Thermodynamics of Water and Aqueous Solutions under Mantle Conditions

Abstract:

Interactions between aqueous solutions and rocks extending from the surface and through the deep mantle control the state and evolution of Earth. The accurate representation of the fluid chemical energy as a function of pressure, temperature and composition over a wide range of conditions is prerequisite in understanding phase equilibria and solubilities in multicomponent systems. End-member thermodynamic properties of water (densities, specific heats, sound speeds, and more) have been extensively explored in a regime below about 100 MPa and an available complex formulation for the Helmholtz free energy (IAPWS-95) accurately represents these data and a smaller number of measurements extending to 1 GPa. However, this parameterization systematically misfits higher pressure data and is not easily adjusted to provide a better description. To address these points, we developed a flexible framework for the acquisition and description of Gibbs’ free energy of water and aqueous solutions. Through use of local basis functions, the thermodynamic state surface can be adjusted to account for improved experimental constraints or for results in new regimes of pressure and temperature. Based on our experimental work on pure water, MgSO_4(aq), Na₂SO_4(aq), and ammonia-water mixtures, new insights are provided on the volumetric behavior of fluids at high pressure. For the ionic solutions, where the partial molar volume at infinite dilution, V_o, is dominated by electrostriction at low pressure, the initial pressure derivative of V_o is large. At high pressure, where V_o is more related to the “size” of the ions, it is only weakly pressure dependent. The non-ideal behavior of these ionic solutions over an extended range of pressures and temperatures is successfully described using a standard three-term parameterization representing solvent (Debye-Hückel), solvent-ion, and ion-ion interactions. The solvent-ion and ion-ion interaction parameters show less dependence on pressure and temperature than V_o or the Debye-Hückel term and non-ideal behavior is generally suppressed at higher pressures.