Prediction of trace metal partitioning between minerals and aqueous solutions: a linear free energy correlation approach
Trace metal partitioning between authigenic minerals and aqueous solutions is of great interest to both geochemical and environmental communities. In this paper, we have developed a linear free energy correlation model that correlates metal partition coefficients with metal cation properties: -2.303 RT log Kd + ∆G f,MZ+0 = a∗MHX∆ Gn,MZ+0 + β ∗MHXrMZ+ + b∗MHX where a∗MHX, β ∗MHX, and b∗MHX are constants, which can be determined by a regression analysis. For isovalent metal partitioning, because of the constraint of Kd = 1 for the host metal, this correlation can be also expressed as: -2.303 RT log Kd = a∗MHX(∆ Gn,MHZ+0 - ∆ Gn,M0) + β ∗MHX( rMZ+ - rn,MHZ+) - (∆ Gf,MZ+0 - ∆ G0f,MHZ+). Host minerals from an isostructural family have the same linear free energy relationship, as long as the relationship is expressed as a function of the differences in cation properties between substituent and host metals. We have applied our model to both isovalent and non-isovalent metal partitioning in carbonate minerals. The model closely fits experimental data, demonstrating the robustness of the proposed linear free energy relationship. Using the model, we have predicted the partition coefficients of divalent and trivalent metals between various carbonate minerals and aqueous solutions. The differences between the predicted and experimental values are generally less than 1 logarithmic unit for divalent cations and less than 0.4 logarithmic unit for trivalent cations. Magnesite is predicted to have the largest partition coefficients among the carbonate minerals with a calcite structure and therefore, can be a good scavenger for toxic metals. The kinetic effect on metal partitioning can be described graphically by a "seesaw" line anchored at a host cation. To explain the rate dependence of partition coefficients, we have proposed a conceptual model that relates metal partitioning to surface adsorption. The conceptual model suggests that as the rate of host mineral precipitation increases, the ratio of substituent to host cation in a solid approaches what is in the adsorbed layer. The linear free energy correlation model developed in this paper provides a useful tool for systematizing the existing experimental data and for predicting unknown partition coefficients.