Variation of element fractionation as a function of pH for oxide, hydroxide and oxide—hydroxide solidsolution—aqueous-solution systems

Abstract

The equations relating element fractionation and pH are derived for systems containing an oxide, hydroxide, or oxide—hydroxide solid solution in equilibrium with an aqueous solution. These expressions demonstrate that the fractionation coefficient for a two-component solid solution in equilibrium with an aqueous solution at any specified pH is equal to the ratio of the solubilities of the pure end-member components at that pH, assuming both solutions are ideal and only mono-hydroxo complexes form. For such a system containing a multi-component solid solution, the ratio of the partition coefficients for the individual components at any pH is inversely proportional to the solubilities of the pure components at that pH. The fractionation coefficient for a two-component solid solution and the ratio of partition coefficients for a multi-component solid solution will be unaffected by changes in pH within any interval in which the ratio of end-member solubilities remains constant. The ratio of two components will be identical in the solid and aqueous phases at any pH at which the end-member solubilities are equal. A reversal in the relative solubilities of two components as a result of a change in pH will produce a corresponding reversal in the component preferentially incorporated into the solid solution. Systems in which only the neutral and singly-charged complexes are present in significant concentrations produce simplified equations for the relationship of element fractionation to pH. Various pH intervals are recognized in which specific combinations of these complexes dominate and the corresponding curves for log of the fractionation coefficient vs. pH are determined. These intervals are also applicable to the ratio of the partition coefficients for any two components in a multi-component solid solution. The effect of pH on element fractionation in naturally-occurring solid solutions will be determined by the relationship between the pH range which may reasonably be expected in nature and the pH dependence of the system under consideration. Element fractionation will be pH-independent if the ratio of solubilities for the end-member components is constant throughout the pH range associated with natural systems, but will be pH-dependent if this ratio varies within those limits.