Using Linear Free Energy Relationship to Predict the Stability Constants of Aqueous Complexes of Metal-Organic Ligands
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Using Linear Free Energy Relationship to Predict the Stability Constants of Aqueous Complexes of Metal-Organic Ligands Huifang Xu* and Yifeng Wang** * Department of Earth and Planetary Sciences, The University of New Mexico, Albuquerque, New Mexico 87131, [email protected] **Sandia National Laboratories, Albuquerque, NM 87185, [email protected] ABSTRACT The Sverjensky-Molling linear free energy relationship was originally developed to correlate the Gibbs free energies of formation of an isostrutural family of solid phases to the thermodynamic properties of aqueous cations. In this paper, we demonstrate that the similar relationship also exists between metal complexes and simple metal cations in aqueous solutions. We extend the Sverjensky-Molling relationship to predict the Gibbs free energies of formation or dissociation constants for a family of metal complexes with a given complexing ligand. The discrepancies between the predicted and experimental data are generally less than 1.5 kcal/mol (or one log unit for stability constants). The use of this linear free energy correlation can significantly enhance our ability to predict the speciation, mobility, and toxicity of heavy metals in natural environments. According the obtained results, Gibbs free energies of formation of cations (∆G0f, Mn+) can be used as an indicator for the hardness/softness of a metal cation (acid). The higher negative value of a metal cation, the harder acid it will be. It is logical to postulate that the coefficient a*ML characterizes the softness of a complexing ligand (base). INTRODUCTION Metal complexation with various inorganic or organic ligands in aqueous solutions directly controls the solubility, sorption, and toxicity of toxic metals including radionuclides in natural environments [1-4]. The quantitative calculations of metal complexation thus have been routinely used in predicting the fate and impact of heavy metals in natural environments [2, 5]. The effectiveness of these calculations heavily depends on the completeness and quality of the thermodynamic databases on which the calculations are based. Unfortunately, the thermodynamic data for many metal complexes, especially those with radionuclides, are currently either unknown or poorly constrained. Therefore, there is a need for (1) developing a method to predict the unknown thermodynamic data based on a limited number of the existing measurements and (2) using this method to check the internal consistency of the thermodynamic databases that are used in the calculations. It is essential to have reliable data for metal organic complexes in order to evaluate impacts of pollutants on water and soils. Empirical linear free energy relationships have been proven useful for correlating thermodynamic properties and predicting unknown thermodynamic data [6-9]. The Hammett linear free energy relationship is a classic example that has been widely used for substituted aqueous organic reactions [6-8]. Directly analog to the Hammett relationship and explicitly accounting for Born solvation en
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