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Theoretical Prediction of Gibbs Free Energies of Formation for Crystalline α‐MOOH and α‐M 2 O 3 Based on a Linear Free‐Energy Relationship
Author(s) -
SUN Xiaoming
Publication year - 2011
Publication title -
acta geologica sinica ‐ english edition
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.444
H-Index - 61
eISSN - 1755-6724
pISSN - 1000-9515
DOI - 10.1111/j.1755-6724.2011.00458.x
Subject(s) - gibbs free energy , chemistry , ionic radius , crystallography , aqueous solution , ionic bonding , solvation , solid solution , thermodynamics , ion , physics , organic chemistry
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 α‐MOOH (with a goethite structure) and α‐M 2 O 3 (with a hematite structure) from the known thermodynamic properties of the corresponding aqueous trivalent cations (M 3+) . The modified equation is expressed as Δ G 0 f , M V X = a M V X Δ G 0 n , M 3+ + b M V X +β M V X γ M 3+ , where the coefficients a M V X , b M V X , and β M V X characterize a particular structural family of M v X (M is a trivalent cation [M 3+ ] and X represents the remainder of the composition of solid); γ 3+ is the ionic radius of trivalent cations (M 3+ ); Δ G 0 f , M V X is the standard Gibbs free energy of formation of M v X; and Δ G 0 n , M 3+ is the non‐solvation energy of trivalent cations (M 3+ ). By fitting the equation to the known experimental thermodynamic data, the coefficients for the goethite family (α‐MOOH) are a M V X =0.8838, b M V X =–424.4431 (kcal/mol), and β M V X =115 (kcal/mol.Å), while the coefficients for the hematite family (α‐M 2 O 3 ) are a M V X =1.7468, b M V X =–814.9573 (kcal/mol), and β M V X =278 (kcal/mol.Å). 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 (α‐MOOH) and hematite (α‐M 2 O 3 ) if the standard Gibbs free energies of formation of the trivalent cations are known.