Chemical Kinetics Ques 26
26. The bromination of acetone that occurs in acid solution is represented by this equation.
[2008]
$CH_3 COCH_3(aq)+Br_2(aq) \to$ $CH_3 COCH_2 Br(aq)+H^{+}(aq)+Br^{-}(aq)$
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 $Br_2,Ms^{-1}$
$\begin{aligned} & 5.7 \times 10^{-5} \\ & 5.7 \times 10^{-5} \\ & 1.2 \times 10^{-4} \\ & 3.1 \times 10^{-4}\end{aligned}$
Base on these data, the rate equation is:DD
(a) Rate $=k\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]\left[\mathrm{H}^{+}\right]$
(b) Rate $=k\left[\mathrm{CH}=\mathrm{COCH}_3\right]\left[\mathrm{Br}_2\right]$
(c) Rate $=k\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]\left[\mathrm{Br}_2\right]\left[\mathrm{H}^{+}\right]^2$
(d) Rate $=k\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]\left[\mathrm{Br}_2\right]\left[\mathrm{H}^{+}\right]$
Show Answer
Answer:
Correct Answer: 26.(a)
Solution:
(a) Rewriting the given data for the reaction
$ \begin{aligned} & \mathrm{CH}_3 \mathrm{COCH}_3(\mathrm{aq})+\mathrm{Br}_2(\mathrm{aq}) \xrightarrow{\mathrm{H}^{+}} \\ & \quad \mathrm{CH}_3 \mathrm{COCH}_2 \mathrm{Br}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Br}^{-}(\mathrm{aq}) \end{aligned} $
| S No. | Initial concentration of $CH_3COCH_3$ in M |
Initial concentration of $Br_2$ in M |
Initial concentration of $H^+$ in M |
Rate of disappearance of $Br_2$ in MS^{-1}$ i.e. $-\frac{d}{dt} [Br_2]$ or $\frac{dx}{dt}$ |
|---|---|---|---|---|
| 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 | $3.1 \times 10^{-4}$ |
This raction 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 $Br_2$).
From data (1) and (2) in which concentration of $\mathrm{CH}_3 \mathrm{COCH}_3$ and $\mathrm{H}^{+}$remain unchanged and only the concentration of $\mathrm{Br}_2$ is doubled, there is no change in rate of reaction. It means the rate of reaction is independent of concentration of $\mathrm{Br}_2$. Again from (2) and (3) in which $\left(\mathrm{CH}_3 \mathrm{CO} \mathrm{CH}_3\right)$ and $\left(\mathrm{Br}_2\right)$ remain constant but $\mathrm{H}^{+}$increases from $0.05 \mathrm{M}$ 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 $\left[\mathrm{H}^{+}\right]$. From (3) and (4), the rate should have doubled due to increase in conc of $\left[\mathrm{H}^{+}\right]$from $0.10 \mathrm{M}$ to $0.20 \mathrm{M}$ 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 $\mathrm{CH}_3 \mathrm{COCH}_3$ from $0.30 \mathrm{M}$ to $0.40 \mathrm{M}$. Thus, the rate is directly proportional to $\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]$.
$\text{rate} = k[CH_3COCH_3]^1[Br_2]^0[H^+]^1$
$ =k[CH_3COCH_3][H^+] $
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