Prediction of Gibbs free energies of calcite-type carbonates and the equilibrium distribution of trace elements between carbonates and aqueous solutions

Abstract

A linear correlation exists between the standard Gibbs free energies of formation of calcite-type carbonates (MCO 3) and the corresponding conventional standard Gibbs free energies of formation of the aqueous divalent cations (M 2+) at 25 °C and 1 bar ΔG MCO 3 0 = m( ΔG f, M 2+ 0) − 141,200 cal · mole −1 where m is equal to 0.9715. This relationship enables prediction of the standard free energies of formation of numerous hypothetical carbonates with the calcite structure. Associated uncertainties typically range from about ± 250 to 600 cal · mole −1. An important consequence of the above correlation is that the thermodynamic equilibrium constant for the distribution of two trace elements M and N between carbonate mineral and aqueous solution at 25 °C and 1 bar is proportional to the free energy difference between the corresponding two aqueous ions: In K M-N = m − 1 298.15R (Δ G ̄ f,M 2+ 0 − Δ G ̄ f,N 2+ 0) Combination of predicted standard free energies, entropies and volumes of carbonate minerals at 25°C and 1 bar with standard free energies of aqueous ions and the equation of state in Helgeson et al. (1981) enables prediction of the thermodynamic equilibrium constant for trace element distribution between carbonates and aqueous solutions at elevated temperatures and pressures. Interpretation of the thermodynamic equilibrium constant in terms of concentration ratios in the aqueous phase is considerably simplified if pairs of divalent trace elements are considered that have very similar ionic radii ( e.g., Sr 2+ Pb 2+ , Mg 2+ Zn 2+ ). In combination with data for the stabilities of complex ions in aqueous solutions, the above calculations enable useful limits to be placed on the concentrations of trace elements in hydrothermal solutions.