Practical hardness scales for metal ion complexes

Abstract

Experimentally determined log stability constant differences for substitution reactions of one ligand for another on a metal ion are used to derive practical metal ion hardness–softness scales applicable to aqueous solutions. These scales probably correspond to what most investigators imply when they use the terms hardness and softness. The correlation between the halide scale for fluoride minus bromide and the oxygen minus nitrogen scales of hydroxide or acetate minus ammonia is high but not perfect. The differences indicate hardness and softness depend to some extent upon the ligands considered, and thus it is not possible to derive a single hardness scale that is applicable to all complexes in aqueous solutions. Based on these quantitative scales, Mn2+ previously assigned as hard, fits better in the borderline category. Depending upon the ligands, Tl+ may be harder or softer than Tl3+. The proton displays strong anti-borderline behavior, acting either as a very hard or a very soft cation. To a lesser degree, Pb2+ behaves similarly. Consideration of the log stability constant difference for substitution of one metal ion for another on a ligand leads to a generally applicable practical hardness scale for 16 ligands in aqueous solutions: F−(−3), H2O(0), acetate(2), HCO3−(4), CO32−(5), OH−(5)>pyridine(6), benzimidazole(6), imidazole(7), Cl−(7), NH3(8), SCN−(9), Br−(9)>I−(13), CN−(13), S2O32−(14). Based on the logarithmic magnitudes in parentheses, it is recommended that the first six ligands be classified as hard, the next seven after the first inequality sign as borderline, and the last three after the last inequality sign as soft. Thus all oxygen donors are designated hard and now all nitrogen donors borderline. Within the borderline group, aliphatic amines are softer than aromatic amines. The principle of hard and soft acids and bases finds its most consistent application, not in direct stability constant comparisons, but rather in log stability constant differences of appropriate substitution reactions.