Thus,

Rate $\propto\left[\mathrm{CH}_{3} \mathrm{COOH}_{3}\right]^{\mathrm{X}}\left[\mathrm{Br}_{2}\right]^{\mathrm{Y}}\left[\mathrm{H}^{+}\right]^{z}$

$5.7 \times 10^{-5}=[0.30]^{x}[0.05]^{y}[0.05]^{z}$ ..... $(i)$

$5.7 \times 10^{-5}=[0.30]^{\times}(0.10)^{y}(0.05)^{z}$ ..... $(ii)$

$1.2 \times 10^{4}=[0.30)^{x}(0.10)^{y}(0.10)^{z}$ ..... $(iii)$

$3.1 \times 10^{-4}=[0.40]^{x}(0.05)^{y}(0.20)^{z} $ ..... $(iv)$

From eqs $(i)$ and $(ii)$

$\mathrm{v}=0$

From eqs $(ii)$ and $(iii)$

$z=1$

From eqs $(i)$ and $(iv)$

$x=1$

Thus, rate law $\propto\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{H}^{+}\right]$

$=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{H}^{+}\right]$