# The role of hydrogen sulfide and trisulfur radical ion in molybdenum transport by hydrothermal fluids: implications for porphyry-epithermal Cu-Au-Mo deposits

Maria A Kokh, Gleb S. Pokrovski, Stephan Klemme, Christian Schmidt, Clément Laskar, Jean-Louis Hazemann, Denis Testemale, Isabelle Kieffer, Olivier Proux, Eric Lahera, et al.

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Maria A Kokh, Gleb S. Pokrovski, Stephan Klemme, Christian Schmidt, Clément Laskar, et al. The role of hydrogen sulfide and trisulfur radical ion in molybdenum transport by hydrothermal fluids: implications for porphyry-epithermal Cu-Au-Mo deposits. Geochimica et Cosmochimica Acta, 2026, 412, pp.90-109. 10.1016/j.gca.2025.10.007. hal-05355819

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Geochimica et
Cosmochimica Acta

JOURNAL OF THE GEOCHEMICAL SOCIETY
AND THE METEOROLOGICAL SOCIETY

The role of hydrogen sulfide and trisulfur radical ion in molybdenum transport by hydrothermal fluids: implications for porphyry-epithermal Cu-Au-Mo deposits

Maria A. Kokh, Gleb S. Pokrovski, Stephan Klemme, Christian Schmidt, Clément Laskar, Jean-Louis Hazemann, Denis Testemale, Isabelle Kieffer, Olivier Proux, Eric Lahera, Harald Müller, Elena F. Bazarkina, Christoph Moeller, Daria Ryaboshapka, Max Wilke

PII: S0016-7037(25)00538-1

DOI: https://doi.org/10.1016/j.gca.2025.10.007

Reference: GCA 14038

To appear in: *Geochimica et Cosmochimica Acta*

Received Date: 11 February 2025

Accepted Date: 6 October 2025

Please cite this article as: Kokh, M.A., Pokrovski, G.S., Klemme, S., Schmidt, C., Laskar, C., Hazemann, J-L., Testemale, D., Kieffer, I., Proux, O., Lahera, E., Müller, H., Bazarkina, E.F., Moeller, C., Ryaboshapka, D., Wilke, M., The role of hydrogen sulfide and trisulfur radical ion in molybdenum transport by hydrothermal fluids: implications for porphyry-epithermal Cu-Au-Mo deposits, *Geochimica et Cosmochimica Acta* (2025), doi: https://doi.org/10.1016/j.gca.2025.10.007

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# The role of hydrogen sulfide and trisulfur radical ion in molybdenum transport by hydrothermal fluids: implications for porphyry-epithermal Cu-Au-Mo deposits

Maria A. Kokh<sup>1,2,3</sup>, Gleb S. Pokrovski<sup>3</sup>, Stephan Klemme<sup>1</sup>, Christian Schmidt<sup>4</sup>, Clément Laskar<sup>3,5</sup>, Jean-Louis Hazemann<sup>6,7</sup>, Denis Testemale<sup>6,7</sup>, Isabelle Kieffer<sup>7,8</sup>, Olivier Proux<sup>7,8</sup>, Eric Lahera<sup>7,8</sup>, Harald Müller<sup>9</sup>, Elena F. Bazarkina<sup>10,11</sup>, Christoph Moeller<sup>2,4</sup>, Daria Ryaboshapka<sup>12</sup>, Max Wilke<sup>2</sup>

<sup>1</sup> Institut für Mineralogie, Universität Münster, Münster, Germany

<sup>2</sup> Institut für Geowissenschaften, Universität Potsdam, Potsdam, Germany

<sup>3</sup> Géosciences Environnement Toulouse, GET, CNRS, Université de Toulouse, IRD, CNES, Toulouse, France

<sup>4</sup> GFZ Helmholtz Centre for Geosciences, Potsdam, Germany

<sup>5</sup> Department of Chemistry, KU Leuven, Leuven, Belgium

<sup>6</sup> Institut Néel, CNRS, Grenoble, France

<sup>7</sup> Institut d'ingénierie et de management, Université Grenoble Alpes, Grenoble, France

<sup>8</sup> Unités d'Appui et de Recherche, Observatoire des Sciences de l'Univers de Grenoble, CNRS, Grenoble, France

<sup>9</sup> European Synchrotron Radiation Facility, ESRF, Grenoble, France

<sup>10</sup> Institute of Resource Ecology, HZDR, Dresden, Germany

<sup>11</sup> The Rossendorf Beamline, ESRF, Grenoble, France

<sup>12</sup> Ircelyon, CNRS, Université Claude Bernard Lyon I, Villeurbanne, France

*correspondence: kokh@uni-potsdam.de, mariakokh175@gmail.com
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Revision 1

*Submitted to Geochimica et Cosmochimica Acta*

October 2025
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**Keywords:**

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Hydrothermal fluid; Sulfur; Molybdenum; Molybdenite; Porphyry deposit; Epithermal

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deposit; Speciation; X-ray absorption spectroscopy; XANES; EXAFS; FDMNES;

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Thermodynamic modeling; Trisulfur radical ion, hydrogen sulfide.

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**Abstract**

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Knowledge of the chemical speciation of molybdenum in fluids under hydrothermal conditions is key to understanding the formation of porphyry Cu-Au-Mo deposits, which are the primary economic source of copper, molybdenum and rhenium. However, the chemical identity and thermodynamic stability of aqueous complexes of molybdenum and the role of different ligands on Mo metal transport yet remain inconsistent and incomplete, in particular for sulfur-bearing fluids typical of such environments. We have experimentally studied the role of hydrogen sulfide ($H_2S$ and $HS^−$) and the trisulfur radical ion ($S_3^{•−}$) in the transport of molybdenum by hydrothermal fluids at 300 °C and 500 bar as a function of pH, redox conditions as well as sulfur speciation and concentration. We combined solubility measurements of molybdenite in hydrothermal reactors using fluid quenching or sampling, with *in situ* synchrotron X-ray absorption spectroscopy experiments and thermodynamic and molecular modeling. Our solubility and spectroscopic dataset is consistent with the formation of the tetrathiomolybdate complex, $MoS_4^{2−}$, in reduced, $H_2S/HS^−$-dominated fluids of neutral-to-alkaline pH. In contrast, a mixed-ligand complex with three sulfide ions and one trisulfur radical ion, $MoS_3(S_3)^−$, prevails in more oxidized and more acidic fluids at the sulfide-sulfate transition where $S_3^{•−}$ is far more abundant. In both complexes, Mo is nominally hexavalent and in a first-shell tetrahedral coordination with sulfur atoms. The derived equilibrium constants of the formal solubility reactions ($log_{10}K$):

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$$MoS_{2(s)} + 2 H_2S^{0}_{(aq)} + 0.5 O_{2(g)} = MoS_4^{2-} + 2 H^+ + H_2O_{(liq)} \text{ and}$$

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$$MoS_{2(s)} + H_2S^{0}_{(aq)} + S_3^{•−} + 0.5 O_{2(g)} = MoS_3(S_3)^− + H_2O_{(liq)},$$

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at 300 °C and 500 bar are 0.5±0.4 and 14.6±0.4, respectively. The solubility of $MoS_{2(s)}$ predicted using these constants aligns well with Mo concentrations measured in natural fluid inclusions in quartz that record S-rich fluids from porphyry-epithermal systems. In contrast, other types of Mo complexes invoked so far (molybdates, alkali ion pairs, oxy-chlorides or oxysulfides) are negligible at such conditions. Thus, trisulfur radical ion complexes may be important carriers of Mo in hydrothermal fluids and would require further systematic investigation across a wide range of temperature and pressure.

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# 1. Introduction

Knowledge of the solubility and chemical speciation of molybdenum in hydrothermal fluids is key to understanding the formation of Mo hydrothermal ore deposits including porphyry Cu-Au-Mo deposits, which are the primary economic source of these elements and some other critical metals such as rhenium (e.g., Sillitoe, 2010; Heinrich, 2024). Previous studies have proposed various Mo complexes in aqueous solution, including molybdic acid, hydrogenomolybdate and molybdate ions ($H_2MoO_4^{0}_{(aq)}$, $HMoO_4^-$, $MoO_4^{2-}$; Minubayeva and Seward, 2010; Dadze et al., 2017) and their ion pairs with alkalis (e.g., $NaHMoO_4^{0}$, $KHMoO_4^{0}$; Zotov et al. 1995; Kokh et al., 2017; Shang et al., 2020) in S- and Cl-poor fluids, oxy-chloride species in strongly acidic saline fluids ($MoO_mCl_n^{(6-2m-n)-}$; Borg et al., 2012; Dadze et al., 2018; Guan et al., 2023), as well as thiomolybdate complexes in $H_2S$-bearing liquids and vapors (e.g., $MoO_{4-n}S_n^{2-}$; Kokh et al., 2016; Liu et al., 2020). However, some of those data are both inconsistent and controversial, particularly regarding the formation constants for a given species that vary over many orders of magnitude across different data sources and published thermodynamic sets of parameters (e.g., Pokrovski et al., 2024, see also Table S1).

In particular, studies of the effect of hydrogen sulfide on Mo transport remain both sporadic and controversial. For example, solubility experiments of Zotov et al. (1995) and Kokh et al. (2017) have not detected sulfide complexes in reduced $H_2S$-bearing fluids at 350–450 °C. In contrast, Zhang et al. (2012) tentatively suggested Mo oxy-sulfide-alkali complexes to interpret their molybdenite solubility data at 600–800 °C in fluids buffered by iron sulfide mineral assemblages. Fang et al. (2025) complemented that study for $H_2O-S-NaCl+HCl$ solutions at 800 °C and 2 kbar and suggested a range of possible complexes, $NaHMoO_4^{0}_{(aq)}$, $NaHMoO_3S^{0}_{(aq)}$, $H_2MoO_2S_2^{0}_{(aq)}$ and/or $NaHMoO_2S_2^{0}_{(aq)}$, depending on redox, NaCl and S concentrations and the chosen speciation model for sulfur. Kokh et al. (2016) observed an increase of $MoS_2(s)$ solubility with increasing $H_2S$ concentration at 350°C in aqueous solutions at $H_2S > 0.03 m^1$, that could not be matched by the known molybdate species, pointing to the presence of additional complexes in S-rich solutions (e.g., oxysulfides). Spectroscopic evidence of thiomolybdate complexes $Mo^{VI}O_{4-n}S_n^{2-}$ in hydrothermal fluids was provided by Liu et al. (2020), who tentatively extrapolated the 25 °C data of Erickson and Helz (2000) to 300 °C using an isocoulombic approach. However, such extrapolations require an experimental validation at hydrothermal conditions.

The available solubility data and thermodynamic models are currently unable to account for the massive transport of Mo in porphyry-related fluids as revealed by direct fluid inclusion analyses, demonstrating Mo concentrations of hundreds ppm (e.g., Kouzmanov and Pokrovski, 2012). A potential missing ligand for Mo that was ignored so far could be the trisulfur radical ion, $S_3^{2-}$. This sulfur form, well-known in nonaqueous chemistry since the early 1970s (Chivers and Drummond, 1972, Seel and Güttler, 1973, Chivers, 1974, Chivers and Elder, 2013), is stable across a very wide temperature (T) and pressure (P) range of magmatic-to-epithermal sulfate/sulfide-bearing fluids as independently confirmed by Raman and UV-Vis spectroscopy and molecular and thermodynamic modeling (Pokrovski and Dubrovinsky, 2011; Jacquemet et al., 2014; Pokrovski and Dubessy, 2015; Barré et al., 2017; Colin et al., 2020; He et al., 2024; references therein). Moreover, this ligand has recently been demonstrated to form stable soluble complexes with Au, Pt and Pd, greatly enhancing the transport of these metals to hydrothermal-magmatic porphyry and metamorphic ore deposits associated with subduction

<footnote n="1">¹ Note that, in this article, “m” is used to denote units of molality, except in figure axes where units are expressed explicitly as [mol/kg H₂O].</footnote>
113 zone settings, which commonly involve S-rich fluids (Pokrovski et al., 2015; 2021; Laskar, 2022; He et al., 2024; Laskar et al., 2025). At present, the stability constants of S₃⁻ are 114 quantitatively constrained by UV-Vis and Raman spectroscopy in-situ measurements at 115 temperatures from 25 to 500 °C and pressures from saturated vapor pressure (Pₐ₅) to ~15 kbar 116 (Giggenbach, 1971; Pokrovski and Dubrovinsky, 2011; Pokrovski and Dubessy, 2015) and can 117 reasonably be extrapolated to the lower-end magmatic temperatures (≤700 °C) using the HKF 118 model coefficients generated from these data (Pokrovski and Dubessy, 2015). Likewise, robust 119 data exist on the properties of aqueous hydrogen sulfide, H₂S⁰(aq), (Schulte et al., 2001; 120 Akinfiev and Diamond, 2003) and its dissociation counterpart, HS⁻ ion (Shock and Helgeson, 121 1988), at least under moderate-temperature hydrothermal conditions (<450 °C, <3 kbar). In 122 contrast, under magmatic conditions of fluid degassing from silicate melts of the shallow-crust 123 (700–900 °C, ≤2 kbar), data on the speciation of sulfur and, in particular, on the relative 124 abundances of H₂S⁰(aq), SO₂⁰(aq), HS⁻ and S₃⁻, remain both erratic and controversial (e.g., 125 Farsang and Zajacz, 2025; see section 2.9) as compared with the large body of knowledge from 126 the hydrothermal sensu lato domain. More studies combining experimental, spectroscopic and 127 modeling approaches are required to constrain the role of the different sulfur ligands in metal 128 transport and fractionation at the magmatic-hydrothermal transition. 129

130 To quantify the effect of hydrogen sulfide and S₃⁻ on Mo speciation in hydrothermal 131 fluids, here we combined in situ X-ray absorption spectroscopy (XAS), solubility 132 measurements and molecular and thermodynamic modeling to constrain the stability of Mo 133 complexes with these two major sulfur ligands at the conditions of porphyry-epithermal Cu- 134 Au-Mo deposits. Our results reveal a key role of both types of complexes in Mo transport and 135 deposition in such environments. 136

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## 2. Materials and methods

### 2.1. Solid phases

139 For all solubility experiments, we used natural molybdenite from the Wolfram Camp 140 deposit, Queensland, Australia (courtesy of P. Kartashov, IGEM RAS). A ~6 cm long mono- 141 mineral coarse-crystalline molybdenite sample was crushed in pieces of ~5 mm size and 142 washed several times with deionized water in an ultrasonic bath. The major element 143 composition and identity of the mineral phases, before and after experiments, were checked by 144 powder X-ray diffraction (XRD) and scanning electron microscopy (SEM) equipped with an 145 energy-dispersive spectrometer. Molybdenite was found to be an almost pure Mo:S of 1:2 146 phase with less than 1 wt.% of trace constituents such as Fe, W, Cu, Re, and As, as selectively 147 checked by electron probe microanalyser (EPMA). Molybdenite was always identified after all 148 experiments with no compositional changes. 149

To buffer oxygen fugacity in one of the solubility experiments, pyrite FeS₂(s) (Aldrich, 150 >99%) and troilite FeS(s) (Aldrich, >95%, that transformed to pyrrhotite, FeS(1+x)(s)) were 151 loaded in the reactor, together with an aqueous solution whose H₂S concentration was large 152 enough (0.5–1 m) to remain almost constant, thereby constraining fO₂ by the following reaction 153 (where Fe is normalized to 1 for simplicity): 154

$$ \mathrm{FeS}_{(1+x)(s)} + (1-x) \mathrm{H}_2\mathrm{S}^0_{(aq)} + (1-x)/2 \mathrm{O}_2 = \mathrm{FeS}_{2(s)} + (1-x) \mathrm{H}_2\mathrm{O} \quad (x \le 0.1) \quad (1) $$
This reaction yields equilibrium $fO_2$ values close to those of the conventional quartz-fayalite-magnetite mineral buffer (QFM), which are ~5 orders of magnitude lower than those in a sulfide-sulfate system (see section 2.2). Pyrite loaded in the beginning of this experiment was identified after the experiment with no compositional changes, whereas troilite was totally transformed to pyrrhotite in line with thermodynamic predictions. The consumption of troilite with time demonstrates that the sulfide mineral mixture of reaction (1) was reactive during the experiment and ensured buffering of $fO_2$ and $fS_2$. XRD analyses of solid phases after this experiment are available in Laskar et al. (2025).

Solid reference compounds for X-ray absorption spectroscopy, such as MoO$_{3}$(s) (Alfa Aesar, ThermoFisher (Kandel) GmbH, 99.5%) and Na$_{2}$MoO$_{4}$(s) (Carl Roth GmbH + Co. KG, ≥99.5%) were purchased, whereas others, namely (NH$_{4}$)$_{2}$MoS$_{4}$(s), K$_{2}$MoS$_{4}$(s), (NH$_{4}$)$_{2}$Mo$_{2}$S$_{12}$(s), (NH$_{4}$)$_{2}$Mo$_{3}$S$_{13}$(s), and MoOS$_{2}$(s), were synthesized at the Université Claude Bernard, Lyon-I (France). The synthesis protocols can be found in the Electronic Supplement (section S1), whereas the structural characterization of MoOS$_{2}$(s) is reported in Ryaboshapka and Afanasiev (2023).

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## 2.2. Aqueous solutions: redox, pH and sulfur ligand control

The activity (or concentration) of sulfur ligands capable of complexing molybdenum in aqueous solution (e.g., sulfide, sulfate, polysulfides, sulfur radical ions) and the resulting solubility of molybdenite (MoS$_{2}$) are complex functions of sulfur concentration, redox potential ($fO_2$), and acidity (pH) of the fluid phase. Therefore, the choice of model experimental systems that would enable control of these parameters is crucial.

To prepare the experimental solutions, the following sources of sulfur were used: potassium and sodium thiosulfate (Na$_{2}$S$_{2}$O$_{3}$×5H$_{2}$O, ≥99.5%; K$_{2}$S$_{2}$O$_{3}$, ≥95%, both Sigma Aldrich), sodium hydrosulfide (NaHS solutions, see below), native sulfur (S$_{(s)}$, 99.998%, Sigma Aldrich) and thioacetamide (CH$_{3}$CNH$_{2}$S, ≥99%, Sigma Aldrich). In most solubility experiments, solutions of 0.15–1.2 m Na$_{2}$S$_{2}$O$_{3}$ or K$_{2}$S$_{2}$O$_{3}$ were used, with acidity (3<pH<8) adjusted by adding HCl or KOH/NaOH. For some *in situ* XAS experiments, native sulfur was also used. Such experimental systems provide both pH and redox buffering of the fluid phase through equilibria between the sulfate and sulfide species, which are the major S forms in solution produced by complete hydrolysis of thiosulfate and sulfur in aqueous solution above 150 °C according to the reactions (e.g., Jacquemet et al., 2014):

$$S_2O_3^{2-} + H_2O_{(liq)} = SO_4^{2-} + H_2S^{0}_{(aq)} \quad (2)$$

$$4 S_{(s)} + 4 H_2O_{(liq)} = 3 H_2S^{0}_{(aq)} + SO_4^{2-} + 2 H^{+} \quad (3)$$

$$H_2S^{0}_{(aq)} + 2 O_2^{0}_{(aq)} = SO_4^{2-} + 2 H^{+} \quad (4)$$

$$SO_4^{2-} + H^{+} = HSO_4^{-} \quad (5)$$

$$HS^{-} + H^{+} = H_2S^{0}_{(aq)} \quad (6)$$

The sulfate-sulfide coexistence also favors the formation of the trisulfur ion according to the formal reaction (e.g., Colin et al., 2020):

$$19 H_2S^{0}_{(aq)} + 5 SO_4^{2-} + 2 H^{+} = 8 S_3^{2-} + 20 H_2O_{(liq)} \quad (7)$$
In addition, ion pairs of the sulfate and sulfide anions with alkalis ($K^+$, $Na^+$) along with minor amounts of $SO_2^{0(aq)}$, molecular sulfur ($S_8^{0(aq)}$, both aqueous and molten), and polysulfide dianions $S_n^{2-}$ contribute to aqueous sulfur speciation, depending on pH (e.g., Pokrovski et al., 2022). The temperature of our runs (300 °C) is high enough to allow the system to reach both sulfur redox and fluid-mineral equilibrium within run durations of few hours to few days depending on the specific system as will be discussed in section 3. These systems correspond to oxygen fugacity values close to the conventional hematite-magnetite (HM) mineral buffer at the experimental temperature.

For more reducing conditions (sulfate- and $S_3^{2-}$-poor, close to those of reaction (1)), solutions of NaHS were prepared by bubbling $H_2S(g)$ through an NaOH aqueous solution (1 mol/L) until saturation ($P_{H_2S(g)} = 1$ bar). The obtained NaHS solutions were diluted (if necessary) with deoxygenated water and used both in the autoclave experiment with pyrite-pyrrhotite (flexible cell reactor, m35, see section 2.1) and in situ XAS experiments (4x, 5x), with total sulfide concentrations of 0.15–1.2 m (see section 2.3 for explanation of run numbering). NaHS solutions are prone to rapid oxidation yielding polysulfide dianions ($S_n^{2-}$) whose presence was examined by in situ laser Raman spectroscopy (514.5 nm excitation) in a sapphire cell using the hydrothermal apparatus of the Néel Institute (Testemale et al., 2005). The freshly synthesized NaHS solutions (<2 days) were found to be free of polysulfides (detection limit 0.001 m S), from 25 °C to at least 200 °C (at $P_{sat}$ to 600 bar pressure). In contrast, a one-year-old NaHS solution showed a bright-yellow coloration and yielded a Raman spectrum with a large peak at 390–510 cm$^{-1}$ at 25 °C likely arising from $S_n^{2-}$ anions (Trofimov et al., 2009; Pokrovski and Dubessy, 2015; Steudel and Chivers, 2019; Laskar et al., 2022). Therefore, extreme care has been taken in this study to use only fresh colorless NaHS solutions to avoid any complexation of Mo with polysulfide ions. The solution pH was measured using a combination glass electrode, at ambient T-P before loading into the autoclave or spectroscopic cell, to quantify the amount of $H_2S$ using the dissociation constant:

$$H_2S^{0(aq)} = H^+ + HS^- \quad (\log_{10}K = -7.0 \text{ at } 25 \,^{\circ}\text{C}, 1 \text{ bar}) \quad (8)$$

The value of this constant imposes limitations as to the practical use of NaHS-$H_2S$ solutions at pH<6–7 due to the rapid massive degassing of volatile $H_2S$ whose solubility in water is rather small (<0.1 m at 25 °C, 1 bar). Therefore, to cover the acidic pH region, another sulfur source, thioacetamide, was used. Thioacetamide-bearing solutions were prepared by dissolution of the solid compound in deoxygenated water. In moderately-acidic to neutral pH solutions, thioacetamide stoichiometrically decomposes to acetic acid ($CH_3COOH$), ammonia ($NH_3$) and $H_2S$ on heating (e.g., Pokrovski et al., 2008):

$$CH_3CNH_2S^{0(aq)} + 2 H_2O = CH_3COOH^{0(aq)} + NH_3^{0(aq)} + H_2S^{0(aq)} \quad (9)$$

Acetic acid and acetate ion are kinetically stable at our moderate temperatures (<300 °C) within the run duration. It is only above 320–350 °C that acetate starts appreciably decomposing to formic acid and $CO_2/CO$ (Li et al., 2017). Care was also taken when preparing HCl-acidified solutions, to avoid early decomposition of thioacetamide and partial $H_2S$ release, by quickly loading the solution and pressurizing the spectroscopic cell within <10 min.

## 2.3. Summary of experiments performed in this study
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The results of the most reliable solubility experiments, judged suitable for deriving the thermodynamic properties of aqueous molybdenum species, are presented in Table 1. The solubility of molybdenite was studied at the GET laboratory (Géosciences Environnement Toulouse, France) using batch reactors quenched after the experiment and a flexible-cell reactor allowing rapid fluid sampling. Both liquid and solid products from the experiments were analyzed in the same laboratory using methods described in sections 2.1 and 2.6. The experiments in the flexible-cell reactor with rapid sampling have a consecutive numbering inherent to the reactor used at GET and are labeled by the letter “m” (“multiple elements”). Here we present a new dataset of two experiments with the flexible-cell reactor labeled m35 (37 samplings, Table S2) and m33 (10 samplings, Table S3). The experiments performed in batch reactors with quenching are labeled in this study with the letter “q” (“quench experiment”). In total, we have performed seven quench experiments for molybdenite solubility measurements (labeled 1q to 7q, Table S4).

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Eight experiments were performed at the ESRF (European Synchrotron Radiation Facility, Grenoble, France) using in situ X-ray absorption spectroscopy (XAS). They are labeled as 1x to 8x (where “x” refers to “X-ray”, Table S5). The time series measurements for these experiments are detailed in Tables S6 to S9. Two experiments were also conducted on Mo-bearing solutions at ambient conditions and at 300°C/500 bar in the absence of solid phase; they are labeled as “reference solution” 1 and 2 (Table S10). Spectra of Mo solid reference materials acquired during the ESRF experiments are available via SSHADE database (Kokh et al., 2022; Kokh et al., 2023) and displayed in Appendix A.

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## 2.4. Solubility measurements in the flexible-cell reactor with rapid sampling

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The solubility of molybdenite was measured in aqueous $K_2S_2O_3$ solutions in experiment m33 at 300°C and pressures of 350–500 bar, and in aqueous NaHS-NaCl solutions in experiment m35 in the temperature range 50–300 °C and the pressure range 100–600 bar, using a flexible-cell reactor that allows controlled fluid sampling and injection (Coretest; Rosenbauer et al., 1993). The reactor is equipped with a 100–200 cm³ flexible inner cell made of gold (99.99% purity) and a rapid-sampling device adapted to S-rich fluids (Kokh et al., 2017). The cell was loaded with the solids (0.5 g $MoS_2$ in both m33 and m35 and, additionally 2.0 g $FeS$ and 1.8 g $FeS_2$ in m35) and freshly prepared NaHS (in m35) and $K_2S_2O_3$ (in m33) solutions under argon atmosphere. The cell was then rapidly compressed to remove the gas phase; the experiments were conducted in the single-phase liquid domain. Multiple fluid extractions were periodically taken at different temperature steps and time. Injections of water, HCl/NaOH or $H_2O_2$ solutions were performed through the sampling line at given steps and moments to modify in situ the sulfur concentration, pH or redox conditions in the experimental fluid. The fluid was sampled under pressure into a trap solution placed in a rigid titanium vial attached to a pressure valve to avoid any degassing or solute loss. Sampling procedures using different trap solutions are detailed in Kokh et al. (2017, 2020) and briefly summarized in section 2.6.

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## 2.5. Solubility measurements in batch reactors with quenching

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In addition to the experiments in the flexible-cell reactor, seven dissolution runs (termed “q”) were conducted in the $H_2O-K_2S_2O_3-Na_2S_2O_3-NaOH-HCl$ and $H_2O-C_2H_5NS$ systems at 300 °C and 500 bar using batch-reactor vessels (volume ~20 cm³) made of a titanium-based
281 alloy (grade VT-8, Ti-Cr-Zr-Al). Details about the procedure are given elsewhere (e.g.,
282 Pokrovski et al., 2002). The vessel was loaded with a weighed amount of experimental aqueous
283 solution. A weighed piece of molybdenite was placed into the titanium container affixed in the
284 upper part of the reactor. Several vessels were introduced together into a vertical oven
285 (temperature control ±1 °C; thermal gradients across reactor height <2 °C). The pressure was
286 estimated at the run temperature using the pressure-volume-temperature-composition (PVTX)
287 properties of H₂O-NaCl fluids (Driesner and Heinrich, 2007) and assuming that the presence
288 of H₂S does not significantly change these properties. At the end of the experiment, the
289 autoclave was cooled in cold water for 20 min, unloaded while being frozen in liquid nitrogen
290 to avoid H₂S degassing, and washed with hot aqua regia to recover all Mo that was dissolved
291 in the experiment but may have precipitated on reactor walls upon cooling. The weight loss of
292 the dried molybdenite after the experiment was within the analytical balance sensitivity (<0.01
293 mg); consequently, dissolved Mo was analyzed in aqua-regia treated samples as described in
294 the following section.
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296 **2.6. Analytical methods**

297 At each step of a solubility experiment performed in the flexible cell reactor
298 (experiments m33 and m35), multiple fluid samples (usually 3 to 4, 1 to 2 g each) were
299 extracted for different analyses (for more details see Kokh et al., 2017, 2020). Sample 1
300 removed the residual solution present in the sampling tube from previous injections or
301 samplings to avoid cross-contamination; sample 2 was titrated for reduced sulfur with iodine
302 (I₂) placed in the sampling vial; sample 3 was trapped in ultrapure aqueous 30 wt.% NH₃
303 solution to measure total metal and sulfur contents; sample 4 was trapped in a 1 m zinc acetate
304 (Zn(CH₃COO)₂) or cadmium acetate (Cd(CH₃COO)₂) aqueous solution to precipitate ZnS or
305 CdS (titrated afterwards with I₂, see below) and to measure sulfate (SO₄²⁻) concentrations in
306 the supernatant. Iodine reacts with sulfide, polysulfide, and thiosulfate species, while zinc
307 acetate and cadmium acetate react only with sulfide species (H₂S+HS⁻+NaHS⁰*(aq)) to form ZnS
308 or CdS. Vials containing ZnS or CdS (sample 4) were acidified with HCl (18 wt.%) in the
309 presence of an excess of I₂, which was back-titrated with sodium thiosulfate (Na₂S₂O₃, 0.1
310 mol/L) to determine the total sulfide concentration. Sample 3 was split into two fractions, one
311 for metal concentration analyses, and the other for HPLC analyses of chloride anion and total
312 sulfur – after converting all S to sulfate by adding 2 mL of 30 wt.% H₂O₂ aqueous solution.
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313 The fluid fractions for metal analyses from flexible-cell reactor, as well as autoclave
314 wash solutions from batch reactors, were transferred into clean Teflon beakers (Savillex®) and
315 processed as followed: i) evaporation of the solution in the vial on a hot plate (70 °C); ii)
316 addition of ~5 mL of aqua regia (1/4 volume 65 wt.% HNO₃, 3/4 volume 37 wt.% HCl) in the
317 closed beaker (~120 °C for 3 hours); iii) evaporation of aqua regia on a hot plate until wet
318 residue (70 °C); iv) dilution of the residue with ultra-pure doubly-distilled acids (0.5 wt.%
319 HNO₃ plus 1.5 wt.% HCl). The use of aqua regia and an HCl-HNO₃ matrix is indispensable to
320 fully dissolve the poorly soluble MoS₂(s) precipitates and to keep Mo in solution as soluble
321 chloride species.
322

322 Concentrations of Mo in sampled fluids were measured by inductively coupled plasma
323 - mass spectrometry (ICP-MS). Samples for ICP-MS were further diluted in 2 wt.% HNO₃, just
324 before the analytical session, to reduce the Cl⁻ and SO₄²⁻ ion concentration in solution, which
325 is a source of plasma instability and elevated analytical background in the ICP-MS analysis.
326 The maximum total dissolved load (alkalis + chloride + metals) did not exceed 100 ppm in our
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samples, with S content less than 5 ppm. An ICP-MS Element XR spectrometer was used in our study, enabling detection limits (DL) as low as 0.02 ppb Mo and quantification limits (QL) of 0.1 ppb Mo. Two standard solutions (0.19±0.01 and 18.30±0.01 ppb Mo) were used for calibration, and showed excellent signal linearity through zero ($R^2_{xy}$>0.999). Both $^{95}$Mo and $^{97}$Mo isotopes analyzed yielded identical Mo concentrations (within ±2%) demonstrating the absence of spectral interferences. Inductively coupled plasma – optical emission spectrometry (ICP-OES) was used to analyze total sulfur. Chloride and sulfate ion concentrations were determined by high pressure liquid chromatography (HPLC) in water-diluted samples. Sodium and potassium concentrations were measured using flame atomic absorption spectrometry (FAAS).

## 2.7. *In situ* X-ray absorption spectroscopy

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Molybdenum K-edge (20,000 eV) X-ray Absorption Near Edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) spectra were measured at beamline BM30 (FAME) at ESRF in Grenoble, France. The FAME setup has been described by Proux et al. (2005) and Testemale et al. (2024). The beamline has an X-ray optics setup with a liquid nitrogen cooled Si (220) double-crystal monochromator with sagittal focusing for selecting the energy of X-rays delivered from a bending magnet and horizontal focusing, and two Rh-coated mirrors for harmonic rejection and vertical focusing, yielding a beam spot on the sample of 150×200 µm². In transmission mode, silicon diodes collect scattered radiation from a Kapton foil placed in the incidental and transmitted X-ray beam. In fluorescence mode, a multi-element solid-state germanium detector (SSD, Canberra 13-element) is placed at 90° to the incident beam. The strong elastic and inelastic scatter signal, which easily leads to detector saturation, was reduced by using a zirconium filter with an X-ray absorption amplitude ($\Delta\mu$) of 3 and 6, thus optimizing the signal to background ratio of the Mo fluorescence signal. The incident energy was scanned from 19,800 to 20,800 eV. Attention was paid to remove all Mo-bearing components from the experimental setup (beamline and autoclave) to achieve a detection limit of 0.03 ppm Mo for the solubility measurements in fluorescence mode. The detection limit is constrained by the spectra in the beginning of the experimental run 2x, which essentially showed no visible edge-jump, i.e., the apparent edge-jump determined by the fit (0.01 ppm Mo) was given by the statistical scatter in the spectra. The energy position during each scan was monitored in transmission using a Mo metal foil placed after the sample and whose K-edge was set to 20,000 eV for the maximum of the spectrum first derivative.

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Solid reference compounds (section 2.1) were diluted either with boron nitride (BN) or with cellulose powder to achieve an absorption value above the edge of one, pressed in 5-mm diameter pellets and recorded in transmission mode at ambient conditions. The experimental solutions were placed in the glassy-carbon inner cell (0.2–0.3 mL volume) of the hydrothermal apparatus. The autoclave, developed at the Néel Institute (Testemale et al., 2005, 2024; see also Pokrovski et al., 2006 for details), is equipped with Be windows and operated with helium pressure. Spectra from the experimental solutions were recorded at 300 and 350 °C at 500 bar in fluorescence mode as all solutions were low-concentrated (≤ 100 ppm). A molybdenite sample (0.3 mm thickness) cut to round-shape pieces was placed at the cell bottom outside the X-ray beam passage. The progress of the $MoS_{2}(s)$ crystal dissolution was monitored by the height of the Mo edge jump in the spectra of the fluid. In preliminary experiments (4x, 6x), the molybdenite crystal was glued to the lower piston with cyanoacrylate to exclude the possible floatation of molybdenite crystal towards the beam position that might occur due to the solution
convection in the cell. Later, we repeated those experiments (5x, 7x) without any glue to check the possible effect of cyanoacrylate on the molybdenite dissolution.

To achieve the necessary signal statistics required for accurate analysis of the extended X-ray absorption fine structure (EXAFS) of the solutions at low Mo concentrations (0.1–5 ppm Mo), 15 to 45 scans of 23 min acquisition time each were necessary. The EXAFS region was analyzed using the xafsX software package (Winterer, 2022), which was used to extract the oscillating part of the signal from the measured absorption spectra and to fit the resulting EXAFS. A polynomial fit was used to remove the background in the energy region below the edge; the edge position E₀ was determined using the inflection point of an error function that was fitted together with a Gaussian function to the edge; the step height of the error function was used for normalization. The background of the EXAFS was determined using a cubic spline function minimizing the signal at < 1 Å in the Fourier transform. A Kaiser-Bessel filter was applied to Fourier-transform (FT) of the k³-weighted EXAFS oscillations (χ(k)×k³). Exploitable k-ranges were 3–10 Å⁻¹ for dissolution experiments and 3–14 Å⁻¹ for Mo-bearing reference solutions and solids. The EXAFS data were fitted to derive structural information (first shell only) on Mo complexes formed in solution. Theoretical amplitude and phase functions were calculated using FEFF 9.0 from simple molecular structure models, which are in accordance with crystallographic data of crystalline phases such as Na₂MoO₄×H₂O, (NH₄)₂MoS₄ and MoS₂. Fits were performed in k-space to determine the interatomic distance (R) and its mean square displacement (so-called Debye-Waller factor, σ²), as well as ΔE, which is a non-structural parameter accounting for energy shift between the experimental spectrum and FEFF calculation. The coordination number N was not fitted but set to a physically meaningful value for a given interatomic distance. Further, the amplitude reduction factor, S₀² was set to 1.0. This approach was tested successfully on spectra of reference materials such as (NH₄)₂MoS₄ (tetrahedral coordination by S) and MoS₂ (trigonal prismatic coordination by S).

The absorption edge height in transmission mode, which may be used for straightforward determination of dissolved absorber concentrations from XAS spectra (e.g., Pokrovski et al., 2006; Testemale et al., 2024), was too small to be quantified for the low Mo concentrations of our experiments that were from 0.1 to 5 ppm. In contrast, the edge height in fluorescence spectra is more sensitive, but requires calibrations as a function of detector position, beam position on the sample, fluorescence filter as well as matrix absorption corrections to be converted into metal concentration (e.g., Bazarkina et al., 2014; Pokrovski et al., 2022). These calibrations of the fluorescence signal were performed using two aqueous solutions of ~10 and 100 ppm Mo prepared by weight from the Na₂MoO₄×2H₂O(s). The calibrations were made as a function of the detector position, because the position was varied during the different runs to optimize the fluorescence signal depending on Mo concentration.

The Mo concentration cₚₐ₉₆ in each scan was determined as:

$$c_{\text{sample}} = c_{\text{ref}} \cdot \frac{eH_{\text{fl sample}} \cdot \sigma_{1 \text{ ref}} \cdot \sigma_{2 \text{ ref}} \cdot \rho_{\text{ref}}}{eH_{\text{fl ref}} \cdot \sigma_{1 \text{ sample}} \cdot \sigma_{2 \text{ sample}} \cdot \rho_{\text{sample}}} \quad (10)$$

where cₚₐ₉₆ and cₚₐ₉₄ are, respectively, the Mo experimental and reference concentrations (in mol/kg solution); eHₚₐ₉₆ and eHₚₐ₉₄ are the fluorescence edge height of the sample and the edge height of the reference solution corrected to the same position of the detector; σ₁ₚₐ₉₆ and σ₁ₚₐ₉₄ are the absorption cross sections of the experimental sample and the reference solution at E₁ = 17,800 eV (fluorescence energy); σ₂ₚₐ₉₆ and σ₂ₚₐ₉₄ are the absorption cross sections of the experimental sample and the reference solution at E₂ = 20,300
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eV (highest excitation energy considered for the edge height determination); ρ<sub>sample</sub> and ρ<sub>ref</sub>
are, respectively, the densities of the experimental sample and reference solution.

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Volumetric concentrations were converted to molality using the fluid density at the experimental *T-P* conditions assuming that density is equal to that of aqueous NaCl solution of the same solute weight concentration (Pokrovski et al., 2009). The amplitude of the edge height (*eH*) was extracted from each experimental spectrum using a fitting routine that combines a polynomial function for background removal, an error function to determine *eH* and a Gaussian function to determine the peak location and width of the white line. The combined uncertainty on Mo concentration determination is 5% (for concentrations above 1 ppm Mo) to 30% (for concentrations below 0.1 ppm Mo that start to approach the detection limit) of the total value, depending on the experiment.

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The nature and extent of possible beam-induced chemical changes in our experimental systems remain difficult to quantify. Photo-induced chemistry depends on numerous parameters, including X-ray flux, beam focus, energy, exposure time, sample composition, surrounding chemical environment, temperature, and pressure. However, we believe that beam-induced chemical changes were negligible in our experimental setup, for the following reasons. First, the experimental setup has been used to study molybdenum speciation in previous studies conducted by independent research groups (e.g., Borg et al., 2012, Liu et al., 2020), under similar energy ranges and in similar chemical systems (i.e., H₂O-based solutions containing dissolved Cl, S and Mo), without indication of beam damage. Particularly, convection of the fluid in the cell leads to an intrinsically reduced effective exposure of a given volume. Second, experiments were performed on a bending-magnet beamline at ESRF, using a relatively large beam size (150 × 200 µm²). This configuration is known to significantly reduce the likelihood of beam-induced effects. Third, multiple spectra were collected for each data point. Before averaging, individual scans were carefully compared to check for any time-dependent evolution over several hours. Fourth, all solid Mo reference phases showed very good stability under beam exposure, with similar exposure times to those used for the solutions. EXAFS-derived structural parameters confirmed the absence of detectable beam-induced alterations. Fifth, the reference solutions were stable under beam during experimental runs. Finally, the absolute solubility values measured in situ are in excellent agreement with those obtained in autoclave experiments with no beam exposure, which further supports the stability of the system under X-ray irradiation.

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2.8. *Density Functional Theory (DFT) and Finite Difference Method Near Edge Structure (FDMNES) simulations*

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To better constrain the identity of Mo species, local molecular structures of different Mo complexes and their corresponding XANES spectra were simulated using complementary tools and compared with the experimental XANES spectra. Geometrical parameters of a given species were first optimized using the Molecular Mechanics tool implemented in the Avogadro software (Neese, 2022). The atomic coordinates provided by Avogadro were then used for Density Functional Theory (DFT) calculations using the ORCA version 5.0.2 software. Generalized gradient BP86 functional exchange (Becke, 1988) and Perdew energy correlation (Perdew, 1986) were applied. The basis sets developed by the Karlsruhe group were applied in combination with the def2-SVP and def2-TZVP functionals (Weigend et al., 2005). An auxiliary basis set, def2/J, for Coulomb fitting was also applied. The RIJCOSX approximation was added, in which RI-J is used for the Coulomb integrals and COSX for Hartree-Fock (HF)
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exchange integrals. RIJCOSX significantly speeds up the calculations without losing accuracy.

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Grimme's D3BJ method (Grimme et al., 2011) was used to introduce the dispersion correction.

465

To achieve convergence, a two-step scheme was applied, including first geometrical

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optimization with the def2-SVP basis and loose convergence criteria, followed by a second

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optimization using the def2-TZVP basis, fine grid, tight convergence tolerance, and the

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'SlowConv' or 'VerySlowConv' options.

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The optimized atomic coordinates of a given molecular complex were used as input

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data for Finite Difference Method Near Edge Structure (FDMNES) simulations of XANES

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spectra (Joly et al., 2009). The cluster radius around the absorbing atom was chosen at 5 Å,

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increasing the radius further yielded insignificant spectral changes. Self-consistent calculations

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SCF were performed, meaning that after the first iteration the obtained electronic density is

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used in the next one, until convergence is achieved (Bunau and Joly, 2009). Convolution with

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the Mo 1s core-hole life-time broadening yields the absorption cross-section spectra. The core

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level width at Mo K-edge was taken to be 4.5 eV (Krause and Olivier, 1979) for the keyword

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"Gamma_hole" in FDMNES.

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The FDMNES calculations presented in this study have certain limitations that are

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inherent to this method. First, these calculations do not take into account any thermal vibrations

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at experimental conditions. Second, they do not explicitly incorporate the experimental

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resolution. As a result, some spectral features in the theoretical FDMNES spectra may not be

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observable as distinct features in experimental data due to both thermal effects and limited

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resolution. To compensate at least partly this imperfection, a convolution with the "Gaussian"

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keyword was used to incorporate experimental resolution broadening (Fig. S9).

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## 2.9. *Thermodynamic data sources and models*

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The mineral solubility and chemical speciation in aqueous solution in our experiments

488

were simulated via equilibrium thermodynamic calculations and compared with the

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experimental data. Modeling was performed using the HCh software package (Shvarov, 2008,

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2015) based on the minimization of the Gibbs energy in multicomponent and multiphase

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systems. The thermodynamic properties of H₂O were calculated using the Haar-Gallagher-

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Kell and Marshall-Franck models (Marshall and Franck, 1981; Kestin et al., 1984), which must

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be used to reproduce our results. Although the HCh software supports more recent

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thermodynamic models for water properties (Wagner and Pruß, 2002; Bandura and Lvov,

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2006), our tests showed that they yield results indistinguishable within errors at the T-P

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conditions relevant to this study. The thermodynamic properties of pyrite, magnetite and

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molybdenite were taken from Robie and Hemingway (1995), those of pyrrhotite from the

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Ivtantermo database (Gurvich et al., 1983), and those of quartz, microcline and muscovite from

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the SUPCRTBL database (Zimmer et al., 2016). The thermodynamic properties of major

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cations, anions and their ion pairs (Na⁺, K⁺, Cl⁻, NaCl⁰(aq), KCl⁰(aq), OH⁻, KOH⁰(aq), NaOH⁰(aq),

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HS⁻, HSO₄⁻, SO₄²⁻, KSO₄⁻, KHSO₄⁰(aq), CH₃COOH⁰(aq), CH₃COO⁻) were taken from

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SUPCRT92 database (Johnson et al., 1992), based on the revised Helgeson-Kirkham-Flowers

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(HKF) equation of state (Tanger and Helgeson, 1988; Oelkers et al., 2009). This list of species

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was complemented by more recent HKF data sets for HCl⁰(aq) (Tagirov et al., 1997), S₃⁻

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(Pokrovski and Dubessy, 2015), NaSO₄⁻ (Pokrovski et al., 1995), NaHS⁰(aq) and KHS⁰(aq)

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(Jacquemet et al., 2014), Al hydroxide complexes (Tagirov and Schott, 2001), SiO₂⁰(aq) and

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Si₂O₄⁰(aq) (Sverjensky et al., 2014), and polysulfide dianions Sₙ²⁻ (Barré et al., 2017). Stability

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constants for mono- and dichloride Fe(II) species (FeCl⁺, FeCl₂⁰(aq)) were taken from
Sverjensky et al. (1997) and those for the additional tetrachloride complex (FeCl₄²⁻) from Testemale et al. (2009). The properties of aqueous volatile nonelectrolyte species (H₂S⁰(aq), SO₂⁰(aq), O₂⁰(aq), and H₂⁰(aq)) were adopted according to the equation of state of Akinfiev and Diamond (2003), based on the water density and the properties of ideal gas species, that provide a slightly better description of the measured Henry coefficients and Cₚ and V functions of those species at moderate pressures (<1 kbar) than the HKF dataset from SUPCRTBL. The activity coefficients of ionic species were calculated using the extended Debye-Hückel equation (Helgeson et al., 1981), whereas those of uncharged species were assumed to be unity, which is a reasonable approximation for the moderately saline fluids used in this study.

Thermodynamic properties of the two major ligands, HS⁻ and S₃⁺⁻, are key to quantitative assessment of metal complexing in hydrothermal fluids. The HKF parameters of HS⁻ were derived by Shock and Helgeson (1988) from selected experimental data of the H₂S⁰(aq) dissociation constant to 300 °C (reaction 8) combined with HKF parameters for H₂S⁰(aq) from the same study slightly updated in a subsequent study of Schulte et al. (2001) who regressed values of isobaric heat capacity (Cₚ) of H₂S⁰(aq) measured by Hnědkovský and Wood (1997) to 430 °C and 350 bar. Note that HKF model predictions for such type of dissociation reaction constant perform exceptionally well beyond the T-P range within which the HKF parameters were derived, and are in agreement with more recent measurements of the dissociation constant of reaction (8) (Suleimenov and Seward, 1997). The log₁₀K₈ shows a similar pattern as a function of temperature as many similar weak acids such as silicic, boric or carbonic for which more T-P extended experimental datasets exist. Note that the use of H₂S⁰(aq) properties from Akinfiev and Diamond (2003) instead of those from SUPCRT92 yields similar within errors log₁₀K₈ to at least 400 °C (<1 kbar) but attains 1 log unit difference at 900 °C and 2 kbar (Fig. S1). Therefore, this minor thermodynamic inconsistency of using different sources of thermodynamic data for HS⁻ and H₂S⁰(aq) introduces negligible error at the T-P covered by our experiments (300 °C, < 1 kbar).

The thermodynamic properties of the S₃⁺⁻ ion used in this study were derived in the form of HKF-model parameters by Pokrovski and Dubessy (2015) from the equilibrium constant (K₁₁) of the formal reaction:

$$2 \text{H}_2\text{S}_{\text{(aq)}} + \text{SO}_4^{2-} + \text{H}^+ = \text{S}_3^{\bullet-} + 0.75 \text{O}_{2(\text{g})} + 2.5 \text{H}_2\text{O} \quad (11)$$

They stem from Raman spectroscopy analyses from 200 to 500 °C and pressures from Pₘₐₜ to 15 kbar in different optical cell configurations (diamond-anvil cell and silica capillaries) at 3 different laser wavelengths (457, 514 and 623 nm), and covering 2 log units of [S₃⁺]⁻ concentrations (Pokrovski and Dubrovinsky, 2011; Pokrovski and Dubessy, 2015), along with UV-Vis absorption spectroscopy measurements from 25 to 300 °C at Pₘₐₜ of Giggenbach (1971) (see Pokrovski and Dubessy, 2015 for details). They are also supported at high temperatures by theoretical quantum-chemistry DFT calculations of Tossell (2012). These independent data are all in excellent mutual agreement (Fig. S2), confirming the validity of the K₁₁ value across the whole T-P range covered (25–500 °C, 1 bar–15 kbar), with no evidence for potential artefacts related to Raman signal absorption in colored solutions as claimed by Schmidt and Seward (2017). The thermodynamic properties of H₂S⁰(aq), which are internally consistent with those of S₃⁺⁻ according to reaction (11), are from Schulte et al. (2001). Like in the case of reaction (8), within the experimentally covered T-range (<500 °C), the use of H₂S⁰(aq) from Akinfiev and Diamond (2003) introduces negligible within error inconsistency. However, it becomes more significant towards magmatic temperatures yielding differences in predictions of S₃⁺⁻ abundance of several log units above 700 °C in hydrothermal-magmatic fluids (see Pokrovski and Dubessy, 2015 for details).
A very recent controversy to the significance of both $HS^-$ and $S_3^{3-}$ ions in hydrothermal-556 magmatic fluids was introduced by the study of Farsang and Zajacz (2025) who used Raman557 spectroscopy measurements on aqueous $H_2SO_4$(-NaCl, -KCl) solutions trapped as synthetic558 fluid inclusions in quartz at 875 °C and 2 kbar. They interpreted the data by dominant $SO_2^{0(aq)}$559 and $HS^-$, along with subordinate $H_2S^{0(aq)}$, whereas the trisulfur radical ion was undetectable in560 their Raman non-resonant spectra. On the basis of thermodynamic calculations that returned561 negligible $HS^-$ but large $S_3^{3-}$ concentrations (expected to be Raman detectable) at their562 experimental conditions, the authors claimed that the $S_3^{3-}$ and $HS^-$ thermodynamic properties563 were incorrect and that the major sulfur species controlling gold transport in hydrothermal-564 magmatic fluids is the $HS^-$ anion. However, these conclusions stem from the use of inconsistent565 thermodynamic data for S species as well as incorrect Raman spectra assignments. First, the566 Raman feature around 2570 cm$^{-1}$, mistaken for the stretching vibration of the $HS^-$ ion by567 Farsang and Zajacz (2025), belongs in fact to the $H_2S^{0(aq)}$ v1 peak (nominally at ~2590 cm$^{-1}$)568 that has an asymmetry at the lower energy side. This intrinsic feature is due to hot bands and569 hydrogen bonding as was shown both in gaseous phase and acidic aqueous solution in which570 the $HS^-$ is virtually zero (Pokrovski and Dubessy, 2015; Jiang et al., 2017). Second, the571 $HS^- / H_2S^{0(aq)}$ ratios reported in the Farsang and Zajacz (2025) study at 875 °C and 2 kbar (~2:1)572 would require an $H_2S^{0(aq)}$ dissociation constant of reaction (8) to be at least 8 log units higher573 than predicted using $H_2S^{0(aq)}$ and $HS^-$ thermodynamic properties discussed above (Fig. S1).574 Such a large difference is in sharp contrast with the ionization patterns of other similar weak575 acids and would be unphysical. Finally, Farsang and Zajacz (2025) calculations of sulfur576 speciation, used as the basis for the comparison with their own experiments, lacked necessary577 corrections for the $H_2S-SO_2$ equilibrium boundary between model and experiment, and578 employed inconsistent thermodynamic data sources for $S_3^{3-}$ and $H_2S^{0(aq)}$ (see above) as well as579 ignored important sulfur species such as sulfate alkali ion pairs that become increasingly580 abundant towards magmatic temperatures (Pokrovski and Dubessy, 2015; Beaudry and581 Sverjensky, 2024). As a result, the predictions of Farsang and Zajacz (2025) largely582 overestimate the abundance of $S_3^{3-}$ ion at the conditions of their experimental fluids. If the583 necessary corrections above were applied, the predicted abundances would have been several584 orders of magnitude less, in excellent agreement with the experiment and the existing585 thermodynamic properties of $S_3^{3-}$, $H_2S^{0(aq)}$ and $HS^-$ (Pokrovski and Dubessy, 2015). In light of586 the above arguments, there is yet no quantitative evidence for questioning the abundance of587 $H_2S^{0(aq)}$, $HS^-$ and $S_3^{3-}$ and their metal complexes in hydrothermal fluids. Details of this analysis588 and numerical data can be found in Pokrovski (2025). Therefore, in the present study, we589 adopted the sources of thermodynamic parameters of sulfur species as discussed above.590

Thermodynamic data for existing Mo complexes are poorly consistent among different591 data sources (Table S1 and references therein). We chose the HKF set of parameters for the592 basis anions $MoO_4^{2-}$ and $HMoO_4^-$ from Shock et al. (1997), which are independently supported593 by more recent experimental data acquired at T-P conditions close to our experiments (e.g.,594 Minubayeva and Seward, 2010; Dadze et al., 2018), thereby lending credibility on the seminal595 HKF predictions. In contrast, no reliable HKF parameters are currently available for any other596 Mo species; e.g., some recent work reported unphysical values for $NaHMoO_4^{0(aq)}$ (see597 Pokrovski et al., 2024 for details). In the face of these limitations and in order to account for598 other Mo species in our speciation model, we used two approaches, depending on the species’599 available T-P set of reaction constant values. Note, that even if these different sources of data600 are independent, they are all based on the thermodynamic properties of $MoO_4^{2-}$ and the major601 cations and anions from the same data source (SUPCRTBL, see above), thereby ensuring602 internal consistency.603
For the H₂MoO₄⁰(aq) species, a set of tabulated dissociation constant values is available to 300 °C and P₃₉₈K (Dadze et al., 2018) that we fitted using the Ryzhenko-Bryzgalin two-parameter model (Ryzhenko, 1981; Ryzhenko et al., 1985; Bryzgalin and Rafal'sky, 1982; modified by Shvarov and Bastrakov, 1999) incorporated into the OptimC software (Shvarov 2015):

$$609 \qquad pK_{T,P} = pK_{298K,1 \text{ bar}} \times 298.15/T + f(T,P) \times (A+B/T) \qquad (12)$$

where T is temperature in Kelvin, pKₜₚ and pKₜ₉₈K,₁ bar are the negative logarithms of the dissociation constant value of a complex (pK = -log₁₀K) at the given T-P and reference conditions, respectively, f(T,P) is a species-independent function computed from the dissociation constant of water as a function of T and P (Marshall and Franck, 1981), and A and B are T-P-independent adjustable parameters for each complex.

The formation constants of molybdate alkali-ion pairs KHMoO₄⁰(aq), KMoO₄⁻ and NaMoO₄⁻ were assumed to be equal, respectively, to those of KHSO₄⁰(aq), KSO₄⁻ and NaSO₄⁻ for which sets of HKF parameters are available (Pokrovski et al. 1995; Sverjensky et al., 1997). This assumption translates to Kₜₚ = 1 for the following isocoulombic ion exchange reactions at all temperatures and pressures (Table 2):

$$620 \qquad KHSO_4^0(aq) + Na^+ = NaHSO_4^0(aq) + K^+ \qquad (13)$$

$$621 \qquad KHSO_4^0(aq) + MoO_4^{2-} = KHMoO_4^0(aq) + SO_4^{2-} \qquad (14)$$

$$622 \qquad NaSO_4^- + MoO_4^{2-} = NaMoO_4^- + SO_4^{2-} \qquad (15)$$

$$623 \qquad KSO_4^- + MoO_4^{2-} = KMoO_4^- + SO_4^{2-} \qquad (16)$$

A large range of formation constant values over different narrow T-P ranges can be found in the literature for NaHMoO₄⁰(aq) (Zotov et al. 1995, Shang et al. 2020; Guan et al. 2023; see Table S1); however, they appear to be inconsistent and controversial and no reliable selection can be made at present (Pokrovski et al., 2024). Therefore, for consistency, the formation constant of NaHMoO₄⁰(aq) was assumed to be equal to that of KHMoO₄⁰(aq) as derived above from equation (14).

The thiomolybdate species considered in our study include a series of four thiomolybdate MoO₄S₄·n²⁻ anions whose stability constants were measured by Erickson and Helz (2000) at 25°C, and later extrapolated by Liu et al. (2020) to higher temperatures using an isocoulombic approach (Gu et al., 1994):

$$634 \qquad \log_{10}K_T = 298/T(K) \times \log_{10}K_{298K} \qquad (17)$$

for the following exchange reactions:

$$636 \qquad MoO_4^{2-} + H_2S^0(aq) = MoO_3S^{2-} + H_2O \qquad (18)$$

$$637 \qquad MoO_3S^{2-} + H_2S^0(aq) = MoO_2S_2^{2-} + H_2O \qquad (19)$$

$$638 \qquad MoO_2S_2^{2-} + H_2S^0(aq) = MoOS_3^{2-} + H_2O \qquad (20)$$

$$639 \qquad MoOS_3^{2-} + H_2S^0(aq) = MoS_4^{2-} + H_2O \qquad (21)$$
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Although alternative or complementary speciation schemes for Mo were proposed in saline (NaCl, KCl) aqueous fluids and HCl-rich vapors, with the formation of oxy-chlorides (e.g., MoO₂Cl₂⁰(aq), MoO₂Cl⁺, MoO₂(OH)₂Cl⁻) rather than alkali molybdate ion pairs (e.g., Ulrich and Mavrogenes, 2008; Rempel et al., 2009; Borg et al., 2012; Guan et al., 2023), the data are either inconsistent or far beyond our experimental pH and T-P ranges. We therefore ignored chloride complexes in our modeling.

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## 3. Results

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### 3.1. Solubility experiments in the flexible-cell reactor

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In the solubility experiments performed in the flexible-cell reactor (m33 and m35), molybdenum concentrations varied from 10s ppb to a few ppm (Table 1) except for two samples where the Mo concentrations reached more than 10 and 100 ppm (for the complete set of data see Tables S2 and S3). Molybdenum concentrations in experimental solutions depended primarily on temperature and solution composition. These solubility trends are further complicated by analytical difficulties of accurately measuring the low metal concentrations in sulfur-rich solutions at high temperatures and pressures, as well as by equilibration kinetics issues that arise from changes in solution composition during injections. Therefore, care has been taken in this study to carefully select the datapoints that were judged to be most reliable and representing equilibrium solubility. Our analysis is limited to the 300 °C dataset, because of paucity of data at lower temperatures, complex sulfur speciation in the presence of poorly quantified polysulfide dianions and their protonated counterparts, as well as stronger kinetic issues that likely have prevented attainment of mineral-fluid equilibrium at lower temperatures. The critically selected solubility data are summarized in Table 1, whereas the whole set of experimental datapoints is reported in the Electronic Supplement (Tables S2, S3). The data choice is discussed below.

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Experiment m35 was designed to measure molybdenite solubility in reduced sulfide-bearing fluids using freshly prepared NaHS solutions (Table S2), in which the concentrations of S₃⁺⁻ and other polysulfide ions are too low (<10⁻⁴ m) to significantly affect Mo solubility. This experiment thus specifically targeted Mo (hydro)sulfide complexes. The different temperature steps and multiple fluid injections resulted in significant fluctuations of Mo concentrations and their subsequent evolution upon time. After each injection, Mo concentrations usually increased likely due to introduction of oxygen, followed by a decrease reflecting the buffering reaction of the pyrite-pyrrhotite assemblage that consumed the introduced O₂ excess with time. Such samples reflect equilibration kinetics (see section 4.1.2 for discussion of data choice). It is only at 300 °C that a consistent and stable solubility pattern could be identified. The Mo concentrations attained a steady state of ~0.05 mmol after a few days of the temperature reach and showed a consistent pattern upon two consecutive HCl injections as a function of pH, first increasing to ~0.1 mmol, and then decreasing to ~0.005 mmol Mo upon further acidification (Table 1).

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Experiment m33 was designed to explore MoS₂(s) solubility in the sulfide-sulfate system, which favors elevated S₃⁺⁻ concentrations (>10⁻² m), whereas polysulfide dianions are very minor (≤ 10⁻⁶ m for any of Sₙ²⁻ species, where n varies from 2 to 8). The Mo concentrations are of the same order of magnitude as those in m35 at 300°C (Table S2), first increasing upon each water injection and then decreasing with time toward a steady state (Table S3).

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### 3.2. Solubility experiments in batch-reactors with quenching
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The results of solubility experiments in batch reactors with quenching are summarized in Table 1 and detailed in Table S4. Three molybdenite dissolution experiments with Na₂S₂O₃ solutions (1q, 2q and 3q) lasted 3 to 5 days and yielded Mo concentrations of ~10 ppm. These results encouraged us to perform *in situ* XAS experiments at similar fluid compositions to constrain the molecular structure of species (see section 3.3). Experiment 4q in a highly reduced C₂H₅NS solution yielded Mo concentrations below detection limits (<0.03 ppm) (Table S4). Experiments 5q, 6q and 7q in K₂S₂O₃-bearing solutions lasted for 1 month and yielded from a few ppm Mo at acidic and neutral pH to ~50 ppm at alkaline pH. Note that identical (within errors) Mo concentrations (~1.5 ppm Mo) were measured in an 0.5 m K₂S₂O₃ solution at neutral pH in experiment 6q and in experiment m33 (flexible cell reactor) lending further support for the quench-based data.

### 3.3. *In situ* XAS experiments

#### 3.3.1. Solubility data

The results of *in situ* XAS experiments on molybdenite dissolution are reported in Table 1, and time series are plotted in Fig. 1 (for full numerical details see Tables S5-S9).

In experiment 1x (Na₂S₂O₃-HCl, pHₜₚ = 4.9, 4.5 ppm Mo), the measured Mo concentrations were stable over time (Fig. 1a). In contrast, chemical equilibrium was not reached in experiment 2x (Na₂S₂O₃, pHₜₚ = 5.3) where the concentration of Mo could reach only ~0.3 ppm Mo within 8 hours (Fig. 1b). Note, that an equilibrium concentration for such an experiment should be around ~1.5 ppm Mo according to a long-term (1 month long) quench experiment 6q of similar composition (Table 1, Table S4). Experiment 3x (S-NaOH system, pHₜₚ = 4.9) was heated to 350 °C to accelerate the sulfur dissolution and disproportionation reaction (3), and then cooled down to 300 °C once the reaction started (Fig. 1c). The Mo concentrations (4.2 ppm) remained constant at 300 °C for at least 1.5 h, suggesting attainment of equilibrium, which is supported by the results of the longer experiment 1x in a thiosulfate solution of similar pH and S speciation but with different starting chemicals at the beginning of experiment.

Two experiments (4x and 5x) were performed with NaHS solutions (Fig. 1d). These are more reducing conditions than the thiosulfate runs, with negligibly low concentrations of S₃⁻ and sulfate. To avoid floating of small MoS₂(s) particles at the X-ray beam passage, the solid was glued at the cell bottom with a cyanoacrylate glue in experiment 4x. A similar experiment (5x) was performed with a bigger MoS₂ crystal and a lower solid/solution ratio and without the glue to check if cyanoacrylate could affect the results. However, this experiment faced another difficulty related to the precipitation of MoS₂ at the cell walls in to the beam path. The beam position was therefore changed by moving the autoclave to find a clean area devoid of precipitates. The measured Mo concentrations in experiment 5x (3 ± 1 ppm) are identical within errors to those found in experiment 4x and in the flexible-cell reactor of much longer run duration (experiment m35, samples 8-10, Table 1), providing further support for the XAS results.

In the case of experiments 6x and 7x (Na₂S₂O₃-NaOH, pHₜₚ = 6.1), the steady state was achieved straight away and no significant changes in measured concentrations were observed within 12 hours (Fig. 1e). The use of cyanoacrylate glue in experiment 6x had no effect on Mo solubility compared to experiment 7x (without glue) within 2 SD (standard deviation) uncertainty of the measured concentration value (Table S5).

Molybdenum concentrations were below detection limit (<0.03 ppm) in experiment 8x with thioacetamide after 5 hours of reaction. Experiment 8x with thioacetamide showed the same result as experiment 4q in the batch reactor, providing more evidence that at acidic conditions in sulfur-rich reduced systems dominated by H₂S⁰(aq) molybdenite solubility is much lower compared to similar reduced systems but at alkaline pH.
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### 3.3.2. XANES spectra of reference compounds

Selected XANES spectra of molybdenum solid compounds of known crystal structures are shown in Fig. S3. The pre-edge feature at ~20,004 eV (dashed vertical line in Fig. S3) may be used as a fingerprint of the Mo local environment. The most pronounced pre-edge feature is found for the tetrahedral coordination of MoVI with oxygen atoms in Na₂MoO₄×2H₂O(s), whereas it is much less pronounced for the distorted octahedral-like coordination of Mo⁶⁺ with oxygen, such as in MoO₃(s). All compounds with Mo-S coordination polyhedra display weak to undetectable pre-edge features: only for the most symmetrical tetrahedral coordination of Mo with sulfide ligands, as realized for (NH₄)₂MoS₄(s), a clear pre-edge shoulder is displayed. In the case of MoOS₂(s) in which Mo⁶⁺ has four sulfur atoms and one oxygen atom in the first coordination shell, only a very weak pre-edge is observed. The spectrum of molybdenite, in which Mo is surrounded by 6 S atoms in trigonal prismatic coordination, is very distinct from a tetrahedral coordination, such as in (NH₄)₂MoS₄(s). It has no pre-edge and shows a pronounced main-edge shoulder at 20,011 and a maximum at 20,027 eV followed, toward the EXAFS region, by a broad double peak with maximums at 20,075 and 20,092 eV. For (NH₄)Mo₃S₁₃(s) and (NH₄)₂MoS₄(s), a shoulder is also visible at 20,011 eV. The maximum at 20,027 eV is characteristic of all measured sulfur-bearing compounds, except (NH₄)₂MoS₂(s) that has the main maximum at 20,042 eV.

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### 3.3.3. XAS spectra of Mo sulfide aqueous species in reference solutions

The MoS₄²⁻ ion is the most stable of the MoVI thiomolybdates in aqueous solution at ambient conditions (Erickson and Helz, 2000) and thus may serve as a direct reference for our XAS experiments. This ion was prepared by dissolving (NH₄)₂MoS₄ in 1M NaHS solution (78 ppm Mo, pH₂₃°C = 8.2). Both XANES and EXAFS spectra of the prepared solution at ambient conditions are similar to those of the solid (NH₄)₂MoS₄, confirming that Mo is coordinated by 4 S nearest atoms at 2.18 Å (Fig. S4). This solution was brought to 300 °C and 500 bar, resulting in irreversible MoS₂(s) precipitation so that no spectrum of the solution could be acquired at 300 °C.

A second solution of MoS₄²⁻ (71 ppm Mo, pH₂₃°C = 12.5) was prepared by adding 1 M NaOH to the first solution. At ambient conditions, this solution has XANES and EXAFS spectra identical to those of the solid (NH₄)₂MoS₄. Upon heating to 300°C and 500 bar, the second solution remained stable and no MoS₂(s) precipitation was observed. Its XANES spectrum showed a more pronounced pre-edge peak at 20,004 eV than that of MoS₄²⁻ (Fig. S5, a). After cooling, the spectrum regained its initial shape of MoS₄²⁻. The higher pre-edge at 300 °C is a strong indication of the presence of tetrahedral coordination with some oxygen atoms in addition to sulfur atoms. The oxygen atom contribution is independently confirmed by EXAFS spectra fits (Fig. S5, d, e) that show 3 O and 1 S around Mo at 1.75 and 2.22 Å, respectively (Table 3). Thus, this spectrum can serve as a generic reference for mixed Mo-(S,O) coordinations. The FDMNES calculated XANES spectra along with the EXAFS results, coupled with thermodynamic considerations, collectively indicate that this solution likely contains a mixture of different thiomolybdate species with an average O:S ratio of 3 (see Fig. S6, S7 and Appendix A for more detail).

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### 3.3.4. In situ XAS spectra of the fluid phase from molybdenite dissolution experiments

The analysis of most XAS spectra from molybdenite dissolution experiments is restricted to the XANES region (Fig. 2a), because the low Mo concentrations (<5 ppm; Table 1) do not provide the necessary data statistics for EXAFS analyses. Only one EXAFS spectrum obtained in the longest experiment 6x (Na₂S₂O₃-NaOH, fO₂ = HM, pHₜₚ = 6.1, 4.4 ppm Mo)

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could be exploited (Fig. 3). The XANES spectrum of the fluid from experiment 6x is similar to that of $(NH_4)_2MoS_4(s)$, and the corresponding EXAFS spectrum is consistent with four S atoms at 2.19 Å around the Mo atom (Table 3). These results point to the predominance of the $MoS_4^{2-}$ anion in experiment 6x. In contrast, XANES spectra of experiment 1x at more acidic conditions $(Na_2S_2O_3-HCl, pH_{TP} = 4.9, fO_2 = HM, 4.5 ppm Mo)$ and of experiment 4x of more reducing and more alkaline composition $(NaHS-H_2S, pH = 8.3, logfO_2 = QFM)$ present between them small energy shifts around 20,020 and 20,060 eV. Similar shifts are observed between $(NH_4)_2MoS_4(s)$ and experiment 6x $(pH_{TP} = 6.1, thiosulfate)$ (Fig. 2b). These differences, even though partly obscured by the noise intrinsic to such low Mo concentrations, could be due to different Mo speciation at acidic, neutral and alkaline solutions. The XANES spectra of experiments 2x and 3x $(pH_{TP} = 5.6$ and 4.5, respectively) have overall similar features of the $Mo(S)_4$ coordination, but are too noisy for further interpretation. In these and other spectra from dissolution experiments (e.g., 5x, not shown), we must caution a possibility of minor contributions from $MoS_{2(s)}$ to some of the solution spectra.

# 4. Discussion

## 4.1. Attainment of equilibrium in solubility experiments

### 4.1.1. Kinetics of molybdenite dissolution in XAS experiments

The *in situ* XAS solubility measurements provide the following insights into the kinetics of molybdenite dissolution and thiosulfate decomposition thereby allowing us to establish accurate equilibrium criteria.

In experiment 2x (Fig. 1b) chemical equilibrium was not achieved, whereas in experiment 1x (Fig. 1a), steady state was reached within minutes of heating. This difference likely reflects the slower rate of thiosulfate decomposition at various pH. At a temperature of 300 °C, the rate of thiosulfate decomposition reaction was measured as $log_{10}k_r$ (in hour$^{-1}$) = -2.4 at pH 6.9 and -1.9 at pH 5.3 (Kokh et al., 2020). Therefore, a similar trend in thiosulfate decomposition rates could be expected between acidic (experiment 1x) and neutral (experiment 2x) solutions, with thiosulfate decomposition rate being lower in neutral than in acidic media. At the same time, an unexpected result was observed in alkaline thiosulfate solutions (experiments 6x and 7x, Fig. 1e), where no initial reaction was detected and the Mo concentrations seem to reach steady state from the beginning of the experiment, despite the expectation of slower $MoS_{2(s)}$ dissolution, consistent with slower thiosulfate decomposition relative to the experiment 2x at neutral pH. This discrepancy may arise from the timing of Mo concentration measurements: in experiments 6x and 7x, measurements were taken approximately one hour after loading, whereas in experiment 2x, measurements began immediately after the cell loading. Such delays at room temperature, prior to measurements at high temperature, could affect the apparent reaction kinetics. Furthermore, the strongly alkaline NaOH solution (pH 13 at 25 °C) may have influenced $MoS_2$ dissolution prior to thiosulfate decomposition establishing redox control at elevated T–P conditions. It cannot be excluded that our experiments 6x and 7x $(Na_2S_2O_3-NaOH, pH_{TP} = 6.1)$ at alkaline conditions underestimate molybdenite solubility, first, because of slow rate of thiosulfate decomposition at alkaline conditions and, second, because one-order-of-magnitude higher Mo concentration was measured in a similar long-term experiment 7q $(K_2S_2O_3-NaOH, pH_{TP} = 6.8)$ (Table 1).

The kinetics of elemental sulfur dissolution, as observed in experiment 3x (Fig. 1c) to be very slow (showing no progress over more than 13 hours), differs significantly from that of thiosulfate in experiment 1x (Fig. 1a). Therefore, to initiate the reactions of native sulfur disproportionation and molybdenite dissolution, we heated the cell to 350 °C. The temperature
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increase boosted molybdenite dissolution because of much faster sulfur dissolution rates and ligand supply. The estimated densities of the solution in experiment 3x are 0.82 and 0.75 g cm⁻³ at 300 °C and 350 °C, respectively. If the density was the only driving force of solubility, a decrease in temperature from 350 °C to the target temperature 300 °C would have caused only ~10% increase in the Mo concentration (from 0.61 ppm to 0.67 ppm). In contrast, in experiment 3x, the measured Mo concentration rather increased by an order of magnitude (4.2 ± 0.1 ppm). This value is in excellent agreement with that of experiment 1x, where steady-state concentrations were reached at 4.5 ± 1.2 ppm Mo. The Mo concentration in experiment 3x remained stable for at least 1 hour and 20 minutes at 300 °C. Subsequent reheating resulted in a sharp decrease in concentration that cannot be attributed to a density effect either. The last step of this experiment is indicative of a retrograde solubility behavior, which may be due to a decrease in the S₃⁻ abundance with increasing temperature from 300 °C to 350 °C.

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Experiments 4x and 5x (Fig. 1d) both ultimately yielded consistent and reproducible molybdenite solubility results, as expected given the identical chemical systems employed. The measured Mo solubilities also agree well with those obtained in experiment m35, conducted using a flexible cell reactor (Table 1). The different dissolution trends observed at the start of experiments 4x and 5x (i.e., a decrease in Mo concentration in 4x with time and an increase in 5x) are attributable to the variable duration of molybdenite exposure to the solution at room temperature prior to the beginning of *in situ* XAS measurements (~2 h longer in 4x than 5x).

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Thus, all *in situ* XAS solubility experiments have been retained for thermodynamic modeling, with only two exceptions of experiment 2x, in which chemical equilibrium was not reached, and experiment 8x, in which the Mo concentration was below the detection limit (Table S5).

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### 4.1.2. Criteria for choosing solubility data at equilibrium

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Strictly speaking, the best criterion to demonstrate equilibrium is to perform solubility experiment both from under- and super-saturation. However, studies that demonstrate equilibrium from both supersaturation and undersaturation conditions under hydrothermal conditions are extremely rare and challenging. This is because solubility measurements from supersaturated solutions are virtually impossible to perform using ex situ setups such as quench based reactors and they are extremely challenging using sampling-based reactors. They are equally difficult to implement in an *in situ* XAS spectroscopic setup. Robust solubility data showing equilibrium only from undersaturated conditions are far more common and, in many cases, the only possible ones such as in our study. Thus, care has been taken in our study to exclude data that do not present convincing equilibrium evidence.

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First, we excluded results of experiment 2x from further consideration, because Mo concentrations obviously have not reached a steady state (Fig. 1b; section 4.1.1). Second, we systematically excluded the first samples following the fluid injections in the flexible-cell reactor (experiments m33 and m35, Tables S2 and S3). Furthermore, in these experiments we also excluded the datapoints obtained by sampling with a syringe that is notoriously slower and could induce solute loss compared to sampling into the titanium vial (Table S2). Third, we omitted data of experiment m35 at lower temperatures (50–250 °C), because they require more experimental data in different systems and *in situ* XAS confirmation (Table S2). Fourth, because of kinetic issues of thiosulfate breakdown (see above), we excluded data of short-term quench experiments (experiments 1q, 2q, 3q, Table S4). Finally, all the remaining experiments at 300 °C were retained for the thermodynamic modeling. Most importantly, results from *in situ* XAS short-term experiments were in most cases confirmed by much longer hydrothermal
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reactor experiments (from a few days to one month) which were not concerned by X-ray exposure compared to the XAS series. In light of previously published solubility data on similar hydrothermal systems (Laskar et al., 2022, 2025), we believe that equilibrium has been reached in the chosen experiments that satisfied the criteria listed above. The critically selected dataset is robust, with Mo solubility values reproducible within one order of magnitude for the similar chemical compositions. Such an uncertainty is consistent with the typical reproducibility of hydrothermal experiments in general, especially when comparing various experimental techniques (e.g., Borchert et al., 2025; Laskar et al., 2025). As an additional proof of our selection, the formation constant value of MoS₄²⁻ obtained in our study (section 4.3.1; Table 4) is in excellent agreement with independent previously published measurements (Liu et al., 2020 and references therein).

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## 4.2. Spectroscopic and coordination chemistry constraints on Mo species structures and stoichiometry

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In complement to the solubility data, our XAS results, coupled with available data on Mo coordination chemistry, allow us to place independent constraints on the identity of the Mo species in our hydrothermal experiments.

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The XANES spectra of our S-rich fluids clearly indicate a tetrahedral coordination by 4 S atoms in the Mo first atomic shell (Fig. 2), in agreement with the spectral data for the thiomolybdate solid reference compounds available in the literature and investigated in this study (K₂MoS₄(s), (NH₄)₂MoS₄(s)). Our XANES data from MoS₂(s) dissolution experiments exclude significant presence of oxygen in the Mo first coordination shell that would have induced a more intense pre-edge feature at 20,004 eV as known in thiomolybdates both in solution and solid phase (Fig. S5, Liu et al., 2020) and qualitatively confirmed by our FDMNES calculations for such mixed Mo-(O,S)₄ structures (Fig. S6). Mo VI-S coordinations other than tetrahedral are much rarer. Although coordinations with 6 S atoms are more common for Mo IV, such as trigonal prismatic in molybdenite or octahedral in 1T-type phases of MoS₂ (e.g., Xu et al., 2020), such structures yield XANES spectra very different from those in our solutions (Fig. 2). Molybdenum-bearing solids with the trisulfur radical anion have not been isolated in coordination chemistry; however, a complex in which Mo VI is present in a polynuclear anion bound to 1 S₃⁺⁻, [(Mo₂O₂S₂)(S₂)(HS)(S₃)]³⁻, was suggested as a reaction intermediate in the formation of the Mo₂O₂S₈²⁻ dianion during reactions of Mo catalyzed hydrogen production (Chirdon et al., 2020). FDMNES-calculated XANES spectra of [MoS₃(S₃)] clusters in which S₃⁺⁻ is bound to Mo in both mono-dentate (tail-like) and bi-dentate (ring-like) arrangements are virtually identical and very similar to that of [MoS₄] within spectral resolution (Fig. S8).

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Independent arguments in favor of mono-dentate binding of S₃⁺⁻ to metals stem from spectroscopic and MD studies of other metal complexes in hydrothermal fluids (Pokrovski et al., 2015, 2021, 2022). These studies have exclusively demonstrated such type of bonds for AuI, PtII and PtIV, whereas ring structures involving an S₃⁺⁻ moiety appear to be unstable in MD simulations and do not match the metal-sulfur distances determined by EXAFS. The Au and Pt complexes are negatively charged and involve one to two S₃⁺⁻ ligands along with additional HS⁻ ligands to complete the AuI (linear), PtII (square-planar) and PtIV (octahedral) coordination spheres. By analogy, the most plausible complex of Mo in S₃⁺⁻-rich solutions of our study would be the tetrahedral mono-dentate MoS₃(S₃)⁻, with one S₃⁺⁻ ligand substituting for one S²⁻ ligand in MoS₄²⁻. Such a complex has also a negative charge, which is an important condition for stabilizing metal complexes in aqueous solution of relatively high dielectric constant (e.g.,
Jolivet, 1994). An uncharged complex with 2 S₃⁻ and S²⁻ ligands bound in the tetrahedral mono-dentate mode, MoS₂(S₃)₂⁰(aq) (Fig. S8), cannot be excluded spectroscopically. However, it does not match the experimental solubility trends vs pH of our study at 300°C. Such a complex might be more stable closer to magmatic temperatures in S-rich fluids of lower dielectric constant favoring neutral species stability (e.g., Kokh et al., 2017).

Thus, based on these arguments, molybdenite solubility in our S-bearing solutions can be thermodynamically analyzed in terms of sulfide and trisulfur ion complexes.

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## 4.3. Thermodynamic interpretation of molybdenite solubility experiments

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### 4.3.1. Sulfide solutions

We have modeled, in terms of thiomolybdate complexes, MoS₂(s) solubility in reduced, H₂S/HS⁻-dominated, S₃⁻-poor (<10⁻⁵ m) solutions from flexible-cell reactor experiment m35 (samples 8, 9, 10, 12, 13, 15, 16), and from *in situ* XAS experiments 4x and 5x. The results are illustrated in Fig. 4a for a representative 1 m NaHS solution at 300°C and 500 bar as a function of pH. The modeling was performed using the HCh package with auxiliary modules (Shvarov, 1999, 2008, 2015) that uses the standard thermodynamic properties of the species and minerals discussed in section 2.8 and returns equilibrium activities (concentrations) of the aqueous species in the fluid phase and the identity and amount of the solid phases stable at a given total system chemical composition, *T* and *P*. The inverse calculations are performed by the module OptimA (Shvarov, 2015) that seeks for the optimal apparent standard Gibbs energy of the solubility-controlling species of a given stoichiometry that would match the best the experimental solubility datapoints (i.e., Mo concentration in solution). The optimized Gibbs energies of the species are then converted to a reaction constant using those of the other reaction constituents. It can be seen in Fig. 4a that the MoS₄²⁻ complex matches well the solubility in the reduced sulfur solutions whereas the contribution of other O-bearing thiomolybdate ions is one to two orders of magnitude lower at pH<7, as predicted according to extrapolations using isocoulombic reactions (see section 2.8). It is only at more alkaline pH, beyond the experimentally covered range, that these anions could significantly contribute to MoS₂(s) solubility. Other Mo-sulfide species, such as with HS⁻ ion (Mo(HS)₆⁻ₙ, n≤4), or mixed-type Mo(HS)ₙS₄⁻(n⁻²) complexes were also checked, but because of their charges, they show a clear mismatch of the observed pH vs solubility trend.

The ligand exchange constant of MoS₄²⁻ with MoO₄²⁻ of the following reaction was found to be log₁₀K₂₂ = 9.9±0.4:

$$ \mathrm{MoO_4^{2-} + 4 H_2S^{0}_{(aq)} = MoS_4^{2-} + 4 H_2O_{(liq)} \qquad (22)} $$

The reported uncertainty corresponds to ± 2 s.d, and includes errors from Mo concentration analyses, experimental data-point scatter, and Gibbs energy optimization by OptimA. This value is in excellent agreement with isocoulombic extrapolations of ambient *T*-*P* data reported by Erickson and Helz (2000) and Brule et al. (1988) (Table 4; log₁₀K₂₂(iso) = 10.3±0.3). Molybdenite solubility for the mentioned experiments is thus described by the formal reaction:

$$ \mathrm{MoS_2(s) + 2 H_2S^{0}_{(aq)} + 0.5 O_2(g) = MoS_4^{2-} + 2 H^+ + H_2O_{(liq)} \qquad (23)} $$

with an equilibrium constant value log₁₀K₂₃(300°, 500 bar) = 0.5±0.4.
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### 4.3.2. $S_3^{\cdot-}$ bearing solutions

In more oxidized (coexistence of sulfate and sulfide) and more $S_3^{\cdot-}$-rich solutions, the $MoS_4^{2-}$ complex with the derived stability constant above (reaction 22) could describe the measured $MoS_2(s)$ solubilities only at alkaline pH, but was found insufficient to match the measured Mo concentrations at pH <6, thereby invoking the presence of additional complexes (Fig. 4b). Known molybdenum aqueous species such as $MoO_4^{2-}$, $HMoO_4^-$, $H_2MoO_4^{0(aq)}$, $NaMoO_4^-$, $NaHMoO_4^{0(aq)}$, $KMoO_4^-$, and $KHMoO_4^{0(aq)}$ show predicted concentrations at our conditions of <10⁻¹¹ m. They, therefore, clearly cannot account for the measured Mo concentrations of at least 10⁻⁵ m at pH<5.5. Similarly, concentrations of O-bearing thiomolybdate ions are at least 2 to 4 orders of magnitude lower as per thermodynamic predictions for reactions (17) to (20). Following the spectroscopic and coordination chemistry considerations above (section 4.2), we included the $MoS_3(S_3)^-$ complex in the speciation model. This species was found to adequately match the measured solubilities at pH <6 in the sulfate-sulfide solutions (Fig. 4b) according to the $MoS_2(s)$ formal dissolution reaction

$$MoS_{2(s)} + H_2S_{(aq)} + S_3^{\cdot-} + 0.5 O_{2(g)} = MoS_3(S_3)^- + H_2O_{(liq)} \quad (24)$$

with an equilibrium constant value $log_{10}K_{24}$ (300°C, 500 bar) = 14.6±0.4 (Table 4).

Other potential species stoichiometries, such as $MoS_2(S_3)_2^0$ and $Mo(HS)_nS_{4-n}^{(n-2)}$, were also optimized in an attempt to match the solubility datapoints at pH <6 but were found to yield solubility-vs-pH trends opposite to the measured one or predict much higher solubilities at more alkaline conditions that those found in our experiments. Similarly, complexes with polysulfide dianions may also be excluded because of very low concentrations of such ligands in our acidic solutions (≤ 10⁻⁶ m for any of $S_n^{2-}$ species).

990

991

## 5. Geochemical implications

992

### 5.1. Factors controlling Mo speciation and solubility in porphyry-epithermal fluids

The stability constants of $MoS_4^{2-}$ and $MoS_3(S_3)^-$ derived in this study, coupled with available thermodynamic properties of other Mo species and major fluid constituents, enable a quantitative assessment of the effect of key fluid parameters, such as sulfur concentration, redox and acidity, on Mo speciation and solubility, as predicted using the reaction constants of Mo sulfide and trisulfur ion complexes generated in this study and those of other system constituents from sources discussed in section 2.9 (Fig. 5).

Among these parameters, sulfur concentration plays a major role as shown in Fig. 5a for a typical moderate temperature (300 °C, 500 bar) and a moderately saline (10 wt.% NaCl equivalent) epithermal fluid. In these calculations, the fluid acidity and redox potential were assumed to be buffered, respectively, to pH ≈ 5 by the quartz-muscovite-K-feldspar (hereafter, QMK) mineral assemblage and to the sulfide-sulfate redox buffer with a total sulfide to sulfate molal ratio of 4:1 corresponding to the maximum of $S_3^{\cdot-}$ abundance (according to reaction 7). Such conditions are typical for many high-sulfidation epithermal deposits (e.g., Kouzmanov and Pokrovski, 2012; Pokrovski et al., 2025). It can be seen in Fig. 5a that $MoS_2(s)$ solubility increases very strongly (3 orders of magnitude) with increasing S concentration to 0.1–0.2 m S (>3000 ppm S) due to the growing abundance of $S_3^{\cdot-}$ stabilizing the $Mo(S_3)S_3^-$ complex,
which may account for as high as 0.1 ppm Mo at S concentration of 1 wt.%, whereas the contribution of MoS₄²⁻ is at least one order of magnitude less. The novel solubility model of molybdenite implies that loss of sulfur, e.g., via fluid boiling, sulfidation of FeII-bearing rocks or deposition of major metal sulfides (FeS₂, CuFeS₂) upon cooling and/or boiling, would be the main cause of molybdenite formation in porphyry-epithermal as well as in some metamorphic systems hosting orogenic-type deposits. Our solubility pattern contrasts with that of previous studies that assumed, in the absence of constrained sulfide and trisulfur ion complexes, the hydrogenomolybdate ion (HMoO₄⁻) and its alkali ion pair (NaHMoO₄⁰(aq)) to be the dominant species. Such a speciation implied an opposite, strongly negative, effect of reduced sulfur on MoS₂(s) solubility (e.g., Zotov et al., 1995; Kouzmanov and Pokrovski, 2012; Guan et al., 2023). A recent overview of available data suggested, however, that the stability of such ion pairs is likely to be largely overestimated at hydrothermal conditions (Pokrovski et al., 2024). Our revised stability constants for such species (Table 2, section 2.9) predict negligible Mo concentrations at the conditions of Fig. 5a.

Another key parameter affecting Mo solubility is the oxygen fugacity as illustrated in Fig. 5b for a 1 wt.% S solution at pH ≈ 5 (QMK) as a function of fO₂ corresponding to the conventional mineral redox buffers (QFM, quartz-fayalite-magnetite; NNO, nickel-nickel oxide; PPM, pyrite-pyrrhotite-magnetite; and HM, hematite-magnetite). It can be seen that the MoS₂(s) solubility maximum matches that of the S₃⁻ around the HM buffer. Oxidizing conditions corresponding to the sulfide-sulfate coexistence are thus the most favorable for Mo transport and often occur in porphyry-epithermal deposits, in particular of high-sulfidation type (Einaudi et al., 2003; Fontboté et al., 2017). In contrast, more reducing conditions, at which the dominant MoS₄²⁻ species has very low concentrations (<1 ppb Mo), are favorable for MoS₂(s) precipitation. Such conditions are realized in contact of the fluid with FeII-rich mafic- or organic carbon-bearing rocks, in agreement with a number of natural observations of molybdenite associated with such types of settings (e.g., Walter et al., 2009, 2020).

The fluid acidity (pH) is a third major factor affecting mineral solubility (Kouzmanov and Pokrovski 2012; references therein). Its effect on MoS₂(s) solubility is illustrated in Fig. 5c at fO₂ buffered by the sulfide-sulfate equilibrium (ΣH₂S:ΣSO₄ = 4:1, corresponding to the solubility maximum in Fig. 5b). In S-rich solutions (>0.2 m S), the solubility of MoS₂(s) as the dominant Mo(S₃)S₃⁻ complex is only weakly affected over a wide pH range, from 1 to 6, staying at 0.ₙ ppm Mo levels. This finding contrasts with previous solubility models that ignored sulfide and trisulfur ion complexes in favor of oxychloride and molybdic acid whose stability is poorly constrained (Ulrich and Mavrogenes, 2008; Rempel et al., 2009; Borg et al., 2012; Guan et al., 2023). Note that such acidic pH values are typical of oxidized fluids from porphyry-epithermal deposits due to the hydrolysis of magmatic SO₂ to H₂S and sulfuric acid on fluid cooling:

$$4 \text{SO}_2 + 4 \text{H}_2\text{O} = 3 \text{SO}_4^{2-} + 6 \text{H}^+ + \text{H}_2\text{S} \quad (25)$$

This reaction generates strongly acidic pH that can be neutralized to a variable degree by interactions with alkali aluminosilicate rocks (e.g., Heinrich, 2005; Pokrovski and Kouzmanov, 2012; Hedenquist and Arribas, 2024). At moderately alkaline pH (6<pH<8), more relevant to fluids interacting with basalts and limestones, MoS₄²⁻ becomes the dominant species accounting for 0.1–1 ppm Mo at 300 °C. At strongly alkaline pH (pH>8–9 at 300 °C) and strongly oxidized conditions (>HM+2), the molybdate anions and their ion pairs with alkalis might further increase MoS₂(s) solubility, up to 10–1000 ppm levels; however, such conditions are unlikely to be realizable in most S-bearing hydrothermal settings. The quantitative stability of such types of ion pairs for Mo yet awaits direct experimental constraints.

## 5.2. Comparison with natural fluid inclusions from porphyry-epithermal settings

The new speciation model of Mo in S-bearing hydrothermal fluids developed in this
study at 300 °C allows a first semi-quantitative assessment of Mo transport over the temperature range of porphyry-epithermal fluids. This assessment benefits from the validity of the isocoulombic approach experimentally demonstrated in this study for MoS₄²⁻ as well as for a number of other complexes in previous work (Gu et al., 1994; Liu et al., 2020). By analogy, we applied this approach to extrapolate, using equation (17), the formation constants of Mo(S₃)S₃⁻ to temperatures above and below 300 °C. We used the isocoulombic reaction of S²⁻ and S₃⁺ exchange with O²⁻ and OH⁻ involving the hydrogenomolybdate ion:

$$1067 \quad HMoO_4^- + 3 H_2S^{0}_{(aq)} + S_3^{\cdot -} = Mo(S_3)S_3^- + 3 H_2O + OH^- \quad (26)$$

The results are reported in Table 4 and illustrated in Fig. 6. Note that, except Mo(S₃)S₃⁻, all constituents of reaction (26) have well-constrained thermodynamic properties within the HKF model thereby allowing reliable extrapolations to high T-P conditions of porphyry deposits.

Our resulting thermodynamic predictions of Mo concentrations in equilibrium with molybdenite for a typical magmatic metal- and sulfur-bearing fluid evolving in a porphyry-epithermal context are shown by the curves in Fig. 7. The initial magmatic fluid composition is 10 wt.% NaCl equivalent, 0.75 wt.% Fe (as FeCl₂), 0.30 wt.% Cu (as CuCl), 0.02 wt.% Mo (as Na₂MoO₄), H₂S:SO₂=2.6; and 1 or 2 wt.% S, which is a typical model composition for porphyry-type fluids (Heinrich et al., 2005; Kouzmanov and Pokrovski, 2012). The fluid pH was assumed to be buffered either by equilibria among the sulfur species (reactions 3–6 and 25) yielding acidic pH or by the QMK mineral assemblage (4<pH<6). The fluid degasses from magma at 700°C and 2 kbar and cools down and decompresses in the liquid phase in a close system. Our calculations are compared with Mo concentration data analyzed by LA-ICP-MS in natural fluid inclusions from porphyry systems and plotted as a function of inclusion's homogenization temperature. Datapoints are color-coded according to the four major types of fluid inclusions such as supercritical, aqueous, brine or vapor as per the classification of Kouzmanov and Pokrovski (2012).

It can be seen in Fig. 7 that molybdenite precipitation from the magmatic fluid is predicted to start at temperatures of 450–350 °C, which are the typical temperature window of Mo ore formation in porphyry systems (Sillitoe, 2010 and references therein). The predicted MoS₂(s) solubility (shown by curves) overlaps with a large part of the fluid inclusion dataset, strengthening the plausibility of our speciation model. Considering the wide range of pH values in porphyry fluids depending on the degree of fluid buffering by rocks, large variations of sulfur and major metal (Fe, Cu) concentrations, and fluid unmixing phenomena, our simple calculations account reasonably well for Mo transport, which is dominated by the MoS₃(S₃)⁻ species in such systems.

Note that Mo concentrations higher than 200 ppm – the concentration representative of supercritical fluids degassed from magmas – correspond to fluid inclusions that record vapor-brine immiscibility. These phenomena may lead to variable enrichment of Mo of the brine or vapor phase, depending on S and CO₂ concentrations, as shown by direct experiments (Kokh et al., 2016) and natural fluid-inclusion analyses (e.g., Seo et al., 2012). Quantification of these phenomena on Mo transfer awaits more speciation and thermodynamic data, in particular for the vapor phase. Some inclusions of aqueous and supercritical fluid types with homogenization temperatures between 250 and 350 °C also demonstrate Mo concentrations that are higher than our predicted values. There may be several reasons of such a discrepancy. These include, for example, methodological issues related to fluid inclusion data such as the necessity for correction of the homogenization temperature due to fluid true entrapment temperature (e.g., Pokrovski et al., 2025; references therein), entrapment of molybdenite during the inclusion formation, and/or accidental ablation of Mo solids in the proximity of the fluid inclusion during LA-ICP-MS analyses. Other issues may be related to the nature of the fluid, such as more alkaline pH (pH >7–8) resulting in elevated MoS₂(s) solubility (e.g., Fig. 5c), as well as additional Mo complexes in S-rich moderate-temperature fluids such as those with polysulfide
1110
1111

dianions forming at the expense of S<sub>3</sub><sup>•</sup> on fluid cooling below 250–300 °C (e.g., Pokrovski and Dubessy, 2015).

1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137

Our chemical thermodynamics model can be compared with an empirical equation of
Fang et al. (2025) who fitted selected MoS<sub>2</sub>(s) bulk solubility data from experiments available
in the literature as a function of T, P, salinity, fO<sub>2</sub>, fS<sub>2</sub> and pH. We applied this equation for the
four cases of fluid composition and evolution, as shown in Fig. S10, to allow comparisons with
our speciation-based model of Fig. 7. The following differences can be identified. First, a
significant amount of natural fluid inclusion data within the temperature window of 450–350
°C plots well above the Fang et al. (2025) predictions. Second, different trends are predicted
compared to our model. Molybdenum is predicted by Fang et al. (2025) to be best transported
by fluids of low sulfur fugacity and near-neutral pH (rock-buffered scenario; Fig. S10), whereas
our speciation model favors sulfur-rich and acidic fluids (fluid-buffered scenario, Fig. 7). Our
thermodynamic model generally better accounts for the majority of fluid inclusions within the
temperature window of 450–350 °C. The major advantage of our model is that it allows the
effect of each formal thermodynamic parameter of the fluid (pH, fO<sub>2</sub>, fS<sub>2</sub>) to be linked with real
sulfur speciation that evolves in solution as a function of those parameters and defines the
corresponding dominant Mo chemical complexes. Our speciation-based model can easily be
integrated in common computer codes for equilibrium thermodynamic calculations of fluid-
rock interactions in multicomponent systems (e.g., HCh, GEMS). The model is open to
improvements, especially regarding other potential Mo bearing complexes such as alkali ion
pairs of molybdate and hydrogenomolybdate and oxy-chloride complexes, which may be more
important in magmatic fluids at oxidizing conditions, as well as polysulfide dianion complexes,
which could control Mo solubility in lower-temperature (<250 °C) S-rich epithermal or
sedimentary fluids. Thus, more systematic data on the fluid composition, sulfur speciation, and
Mo complexes with different ligands are required for more accurate interpretations of Mo
transport in epithermal, metamorphic and sedimentary settings across a wide temperature
range.

6. Conclusions

1138
1139
1140
1141
1142
1143
1144

In this study, we combined solubility experiments with accurate sampling procedures, *in situ* synchrotron X-ray absorption spectroscopy and thermodynamic modeling. These data demonstrate the dominant formation of the MoS<sub>4</sub><sup>2-</sup> and MoS<sub>3</sub>(S<sub>3</sub>)<sup>-</sup> complexes, at alkaline and acidic-to-neutral pH values, respectively, in sulfur-rich (up to 1 m S) moderate-temperature and pressure (300 °C, 500 bar) hydrothermal fluids. In both species, Mo<sup>VI</sup> is tetrahedrally coordinated to 4 S atoms with Mo-S bond distances of 2.2 Å.

1145
1146
1147
1148
1149

The derived stability constants of these complexes coupled with analyses of literature
data demonstrate that isocoulombic reactions between MoS<sub>4</sub><sup>2-</sup> and MoO<sub>4</sub><sup>2-</sup>, and between
MoS<sub>3</sub>(S<sub>3</sub>)<sup>-</sup> and HMoO<sub>4</sub><sup>-</sup> allow a plausible extrapolation of such reaction constants both to
higher and lower temperatures. These isocoulombic relationships require further validation by
experimental data over a large T-P range for Mo sulfide and trisulfur anion radical complexes.

1150
1151
1152
1153
1154
1155
1156

The new thermodynamic and speciation model was used to predict Mo transport in
fluids that form porphyry-epithermal Cu-Au-Mo deposits. Our results suggest that MoS<sub>3</sub>(S<sub>3</sub>)<sup>-</sup>
is the molybdenum solubility controlling species in typical porphyry-epithermal settings
characterized by elevated sulfur concentrations, oxidizing conditions (sulfate-sulfide
coexistence) and acidic-to-neutral pH. The predicted MoS<sub>2(s)</sub> solubility accounts for a large
fraction of data points of Mo concentration analyses of natural fluid inclusions from such
settings. At temperatures below 250-300 °C, however, other Mo complexes such as those with
1157 polysulfide dianions may also contribute to Mo transport and would require further

1158 investigation.
Data availability

1160

1161

Data are available through Mendeley Data

1162

at https://data.mendeley.com/datasets/zk4cjx8cpk/7. The same data will be also available

1163

through https://dataservices-cms.gfz.de.

1164

Spectroscopic data for solid reference materials are available via SSHADE database at

1165

https://www.sshade.eu/data/EXPERIMENT_MK_20220405_001,

1166

https://www.sshade.eu/data/EXPERIMENT_MK_20230604_001.

1167

CRediT author statement

1168

1169

Conceptualization M.A.K., G.S.P., M.W., J.-L.H., C.L. and data curation M.A.K.,

1170

G.S.P., M.A.K., C.L., M.W., C.M., I.K.; formal analysis M.A.K., G.S.P., C.L., M.W., C.S.,

1171

C.M., D.R., O.P.; funding acquisition G.S.P., J.-L.H., D.T., M.W., S.K., C.S.; investigation

1172

M.A.K., C.L., C.M., E.F.B., G.S.P., M.W., I.K., J.-L.H.; methodology M.A.K., G.S.P., M.W.,

1173

E.F.B., C.L., J.-L.H., I.K., H.M., D.T., O.P., E.L.; project administration G.S.P., M.W., S.K.

1174

and C.S.; resources G.S.P., J.-L.H., H.M., D.R., E.L., O.P.; software G.S.P., M.W., C.M. and

1175

D.T.; supervision M.W., G.S.P., S.K. and C.S.; validation M.A.K. and G.S.P.; visualization

1176

M.A.K., M.W., D.R.; writing of the original draft M.A.K., G.S.P., M.W., D.R. and C.L.; all

1177

authors have read and reviewed the text of manuscript.
ACKNOWLEDGMENTS

This work was funded by the French National Research Agency (grant ANR-16-CE31-0017 to G.S.P.), the Institut Carnot ISIFoR (grants OrPet and AsCOCrit to G.S.P.), and the CNRS through the MITI interdisciplinary programs MetalloMix 2021 and Conditions Extremes 2024 (grants PtS3 and ExtremeS to G.S.P.), and Deutsche Forschungsgemeinschaft (grant WI 2000/25-1, KL 1368/13-1, SCHM 2415/6-1 to M.W., S.K. and C.S.). C.L. acknowledges support from the University of Toulouse (PhD fellowship of the Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, MESRI). C.M. acknowledges the support from the University of Potsdam (PhD fellowship). D.R. acknowledges support from the University of Lyon (PhD fellowship). We acknowledge ESRF (European Synchrotron Radiation Facility) for providing beamtime and facilities (projects ESRF ES-1050, ESRF ES-1278). This research was partially supported by DESY-CMWS-Early Science Project "Unraveling the formation of economic Cu, Mo and W deposits in the Earth's crust by hydrothermal supercritical hydrous fluids using in-situ X-ray Absorption and Fluorescence spectroscopy". The HP/HT vessel was financially supported by the French "grand emprunt" EquipEx (PlanEx, ANR-11-EQPX-36). We thank A. Aguilar, P. Gisquet, A. Castillo, C. Causserand, L. Menjot, A. Musiol and C. Günter for their professional help with hydrothermal experiments and tedious chemical analyses. We are grateful to J. Schott and A. Zotov for fascinating discussions about molybdenum complexation. Comments of Associate Editor J-F. Boily and three anonymous reviewers greatly improved this article.

Appendix A. Supplementary Material

Supplementary material includes additional figures (Fig. S1–S10), tables (Table S1–S10) and supplementary text. Supplementary text contains synthesis protocols for solid reference materials and discussion about Mo speciation in reference solutions. Fig. S1 and S2 provide information about the dissociation constants of H₂S⁰(aq) and thermodynamic properties of S₃⁻. Fig. S3-S5 report XANES and EXAFS spectra of molybdenum solid reference materials and solutions. Fig. S6-S9 report results of FDMNES calculations. Fig. S10 compares Mo concentrations in fluid inclusions and simulated MoS₂(s) solubility values using the empirical equation of Fang et al. (2025). Table S1 gives the values of reaction constants for aqueous molybdate species. Tables S2-S9 give analytical details of MoS₂(s) solubility experiments. Table S10 gives results of linear combination fits for the reference solutions.
1212

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<table><caption>1547 Table 1. Fluid composition data in MoS₂(s) dissolution experiments at 300°C selected for the thermodynamic analysis of Mo speciation.</caption><thead><tr><th rowspan="2">Sample number</th><th>P</th><th colspan="2">pH<sub>TP</sub></th><th colspan="10">Bulk system composition, m</th></tr><tr><th>bars</th><th>calc.</th><th>NaHS</th><th>H<sub>2</sub>S</th><th>S<sub>(s)</sub></th><th>HCl</th><th>NaOH</th><th>KOH</th><th>K<sub>2</sub>S<sub>2</sub>O<sub>3</sub></th><th>Na<sub>2</sub>S<sub>2</sub>O<sub>3</sub></th><th>Mo</th><th>Mo, ppm</th></tr></thead><tbody><tr><td colspan="13">flexible-cell experiments*</td></tr><tr><td colspan="13">experiment m35: H<sub>2</sub>O-NaHS-H<sub>2</sub>S-HCl-MoS<sub>2</sub>-pyrite-pyrrhotite</td></tr><tr><td>8</td><td>523</td><td>7.5</td><td>1.04</td><td>0.13</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>2.13&middot;10<sup>-5</sup></td><td>1.9</td></tr><tr><td>9</td><td>464</td><td>7.5</td><td>1.04</td><td>0.13</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>4.26&middot;10<sup>-5</sup></td><td>3.9</td></tr><tr><td>10</td><td>425</td><td>7.5</td><td>1.04</td><td>0.13</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>4.92&middot;10<sup>-5</sup></td><td>4.5</td></tr><tr><td>12</td><td>416</td><td>6.8</td><td>1.01</td><td>0.11</td><td>—</td><td>0.29</td><td>—</td><td>—</td><td>—</td><td>—</td><td>8.46&middot;10<sup>-5</sup></td><td>7.6</td></tr><tr><td>13</td><td>462</td><td>6.8</td><td>1.01</td><td>0.11</td><td>—</td><td>0.29</td><td>—</td><td>—</td><td>—</td><td>—</td><td>9.35&middot;10<sup>-5</sup></td><td>8.4</td></tr><tr><td>15</td><td>477</td><td>5.7</td><td>0.81</td><td>0.10</td><td>—</td><td>0.71</td><td>—</td><td>—</td><td>—</td><td>—</td><td>1.07&middot;10<sup>-5</sup></td><td>1.0</td></tr><tr><td>16</td><td>434</td><td>5.7</td><td>0.81</td><td>0.10</td><td>—</td><td>0.71</td><td>—</td><td>—</td><td>—</td><td>—</td><td>3.33&middot;10<sup>-6</sup></td><td>0.3</td></tr></tbody></table>
experiment m33: H₂O–K₂S₂O₃–MoS₂

<table><tr><td>3,4</td><td>410</td><td>5.3</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.49</td><td>—</td><td>4.43·10<sup>-5</sup></td><td>3.9</td></tr><tr><td>7</td><td>395</td><td>5.3</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.31</td><td>—</td><td>2.31·10<sup>-6</sup></td><td>0.2</td></tr><tr><td>10</td><td>359</td><td>5.4</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.21</td><td>—</td><td>2.28·10<sup>-6</sup></td><td>0.2</td></tr></table>

experiments in autoclaves with quenching: H₂O–K₂S₂O₃–MoS₂ ± HCl ± KOH

<table><tr><td>5q</td><td>500</td><td>4.4</td><td>—</td><td>—</td><td>—</td><td>0.22</td><td>—</td><td>—</td><td>0.56</td><td>—</td><td>1.78·10<sup>-5</sup></td><td>1.5</td></tr><tr><td>6q</td><td>500</td><td>5.3</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.55</td><td>—</td><td>1.68·10<sup>-5</sup></td><td>1.5</td></tr><tr><td>7q</td><td>500</td><td>6.8</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.34</td><td>0.56</td><td>—</td><td>5.80·10<sup>-4</sup></td><td>50</td></tr></table>

in situ XAS experiments: H₂O–MoS₂ ± HCl ± NaOH ± Na₂S₂O₃ ± S ± NaHS ± H₂S
<table><tr><td>1x</td><td>500</td><td>4.9</td><td>-</td><td>-</td><td>-</td><td>0.33</td><td>-</td><td>-</td><td>-</td><td>1.06</td><td>5.53·10<sup>-5</sup></td><td>4.5</td></tr><tr><td>3x</td><td>500</td><td>4.9</td><td>-</td><td>-</td><td>1.02</td><td>-</td><td>0.40</td><td>-</td><td>-</td><td>-</td><td>4.13·10<sup>-5</sup></td><td>4.2</td></tr><tr><td>4x</td><td>500</td><td>8.3</td><td>0.98</td><td>0.01</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>2.75·10<sup>-5</sup></td><td>2.5</td></tr><tr><td>5x</td><td>500</td><td>7.4</td><td>0.98</td><td>0.13</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>3.08·10<sup>-5</sup></td><td>2.8</td></tr><tr><td>6x</td><td>500</td><td>6.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.36</td><td>-</td><td>-</td><td>1.19</td><td>5.52·10<sup>-5</sup></td><td>4.4</td></tr><tr><td>7x</td><td>500</td><td>6.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.36</td><td>-</td><td>-</td><td>1.21</td><td>2.63·10<sup>-5</sup></td><td>2.0</td></tr></table>

<footnote>* The reported fluid compositions for experiments m33 and m35 are those that were adopted in the thermodynamic analysis of this study; for analytical and experimental details as well as for sulfur speciation in experiments see Table S2-S5; “m” – mol/kg H₂O.</footnote>
1550 Table 2. Reaction constant values at 300°C, 500 bar for aqueous molybdenum species
1551 considered in this study.

<table><thead><tr><th>Species</th><th>Reaction</th><th>log<sub>10</sub>K<sub>300°C, 500 bar</sub></th><th>Data source</th></tr></thead><tbody><tr><td>HMoO<sub>4</sub><sup>-</sup></td><td>H<sup>+</sup> + MoO<sub>4</sub><sup>2-</sup> = HMoO<sub>4</sub><sup>-</sup></td><td>7.10</td><td>Sh97</td></tr><tr><td>H<sub>2</sub>MoO<sub>4</sub><sup>0</sup></td><td>2 H<sup>+</sup> + MoO<sub>4</sub><sup>2-</sup> = H<sub>2</sub>MoO<sub>4</sub><sup>0(aq)</sup></td><td>9.12</td><td>Da18</td></tr><tr><td>NaHMoO<sub>4</sub><sup>0</sup></td><td>Na<sup>+</sup> + HMoO<sub>4</sub><sup>-</sup> = NaHMoO<sub>4</sub><sup>0(aq)</sup></td><td>-0.21</td><td>this study</td></tr><tr><td>KHMoO<sub>4</sub><sup>0</sup></td><td>HMoO<sub>4</sub><sup>-</sup> + KHSO<sub>4</sub><sup>0(aq)</sup> = KHMoO<sub>4</sub><sup>0(aq)</sup> + HSO<sub>4</sub><sup>-</sup></td><td>0</td><td>this study</td></tr><tr><td>NaMoO<sub>4</sub><sup>-</sup></td><td>MoO<sub>4</sub><sup>2-</sup> + NaSO<sub>4</sub><sup>-</sup> = NaMoO<sub>4</sub><sup>-</sup> + SO<sub>4</sub><sup>2-</sup></td><td>0</td><td>this study</td></tr><tr><td>KMoO<sub>4</sub><sup>-</sup></td><td>MoO<sub>4</sub><sup>2-</sup> + KSO<sub>4</sub><sup>-</sup> = KMoO<sub>4</sub><sup>-</sup> + SO<sub>4</sub><sup>2-</sup></td><td>0</td><td>this study</td></tr><tr><td>MoO<sub>3</sub>S<sup>2-</sup></td><td>MoO<sub>4</sub><sup>2-</sup> + H<sub>2</sub>S<sup>0(aq)</sup> = MoO<sub>3</sub>S<sup>2-</sup> + H<sub>2</sub>O<sub>(liq)</sub></td><td>2.70</td><td>Li20</td></tr><tr><td>MoO<sub>2</sub>S<sup>2-</sup></td><td>MoO<sub>4</sub><sup>2-</sup> + 2 H<sub>2</sub>S<sup>0(aq)</sup> = MoO<sub>2</sub>S<sup>2-</sup> + 2 H<sub>2</sub>O<sub>(liq)</sub></td><td>5.20</td><td>Li20</td></tr><tr><td>MoOS<sub>3</sub><sup>2-</sup></td><td>MoO<sub>4</sub><sup>2-</sup> + 3 H<sub>2</sub>S<sup>0(aq)</sup> = MoOS<sub>3</sub><sup>2-</sup> + 3 H<sub>2</sub>O<sub>(liq)</sub></td><td>7.80</td><td>Li20</td></tr><tr><td>MoS<sub>4</sub><sup>2-</sup></td><td>MoO<sub>4</sub><sup>2-</sup> + 4 H<sub>2</sub>S<sup>0(aq)</sup> = MoS<sub>4</sub><sup>2-</sup> + 4 H<sub>2</sub>O<sub>(liq)</sub></td><td>10.34<sup>a</sup></td><td>Li20</td></tr></tbody></table>

1552

1553 Data sources: Sh97 – Shock et al., 1997; Da18 – Dadze et al., 2018; Li20 – Liu et al. 2020.

1554 log<sub>10</sub>K values of the indicated isocoulombic exchange reactions are assumed to be zero at all T and P.

1555 a – initial approximation (see Table 4 for the updated experimental values).
Table 3. Summary of EXAFS analysis results of the first coordination shell in the indicated experimental aqueous solutions of this study.

1557

<table><thead><tr><th>Sample</th><th>T<br>(°C)</th><th>nS<br>fixed</th><th>rS<br>(Å)</th><th>σ<sup>2</sup><br>(Å<sup>2</sup>)</th><th>nO<br>fixed</th><th>rO<br>(Å)</th><th>σ<sup>2</sup><br>(Å<sup>2</sup>)</th><th>Δ E<sub>0</sub> (eV)</th><th>χ<sup>2</sup><sub>reduced</sub></th><th>R<br>(%)</th><th>R-factor</th><th>k-range</th></tr></thead><tbody><tr><td>Reference solution 1</td><td>25 °C</td><td>4</td><td>2.18±0.01</td><td>0.004</td><td>0</td><td>—</td><td>—</td><td>4.8±0.1</td><td>1.40</td><td>26.27</td><td>1.0000</td><td>3–13</td></tr><tr><td>Reference solution 2</td><td>25°C</td><td>4</td><td>2.19±0.01</td><td>0.003</td><td>0</td><td>—</td><td>—</td><td>7.7±0.1</td><td>1.99</td><td>33.16</td><td>1.0000</td><td>3–14</td></tr><tr><td>Reference solution 2</td><td>300°C</td><td>1</td><td>2.20±0.80</td><td>0.003</td><td>3</td><td>1.76±0.01</td><td>0.004</td><td>7.2±0.1</td><td>1.50</td><td>32.22</td><td>1.0000</td><td>3–14</td></tr><tr><td>Experiment 6x</td><td>300°C</td><td>4</td><td>2.19±0.01</td><td>0.013</td><td>0</td><td>—</td><td>—</td><td>5.5±0.1</td><td>4.60</td><td>66.06</td><td>0.6839</td><td>3–12</td></tr></tbody></table>

1558

Comment: nO and nS = number of oxygen and sulfur ligands; rO and rS = Mo–O and Mo–S bond distances; σ² = Debye-Waller factor; Δ E₀ = shift of energy; χ²<sub>reduced</sub> = reduced χ², R-factor = goodness of fit. The minimized normalized square difference (χ²<sub>reduced</sub>) between data and model function is defined as follows: $χ² = \frac{N}{F·M} \sum_{i=1,M} \frac{(d_i^2 - f_i^2)}{e_i^2}$, where N = number of independent data; (INT(2Δk*Δr/π) for Fourier filtered data, F = degrees of freedom (= N – p) for p number of free fit parameters, M = number of data fitted, d = data (experiment), f = fit function (model), e: absolute error of data (standard deviations, if no error is given, e is set to 1). Estimate for the R-factor (goodness of fit) = 1 too good to be true (e.g., for smoothed data); > 0.5 good; > 0.01 reasonable; > 0.001 doubtful.

1564
1565 Table 4. Reaction constant values at 300°C, 500 bar for aqueous molybdenum species
determined in this study and compared with literature data.
1566

<table><thead><tr><th rowspan="2">Reaction</th><th colspan="3">log<sub>10</sub>K<sub>300°C, 500 bar</sub></th></tr><tr><th>this study</th><th>EH00*</th><th>Br88*</th></tr></thead><tbody><tr><td>MoS<sub>2(s)</sub> + H<sub>2</sub>S<sup>0</sup><sub>(aq)</sub> + S<sub>3</sub><sup>•−</sup> + 0.5 O<sub>2(g)</sub> = MoS<sub>3</sub>(S<sub>3</sub>)<sup>−</sup> + H<sub>2</sub>O<sub>(liq)</sub></td><td>14.6 ±0.4</td><td></td><td></td></tr><tr><td>HMoO<sub>4</sub><sup>−</sup> + 3 H<sub>2</sub>S<sup>0</sup><sub>(aq)</sub> + S<sub>3</sub><sup>•−</sup> = Mo(S<sub>3</sub>)S<sub>3</sub><sup>−</sup> + 3 H<sub>2</sub>O + OH<sup>−</sup></td><td>5.9 ±0.4</td><td></td><td></td></tr><tr><td>MoS<sub>2(s)</sub> + 2 H<sub>2</sub>S<sup>0</sup><sub>(aq)</sub> + 0.5 O<sub>2(g)</sub> = MoS<sub>4</sub><sup>2−</sup> + 2 H<sup>+</sup> + H<sub>2</sub>O<sub>(liq)</sub></td><td>0.5 ±0.4</td><td></td><td></td></tr><tr><td>MoO<sub>4</sub><sup>2−</sup> + 4 H<sub>2</sub>S<sup>0</sup><sub>(aq)</sub> = MoS<sub>4</sub><sup>2−</sup> + 4 H<sub>2</sub>O<sub>(liq)</sub></td><td>9.9 ±0.4</td><td>10.3 ±0.3</td><td>10.0</td></tr></tbody></table>

1567 Data sources: Br88 – Brule et al. 1988; EH00 – Erickson and Helz, 2000. Thermodynamic properties for O₂(g)

(oxygen, ideal gas) were taken from Robie and Hemingway (1995).

1569 * Constants EH00 and Br88 at 300°C, 500 bar were estimated using isocoulombic extrapolation of the constants

1570 reported at 25°C by those authors.
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

experiment 1x
Na₂S₂O₃ 1.063 m
HCl 0.327 m
pHₜₚ = 4.9

experiment 2x
Na₂S₂O₃ 0.963 m
pHₜₚ = 5.3

<figure><img src="image_5.png" /></figure>

experiment 3x
S 1.019 m
NaOH 0.401 m
pHₜₚ = 4.9

<figure><img src="image_6.png" /></figure>

experiment 4x
NaHS 0.983 m
H₂S 0.007 m
pHₜₚ = 8.3
MoS₂ glued

experiment 5x
NaHS 0.981 m
H₂S 0.130 m
pHₜₚ = 7.4
MoS₂ not glued

area of chemical
equilibrium

<figure><img src="image_7.png" /></figure>

experiment 6x
Na₂S₂O₃ 1.186 m
NaOH 0.356 m
pHₜₚ = 6.1
MoS₂ glued

experiment 7x
Na₂S₂O₃ 1.210 m
NaOH 0.363 m
pHₜₚ = 6.1
MoS₂ not glued

1572

1573

1574

1575

<caption>**Fig. 1.** Results of molybdenite dissolution experiments at 300°C and 500 bar. *In situ*</caption>

XAS measured concentrations of molybdenum in solution as a function of time (m = molinity, mol/kg H₂O when reporting the fluid composition). See text for detailed discussions.
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

1576

1577

1578

1579

1580

1581

**Fig. 2.** (a) XANES spectra of solutions from the indicated molybdenite dissolution experiments. Spectra of molybdenite, (NH₄)₂MoS₄(s) and reference solution 2 are given for comparison. (b) Comparison of XANES spectra of the three indicated experiments that showed the best statistics. Arrows show the differences among the spectra at 20,020 eV, 20,070 eV and 20,110 eV.
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

1582

1583 **Fig. 3.** EXAFS spectrum of experimental solution 6x and its Fourier transform

1584 magnitude (for more details see Table 3).
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

1585

1586

1587

1588

1589

1590

1591

1592

1593

1594

1595

1596

**Fig. 4.** Experimental solubility data and their interpretation in terms of the indicated Mo complexes and dominant sulfur species. (a) Results of thermodynamic calculations for a model sodium hydrosulfide solution (NaHS 1 m ± NaOH ± HCl) as a function of pH in equilibrium with molybdenite at 300°C, 500 bar. Lines represent calculated aqueous species concentrations Cᵢ in mol/kg H₂O. (b) Results of thermodynamic calculations for a model sodium thiosulfate solution (Na₂S₂O₃ 1 m ± NaOH ± HCl) as a function of pH in equilibrium with molybdenite at 300°C, 500 bar. The experimental data plotted include datapoints from (a) coretest reactor experiment m35 (samples 8, 9, 10, 12, 13, 15, 16) and *in situ* XAS experiments 4x, 5x; (b) coretest reactor experiment m33 (average of samples 3, 4), quench autoclave experiments 5q, 6q, 7q and *in situ* XAS experiments 1x, 3x, 6x, 7x. Analytical uncertainties are below the size of symbols except of an average for samples 3 and 4 (experiment m33).
1597

1598

1599

1600

1601

1602

1603

1604

1605

1606

1607

1608

1609

1610

1611

1612

1613

1614

1615

1616

1617

1618

1619

1620

1621

1622

1623

1624

1625

1626

1627

1628

1629

**Fig. 5.** Molybdenum dissolved concentrations in equilibrium with MoS₂(s) in a saline hydrothermal fluid at 300°C and 500 bar as a function of (a) total dissolved S concentration at pH ~5 buffered by quartz-muscovite-K-feldspar buffer (QMK) and fO₂ buffered by sulfide-sulfate equilibrium with a (H₂S)ₜotal : (SO₄)ₜotal molal ratio of 4:1 corresponding to the maximum of S₃⁻ abundance; (b) oxygen fugacity corresponding to common redox buffers (QFM, quartz-fayalite-magnetite; NNO, nickel-nickel oxide; PPM, pyrite-pyrrhotite-magnetite; and HM, hematite-magnetite); (c) fluid acidity, pH = -log₁₀a(H⁺) at fO₂ buffered by sulfide-sulfate equilibrium (H₂S:SO₄ = 4:1). Ci means the concentration of an i aqueous species in solution in mol/kg H₂O. In (a) and (b) the concentrations of NaCl vary from 1.0 to 1.8 m and those of KCl from <0.01 to 0.5 m to maintain the chosen pH<sub>TP</sub> value. In (c) concentration of NaCl is 10 wt.%. Only major Mo species are plotted (other Mo species are below 10⁻¹⁰ m Mo).

<figure><img src="image_14.png" /><figcaption>(b) MoS₂(s), QMK, pH 5, 1 wt.% S</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(c) MoS₂(s), H₂S:SO₄ = 4:1, 1 wt.% S</figcaption></figure>

<figure><img src="image_16.png" /></figure>
$$ \mathrm{MoO_4}^{2-} + 4 \mathrm{H_2S^0(aq)} = \mathrm{MoS_4}^{2-} + 4 \mathrm{H_2O_{(liq)}} \quad (22) $$

$$ \mathrm{HMoO_4}^{-} + 3 \mathrm{H_2S^0(aq)} + \mathrm{S_3}^{\cdot -} = \mathrm{MoS_3(S_3)}^{-} + 3 \mathrm{H_2O_{(liq)}} + \mathrm{OH}^{-} \quad (26) $$

<figure><img src="image_17.png" /><figcaption>**Fig. 6.** Isocoulombic extrapolations of the indicated reaction constants versus the reciprocal of absolute temperature. Extrapolation to lower and higher temperatures was performed using results of this study and isocoulombic relation (17) applied to chemical reactions (22) and (26).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 7.** Comparison of Mo concentrations in natural fluid inclusions and simulated MoS₂(s) solubility for a typical porphyry-epithermal system. A magmatic fluid of the initial composition indicated in the figure as degassed from magma at 700°C, cools down in the liquid phase in a closed system. The curves show Mo concentrations calculated in equilibrium with molybdenite, using the stability constants of Mo-S complexes derived in this study, as a function of temperature and pressure. The pressure change upon cooling is calculated according to P (bar) = 0.0032×t² – 0.4064×t + 148.36, where t is temperature in °C, corresponding to a cooling regime in the liquid-like phase. The fluid acidity is buffered by either the quartz-muscovite-K-feldspar (QMK) assemblage or equilibrium among sulfur species in the fluid (Heinrich, 2005). In the chosen acidity range, the dominant Mo complex is MoS₃(S₃)⁻ at all temperatures. Molybdenum concentrations in fluid inclusions are plotted as a function of their homogenization temperature. Fluid inclusion data are taken from Catchpole et al. (2015), Seo et al. (2009, 2012), and Schirra et al (2022).</figcaption></figure>
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

experiment 1x
Na₂S₂O₃ 1.063 m
HCl 0.327 m
pHₜₚ = 4.9

experiment 2x
Na₂S₂O₃ 0.963 m
pHₜₚ = 5.3

<figure><img src="image_21.png" /></figure>

experiment 3x
S 1.019 m
NaOH 0.401 m
pHₜₚ = 4.9

<figure><img src="image_22.png" /></figure>

experiment 4x
NaHS 0.983 m
H₂S 0.007 m
pHₜₚ = 8.3
MoS₂ glued

experiment 5x
NaHS 0.981 m
H₂S 0.130 m
pHₜₚ = 7.4
MoS₂ not glued

area of chemical
equilibrium

<figure><img src="image_23.png" /></figure>

experiment 6x
Na₂S₂O₃ 1.186 m
NaOH 0.356 m
pHₜₚ = 6.1
MoS₂ glued

experiment 7x
Na₂S₂O₃ 1.210 m
NaOH 0.363 m
pHₜₚ = 6.1
MoS₂ not glued
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

1650

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

1651
<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>
<figure><img src="image_30.png" /><figcaption>(b) MoS<sub>2(s)</sub>, QMK, pH 5, 1 wt.% S</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>(c) MoS<sub>2(s)</sub>, H<sub>2</sub>S:SO<sub>4</sub> = 4:1, 1 wt.% S</figcaption></figure>

<figure><img src="image_32.png" /></figure>
$$ \mathrm{MoO_4^{2-} + 4 H_2S^{0}_{(aq)} = MoS_4^{2-} + 4 H_2O_{(liq)} \quad (22)} $$

$$ \mathrm{HMoO_4^{-} + 3 H_2S^{0}_{(aq)} + S_3^{\cdot -} = MoS_3(S_3)^{-} + 3 H_2O_{(liq)} + OH^{-} \quad (26)} $$

<figure><img src="image_33.png" /></figure>
<figure><img src="image_34.png" /></figure>