Kinetics, mechanism, and thermodynamics of the reversible reaction of methylglyoxal (CH₃COCHO) with S(IV)

At pH ≤2 the following rate law for the formation of hydroxyacetylmethanesulfonate (HAMS) from methylglyoxal (MG) and S(IV) (H₂O·SO₂, HSO₃^-, SO₃^2-) is obtained: d[HAMS]/dt = (((k₀α₁[H⁺]/K_a0) + k₁α₁ + k₂α₂)[S(IV)][MG]₀)/(1 + K_d + K_d[H⁺]/K_a0), where α₁ and α₂ are the fractional concentrations of HSO₃^- and SO₃^2-, respectively; k₀ is the rate constant for the reaction of HSO₃^- with the carbocation aldehyde species (CH₃COC⁺HOH); k₁ and k₂ are the rate constants for the reaction of unhydrated MG with HSO₃^- and SO₃^2-, respectively; K_d is the dehydration constant of hydrated MG; and K_a0 is the acid dissociation constant of the carbocation. At pH ≥4 the rate of formation of HAMS is determined by the rate of dehydration of the diol form of (hydrated) MG: d[HAMS]/dt = k_d[MG]/(1 + K_d + K_d[H⁺]/K_a0), where k_d = k_w + k_H[H⁺] + k_OH[OH^-] + k_A[A] + k_B[B], and k_W is the intrinsic (water) rate constant; k_H and k_OH are the specific acid and base rate constants; and k_A and k_B are the general acid (A) and base (B) rate constants. Between pH 2 and 4, biexponential kinetics are observed because, under our conditions, the rates of dehydration and of S(IV) addition become comparable. Over the pH range 0.7-7.0, the dissociation of HAMS follows the rate law: d[S(IV)]/dt = ((k_-0[H⁺] + k_-1 + k_-2K_a3/[H⁺])K_a4[H ⁺][HAMS])/([H⁺]² + K_a4[H⁺] + K_a3K_a4), where k_-0, k_-1, and k_-2 are the reverse of the analogous forward rate constants defined above and K_a3 and K_a4 are the acid dissociation constants of the sulfonate anion and the sulfonic acid, respectively. Experiments to determine the effect of temperature on the rate (and equilibrium) constants indicate a marked effect of ΔS^‡ (and ΔS₂₉₈) on the relative magnitude of these constants.