Early stages of the hydrolysis of chromium(III) in aqueous solution-VII. Kinetics of dimerization of deprotonated forms of doubly bridged dimer

The dimerization of the doubly bridged hydrolytic dimer of CrIII to give tetramer has been followed in the pH range 3.4-5.0, using a pH stat facility. Acid is liberated as the reaction proceeds and initial rates were estimated from the volume of base added to maintain constant pH with time. The reaction was followed only over the first 8% of dimer conversion to ensure that tetramer was the major product. The pH dependence of k_obs has been successfully fitted to an expression which assumes the predominance of three reaction pathways: Cr₂(μ-OH)₂(OH)³⁺+Cr₂(μ-OH)₂(OH)³⁺ → tetramer k₁₁ = (2.18 ± 0.21) × 10^-4 M^-1 s^-1; Cr₂(μ-OH)₂(OH)₂²⁺+Cr₂(μ-OH)₂(OH)³⁺ → tetramer k₂₁ = (5.2 ± 3.2) × 10^-3 M^-1 s^-1; Cr₂(μ-OH)₂(OH)₂²⁺+Cr₂(μ-OH)₂(OH)₂²⁺ → tetramer k₂₂ = (0.83 ± 0.08) M^-1 s^-1. Each deprotonation of dimer affords rate enhancements of 25-160 fold which are in keeping with previous observations for the dimerization of Cr³⁺ and result primarily from labilization of the primary coordination sphere of Cr^III on deprotonation of the aquo ligands. The marginally faster overall rate of dimerization of dimer compared with Cr³⁺ is attributed to the greater acidity of dimer and does not result from a greater reactivity of its deprotonated forms.