$4 \mathrm{KMnO}_{4}+4 \mathrm{KOH} \stackrel{\Delta}{\longrightarrow} 4 \mathrm{K}_{2} \mathrm{MnO}_{4}+\mathrm{O}_{2}+2 \mathrm{H}_{2} \mathrm{O}$
$2 \mathrm{MnO}_{2}+4 \mathrm{KOH}+\mathrm{O}_{2} \stackrel{\Delta}{\longrightarrow} 2 \mathrm{K}_{2} \mathrm{MnO}_{4}+2 \mathrm{H}_{2} \mathrm{O}$
$\mathrm{KMnO}_{4}+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{con}) \stackrel{\Delta}{\longrightarrow} \mathrm{K}_{2} \mathrm{SO}_{4}+\mathrm{Mn}_{2} \mathrm{O}_{7}+\mathrm{H}_{2} \mathrm{O}$
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$CH_3COCH_{3(aq)} + Br_{2(aq)} \rightarrow $$CH_3COCH_2Br_{(aq)} + H^+_{(aq)}+ Br^-_{(aq)}$
These kinetic data were obtained for given reaction concentrations.
Initial concentrations, $M$
| $[CH_3COCH_3]$ | $[Br_2]$ | $[H^+]$ |
| $0.30$ | $0.05$ | $0.05$ |
| $0.30$ | $0.10$ | $0.05$ |
| $0.30$ | $0.10$ | $0.10$ |
| $0.40$ | $0.05$ | $0.20$ |
Initial rate, disappearance of $Br_2, \,\,Ms^{-1}$
$5.7 \times 10^{-5} ,$ $5.7 \times 10^{-5} ,$ $1.2 \times 10^{-5} ,$ $3.1 \times 10^{-5}$
Based on these data, the rate equation is