Question

The bromination of acetone that occurs in acid solution is represented by this equation.
$C{H}_{3}COC{H}_3(aq.)+B{r}_2(aq.)\to$
$C{H}_{3}COC{H}_{2}Br(aq.)+H^{+}(aq.)+B{r}^{-}(aq.)$
These kinetic data were obtained from given reaction concentrations.
Initial concentrations, (M)
$\left[C{H}_{3}COC{H}_3\right]$ $\left[B{r}_2\right]$ $\left[H^{+}\right]$
0.30 0.05 0.05
0.30 0.10 0.05
0.30 0.10 0.10
0.40 0.05 0.20
Corresponding initial rate of disappearance of $B{r}_2,M{s}^{-1}$
$5.7\times {10}^{-5}$
$5.7\times {10}^{-5}$
$1.2\times {10}^{-4}$
$3.1\times {10}^{-4}$
Based on these data, the rate equation is:

• A. $Rate=k\left[C{H}_{3}COC{H}_3\right]\left[B{r}_2\right][H^{+}{]}^2$
• B. $Rate=k\left[C{H}_{3}COC{H}_3\right]\left[B{r}_2\right]\left[H^{+}\right]$
• C. $Rate=k\left[C{H}_{3}COC{H}_3\right]\left[H^{+}\right]$
• D. $Rate=k[CH=COC{H}_3]\left[B{r}_2\right]$

Answer 1

Answer: (C)

$Rate=k\left[C{H}_{3}COC{H}_3\right]\left[H^{+}\right]$

$\left[{CH}_3{COCH}_3\right]\left[{Br}_2\right]\left[H^{+}\right]$ Initial rate of disappearance of ${Br}_2$

(1) 0.30 0.05 0.05 $5.7\times {10}^{-5}$

(2) 0.30 0.10 0.05 $5.7\times {10}^{-5}$

(3) 0.30 0.10 0.10 $1.2\times {10}^{-4}$

(4) 0.40 0.05 0.20 $3.1\times {10}^{-4}$

Here, Rate of disappearance of ${Br}_2$ = Rate of reaction.

$\bullet$ On comparing (1) & (2)

On doubling the concentration of ${Br}_2$, there is no change in the rate of reaction.

$\Rightarrow$ order wrt $H_2=1.$

$\bullet$ On comparing (3) & (4)

$\left[{CH}_{3}COC{H}_3\right]\to \frac{4}{3}\left[{CH}_{3}CO{CH}_3\right]$

and

$\left[H^{+}\right]\to 2\left[H^{+}\right]$

the rate became $\frac{8}{3}$ times of itself.

$\Rightarrow$order wrt ${CH}_3{COCH}_3=1$.

$\therefore$ Rate equation $\Rightarrow$ rate = $K\left[{CH}_{3}CO{CH}_3\right]\left[H^{+}\right]$