides and thus to interfere with the sulfide formation of interest by the reductive dissolution of pyrite. Native sulfur was therefore removed from the pyrite starting material in a two-step procedure: thermal treatment and washing in toluene. S.2-1 Thermal treatment During thermal treatment (80 °C) at vacuum conditions (6.7x10-6 bar), the native S sublimated from the bulk pyrite powder and redeposited along the cool upper wall of a glass phial (Fig. S.2-1). XRD analysis of the pyrite powder after thermal treatment showed the removal of native S whose main peak at ~ 26.9 ° 2ϴ was below the detection limit of XRD (Fig. S.2-1b). Fig. S.2-1a: Bulk pyrite powder with the separated and redeposited native sulfur after thermal treatment at vacuum conditions. Fig. S.2-1b: Close-up of diffractograms (14-40 °) of the non-treated, native S-bearing and the thermally treated pyrite powder. In the latter, the native sulfur peak is below the detection limit. S.2-2 Sulfide release kinetics as a function of native S abundance Measured average aqueous sulfide concentrations over time (Fig. S.2-2) vary systematically with the trace abundance of native sulfur in the pyrite powder. The untreated powder (~ 0.7 wt.% S8) showed highly elevated sulfide release kinetics. After removal of most of the native sulfur by thermal treatment (Suppl. S.2-1) of the same pyrite powder batch (~ 0.1 wt.% S8), the degree of initial sulfide formation significantly, dropped but was still elevated relative to the native sulfur-free reference (pyrite B). The thermal and toluene treatments of the pyrite powder led to a decrease in the measured aqueous sulfide formation, such that it was of the same magnitude as for the S8-free reference. Fig. S.2-2: Measured average aqueous sulfide formation of the 50-100 µm pyrite fraction at different purification stages for the removal of native sulfur: i) untreated, ii) thermally treated, and iii) thermally and toluene treated. Pyrite B is a different pyrite specimen that was free of native sulfur and therefore served as a reference for the efficiency of the native sulfur removal procedure. S.3 Pyrite titration models The reductive dissolution experiments of pyrite were reproduced by geochemical models using the code PHREEQC (Parkhurst and Appelo, 2013) and the Thermoddem database (Blanc et al., 2012). The computations were performed as so called ‘pyrite titration models’ (PTM), where a defined quantity of FeS2 is forced to complete dissolution. These models can be considered to be analogous to a chemical titration in the laboratory. If the number of moles of reacted pyrite at each sampling step is known, the reaction progress in the reactor can be simulated by dissolving (i.e., ‘titrating’) an increasing number of moles of pyrite corresponding to each sampling step. The thermodynamic code then calculates a fluid-mineral-gas equilibrium for each ‘titration’ step of pyrite, from which complementary thermodynamic parameters can be retrieved. Fig. S.3: Workflow for the simulation of reductive pyrite dissolution experiments using a pyrite titration model. The workflow for the PTMs is illustrated in Fig. S.3. Three PHREEQC input scripts are given at the end of this section. The workflow for the PTMs includes the following steps: i) pH correction for in situ experimental conditions (1st PHREEQC input script), ii) estimation of the moles of reacted pyrite based on sulfide in the aqueous, gas, and solid sinks, and iii) reproduction of the experiments as pyrite titration models (3rd PHREEQC input script). We note here that some steps and required parameters can be derived from the experimental data, whereas other parameters require geochemical models. The input to each PTM uses the cumulative number of moles of dissolved pyrite (∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀, [mol]) at each sampling step (𝑖) for a given experiment (Eq. S.1). This quantity corresponds to the total amount of sulfide released into the reactor, which is partitioned into the following sinks: i) aqueous sulfide (∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀), ii) gas phase sulfide (∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 ), and iii) sulfide incorporated into secondary minerals (∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀). Since two moles of sulfide are released for each mole of pyrite dissolved, the stoichiometry factor k [unitless] accounts for the conversion of moles of sulfide to moles of pyrite. The superscript ‘PTM’ is used to indicate that the corresponding variable serves only as input for the pyrite titration models, but is not used for the kinetic evaluation of the experiments. ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀=∑[(∆𝑛𝑆𝑎𝑞 −𝐼𝐼 + ∆𝑛𝐻2𝑆𝑔𝑎𝑠 + ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 )𝑖𝑃𝑇𝑀 𝑘=2 ] 𝑖 (S.1) With respect to the aqueous sink, the number of moles of sulfide produced between sampling step 𝑖 and the previous step 𝑖−1 is given by: ∆𝑛𝑆𝑎𝑞 −𝐼𝐼,𝑖 𝑃𝑇𝑀 =(𝐶𝑆𝑎𝑞 −𝐼𝐼,𝑖 𝑀𝐵 × 𝑉𝑖)−(𝐶𝑆𝑎𝑞 −𝐼𝐼,𝑖−1 𝑀𝐵 × 𝑉𝑖−1) + (𝐶𝑆𝑎𝑞 −𝐼𝐼,𝑖−1 𝑀𝐵 × 𝑉𝑖−1 𝑒𝑥𝑡𝑟) (S.2) where the number of moles of sulfide in the reactor at time point 𝑖 is the product of the methylene blue-measured dissolved sulfide concentration (𝐶𝑆𝑎𝑞 −𝐼𝐼 𝑀𝐵, [M]) and the solution volume 𝑉𝑖 [L] prior to aliquot extraction (first term). Analogously, the second term corresponds to the moles of sulfide in the reactor at the previous sampling step. The third term is a correction for the number of moles of dissolved sulfide removed from the reactor with the extracted solution volume during the previous sampling step (𝑉𝑖−1 𝑒𝑥𝑡𝑟 [L]). To estimate the gaseous sink, a liquid-gas sulfide fractionation factor (𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼 ⁄, [unitless]) is calculated for each sampling step (Eq. S.3). The fractionation factors are determined from an auxiliary model (2nd PHREEQC input script) that solves for the aqueous and gaseous sulfide speciation at equilibrium for an arbitrary input number of moles of sulfide. These models take into account the respective experimental T, total P, partial pressures of gases (H2, Ar, CO2), the -pressure 69.0846 # atm -volume 0.16007 # liter -temperature 120 Ar(g) 62.1915 # unit: atm H2(g) 6.9102 # unit: atm H2S(g) 0 SELECTED_OUTPUT -file P8-PY13_PTM.prn -reset false -temperature -pH -pe -totals Fe Ca S -molalities Fe+2 Ca+2 H2S HSS-2 -activities Fe+2 Ca+2 H2S HSS-2 -equilibrium_phases Pyrite Calcite Pyrrhotite Magnetite -saturation_indices Pyrite Pyrrhotite Fe7.016S8 Fe9S10 Fe10S11 Fe11S12 Troilite Mackinawite Marcassite Greigite Wustite FeO Fe(OH)2 Lepidocrocite Hematite Magnetite Goethite Siderite Calcite C(element) H2(g) H2S(g) O2(g) S2(g) -gases H2(g) H2S(g) USER_PUNCH 1 -headings aq_density m_H2S(g) m_CO2(g) -start 10 punch RHO 20 punch GAS("H2S(g)") 30 punch GAS("CO2(g)") -end END S.3-1 PY12 Table S.3-1: Input data for the pyrite titration model of experiment PY12. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 6 200.00 8.26 0.004819 7.32E-06 3.53E-08 7.36E-06 7.36E-06 P2 21 191.74 9.25 0.004297 4.40E-09 1.89E-11 4.42E-09 7.36E-06 P3 70 182.49 9.21 0.004498 3.26E-06 1.47E-08 3.28E-06 1.06E-05 P4 170 173.28 12.72 0.004396 0.00E+00 0.00E+00 0.00E+00 1.06E-05 P5 265 160.56 12.38 0.004709 1.45E-06 6.85E-09 1.46E-06 1.21E-05 P6 387 148.19 25.64 0.004709 0.00E+00 0.00E+00 0.00E+00 1.21E-05 S.3-2 PY13 Table S.3-2: Input data for the pyrite titration model of experiment PY13. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 15 200.00 8.04 0.014417 1.39E-05 2.00E-07 1.41E-05 1.41E-05 P2 47 191.96 11.77 0.019363 0.00E+00 0.00E+00 0.00E+00 1.41E-05 P3 112 180.19 7.63 0.015088 6.87E-06 1.04E-07 6.97E-06 2.11E-05 P4 209 172.56 8.62 0.025964 1.27E-05 3.30E-07 1.31E-05 3.41E-05 P5 304 163.94 7.75 0.016902 2.72E-05 4.60E-07 2.77E-05 6.18E-05 P6 376 156.19 9.07 0.026555 1.23E-05 3.26E-07 1.26E-05 7.44E-05 P7 448 147.12 7.19 0.015088 1.75E-05 2.64E-07 1.78E-05 9.21E-05 P8 520 139.93 15.71 0.016152 1.43E-05 2.31E-07 1.45E-05 1.07E-04 S.3-3 PY14 Table S.3-3: Input data for the pyrite titration model of experiment PY14. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 6 200.00 7.55 0.0016914 5.76E-07 9.74E-10 5.77E-07 5.77E-07 P2 25 192.45 10.83 0.0015429 8.12E-07 1.25E-09 8.14E-07 1.39E-06 P3 71 181.62 11.48 0.0014073 1.46E-06 2.06E-09 1.46E-06 2.85E-06 P4 145 170.14 10.56 0.0016914 3.14E-07 5.30E-10 3.14E-07 3.17E-06 P5 215 159.58 11.07 0.0022799 0.00E+00 0.00E+00 0.00E+00 3.17E-06 P6 311 148.51 11.79 0.0016914 3.26E-08 5.52E-11 3.27E-08 3.20E-06 P7 527 136.71 11.25 0.0024991 0.00E+00 0.00E+00 0.00E+00 3.20E-06 P8 725 125.46 10.81 0.0014073 0.00E+00 0.00E+00 0.00E+00 3.20E-06 P9 912 114.66 22.65 0.0014073 3.73E-09 5.25E-12 3.74E-09 3.20E-06 S.3-4 PY15 Table S.3-4: Input data for the pyrite titration model of experiment PY15. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 6 200.00 7.07 0.262993 3.49E-05 9.18E-06 4.41E-05 4.41E-05 P2 23 192.93 8.50 0.206797 1.17E-05 2.43E-06 1.42E-05 5.82E-05 P3 47 184.43 7.20 0.244617 1.08E-05 2.64E-06 1.35E-05 7.17E-05 P4 94 177.23 8.58 0.481679 4.91E-05 2.36E-05 7.27E-05 1.44E-04 P5 166 168.65 6.84 0.346022 9.43E-05 3.26E-05 1.27E-04 2.71E-04 P6 267 161.81 7.78 0.223017 8.62E-05 1.92E-05 1.05E-04 3.77E-04 P7 432 154.03 6.25 0.363196 9.09E-05 3.30E-05 1.24E-04 5.01E-04 P8 580 147.78 8.42 0.244617 3.20E-05 7.83E-06 3.98E-05 5.41E-04 P9 744 139.36 11.5 0.227205 3.32E-05 7.54E-06 4.07E-05 5.81E-04 S.3-5 PY16 Table S.3-5: Input data for the pyrite titration model of experiment PY16. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 5 200.00 8.92 0.002843 6.46E-06 1.84E-08 6.48E-06 6.48E-06 P2 23 191.08 8.45 0.000430 1.57E-05 6.75E-09 1.57E-05 2.22E-05 P3 70 182.62 7.80 0.000100 2.34E-05 2.34E-09 2.34E-05 4.56E-05 P4 166 174.82 7.05 0.000120 1.62E-05 1.95E-09 1.62E-05 6.18E-05 P5 240 167.78 8.52 0.000093 2.19E-05 2.03E-09 2.19E-05 8.37E-05 P6 357 159.26 7.30 0.000077 3.58E-05 2.76E-09 3.58E-05 1.20E-04 P7 527 151.96 7.89 0.000132 3.17E-05 4.18E-09 3.17E-05 1.51E-04 P8 717 144.06 7.08 0.000110 2.93E-05 3.21E-09 2.93E-05 1.81E-04 S.3-6 PY17 Table S.3-6: Input data for the pyrite titration model of experiment PY17. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 5 200.00 10.46 0.004603 1.50E-06 6.90E-09 1.51E-06 1.51E-06 P2 23 189.54 11.61 0.006342 2.68E-06 1.70E-08 2.70E-06 4.20E-06 P3 69 177.93 10.77 0.006639 3.53E-06 2.35E-08 3.56E-06 7.76E-06 P4 165 167.15 10.44 0.006342 0.00E+00 0.00E+00 0.00E+00 7.76E-06 P5 315 156.71 10.93 0.004199 2.01E-06 8.43E-09 2.02E-06 9.77E-06 P6 484 145.78 10.72 0.007615 0.00E+00 0.00E+00 0.00E+00 9.77E-06 P7 650 135.05 9.95 0.007791 0.00E+00 0.00E+00 0.00E+00 9.77E-06 P8 722 125.11 10.26 0.009789 1.06E-07 1.04E-09 1.07E-07 9.88E-06 S.3-7 PY18 Table S.3-7: Input data for the pyrite titration model of experiment PY18. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 16 215.00 11.31 0.003920 2.87E-06 1.13E-08 2.88E-06 2.88E-06 P2 40 203.69 9.94 0.004199 2.90E-06 1.22E-08 2.91E-06 5.79E-06 P3 111 193.76 9.38 0.005045 5.46E-06 2.75E-08 5.49E-06 1.13E-05 P4 303 184.38 9.32 0.010970 2.71E-06 2.97E-08 2.74E-06 1.40E-05 P5 447 175.06 8.76 0.010482 6.97E-06 7.31E-08 7.05E-06 2.11E-05 P6 617 166.30 7.71 0.011223 9.35E-07 1.05E-08 9.45E-07 2.20E-05 P7 784 158.59 8.06 0.013159 0 0 0 2.20E-05 S.3-8 PY19 Table S.3-8: Input data for the pyrite titration model of experiment PY19. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 5 200.00 7.92 0.000667 3.09E-05 2.06E-08 3.09E-05 3.09E-05 P2 24 192.08 9.50 0.000517 0.00E+00 0.00E+00 0.00E+00 3.09E-05 P3 74 182.57 8.35 0.000383 6.42E-07 2.46E-10 6.43E-07 3.15E-05 P4 148 174.22 8.16 0.000461 2.10E-06 9.68E-10 2.10E-06 3.36E-05 P5 242 166.06 8.17 0.000392 5.39E-06 2.11E-09 5.39E-06 3.90E-05 P6 386 157.89 9.67 0.000230 2.09E-06 4.81E-10 2.09E-06 4.11E-05 P7 646 148.22 9.12 0.000383 9.29E-06 3.56E-09 9.29E-06 5.04E-05 P8 863 139.10 9.11 0.000200 4.90E-06 9.83E-10 4.90E-06 5.53E-05 P9 1054 129.99 8.75 0.000196 8.81E-06 1.72E-09 8.81E-06 6.41E-05 S.3-9 PY20 Table S.3-9: Input data for the pyrite titration model of experiment PY20. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 20 200.00 10.24 0.776862 3.58E-06 2.78E-06 6.36E-06 6.36E-06 P2 67 189.76 10.24 0.731962 1.51E-06 1.11E-06 2.62E-06 8.99E-06 P3 144 179.52 8.86 0.747732 0.00E+00 0.00E+00 0.00E+00 8.99E-06 P4 236 170.66 9.71 0.684750 7.82E-07 5.35E-07 1.32E-06 1.03E-05 P5 481 160.95 9.10 0.642090 4.88E-07 3.13E-07 8.02E-07 1.11E-05 P6 649 151.86 8.21 0.580603 0.00E+00 0.00E+00 0.00E+00 1.11E-05 P7 887 143.64 9.83 0.661461 0.00E+00 0.00E+00 0.00E+00 1.11E-05 S.3-10 PY22 Table S.3-10: Input data for the pyrite titration model of experiment PY22. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 17 200.00 8.92 0.958020 9.50E-06 9.11E-06 0.00E+00 9.30E-06 P2 70 191.08 9.29 0.958365 4.02E-06 3.86E-06 0.00E+00 1.32E-05 P3 165 181.78 9.11 0.958097 1.69E-06 1.62E-06 0.00E+00 1.49E-05 P4 262 172.67 9.06 0.958212 0.00E+00 0.00E+00 0.00E+00 1.49E-05 P5 427 163.62 8.58 0.957905 0.00E+00 0.00E+00 0.00E+00 1.49E-05 P6 593 155.03 10.51 0.957828 0.00E+00 0.00E+00 0.00E+00 1.49E-05 P7 714 144.52 9.89 0.957292 0.00E+00 0.00E+00 0.00E+00 1.49E-05 Remark on PY22: ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 values were set to 0 mol due to missing secondary mineral formation based on SEM observations. S.3-11 PY23 Table S.3-11: Input data for the pyrite titration model of experiment PY23. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 16 215.00 10.24 0.006793 3.25E-06 2.21E-08 3.27E-06 3.27E-06 P2 46 204.76 10.23 0.005281 6.42E-06 3.39E-08 6.45E-06 9.72E-06 P3 112 194.53 8.36 0.005281 1.07E-05 5.63E-08 1.07E-05 2.04E-05 P4 209 186.17 8.50 0.005788 1.44E-05 8.34E-08 1.45E-05 3.49E-05 P5 352 177.67 7.94 0.007275 1.17E-05 8.50E-08 1.18E-05 4.67E-05 P6 520 169.73 9.16 0.009568 1.27E-05 1.22E-07 1.29E-05 5.96E-05 P7 714 160.57 8.73 0.011480 6.68E-06 7.67E-08 6.76E-06 6.63E-05 S.3-12 PY25 Table S.3-12: Input data for the pyrite titration model of experiment PY25. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 17 215.00 9.80 0.004930 7.33E-06 3.61E-08 7.37E-06 7.37E-06 P2 41 205.20 8.78 0.004709 7.75E-06 3.65E-08 7.78E-06 1.52E-05 P3 89 196.42 8.94 0.004603 1.16E-05 5.32E-08 1.16E-05 2.68E-05 P4 160 187.48 8.70 0.004199 1.26E-05 5.29E-08 1.26E-05 3.94E-05 P5 257 178.78 8.29 0.004199 1.64E-05 6.91E-08 1.65E-05 5.59E-05 P6 377 170.50 8.42 0.004498 1.67E-05 7.51E-08 1.68E-05 7.27E-05 P7 497 162.07 8.52 0.004396 2.06E-05 9.07E-08 2.07E-05 9.34E-05 P8 689 153.55 11.30 0.004498 1.51E-05 6.79E-08 1.52E-05 1.09E-04 S.3-13 PY27 Table S.3-13: Input data for the pyrite titration model of experiment PY27. Sulfide production in the aqueous, gaseous, and solid sinks, and corresponding cumulated moles of pyrite dissolution. Sample 𝑖 Time (h) Vsol (mL) Vextr (mL) 𝐷𝐻2𝑆𝑔𝑎𝑠 𝑆𝑎𝑞 −𝐼𝐼,𝑖 ⁄ (unitless) ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∆𝑛𝐻2𝑆 𝑔𝑎𝑠 𝑃𝑇𝑀 (mol) ∆𝑛𝑆𝑚𝑖𝑛 −𝐼𝐼 𝑃𝑇𝑀 (mol) ∑𝑛𝐹𝑒𝑆2 𝑃𝑇𝑀 (mol) P1 20 215.00 7.62 0.004297 8.50E-06 3.65E-08 8.53E-06 8.53E-06 P2 44 207.38 8.26 0.004396 9.18E-06 4.04E-08 9.22E-06 1.78E-05 P3 117 199.12 8.92 0.004709 2.67E-05 1.26E-07 2.68E-05 4.46E-05 P4 212 190.20 8.31 0.004199 1.80E-05 7.56E-08 1.81E-05 6.27E-05 P5 380 181.89 8.27 0.004199 4.06E-05 1.71E-07 4.08E-05 1.03E-04 P6 547 173.62 7.69 0.003920 3.15E-05 1.23E-07 3.16E-05 1.35E-04 P7 692 165.93 8.16 0.004011 8.24E-06 3.31E-08 8.28E-06 1.43E-04 General remark concerning Tables S.3-1 to S.3-13: Decreasing consecutive aqueous sulfide measurements leading to negative ∆𝑛𝑆𝑎𝑞 −𝐼𝐼 𝑃𝑇𝑀 values, were set to 0 mol in the input tables of the PTMs to ensure mole preservation in a closed system. S.4 Uncertainty calculations Uncertainties in the measured dissolved sulfide concentrations were based on precision estimates on the same experiments. The precisions were determined by the measurement of iteratively extracted sample aliquots upon termination of select experiments, from which the relative standard deviations were calculated. These precisions are given in section 2.2.3 and below. The reliability of the concentration of sulfide reference solutions is disputable, given the oxidation and degassing of sulfides over time. An independent verification of standard concentrations is therefore commonly recommended (Baird et al., 2017), which is a part of the measurement uncertainty. For this reason, multiple methods were applied in this study to determine the dissolved sulfide concentration over time as an alternative check of accuracy. Only for the SO42--conversion method was a measured accuracy estimate available from the elemental sulfur control IV-stock 29 (section 2.2.3). In this case, the uncertainty (𝜎) was calculated using Eq. (S.6): 𝜎𝑆𝑂42−−𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛=√(𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛)2+(𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦)2 (S.6) The precision-based uncertainties for spectrophotometry and potentiometry, therefore, are minimum estimates due to the lack of an independent determination of their accuracies. The following uncertainties were applied to the measured concentrations: • Methylene blue spectrophotometry (concentration ranges chosen arbitrarily): o 0-0.030 mM S-II(aq): ± 9.7 % o 0.030-0.150 mM S-II(aq): ± 6.3 % o ≥ 0.150 mM S-II(aq): ± 7.3 % • Ag+/S2ion-selective electrode potentiometry: o For all S-II(aq) concentrations: ± 6.7 % • SO42--conversion: o For all S-II(aq) concentrations: ± 11.4 % The uncertainty of the dissolution rates was estimated based on the deviation between the replicate experiments PY12 and PY17, yielding ± 24 % with respect to their mean dissolution rate (n = 2). S.5 Reductive dissolution experiments of pyrite A description of each experiment is given on the following pages. The measured experimental data (section 2.2.3), corrected solution pH for in situ experimental conditions (section 2.3.1), and modeled parameters from the pyrite titration models (section 2.3.2) are summarized and illustrated. The mathematical fits to the data trends of dissolved pyrite per surface area (𝑛𝐹𝑒𝑆2 from Eq. 4, main article) by the Michaelis-Menten equation (Eq. 5, main article) are given for each experiment. Where necessary, specific individual decisions on data selection are explained. To evaluate the fits, the square root of the sum of squared residuals (√𝑆𝑆𝑅) between the experimental data (𝑛𝐹𝑒𝑆2) and the calculated data after the fit (𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 ) of each sampling step 𝑖 was calculated using Eq. (S.7): √𝑆𝑆𝑅=√∑(𝑛𝐹𝑒𝑆2−𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 )𝑖2 𝑖 (S.7) The fit parameters, m and n, in addition to the √𝑆𝑆𝑅 of the fitted data points are given in the corresponding figure of the Michaelis-Menten fit of each experiment. General remarks: o For experiments with dissolved sulfide formation < ~ 0.1 mM S-II(aq) by the methylene blue method and potentiometry (PY12, PY14, PY17, PY20, and PY22), the SO42-- conversion technique yielded systematically deviating measurements. These often showed fluctuating trends and elevated concentration estimates, which were greater by a factor of two to three relative to the other techniques. One possible explanation are interferences with sulfur oxyanions due to trace amounts of remaining dissolved O2 in the reactor solution. It is emphasized that only data from methylene blue spectrophotometry was used in the kinetic evaluations. o In all experiments conducted in the stainless-steel reactor (PY18, PY23, PY25, PY27) a glass liner was used. Reactors were filled with an initial volume of 250 mL of experimental solution. Upon termination of these experiments, a volume of 30 to 40 mL was found in the reactor vessel outside of the glass liner. The loss of solution most likely was due to the initial Ar-sparging via the dip tube during deoxygenation of the reactor. The solution volumes prior to the first sampling step (Vsol) were therefore adjusted. S.5-1 PY12 Experimental conditions: o T: 90 °C o PH2: 7 bar (Ptotal = 70 bar) o pH buffer: calcite (200-600 µm) o Reactor: Ti Aqueous data: Table S.5-1a: Experimental and modeled data for PY12. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 6 200.00 0.037 0.011 - 2.40E-5 8.34 8.74 8.61 P2 21 191.74 0.037 0.026 - 2.72E-5 8.47 8.79 8.61 P3 70 182.49 0.055 0.043 0.161 4.72E-5 7.91 8.77 8.58 P4 170 173.28 0.049 0.057 0.187 5.42E-5 7.93 8.78 8.58 P5 265 160.56 0.058 0.065 < LOD 7.69E-5 7.68 8.75 8.55 P6 387 148.19 0.056 0.046 0.002 9.25E-5 7.56 8.75 8.55 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-1b: Experimental and modeled data for PY12 (continued). Measured dissolved elemental concentrations, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 6 - 0.010 < LOD 0.241 0.242 < LOD P2 21 - 0.009 < LOD 0.271 0.242 < LOD P3 70 - 0.008 < LOD 0.274 0.250 < LOD P4 170 - 0.011 < LOD 0.276 0.251 < LOD P5 265 - 0.010 < LOD 0.270 0.256 < LOD P6 387 - 0.010 < LOD 0.274 0.259 < LOD Fig. S.5-3a: Measured and modeled results of experiment PY14. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o Sample P8 was taken by a different operator. A problem occurred during the pH measurement (see Tab. S.5-3a) and was therefore ignored in Fig. S.5-3a. In order to apply the pyrite titration model on the complete sampling set of experiment PY14, a solution pH of 7.00 at 25 °C was used as input instead. o See the introductory remark in section S.5 on the SO42--conversion method. o The detection limit for dissolved sulfide by the Ag+/S2ion-selective electrode is 0.01 mM (Mettler Toledo, 2011). Considering the dilution factor required for sample pretreatment in potentiometry (2 mL sample + 2 mL SAOB conservation solution), the measured diluted concentrations were very close to or below the potentiometric limit of detection. Mathematical fit: Table S.5-3c: Data for the mathematical fit of PY14. The fit included P0-P4. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 2.07E+04 1.02E-06 9.25E-07 9.22E-08 P2 8.85E+04 2.41E-06 2.72E-06 3.03E-07 P3 2.55E+05 4.86E-06 4.42E-06 4.40E-07 P4 5.23E+05 5.11E-06 5.34E-06 2.26E-07 P5 7.72E+05 4.66E-06 5.70E-06 1.03E-06 P6 1.12E+06 4.40E-06 5.96E-06 1.56E-06 P7 1.90E+06 2.80E-06 6.22E-06 3.42E-06 P8 2.61E+06 2.56E-06 6.33E-06 3.77E-06 P9 3.28E+06 2.35E-06 6.39E-06 4.04E-06 Fig. S.5-3b: Mathematical fit of PY14 using the Michaelis-Menten equation. S.5-4 PY15 Experimental conditions: o T: 150 °C o PH2: 7 bar (Ptotal = 70 bar) o pH buffer: calcite (200-600 µm) o Reactor: Ti Aqueous data: Table S.5-4a: Experimental and modeled data for PY15. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 6 200.00 0.175 0.149 0.230 1.26E-3 7.10 6.95 7.69 P2 23 192.93 0.235 0.194 0.272 2.20E-3 7.37 7.08 7.60 P3 47 184.43 0.294 0.245 0.393 3.68E-3 7.18 6.99 7.51 P4 94 177.23 0.571 0.374 0.597 1.41E-2 6.73 6.57 7.22 P5 166 168.65 1.130 0.822 1.063 4.52E-2 7.04 6.79 6.96 P6 267 161.81 1.663 1.180 1.462 8.06E-2 7.33 7.04 6.84 P7 432 154.03 2.253 1.640 1.733 1.31E-1 7.04 6.76 6.74 P8 580 147.78 1.161 1.917 1.825 - 8.50 7.65 - P9 744 139.36 2.708 1.668 1.971 1.86E-1 7.35 7.03 6.68 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-4b: Experimental and modeled data for PY15 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 6 - 0.027 0.015 0.320 0.308 < LOD P2 23 - 0.028 0.015 0.334 0.342 < LOD P3 47 - 0.027 0.016 0.410 0.381 < LOD P4 94 - 0.029 0.020 0.482 0.558 < LOD P5 166 - 0.024 0.020 0.700 0.810 0.001 P6 267 - 0.015 0.023 1.036 0.981 < LOD P7 432 - 0.013 0.026 1.140 1.154 < LOD P8 580 - 0.013 0.028 1.312 - < LOD P9 744 - 0.012 0.028 1.297 1.273 < LOD Fig. S.5-4a: Measured and modeled results of experiment PY15. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o Sample P8 was taken by a different operator. The aliquot for spectrophotometry was not sufficiently diluted prior to methylene blue complexation and did not match the reagent concentrations. Consequently, the complexation reaction occurred incompletely. therefore leading to an underestimation of the dissolved sulfide concentration. In addition, the pH measurement significantly deviated from the trend. For these reasons, sample P8 was excluded from the data evaluation of experiment PY15. Mathematical fit: Table S.5-4c: Data for the mathematical fit of PY15. The fit included P0-P3. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 2.09E+04 6.41E-05 6.35E-05 6.59E-07 P2 8.27E+04 8.44E-05 9.04E-05 6.02E-06 P3 1.69E+05 1.03E-04 9.76E-05 5.05E-06 P4 3.38E+05 2.04E-04 1.01E-04 1.03E-04 P5 5.97E+05 4.18E-04 1.03E-04 3.15E-04 P6 9.61E+05 6.20E-04 1.04E-04 5.16E-04 P7 1.55E+06 8.48E-04 1.05E-04 7.43E-04 P8 2.09E+06 - - - P9 2.68E+06 9.99E-04 1.05E-04 8.94E-04 Fig. S.5-4b: Mathematical fit of PY15 using the Michaelis-Menten equation. S.5-5 PY16 Experimental conditions: o T: 90 °C o PH2: 7 bar (Ptotal = 70 bar) o pH buffer: CaCO3 powder (AnalytiChem®, CL00.0302.2500) o Reactor: Ti Aqueous data: Table S.5-5a: Experimental and modeled data for PY16. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 5 200.00 0.032 0.044 0.289 9.76E-6 6.66 8.97 9.21 P2 23 191.08 0.114 0.172 0.056 1.08E-5 10.78 9.79 9.79 P3 70 182.62 0.243 0.292 0.146 6.36E-6 11.78 10.42 10.38 P4 166 174.82 0.336 0.486 0.273 1.18E-5 11.55 10.34 10.29 P5 240 167.78 0.466 0.517 0.343 1.39E-5 11.77 10.45 10.39 P6 357 159.26 0.691 0.752 0.497 1.58E-5 11.90 10.53 10.47 P7 527 151.96 0.899 1.033 0.626 2.23E-5 11.49 10.30 10.24 P8 717 144.06 1.103 1.175 0.821 2.51E-5 11.61 10.38 10.31 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-5b: Experimental and modeled data for PY16 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 5 - 0.007 0.036 0.632 0.630 < LOD P2 23 - 0.012 0.037 1.172 1.172 < LOD P3 70 - 0.015 0.022 2.848 2.847 < LOD P4 166 - 0.014 0.015 3.336 3.335 < LOD P5 240 - 0.010 0.015 3.502 3.505 < LOD P6 357 - 0.009 0.013 3.557 3.554 < LOD P7 527 - 0.010 0.014 3.161 3.159 < LOD P8 717 - 0.021 0.018 3.696 3.693 < LOD Fig. S.5-5a: Measured and modeled results of experiment PY16. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o Experiment PY16 was buffered using a commercial CaCO3 powder instead of grains of crystalline calcite. The reactivity of the commercial powder exceeded that of the crystalline calcite by far, as evidenced by the resulting buffered solution pH > 10 and measured dissolved Ca concentrations > 1 mM relative to other experiments at 90 °C (PY12, PY17). The database used in the pyrite titration models, however, contains only thermodynamic data for calcite as a mineral phase and is thus not representative for the experimental setup of PY16. As an alternative, the moles of calcite corresponding to the measured dissolved Ca concentration by ICP-OES were forced to complete dissolution instead of computing an equilibrium with calcite. For this reason, the corrected and modeled in situ pH in Fig. S.5-5a (B) are nearly identical and no modeled dissolved Ca concentration is given in Fig. S.5-5a (C). Mathematical fit: Table S.5-5c: Data for the mathematical fit of PY16. The fit included P0-P3. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 1.98E+04 1.15E-05 1.11E-05 3.42E-07 P2 8.43E+04 3.89E-05 3.88E-05 7.31E-08 P3 2.54E+05 7.87E-05 7.88E-05 1.01E-07 P4 5.97E+05 1.04E-04 1.12E-04 7.80E-06 P5 8.65E+05 1.39E-04 1.24E-04 1.49E-05 P6 1.29E+06 1.95E-04 1.34E-04 6.11E-05 P7 1.90E+06 2.43E-04 1.42E-04 1.00E-04 P8 2.58E+06 2.82E-04 1.47E-04 1.35E-04 Fig. S.5-5b: Mathematical fit of PY16 using the Michaelis-Menten equation. S.5-6 PY17 Experimental conditions: o T: 90 °C o PH2: 7 bar (Ptotal = 70 bar) o pH buffer: calcite (200-600 µm) o Reactor: Ti Aqueous data: Table S.5-6a: Experimental and modeled data for PY17. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 5 200 0.007 0.007 < LOD 9.03E-6 7.70 8.76 8.64 P2 23 189.54 0.022 0.021 < LOD 1.52E-5 7.37 8.62 8.63 P3 69 177.93 0.041 0.037 < LOD 3.54E-5 7.17 8.60 8.60 P4 165 167.15 0.037 0.048 < LOD 4.13E-5 7.19 8.62 8.60 P5 315 156.71 0.050 0.054 0.017 6.28E-5 7.53 8.80 8.57 P6 484 145.78 0.044 0.053 0.106 7.37E-5 7.03 8.54 8.57 P7 650 135.05 0.036 0.054 0.081 8.65E-5 6.83 8.53 8.56 P8 722 125.11 0.037 0.053 0.094 1.02E-4 6.60 8.43 8.55 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-6b: Experimental and modeled data for PY17 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 5 - 0.004 0.015 0.269 0.234 < LOD P2 23 - 0.016 0.011 0.207 0.237 < LOD P3 69 - 0.017 0.013 0.218 0.244 < LOD P4 165 - 0.016 0.012 0.222 0.245 < LOD P5 315 - 0.017 0.015 0.311 0.251 < LOD P6 484 - 0.016 0.014 0.204 0.253 0.001 P7 650 - 0.017 0.015 0.221 0.255 0.001 P8 722 - 0.016 0.015 0.214 0.258 < LOD Fig. S.5-6a: Measured and modeled results of experiment PY17. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o See the introductory remark in section S.5 on the SO42--conversion method. Mathematical fit: Table S.5-6c: Data for the mathematical fit of PY17. The fit included P0-P5. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 1.86E+04 2.66E-06 3.05E-06 3.83E-07 P2 8.16E+04 7.27E-06 7.76E-06 4.89E-07 P3 2.48E+05 1.31E-05 1.12E-05 1.92E-06 P4 5.93E+05 1.10E-05 1.28E-05 1.78E-06 P5 1.13E+06 1.39E-05 1.35E-05 4.59E-07 P6 1.74E+06 1.16E-05 1.37E-05 2.15E-06 P7 2.34E+06 8.76E-06 1.39E-05 5.12E-06 P8 2.60E+06 8.34E-06 1.39E-05 5.57E-06 chemical products used. The resulting modeled in situ pH was strictly buffered at pH 9.0 (Tab. S.5-8a, Fig. S.5-8a). o The H2O2-oxidized samples for SO42--conversion P1 and P4 were affected by loss of solution during storage by ~ 38 % and ~ 28 %, respectively. Mathematical fit: Table S.5-8c: Data for the mathematical fit of PY19. The fit included P0, P3, and P4. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 1.81E+04 5.49E-05 2.52E-05 2.97E-05 P2 8.59E+04 4.90E-05 4.19E-05 7.03E-06 P3 2.68E+05 4.77E-05 4.77E-05 4.37E-09 P4 5.31E+05 4.93E-05 4.93E-05 5.73E-09 P5 8.71E+05 5.66E-05 4.99E-05 6.65E-06 P6 1.39E+06 5.75E-05 5.03E-05 7.21E-06 P7 2.33E+06 7.06E-05 5.06E-05 2.00E-05 P8 3.11E+06 7.51E-05 5.07E-05 2.44E-05 P9 3.79E+06 8.59E-05 5.08E-05 3.52E-05 Fig. S.5-8b: Mathematical fit of PY19 using the Michaelis-Menten equation. Remarks: o Unrealistic curve fits, yielding negative slopes after a local peak around P1, were obtained if sampling points P1 and P2 were included. Considering the overheating during the launch of experiment PY19, the fit was limited to P0, P3, and P4. S.5-9 PY20 Experimental conditions: o T: 90 °C o PH2: 7 bar (Ptotal = 74 bar) o pH buffer: calcite (200-600 µm) + 4 bar PCO2 o Reactor: Ti Aqueous data: Table S.5-9a: Experimental and modeled data for PY20. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 20 200.00 0.018 0.031 0.095 3.76E-3 6.24 5.82 5.62 P2 67 189.76 0.026 0.033 0.085 5.83E-3 6.34 5.94 5.65 P3 144 179.52 0.025 0.031 0.085 6.38E-3 6.25 5.90 5.67 P4 236 170.66 0.029 0.042 0.167 7.85E-3 6.42 6.05 5.70 P5 481 160.95 0.032 0.049 0.103 8.98E-3 6.52 6.14 5.71 P6 649 151.86 0.030 0.047 0.099 8.89E-3 6.55 6.26 5.73 P7 887 143.64 0.030 0.065 0.088 8.74E-3 6.28 6.10 5.75 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-9b: Experimental and modeled data for PY20 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 20 - 0.016 0.026 5.726 5.505 0.319 P2 67 - 0.017 0.028 5.953 5.302 0.354 P3 144 - 0.017 0.034 5.735 5.158 0.335 P4 236 - 0.017 0.039 5.665 5.016 0.243 P5 481 - 0.017 0.048 5.393 4.904 0.224 P6 649 - 0.021 0.060 6.521 4.777 0.221 P7 887 - 0.017 0.050 5.326 4.656 0.142 Fig. S.5-9a: Measured and modeled results of experiment PY20. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o The data from the SO42--conversion method is not considered reliable at the concentration level of dissolved sulfide formation in PY20 (see introductory remark in section S.5). o The H2O2-oxidized samples for SO42--conversion P1, P2, P4, and P7 were affected by loss of solution during storage by ~ 54 %, ~ 28 %, ~ 42 %, and ~ 93 % respectively. The samples P1 and P7 were additionally diluted to ensure sufficient solution volume for the ICP-OES measurement. Mathematical fit: Table S.5-9c: Data for the mathematical fit of PY20. The fit included P0-P4. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 7.05E+04 1.30E-05 1.29E-05 8.17E-08 P2 2.40E+05 1.90E-05 1.86E-05 3.68E-07 P3 5.18E+05 1.91E-05 2.07E-05 1.58E-06 P4 8.48E+05 2.27E-05 2.15E-05 1.22E-06 P5 1.73E+06 2.50E-05 2.21E-05 2.90E-06 P6 2.33E+06 2.38E-05 2.23E-05 1.45E-06 P7 3.19E+06 2.30E-05 2.24E-05 5.71E-07 Fig. S.5-9b: Mathematical fit of PY20 using the Michaelis-Menten equation. S.5-10 PY21 Experimental conditions: o T: 90 °C o PH2: 0 bar (Ptotal = 70 bar Ar) o pH buffer: calcite (200-600 µm) o Reactor: Ti Aqueous data: Table S.5-10a: Experimental and modeled data for PY21. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 68 200.00 0.000 0.000 0.000 - 6.60 6.58 - P2 165 189.31 < LOD 0.000 0.104 - 6.94 6.88 - P3 285 177.54 < LOD 0.000 0.189 - 7.38 7.23 - P4 405 164.92 < LOD 0.000 0.130 - 7.99 7.48 - MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-10b: Experimental and modeled data for PY21 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 68 - 0.020 0.012 0.279 - 0.001 P2 165 - 0.020 0.017 0.218 - 0.000 P3 285 - 0.022 0.017 0.318 - 0.000 P4 405 - 0.021 0.017 0.324 - 0.000 Fig. S.5-10a: Measured and modeled results of experiment PY21. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o In the H2-free Ar-blank experiment PY21, the positive measurement signal of the SO42- -conversion method is not indicative of sulfide formation from the reductive dissolution of pyrite. The method determines dissolved sulfide indirectly after oxidation as total dissolved elemental S by ICP-OES. It is therefore susceptible to interferences by sulfur oxyanions. An unambiguous indicator for the absence of sulfide formation was that the methylene blue complex did not form in undiluted aliquots for spectrophotometry. o The Ar-blank experiment could not be simulated by a pyrite titration model due to the absence of pyrite dissolution. As an alternative, the fluid composition in equilibrium with pyrite, calcite, and in the absence of H2 was modeled at 90 °C, yielding: ▪ [S-II]aq = 0.001 mM ▪ H2Sgas = 7.72x10-7 mmol ▪ [Ca] = 0.230 mM ▪ pH = 8.66 o The H2O2-oxidized samples for SO42--conversion P1, P2, and P3 were affected by loss of solution during storage by ~ 35 %, ~ 38 %, and ~ 26 %, respectively. S.5-11 PY22 Experimental conditions: o T: 90 °C o PH2: 7 bar (Ptotal = 78 bar) o pH buffer: 8 bar PCO2 o Reactor: Ti Aqueous data: Table S.5-11a: Experimental and modeled data for PY22. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 17 200.00 0.048 0.026 0.490 5.84E-3 5.12 4.08 3.77 P2 70 191.08 0.069 0.070 0.230 9.19E-3 4.85 4.04 3.83 P3 165 181.78 0.078 0.076 0.198 1.15E-2 5.04 4.07 3.89 P4 262 172.67 0.075 0.059 0.155 1.24E-2 4.87 4.06 3.91 P5 427 163.62 0.063 0.055 0.130 1.33E-2 4.98 4.09 3.95 P6 593 155.03 0.036 0.001 0.309 1.42E-2 5.01 4.10 3.98 P7 714 144.52 0.033 - 0.256 1.52E-2 5.28 4.15 4.03 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-11b: Experimental and modeled data for PY22 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 17 - 0.017 0.053 0.297 0.000 1.515 P2 70 - 0.019 0.030 0.082 0.000 0.547 P3 165 - 0.019 0.024 0.064 0.000 0.666 P4 262 - 0.019 0.028 0.072 0.000 0.621 P5 427 - 0.019 0.028 0.073 0.000 0.678 P6 593 - 0.019 0.028 0.075 0.000 0.696 P7 714 - 0.018 0.026 0.067 0.000 0.675 Fig. S.5-11a: Measured and modeled results of experiment PY22. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o Experiment PY22 did not contain calcite. o The Ag+/S2ion-selective electrode started to malfunction after regular usage in strongly alkaline, anti-oxidant-bearing buffer solutions (De Marco et al., 1990) with sample P6. The potentiometric measurement of the latter sample therefore underestimated the dissolved sulfide concentration, and completely failed for sample P7. o The data from the SO42--conversion method is not considered reliable at the concentration level of dissolved sulfide formation in PY22 (see introductory remark in section S.5). o The H2O2-oxidized samples for SO42--conversion P1, P3, and P6 were affected by loss of solution during storage by ~ 38 %, ~ 79 %, and ~ 93 %, respectively. The samples P3 and P6 were additionally diluted to ensure sufficient solution volume for the ICP-OES measurement. Mathematical fit: Table S.5-11c: Data for the mathematical fit of PY22. The fit included P0-P3. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 5.99E+04 2.73E-05 2.76E-05 3.58E-07 P2 2.51E+05 3.96E-05 4.07E-05 1.09E-06 P3 5.95E+05 4.56E-05 4.45E-05 1.08E-06 P4 9.44E+05 4.52E-05 4.57E-05 4.98E-07 P5 1.54E+06 4.19E-05 4.65E-05 4.64E-06 P6 2.14E+06 3.51E-05 4.69E-05 1.18E-05 P7 2.57E+06 3.54E-05 4.70E-05 1.16E-05 Fig. S.5-11b: Mathematical fit of PY22 using the Michaelis-Menten equation. S.5-14 PY27 Experimental conditions: o T: 90 °C o PH2: 150 bar (Ptotal = 150 bar) o pH buffer: calcite (200-600 µm) o Reactor: 316L stainless-steel Aqueous data: Table S.5-14a: Experimental and modeled data for PY27. Measured dissolved sulfide concentrations, modeled gaseous H2S and solution pH. Sample no. Time (h) Vsol (mL) [S-IIMB]aq (mM) [S-IIISE]aq (mM) [S-IISD]aq (mM) [H2S]gas (mmol) measured pH25 °C corrected pHin situ modeled pHin situ P1 20 215.00 0.040 0.035 0.201 8.60E-5 8.67 8.79 8.48 P2 44 207.38 0.084 0.074 0.142 2.27E-4 8.94 8.78 8.38 P3 117 199.12 0.218 0.168 0.223 9.89E-4 8.75 8.75 8.17 P4 212 190.20 0.313 0.283 0.369 2.03E-3 8.78 8.80 8.03 P5 380 181.89 0.536 0.450 0.542 5.86E-3 8.52 8.80 7.79 P6 547 173.62 0.717 0.558 0.654 1.13E-2 8.58 8.83 7.64 P7 692 165.93 0.767 0.338 0.935 1.41E-2 8.54 8.82 7.59 MB: Methylene blue spectrophotometry ISE: Ag+/S2ion-selective electrode potentiometry SD: SO42--conversion Table S.5-14b: Experimental and modeled data for PY27 (continued). Measured dissolved elemental concentrations by ICP-OES, in addition to modeled [Ca]. Sample no. Time (h) [B] (mM) [Al] (mM) [Si] (mM) [Ca] (mM) [Ca]modeled (mM) [Fe] (mM) P1 20 0.035 0.044 0.337 0.366 0.278 0.001 P2 44 0.063 0.043 0.452 0.341 0.308 0.001 P3 117 0.122 0.047 0.661 0.420 0.390 0.001 P4 212 0.168 0.050 0.821 0.519 0.456 0.001 P5 380 0.221 0.049 1.000 0.665 0.597 0.001 P6 547 0.246 0.048 1.098 0.724 0.716 0.001 P7 692 0.280 0.050 1.220 0.777 0.762 0.001 Fig. S.5-14a: Measured and modeled results of experiment PY27. Dissolved sulfide concentrations by methylene blue spectrophotometry, Ag+/S2ion-selective electrode potentiometry, and SO42--conversion (A), solution pH corrected for in situ conditions (B) and dissolved elemental concentrations from ICP-OES (C). Remarks: o The solution volume prior to the first sampling step (Vsol) was adjusted to 215 mL due to a loss of ~ 35 mL that was found in the reactor vessel outside of the glass liner upon termination of experiment PY25. o The measured solution pH at 25 °C (Table S.5-14a) was shifted to more alkaline conditions by leaching of the borosilicate glass liner (see [B] and [Si] in Table S.5-14b and in Fig. S.5-14a), relative to experiments performed at 90 °C without a glass liner in Ti-reactors buffered by calcite. o Malfunctioning of the Ag+/S2ion-selective electrode occurred at sample P7. Five iteratively extracted and measured aliquots yielded systematically negative decreasing electrochemical potential responses ranging from -880.2 mV to -862.9 mV (0.3380.086 mM). Mathematical fit: Table S.5-14c: Data for the mathematical fit of PY27. The fit included P0-P4. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑛𝐹𝑒𝑆2 𝑓𝑖𝑡 (mol m-2) Residuals (mol m-2) P1 7.38E+04 1.22E-05 1.49E-05 2.69E-06 P2 1.60E+05 2.51E-05 2.96E-05 4.49E-06 P3 4.21E+05 6.32E-05 6.16E-05 1.59E-06 P4 7.65E+05 8.76E-05 8.79E-05 3.50E-07 P5 1.37E+06 1.47E-04 1.14E-04 3.29E-05 P6 1.97E+06 1.93E-04 1.29E-04 6.42E-05 P7 2.49E+06 2.01E-04 1.38E-04 6.35E-05 Fig. S.5-14b: Mathematical fit of PY27 using the Michaelis-Menten equation. Remarks: o Attempts to constrain the fit to P0-P3 led to nearly linear fit results. A fourth data point (P4) was used in order to allow the fitted curve to show the anticipated effect of decreasing sulfide release kinetics with time. S.6 Alternative rate equation In geochemical modeling codes the following alternative form of the derived rate equations given in the main article (Eq. 22, 23) can often be found (Marty et al., 2015): 𝑟=𝐴298.15exp[−𝐸𝑎 𝑅(1 𝑇−1 298.15)](𝑎𝐻+)−𝑛(𝑃𝐻2)𝑚(1− 𝑄 𝐾𝑒𝑞) (S.8) In this case, the temperature dependence of the rate constant is based on a reference temperature of 298.15 K. The pre-exponential frequency factor A consequently needs to be linearly extrapolated to the same reference (A298.15), using the following equation: 𝐴298.15= 𝜑× 103 298.15+𝐴 (S.9) Using the parameters given in the main article, the values of log A298.15 = -11.58 and log A298.15 = -10.28 are obtained for the ‘U’ and ‘V’-rate laws, respectively. Recasting all parameters into Eq. S.8, the alternative rate equations yield the following expressions: ❖ 1st alternative kinetic rate law (‘U’-shaped pH dependence): 𝑟=10−11.58exp[−35208 𝑅(1 𝑇−1 298.15)](𝑃𝐻2)0.37(1− 𝑄 𝐾𝑒𝑞) (S.10) ❖ 2nd alternative kinetic rate law (‘V’-shaped pH dependence): 𝑟=10−10.28exp[−29370 𝑅(1 𝑇−1 298.15)](𝑎𝐻+)0.13(𝑃𝐻2)0.37(1− 𝑄 𝐾𝑒𝑞) (S.11) These alternative rate equations produce identical rates relative to the rate equations derived in the main article. S.7 Performance of the kinetic rate laws The two derived kinetic rate laws (Eq. 22, 23), that were based on different assumptions in terms of pH-related dissolution rate domains (section 4.1.2), were tested by calculating the predicted aqueous sulfide concentrations over time at each experimental condition. To this aim, the kinetic rate laws were implemented in the Thermoddem database (Blanc et al., 2012) and the reductive dissolution of pyrite by H2 modelled kinetically using PHREEQC (Parkhurst and Appelo, 2013). In the following two sub-sections, the dissolved sulfide concentrations predicted by the kinetic rate laws as a function of time were compared with the measured concentrations by methylene blue spectrophotometry from the experiments. Further explanations are given in the main article. S.7-1 1st kinetic rate law: ‘U’-shaped pH dependence Fig. S.7-1a: Experimentally measured versus modelled dissolved sulfide concentrations by the first kinetic rate law based on the assumption of three dissolution rate domains in terms of pH (‘U’-shape) for variable PH2 at 90 °C. A: Experimental time scale. B: Extended time scale up to 10 000 h. Fig. S.7-1b: Experimentally measured versus modelled dissolved sulfide concentrations by the first kinetic rate law based on the assumption of three dissolution rate domains in terms of pH (‘U’-shape) for variable temperatures at 7 bar H2. A: Experimental time scale. B: Close-up at low concentrations. C: Extended time scale up to 10 000 h. Fig. S.7-1c: Experimentally measured versus modelled dissolved sulfide concentrations by the first kinetic rate law based on the assumption of three dissolution rate domains in terms of pH (‘U’-shape) for conditions at variable solution pH at 90 °C and 7 bar H2. A: Acidic conditions. B: Alkaline conditions. S.7-2 2nd kinetic rate law: ‘V’-shaped pH dependence Fig. S.7-2a: Experimentally measured versus modelled dissolved sulfide concentrations by the second kinetic rate law based on the assumption of two dissolution rate domains in terms of pH (‘V’-shape) for variable PH2 at 90 °C. A: Experimental time scale. B: Extended time scale up to 10 000 h. Fig. S.7-2b: Experimentally measured versus modelled dissolved sulfide concentrations by the second kinetic rate law based on the assumption of two dissolution rate domains in terms of pH (‘V’-shape) for variable temperatures at 7 bar H2. A: Experimental time scale. B: Close-up at low concentrations. C: Extended time scale up to 10 000 h. S.8-5 PY17 Table S.8-5: Data relevant to the r-∆Gr relation of experiment PY17, including rates (r) from long-term MichaelisMenten fits and Gibbs free energy (∆Gr) values from the pyrite saturation indices (SIFeS2) of the corresponding pyrite titration model. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑟 (mol m-2 s-1) SIFeS2 (unitless) ∆Gr (J mol-1) P1 1,86E+04 2,66E-06 1.331E-10 -3.4929 -24284 P2 8,16E+04 7,27E-06 3.982E-11 -3.2168 -22365 P3 2,48E+05 1,31E-05 8.247E-12 -2.8924 -20109 P4 5,93E+05 1,10E-05 1.823E-12 -2.8617 -19896 P5 1,13E+06 1,39E-05 5.418E-13 -2.7125 -18858 P6 1,74E+06 1,16E-05 2.378E-13 -2.6749 -18597 P7 2,34E+06 8,76E-06 1.339E-13 -2.6346 -18317 P8 2,60E+06 8,34E-06 1.091E-13 -2.5882 -17994 Fig. S.8-5: Long-term mathematical fit of PY17 using the Michaelis-Menten equation. Experimental data points P1-P6 included. The long-term Michaelis-Menten fit was limited to the data points P1-P6 due to decreasing sulfide concentration estimates at longer experimental duration. S.8-6 PY18 Table S.8-6: Data relevant to the r-∆Gr relation of experiment PY18, including rates (r) from long-term MichaelisMenten fits and Gibbs free energy (∆Gr) values from the pyrite saturation indices (SIFeS2) of the corresponding pyrite titration model. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑟 (mol m-2 s-1) SIFeS2 (unitless) ∆Gr (J mol-1) P1 5,70E+04 4,04E-06 5.551E-11 -3.7942 -26379 P2 1,43E+05 7,91E-06 4.038E-11 -3.3651 -23396 P3 4,00E+05 1,53E-05 1.956E-11 -2.9388 -20432 P4 1,09E+06 1,86E-05 5.903E-12 -2.6186 -18206 P5 1,61E+06 2,79E-05 3.300E-12 -2.3309 -16205 P6 2,22E+06 2,80E-05 1.963E-12 -2.2759 -15823 P7 2,82E+06 2,47E-05 1.306E-12 -2.2897 -15919 P8 5,70E+04 4,04E-06 5.551E-11 -3.7942 -26379 Fig. S.8-6: Long-term mathematical fit of PY18 using the Michaelis-Menten equation. All experimental data points (P1-P8) included. S.8-7 PY23 Table S.8-7: Data relevant to the r-∆Gr relation of experiment PY23, including rates (r) from long-term MichaelisMenten fits and Gibbs free energy (∆Gr) values from the pyrite saturation indices (SIFeS2) of the corresponding pyrite titration model. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑟 (mol m-2 s-1) SIFeS2 (unitless) ∆Gr (J mol-1) P1 5,61E+04 4,63E-06 8.646E-11 -4.0941 -28464 P2 1,64E+05 1,36E-05 7.599E-11 -3.4762 -24168 P3 4,03E+05 2,83E-05 5.867E-11 -3.0435 -21160 P4 7,51E+05 4,82E-05 4.232E-11 -2.6641 -18522 P5 1,27E+06 6,36E-05 2.832E-11 -2.3988 -16677 P6 1,87E+06 8,11E-05 1.920E-11 -2.1232 -14761 P7 2,57E+06 8,80E-05 1.328E-11 -2.0102 -13976 Fig. S.8-7: Long-term mathematical fit of PY23 using the Michaelis-Menten equation. All experimental data points (P1-P7) included. S.8-8 PY25 Table S.8-8: Data relevant to the r-∆Gr relation of experiment PY25, including rates (r) from long-term MichaelisMenten fits and Gibbs free energy (∆Gr) values from the pyrite saturation indices (SIFeS2) of the corresponding pyrite titration model. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑟 (mol m-2 s-1) SIFeS2 (unitless) ∆Gr (J mol-1) P1 6.07E+04 1.06E-05 1.275E-10 -3.9745 -27632 P2 1.47E+05 2.14E-05 1.165E-10 -3.5786 -24880 P3 3.20E+05 3.75E-05 9.836E-11 -3.2245 -22418 P4 5.77E+05 5.45E-05 7.833E-11 -2.959 -20572 P5 9.25E+05 7.70E-05 5.966E-11 -2.6612 -18502 P6 1.36E+06 9.98E-05 4.446E-11 -2.4123 -16771 P7 1.79E+06 1.29E-04 3.444E-11 -2.1679 -15072 P8 2.48E+06 1.49E-04 2.423E-11 -1.9905 -13839 Fig. S.8-8: Long-term mathematical fit of PY25 using the Michaelis-Menten equation. All experimental data points (P1-P8) included. S.8-9 PY27 Table S.8-9: Data relevant to the r-∆Gr relation of experiment PY27, including rates (r) from long-term MichaelisMenten fits and Gibbs free energy (∆Gr) values from the pyrite saturation indices (SIFeS2) of the corresponding pyrite titration model. Sample no. Time (s) 𝑛𝐹𝑒𝑆2 (mol m-2) 𝑟 (mol m-2 s-1) SIFeS2 (unitless) ∆Gr (J mol-1) P1 7,38E+04 1,22E-05 1.881E-10 -4.1216 -28655 P2 1,60E+05 2,51E-05 1.697E-10 -3.714 -25821 P3 4,21E+05 6,32E-05 1.280E-10 -3.0895 -21479 P4 7,65E+05 8,76E-05 9.296E-11 -2.7922 -19413 P5 1,37E+06 1,47E-04 5.857E-11 -2.3458 -16309 P6 1,97E+06 1,93E-04 4.036E-11 -2.0741 -14420 P7 2,49E+06 2,01E-04 3.064E-11 -1.9889 -13828 Fig. S.8-9: Long-term mathematical fit of PY27 using the Michaelis-Menten equation. All experimental data points (P1-P7) included.