Theoretical Prediction of Gibbs Free Energies of Formation for Crystalline -MOOH and -M₂O₃ Based on a Linear Free-Energy Relationship

摘要

In the present study, the modified Sverjensky–Molling equation, derived from a linear-free energy relationship, is used to predict the Gibbs free energies of formation of crystalline phases of -MOOH (with a goethite structure) and -M₂O₃ (with a hematite structure) from the known thermodynamic properties of the corresponding aqueous trivalent cations (M3+). The modified equation is expressed as ΔG0_f,MVX=a_MVXΔG0_n,M3++b_MVX+β_MVXM3+, where the coefficients a_MVX, b_MVX, and β_MVX characterize a particular structural family of M_vX (M is a trivalent cation [M3+] and X represents the remainder of the composition of solid); 3+ is the ionic radius of trivalent cations (M3+); ΔG0_f,MVX is the standard Gibbs free energy of formation of M_vX; and ΔG0_n,M3+ is the non-solvation energy of trivalent cations (M3+). By fitting the equation to the known experimental thermodynamic data, the coefficients for the goethite family (-MOOH) are a_MVX=0.8838, b_MVX=–424.4431 (kcal/mol), and β_MVX=115 (kcal/mol.?), while the coefficients for the hematite family (-M₂O₃) are a_MVX=1.7468, b_MVX=–814.9573 (kcal/mol), and β_MVX=278 (kcal/mol.?). The constrained relationship can be used to predict the standard Gibbs free energies of formation of crystalline phases and Active phases (i.e. phases that are thermodynamically unstable and do not occur at standard conditions) within the isostructural families of goethite (-MOOH) and hematite (-M₂O₃) if the standard Gibbs free energies of formation of the trivalent cations are known.