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 for given reaction concentrations.

Based on given data, the rate equations is:

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

Answer 1

Answer: (A)

Rewriting the given data for the reaction
$C{H}_{3}COC{H}_3(aq)+B{r}_2(aq)\stackrel{H^{+}}{\to }C{H}_{3}COC{H}_{2}Br(aq)+H^{+}(aq)+B{r}^{-}(aq)$
Actually this reaction is autocatalyzed and involves complex calculation for concentration terms.
We can look at the above results in a simple way to find the dependence of reaction rate (i.e., rate of disappearance of $B{r}_2)$
From data (1) and (2) in which concentration of $C{H}_{3}COC{H}_3$ and $H^{+}$remain unchanged and only the concentration of $B{r}_2$ is doubled, there is no change in rate of reaction. It means the rate of reaction is independent of concentration of $B{r}_2$
Again from (2) and (3) in which $\left(C{H}_{3}COC{H}_3\right)$ and $\left(B{r}_2\right)$ remain constant but $H^{+}$increases from $0.05M$ to $0.10$ i.e. doubled, the rate of reaction changes from $5.7\times 10^{-5}$ to $1.2\times$ $10^{-4}$ (or $12\times 10^{-5}$ ), thus it also becomes almost doubled. It shows that rate of reaction is directly proportional to $\left[H^{+}\right]$. From (3) and (4), the rate should have doubled due to increase in conc of $\left[H^{+}\right]$from $0.10M$ to $0.20M$ but the rate has changed from $1.2\times 10^{-4}$ to $3.1\times 10^{-4}$. This is due to change in concentration of $C{H}_{3}COC{H}_3$ from $0.30M$ to $0.40$ $M$. Thus the rate is directly proportional to $\left[C{H}_{3}COC{H}_3\right]$. We now get
rate $=k{\left[C{H}_{3}COC{H}_3\right]}^1{\left[B{r}_2\right]}^0{\left[H^{+}\right]}^1$
$=k\left[C{H}_{3}CC{H}_3\right]\left[H^{+}\right]$
Trick : only option (a) can be correct if rate does not depend on $\left[B{r}_2\right]$.