1

### AIPMT 2008

The bromination of acetone that occurs in acid solution is represented by this equation.
CH3COCH3(aq) + Br2(aq)  $\to$
CH3COCH2Br(aq) + H+(aq) + Br$-$(aq)
These kinetic data were obtained for given reaction concentrations.
Initial concentrations, M
[CH3COCH3 [Br2] [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 Br2, Ms$-$1
5.7$\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[CH3COCH3][Br2][H+]2
B
Rate = k[CH3COCH3][Br2][H+]
C
Rate = k[CH3COCH3][H+]
D
Rate = k[CH3COCH3][Br2]

## Explanation

From the first two experiments, it is clear that when concentration of Br2 is doubled, the initial rate of disappearance of Br2 remains unaltered. So, order of reaction with respect to Br2 is zero. The probable rate law for the reaction will be : k[CH3COCH3 ][H+].
2

### AIPMT 2008

The rate constants k1 and k2 for two different reactions are 1016 $\cdot$ e$-$2000/T and 1015 $\cdot$ e$-$1000/T, respectively.
The temperature at which k1 = k2 is
A
2000 K
B
${{1000} \over {2.303}}K$
C
1000 K
D
${{2000} \over {2.303}}K$

## Explanation

k1 = 1016 ${e^{ - {{2000} \over T}}}$

k2 = 1015 ${e^{ - {{1000} \over T}}}$

On taking log of both the equations, we get

$\log {k_1} = 16 - {{2000} \over {2.303T}}$

$\log {k_2} = 15 - {{1000} \over {2.303T}}$

As k1 = k2

$16 - {{2000} \over {2.303T}}$ = $15 - {{1000} \over {2.303T}}$

$\Rightarrow$ T = ${{1000} \over {2.303}}K$
3

### AIPMT 2007

The reaction of hydrogen and iodine monochloride is given as :
H2(g) + 2ICl(g) $\to$ 2HCl(g) + I2(g)
This reaction is of first order with respect to H2(g) and ICl(g),
following mechanisms were proposed.

Mechanism A :
H2(g) + 2ICl(g) $\to$ 2HCl(g) + I2(g)
Mechanism B :
H2(g) + ICl(g) $\to$ HCl(g) + HI(g) ; slow
HI(g) + ICl(g) $\to$ HCl(g) + I2(g) ; fast

Which of the above mechanism(s) can be consistent with the given information about the reaction?
A
A and B both
B
Neither A nor B
C
A only
D
B only

## Explanation

The slow step is the rate determining step and it involves 1 molecule of H2(g) and 1 molecule of ICl(g) . Hence the rate will be,

r = k[H2(g)] [ICl(g)]

$\therefore$ The reaction is 1st order with respect to H2(g) and ICl(g).
4

### AIPMT 2007

In a first-order reaction A $\to$ B, if k is rate constant and initial concentration of the reactant A is 0.5 M, then the half-life is
A
${{\log 2} \over k}$
B
${{\log 2} \over {k\sqrt {0.5} }}$
C
${{\ln 2} \over k}$
D
${{0.693} \over {0.5k}}$

## Explanation

For first order reaction

k = ${{2.303} \over t}\log {a \over {a - x}}$

at ${t_{1/2}}$, x = ${a \over 2}$

${t_{1/2}}$ = ${{2.303} \over k}\log {a \over {a - {a \over 2}}}$

= ${{\ln 2} \over k}$