Free-energy relationships in coordination chemistry. I. Linear relationships among equilibrium constants

After a review of previous semi-empirical free-energy relationships applying to the formation of metal complexes, the following equations are derived within a framework of logical assumptions[Formula: see text]These compare stability constants of complexes formed by a metal ion M and a ligand L with those formed by a reference metal M s and a reference ligand L o . The derivation of these equations reveals an inherent relationship between the constants B and C, which is formulated through an "exactness" test. The application of these relationships to stoichiometric equilibrium constants is discussed.In the testing of the foregoing equations with data for various ligand families reacting with numerous metal ions, two principal modes of behavior were noted. In one, there was a mutual dependence of B on the particular metal ions compared and of C on the particular ligands compared. In the other, all values of B and C were found to equal unity irrespective of metal ion or ligand compared. The cause of this distinction is not yet understood.