Measuring thermodynamically-interpretable solubilities at high pressures and temperatures

Solubilities are useful only if measured in defined systems where at least the minimum number of intensive variables required by the Gibbs' phase rule for invariancy are either fixed, measured, or controlled in the experiment. The array of determined intensive variables and any necessary buffers should be selected also to provide maximum resolution in identifying stoichiometries of solute species and in evaluating equilibrium constants of solubility-controlling reactions. Simultaneous measurements of volumetric properties of solutions and gases present during solubility measurements are practical and simplify thermodynamic analysis of solubilities. Equilibration is best demonstrated by equal solubilities for the same conditions approached from opposite directions. In solubility experiments at high pressures and temperatures, continuous analyses are possible using spectra, cell potentials, or radioactive tracers but they are uncertain indicators of total solute concentration. Methods providing only a single data point per experiment, by nutrient weight-loss or by analysis of quenched fluids, are comparatively slow and are not reversible. Better are periodic sampling and analysis of quenched, filtered fluids from two types of experimental systems. Condensed fluids are investigated effectively with an external-fluid-supported flexible cell but vapor-containing or supercritical experiments are less complex in a fixed-volume, rocking vessel. In both systems the parent solution remains virtually isothermal and isobaric during sampling, replicate sampling is possible, and reversing of reactions is simple. The less-complicated, fixed-volume system also permits P-V-T measurements on liquids and gases together with sampling. The stoichiometry of the dominant solute species is given, commonly with satisfactory resolution, by the exponential dependence of the solubility on the concentration of each potential ligand. The exponent closely approximates the stoichiometric coefficient of the ligand in the solute species. From these ligand and solute concentrations and tabulated or calculated activity coefficients, activities are obtained for dominant solute species, ligands, and gases corresponding to each solubility measurement. These activities permit the calculation of an equilibrium constant for each principal reaction representing equilibration among the solute, its dissolved species, and reacting ligands. The resulting constants, based on individual solubility measurements may then be compared for consistency both isothermally and polythermally. Measurements of solubilities at high temperatures and pressures are now impeded primarily by the lack of (1) well-calibrated buffers of oxidation state and acidity with known reaction rates for hydrothermal use, and (2) inert high-strength alloys that are resistant to hydrogen embrittlement, nonreactive with acidic and other high temperature fluids, and with mechanical properties compatible with use in the bodies or liners of reaction vessels.