Kinetics and Mechanism of Rapid Oxidation of Acetaminophen by Sodium Periodate in the Presence of Catalyst

Abstract

Kinetic studies of the novel oxidation of acetaminophen by sodium periodate are discussed with an emphasis on structure and reactivity by using kinetic approach. The reactions were catalyzed by Os(VIII). The kinetics of the reaction was studied as a function of temperature, ionic strength, dielectric constant of the medium, concentrations of the salt and the added reaction product to learn the mechanism of the reaction. The active species of catalyst and oxidant have been identified. Activation parameters have also been evaluated using the Arrhenius and Eyring plots. A suitable mechanism consistent with the observed kinetic results has been suggested and the related rate law deduced.

APPENDIX

Derivation of rate law for Scheme 2:

Scheme 2.

$[{\text{Os}}{{({\text{VIII}})}_{T}}]$ is equal to sum of concentration of,

$$\frac{{d[{\text{IO}}_{4}^{ - }]}}{{dt}} = {\text{rate}} = {{k}_{3}}[{\text{IO}}_{4}^{ - }][{\text{Complex}}],$$

(1)

$${\text{Os}}{{({\text{VIII}})}_{T}} = ~~[{{{\text{C}}}_{1}}] + [{{{\text{C}}}_{2}}] + [{{{\text{C}}}_{3}}],~$$

(2)

$$\begin{gathered} \frac{{d[{{{\text{C}}}_{1}}]}}{{dt}} = - {{k}_{1}}~[{{{\text{C}}}_{1}}][{\text{O}}{{{\text{H}}}^{ - }}] + {{k}_{{ - 1}}}[{{{\text{C}}}_{2}}] \\ - \;{{k}_{2}}[{{{\text{C}}}_{1}}][{\text{PAM}}] + {{k}_{{ - 2}}}[{{{\text{C}}}_{3}}]. \\ \end{gathered} $$

(3)

On applying steady state approximation to Eq. (3) we get,

$$\begin{gathered} - {{k}_{1}}[{{{\text{C}}}_{1}}][{\text{O}}{{{\text{H}}}^{ - }}] + {{k}_{{ - 1}}}[{{{\text{C}}}_{2}}] \\ - \;{{k}_{2}}[{{{\text{C}}}_{1}}][{\text{PAM}}] + {{k}_{{ - 2}}}[{{{\text{C}}}_{3}}] = 0. \\ \end{gathered} $$

(4)

Similarly we have rate of formation of [${{{\text{C}}}_{2}}]$,

$$\frac{{d[{{{\text{C}}}_{2}}]}}{{dt}} = {{k}_{1}}[{{{\text{C}}}_{1}}][{\text{O}}{{{\text{H}}}^{ - }}] - {{k}_{{ - 1}}}[{{{\text{C}}}_{2}}].$$

(5)

On applying steady state approximation to the above equation we get,

$${{k}_{1}}[{{{\text{C}}}_{1}}][{\text{O}}{{{\text{H}}}^{ - }}] - {{k}_{{ - 1}}}[{{{\text{C}}}_{2}}] = 0,$$

(6)

$$[{{{\text{C}}}_{2}}] = \frac{{{{k}_{1}}[{{{\text{C}}}_{1}}][{\text{O}}{{{\text{H}}}^{ - }}]}}{{{{k}_{{ - 1}}}}}.$$

(7)

From Eqs. (4) and (6) we get,

$$[{{{\text{C}}}_{1}}] = \frac{{{{k}_{{ - 2}}}[{{{\text{C}}}_{3}}]}}{{{{k}_{2}}[{\text{PAM}}]}}.$$

(8)

Putting the value of $[{{{\text{C}}}_{1}}]$ in Eq. (7) we get,

$$\begin{gathered} \text{[}{{{\text{C}}}_{2}}] = \frac{{{{k}_{1}}{{k}_{{ - 2}}}[{\text{O}}{{{\text{H}}}^{ - }}][{{{\text{C}}}_{3}}]}}{{{{k}_{{ - 1~~}}}{{k}_{2}}[{\text{PAM}}]}}, \\ [{{{\text{C}}}_{2}}] = \frac{{{{K}_{1}}[{\text{O}}{{{\text{H}}}^{ - }}][{{{\text{C}}}_{3}}]}}{{{{K}_{2}}[{\text{PAM}}]}}~\quad \left\{ {\because {{K}_{1}} = \frac{{{{k}_{1}}}}{{{{k}_{{ - 1}}}}},\;{{K}_{{2~}}} = \frac{{{{k}_{2}}}}{{{{k}_{{ - 2}}}}}} \right\}. \\ \end{gathered} $$

(9)

Therefore from Eqs. (2), (8), and (9), we get total concentration of catalyst i.e.,

$${\text{Os}}{{({\text{VIII}})}_{T}} = \frac{{[{{{\text{C}}}_{3}}]}}{{{{K}_{2}}[{\text{PAM}}]}} + \frac{{{{K}_{1}}[{\text{O}}{{{\text{H}}}^{ - }}][{{{\text{C}}}_{3}}]}}{{{{K}_{2}}[{\text{PAM}}]}} + [{{{\text{C}}}_{3}}]$$

$$\begin{gathered} = \frac{{[{{{\text{C}}}_{3}}]}}{{{{K}_{2}}[{\text{PAM}}]}} + \frac{{{{K}_{1}}[{\text{O}}{{{\text{H}}}^{ - }}][{{{\text{C}}}_{3}}]}}{{{{K}_{2}}[{\text{PAM}}]}} + ~[{{{\text{C}}}_{3}}] \\ = [{{{\text{C}}}_{3}}]\left\{ {\frac{{1 + ~~{{K}_{1}}[{\text{O}}{{{\text{H}}}^{ - }}] + {{K}_{2}}[{\text{PAM}}]}}{{{{K}_{2}}[{\text{PAM}}]}}} \right\}, \\ \end{gathered} $$

(10)

$$[{{{\text{C}}}_{3}}] = \left\{ {\frac{{{{K}_{2}}[{\text{PAM}}][{\text{Os}}{{{({\text{VIII}})}}_{T}}]}}{{1 + ~{{K}_{1}}[{\text{O}}{{{\text{H}}}^{ - }}] + ~{{K}_{2}}[{\text{PAM}}]}}} \right\}.$$