Parametric correlation of formation constants in aqueous solution. 1. Ligands with small donor atoms

Abstract

It is shown that four-parameter equations proposed by previous authors have poor predictive powers for data of formation constants in aqueous solution. This relates partly to the paucity of data on complexes of ligands such as ammonia which, with most metal ions, cannot exist in water because of hydrolysis. Equations previously proposed that relate the formation constants of polyamine and poly(aminbcarboxy1ate) complexes to those of the ammonia and acetate complexes are used to calculate formatio‘n constants for these hydrolysis-prone ammonia complexes. An equation of the type log K, = EAEB + CACB, where E and C are identified with the tendencies of the Lewis acid A and base B to undergo ionic and covalent bonding, was used to correlate the F-, OH-, and NH, formation constants of 27 Lewis acids to a standard deviation of 0.24 log unit. Hardness parameters l!fA and HB were defined as EA/CA and EB/CB for acids and bases, respectively, and gave reasonable orders of hardness It was found that for ligands with large donor atoms, such as C1-, and for sulfur or phosphorus donor atoms, deviations from the predictions of this equation were observed that appeared to be related to the size of the acid, so that no deviations were observed for large cations such as Ag’ and Pb2+, aith Occurrence of large deviations for smaller cations such as Cu” or Ni2+, with the very largest occurring for the proton. These deviations were attributed to steric hindrance between the large donor atom and adjacent coordinated water molecules. The important contribution of the Edwards equation’ lies in illustrating that formation constant data for complexes of unidentate ligands in aqueous solution need at least a dualbasicity scale for any kind of correlation to be obtained at all. There have been several other multiparameter equation^^-^ proposed for correlating formation constant data. The need for at least a dual-basicity equation has manifested itself in the classification of metal ions’into Schwart~enbach’s~ and Ahrland and Chatt’s6 A- and B-type metal ions and Pearson’s more general classification7 of Lewis acids and bases into hard and soft acids and bases (HSAB). Drago and co-workers* have had considerable success with a more generalized form of a four-parameter equation similar to eq 1 for the correlation of enthalpy changes on adduct formation in solvents of low dielectric constant. In eq 1, which resembles Drago’s expression, except that -AHo has been replaced with log K1, C and E are identified with the tendency of each Lewis acid A or base B to undergo covalent or ionic bonding. This interpretation of the significance of the C and E parameters seems most reasonable in the light of the work of Klopman9 on the origin of hardness and softness in acids and bases. Klopman9 found softness to be associated Rith “frontier-controlled’’ (covalent) and hardness with “charge-controlled’’ (ionic) bonding in calculations based upon polyelectronic pertubation theory. We have therefore adopted the E and C formalism of Drago and co-workers8 in this paper as probably being the best interpretation of the parameters in a four-parameter equation such as (1).