Stepwise and Overall Formation Constants

A free metal ion in aqueous medium is already surrounded by (coordinated to) water molecules, written [MS₆]; adding a ligand that binds more strongly than water displaces the coordinated water molecules one by one, or all at once. If six ligands are added to the metal ion in a single step, [MS₆] + 6L ⇌ [ML₆] + 6S, the overall stability constant is βoverall = [ML₆][S]⁶ / ([MS₆][L]⁶); because the solvent is present in large excess its concentration can be treated as constant and dropped, giving βoverall = [ML₆] / ([MS₆][L]⁶) in practice. If instead the six ligands are added one at a time, the formation of [ML₆] proceeds through six successive steps, each with its own stepwise stability constant k₁ through k₆ (for example k₁ = [MS₅L]/[MS₆][L] for the first substitution, and so on through k₆ = [ML₆]/[MSL₅][L] for the last). A short mathematical derivation shows that the overall stability constant is simply the product of all six ste …