VAPOR PRESSURE, CHEMICAL EQUILIBRIUM, THERMODYNAMICS, AND EARTH AND PLANETARY SCIENCES - A TRIBUTE TO LAWRENCE A. HARDIE

Based on his Ph.D. thesis at The Johns Hopkins Univ. (JHU) on “Phase equilibria involving minerals of the system CaSO₄-Na₂SO₄-H₂O”, Hardie published his influential paper (Hardie, 1967, Am. Mineral., v. 52, 171) right before I started my graduate study at JHU under the supervision of Hans P. Eugster, who was also the mentor of Hardie. In the thermodynamics class given by Eugster and Hardie at JHU, I learned its basic principles. The stability phase boundary between gypsum and anhydrite at one atm. reported by Hardie (1967, ibid., Figs. 2 & 5) was based on the H₂O vapor pressures of his sample solutions, containing gypsum, anhydrite, and either H₂SO₄ or Na₂SO₄, at one atm. and equilibrated temperatures (T’s). He calculated H₂O vapor pressures in his samples using the well-established relationships between vapor pressures and H₂SO₄ or Na₂SO₄ concentrations, assuming CaSO₄-free solutions due to low solubilities of both minerals. Based on the standard state of H₂O he chose, the “activity of H₂O” shown in his mineral stability diagrams is equivalent to the “relative humidity” in the phase diagrams reported by Chou et al. (2002, Am. Mineral., v. 87, 108) in their humidity buffer technique (HBT). The HBT had been widely used for stability studies of hydrated metal sulfate minerals with considerable applications in environmental and planetary sciences (Chou et al., 2013, J. Asian Earth Sci., v. 62, 734, and references therein). Even though most of the samples in the HBT experiments were dry with no aqueous phase, the basic thermodynamic principles in the HBT were the same as those used by Hardie (1967, ibid.). Also, before these studies, new values of equilibrium constants, as well as the related thermodynamic data, for the hydration-dehydration reactions were needed, because most of the previous data contained large uncertainties and difficult to be applied to the natural systems. For example, Hardie (1967, ibid.) pointed out that the uncertainties for the gypsum-anhydrite transition point under one atm., derived from previous thermodynamic data, were as large as ± 22ºC!

Recent advances on the vapor pressure measurements of aqueous solutions in fused silica capillary high-pressure optical cells at temperatures up to 400ºC (Chou, Goldschmidt 2015 Abstr. 551) were also based on the thermodynamic principles that I learned at JHU.