Complexation Equilibria

Metal ions such as Cu2+ are Lewis acids that combine with Lewis bases such as H₂O to form complex ions, e.g.,Cu(OH₂)₄²⁺. The number of ligands, the coordination number, varies from one metal ion to another; the most common coordination numbers are 4 and 6, but 2, 3, 5, 7, and 8 are also known. In the presence of another Lewis base such as NH₃, the H₂O ligands can be replaced in stepwise equilibria:

K₁ = 1.6 × 104, K₂ = 3.2 × 103, K₂ = 9.5 × 102, K₄ = 1.3 × 102. Since ΔH° is nearly the same for each step, -23 kJ/mol, the decrease of Kn with increasing NH₃ substitution is an entropy effect which can be partly explained by statistics. In the first step, any one of four H₂O ligands can be replaced in the forward reaction but only one NH₃ can be replaced in the reverse reaction, contributing a factor of 4 to K₁. In the fourth step, the statistics are reversed, one H₂O can be replaced in the forward reaction but any of four NH₃ ligands can be replaced in the reverse step, contributing a factor of 1/4 to K₄. We sometimes can use the overall formation constant corresponding to the sum of the four steps,