The bromination of acetone that occurs in acid solution is represented by this equation. $\mathrm{CH}_3 \mathrm{COCH}_3(a q)+\mathrm{Br}_2(a q) \longrightarrow \mathrm{CH}_3 \mathrm{COCH}_2 \mathrm{Br}(a q)+\mathrm{H}^{+}(a q)+\mathrm{Br}^{-}(a q)$ These kinetic data were obtained for given…

Question

The bromination of acetone that occurs in acid solution is represented by this equation.
$\mathrm{CH}_3 \mathrm{COCH}_3(a q)+\mathrm{Br}_2(a q) \longrightarrow \mathrm{CH}_3 \mathrm{COCH}_2 \mathrm{Br}(a q)+\mathrm{H}^{+}(a q)+\mathrm{Br}^{-}(a q)$
These kinetic data were obtained for given reaction concentrations.
$\begin{array}{|l|}
\hline \text {Initial concentrations, } M & \\
\begin{array}{c|l|l|l}
{\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]} & {\left[\mathrm{Br}_2\right]} & {\left[\mathrm{H}^{+}\right]} & \text{Initial rate, disappearance of } \mathrm{Br}_2, \mathrm{Ms}^{-1} \\
\hline 0.30 & 0.05 & 0.05 & 5.7 \times 10^{-5} \\
0.30 & 0.10 & 0.05 & 5.7 \times 10^{-5} \\
0.30 & 0.10 & 0.10 & 1.2 \times 10^{-4} \\
0.40 & 0.05 & 0.20 & 3.1 \times 10^{-4}
\end{array} \\ \hline
\end{array}$
Based on these data, the rate equation is

Aicharya · Accepted Answer

Key Idea : By comparing the rate and concentration the order of the reaction can be calculated
Let the rate of the reaction wrt $\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]$, $\left[\mathrm{Br}_2\right]$ and $\left[\mathrm{H}^{+}\right]$are $x, y$ and $z$ respectively. Thus,
$\text {Rate } \propto\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]^x\left[\mathrm{Br}_2\right]^y\left[\mathrm{H}^{+}\right]^z$
$5.7 \times 10^{-5}=[0.30]^x[0.05]^y[0.05]^z$
$5.7 \times 10^{-5}=[0.30]^x(0.10)^y(0.05)^z$
$1.2 \times 10^{-4}=[0.30]^x(0.10)^y(0.10)^z$
$3.1 \times 10^{-4}=[0.40]^x(0.05)^y(0.20)^z$
From Eqs (i) and (ii)
$y=0$
From Eqs (ii) and (iii)
$z=1$
From Eqs (i) and (iv)
$x=1$
Thus, rate law $\propto\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]\left[\mathrm{H}^{+}\right]$
$=k\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]\left[\mathrm{H}^{+}\right]$

The bromination of acetone that occurs in acid solution is represented by this equation. $\mathrm{CH}_3…

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