Acidic Constant of Hydrofluoric Acid in High-Pressure and High-Temperature Geofluids

Fluorine is a key component in many hydrothermal ore-forming fluids, commonly occurring as fluorite and in minerals such as apatite, fluorite, and mica. The availability of fluoride ions (F–) for forming metal fluoride complexes is governed by the equilibrium thermodynamics of hydrofluoric acid [HF(aq); Migdisov et al. Chem. Geol. 2016, 439, 13–42 and Xing et al. Geofluids 2018, 2018 (1), 6835346]. However, obtaining reliable thermodynamic properties of HF(aq) at high pressure–temperature (P–T) conditions, typical of the Earth’s crust and upper mantle, has proven challenging due to limitations in experimental techniques. This study employs an automated machine-learning molecular dynamics (MLMD) approach that is trained on ab initio data [Wang et al. J. Chem. Phys. 2022, 157 (2), 24103 and Wang et al. J. Am. Chem. Soc. 2024, 146 (21), 14566–14575] to calculate the pKa of HF(aq) across a wide range of temperatures (150–600 °C) and pressures (500 bar to 20 kbar). The calculated pKa values were then fitted into the Ryzhenko–Bryzgalin thermodynamic model with a density dependence to derive properties that can predict the role of HF(aq) in controlling the element mobility and pH in deep-Earth fluids. These results suggest that HF(aq) is a stronger acid than previously estimated, particularly under supercritical conditions, leading to enhanced dissociation and increased availability of fluoride ions (F–), which may improve the solubility and transport of metals such as rare-earth elements and uranium.