The catalytic breakdown of hydrogen peroxide () in a diluted aqueous mixture is routinely monitored — Chemical Kinetics Chemistry Question
Question
The catalytic breakdown of hydrogen peroxide ($H_2O_2$) in a diluted aqueous mixture is routinely monitored analytically by titrating identical volume aliquots thoroughly against a standardized $KMnO_4$ solution. If the unadjusted experimental volume of $KMnO_4$ consumed records as $V_0$ at the start and $V_t$ at any elapsed time $t$, the kinetic integrated rate equation properly formulates to:
💡 Solution & Explanation
Unlike ester hydrolysis, $H_2O_2$ decomposition directly consumes the reactant titrated. The volume of $KMnO_4$ applied strictly correlates to the raw undecomposed $H_2O_2$ remaining. Therefore, $V_0$ is directly proportional to initial concentration $a$, and $V_t$ is directly proportional to the residual $(a-x)$. Substituting these directly, $k = \frac{2.303}{t} \log \frac{a}{a-x}$ becomes precisely $k = \frac{2.303}{t} \log \left(\frac{V_0}{V_t}\right)$.