Solid solution — aqueous solution equilibria as a function of pH

The equations relating element distribution and pH are derived for systems containing an ideal solid solution in equilibrium with an ideal aqueous solution, assuming no polymeric complexes form in the aqueous solution and the solid solution does not contain molecular units with multiple atoms of the substituting elements. These expressions demonstrate that the ratio of the partition coefficients describing element distribution for a system containing a multi-component solid solution is inversely proportional to the solubilities of the end member components at any given pH raised to the power equal to the ratio of the sum of the stoichiometric coefficients of the end-member salt to the stoichiometric coefficient of the substituting radical. The coefficient describing distribution between the aqueous phase and a two-component solid solution is equal to the inverse of the ratio of the end member solubilities raised to the above power. Element distribution between the two phases will be homogenous at any pH resulting in identical solubilities for the two end-member components, and a reversal in relative solubilities will result in a corresponding reversal in the element preferentially incorporated into the solid solution. Because of the dependence of element distribution on pH, a crystal could develop both zoning and reverse zoning as a result of changes in pH. The distribution coefficient could provide information regarding the pH of the aqueous solution at the time of mineral formation if independent evidence establishes the ratio of end-member components in the aqueous phase. The equations describing element distribution may be expressed in terms of the solubility products of the end-member components and the ionization constants of the substituting radicals. Based on the relative values of the ionization constants, pH intervals can be established in which only the concentration of a single complex for each substituting radical need be considered. Within such an interval, the curve of the log of the distribution coefficient vs. pH is linear with a slope equal to the difference in the charges of the two complexes. This approach to the examination of element distribution is developed in some detail for the geologically important case of a two component solid solution having composition (A²⁺, B²⁺) X^2?.