Question

The bromination of acetone that occurs in acid solution is represented by this equation $C{H}_{3}COC{H}_3(aq)+B{r}_2(aq)⟶$
$C{H}_{3}COC{H}_{2}Br(aq)+H^{+}(aq)+B{r}^{-}(aq)$
These kinetic data were obtained for given reaction concentrations.
Initial rate, 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

Initial concentrations, $M$
$[C{H}_{3}COC{H}_3]$	$[B{r}_2]$	$[H^{+}]$
0.30	0.05	0.05
0.30	0.10	0.05
0.30	0.10	0.10
0.40	0.05	0.20

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

Answer 1

Answer: (A)

Let the order of reaction wrt $C{H}_{3}COC{H}_3,B{r}_2$ and $H^{+}$ are $x,y$ and $z$ respectively. Thus,
Rate $(r)=[C{H}_{3}C0C{H}_3{]}^x[B{r}_2{]}^y[H^{+}{]}^z$
$5.7\times 10^{-5}=(0.30{)}^x(0.05{)}^y(0.05{)}^z...(i)$
$5.7\times 10^{-5}=(0.30{)}^x(0.10{)}^y(0.05{)}^z...(ii)$
$1.2\times 10^{-4}=(0.30{)}^x(0.10{)}^y(0.10{)}^z...(iii)$
$3.1\times 10^{-4}=(0.40{)}^x(0.05{)}^y(0.20{)}^z...(iv)$
From Eqs. (i) and (ii)
$y=0$
From Eqs. (ii) and (iii)
$z=1$
From Eqs. (i) and (iv)
$x=1$
Thus, rate law $[C{H}_{3}COC{H}_3{]}^1[B{r}_2{]}^0[H^{+}{]}^1$
$k=[C{H}_{3}COC{H}_3][H^{+}]$