For oxygen isotopes, values of isotopic ratios were reported asδO18=(R18sampleR18VSMOW1) × 1000(9)where 18R = 18O/16O and V-SMOW refers to the Vienna Standard Mean Ocean Water international reference scale. Samples for δ18OSO4 were run in triplicates, and the SD of these triplicate analyses was used as the error (~0.3‰, 1σ). Measurements of δ18OSO4 were calibrated according to the following standards: NBS 127, IAEA-SO-6, and IAEA-SO-5 with δ18OSO4 of 8.6, −11.35, and 12.1‰, respectively. δ18OH2O values were measured by a continuous flow gas source isotope ratio mass spectrometer (Thermo Fisher) coupled to a GasBench II interface. Samples were corrected to NBS 127. The uncertainty on the measurement was ±0.1‰. δ18OH2O was reported versus Vienna Standard Mean Ocean Water (V-SMOW). The equilibrium value of δ18OSO4 was calculated by correcting for the small concentration of sulfate carried over with the inoculum according toδ18Ot=δ18Oeq+x(δ18Oinδ18Oeq)(10)where δ18Ot is the value of the sulfate at the time of sampling, δ18Oeq is the value of the sulfate synthesized by sulfide oxidation, δ18Oin is the value of the sulfate carried over with the inoculum, and x is the fraction of the sulfate, which is part of the inoculum in a given sample t.

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