Kinetics and mechanism of the formation of hydroxymethanesulfonic acid at low pH

A spectrophotometric kinetic study of the reaction of sulfur dioxide with formaldehyde to form hydroxymethanesulfonic acid in aqueous solution was performed over the pH range 0.0 to 3.5. A kinetic expression of the following form was verified experimentally: -d[S(IV)]/dt = {(k_1α_1 + k_2α_2)K_d/(K_d + l)}[S(IV)][CH_2O]_t where [CH_2O]_t = [CH_2(OH]_2 + [CH_2O] K_d = k_d/k_(-d) = [CH_2O]/[CH_2(OH)_2], [S(IV)] = [SO_2•H_2] + [HSO_3^-] + SO_3^(2-)], α_1 = [HSO_3-]/[S(IV)] = K_(a1)/[H^+]^2 + K_(a1)[H^+][K_(a1)K_(a2),α_2 = [SO_3^(2-)]/S(IV)] = K_(al)K_(a2)/([H+]^2 + K_(a1)[H^+] + K_(a1)K_(a2), K_(a1) = [H^+][HSO_3^-]/[SO_2•H_2O] and K_(a2) = [H^+][SO_3^(2-)]/[HSO_3^-]. The following kinetic parameters were determined at 25 ºC and µ = 1.0 M: k_1 = (7.90 ± 0.32) x 10^2 M^(-1) s^(-1), k_2 = (2.48 ± 0.05) x 10^7 M^(-1) s^(-1), ΔH_1^* = (24.9 ± 0.8) kJ mol^(-1), ΔS_1^* = (-108.0 ± 2.6) J mol^(-1) K^(-1), ΔH_2^* = (20.4 ± 0.5) kJ mol^(-1), and ΔS_2^* = (-31.7 ± 1.6) J mol^(-1) K^(-1) for values of K_d = 5.50 x 10^(-4), K_(a1) = 1.45 X 10^(-2) M, and K_(a2) = 6.31 x 10^(-8) M. Application of the Davies approximation (log γ = -Az^2/{µ^(1/2)- 0.2µ)} to correct for ionic strength effects yielded ^ck_1 = (4.51 ± 0.15) x 10^2 M^(-1) s^(-1) and ^ck_2 = (5.42 ± 0.07) x 10^6 M^(-1) s^(-1) for concentration-dependent equilibrium constants ^cK_(a1) = K_((a1)γ_(SO_2•H_2O)/γ_(H+γ_HSO_2^-) = 2.92 x 10^(-2) M and ^cK_(a2) = K_(a2)γHSO_3^-/γH+γSO_3^(2-)= 2.58 x 10^(-7) M. The reaction proceeds via each of two parallel pathways involving the nucleophilic addition of HSO_3^- and SO_3^(2-) to the carbonyl C-atom of formaldehyde as follows: CH_2(OH)_2 kd/k-d CH_2O + H_2O (fast); SO_2•H_2O K_(a1) H^+ + HSO_3^- (fast); HSO_3^- + CH_2O K_1 CH_2 (OH)SO_3 (slow); SO_3^(2-) + CH_2O k_2 CH_2(O^-)SO_3^- (slow); CH_2(O^-)SO_3^- + H^+ K_(a2)(HMSA) CH_2(OH)SO_3^- (fast). Previous investigations of this reaction have demonstrated that the dehydration of methylene glycol, CH_2(OH)_2 to form CH_2O becomes rate limiting under neutral pH conditions. The experimental data obtained in the present study indicate that rate of CH_2O production from CH_2(OH)_2 is strongly influenced by specific acid catalysis. Application of the aforementioned results to liquid-phase reaction processes occurring in atmospheric microdroplets is discussed.