Kinetics and mechanism of the oxidation of hydrogen peroxide by the octacyanotungstate(V) ion in alkaline aqueous media

Summary

The oxidation of H₂O₂ by [W(CN)₈]³⁻ has been studied in aqueous media between pH 7.87 and 12.10 using both conventional and stopped-flow spectrophotometry. The reaction proceeds without generation of free radicals. The experimental overall rate law, ${{{\text{d[W(CN)}}_{\text{8}}^{{\text{4 - }}} ]} \mathord{\left/ {\vphantom {{{\text{d[W(CN)}}_{\text{8}}^{{\text{4 - }}} ]} {{\text{d}}t = 2(k_s [{\text{H}}_{\text{2}} {\text{O}}_{\text{2}} ])[{\text{W(CN)}}_{\text{8}}^{{\text{3 - }}} ]}}} \right. \kern-\nulldelimiterspace} {{\text{d}}t = 2(k_s [{\text{H}}_{\text{2}} {\text{O}}_{\text{2}} ])[{\text{W(CN)}}_{\text{8}}^{{\text{3 - }}} ]}}$, strongly suggests two types of mechanisms. The first pathway, characterized by the pH-dependent rate constant k _s, given by ${{2k_s = (k_{\text{a}} + k_{\text{b}} K_5 [{\text{H}}^{\text{ + }} ]^{ - 1} )} \mathord{\left/ {\vphantom {{2k_s = (k_{\text{a}} + k_{\text{b}} K_5 [{\text{H}}^{\text{ + }} ]^{ - 1} )} {[1 + K_5 [{\text{H}}^{\text{ + }} ]^{ - 1} )(}}} \right. \kern-\nulldelimiterspace} {[1 + K_5 [{\text{H}}^{\text{ + }} ]^{ - 1} )(}}1 + K_{{\text{a1}}} [{\text{H}}^{\text{ + }} ]^{ - 1} )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} ]$, involves the formation of [W(CN)₈· H₂O₂]³⁻, [W(CN)₈· H₂O₂·W(CN)₈]⁶⁻ and [W(CN)₈· HO]³⁻ intermediates in rapid pre-equilibria steps, and is followed by a one-electron transfer step involving [W(CN)₈·HO]³⁻ (k _a) and its conjugate base [W(CN)₈·O]⁴⁻ (k _b). At 25 °C, I = 0.20 m (NaCl), the rate constant $k_{\text{a}} = (8.0 \pm 0.9) \times 10^{ - 3} {\text{M}}^{{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{2}}}} \right. \kern-\nulldelimiterspace} {\text{2}}}} {\text{S}}^{{\text{ - 1}}}$ with ΔH ^‡_a =40±6kJmol⁻¹ and ΔS ^‡_a =−151±22JK⁻¹mol⁻¹; the rate constant $k_b = 0.22 \pm 0.03{\text{M}}^{{{{\text{ - 1}}} \mathord{\left/ {\vphantom {{{\text{ - 1}}} {\text{2}}}} \right. \kern-\nulldelimiterspace} {\text{2}}}} {\text{S}}^{{\text{ - 1}}}$ with ΔH ^‡_b =36±1kJmol⁻¹ and ΔS ^‡_b =−136±2JK⁻¹mol⁻¹ at 25 °C, I = 0.20 m (NaCl); the acid dissociation constant of [W(CN)₈·HO]³⁻, K ₅ =(5.9±1.7)×10⁻¹⁰ m, with $\Delta H_{K_5 }^ = 18 \pm 5{\text{kJ mol}}^{{\text{ - 1}}}$ and $\Delta S_{K_5 }^ = - 117 \pm 23{\text{JK}}^{{\text{ - 1}}} {\text{mol}}^{{\text{ - 1}}}$ is the first acid dissociation constant of H₂O₂. The second pathway, with rate constant, k _f, involves the formation of [W(CN)₈· HO₂]⁴⁻ and is followed by a formal two-electron redox process with [W(CN)₈]³⁻. The pH-dependent rate constant, k _f, is given by ${{2k_{\text{f}} = 2k_{\text{7}} } \mathord{\left/ {\vphantom {{2k_{\text{f}} = 2k_{\text{7}} } {(1 + K_{{\text{a1}}}^{{\text{ - 1}}} [{\text{H}}^{\text{ + }} ])}}} \right. \kern-\nulldelimiterspace} {(1 + K_{{\text{a1}}}^{{\text{ - 1}}} [{\text{H}}^{\text{ + }} ])}}$. The rate constant k ₇ =23±6m ⁻¹ s ⁻¹ with $\Delta H_{K_7 }^\ddag = 9 \pm 2{\text{kJ mol}}^{{\text{ - 1}}}$ and $\Delta S_{K_7 }^\ddag = - 188 \pm 7{\text{JK}}^{{\text{ - 1}}} {\text{ mol}}^{{\text{ - 1}}}$ at 25°C, I = 0.20 m (NaCl).