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1

### AIPMT 2009

In the reaction,
BrO$$_{3(aq)}^ -$$ + 5Br$$_{(aq)}^ -$$ + 6H+ $$\to$$ 3Br2(l) + 3H2O(l).
The rate of appearance of bromine (Br2) is related to rate of disappearance of bromide ions as
A
$${{d\left[ {B{r_2}} \right]} \over {dt}} = - {5 \over 3}{{d\left[ {B{r^ - }} \right]} \over {dt}}$$
B
$${{d\left[ {B{r_2}} \right]} \over {dt}} = {5 \over 3}{{d\left[ {B{r^ - }} \right]} \over {dt}}$$
C
$${{d\left[ {B{r_2}} \right]} \over {dt}} = {3 \over 5}{{d\left[ {B{r^ - }} \right]} \over {dt}}$$
D
$${{d\left[ {B{r_2}} \right]} \over {dt}} = - {3 \over 5}{{d\left[ {B{r^ - }} \right]} \over {dt}}$$

## Explanation

Rate = $${1 \over 3}{{d\left[ {B{r_2}} \right]} \over {dt}} = - {1 \over 5}{{d\left[ {B{r^ - }} \right]} \over {dt}}$$

$$\therefore$$ $${{d\left[ {B{r_2}} \right]} \over {dt}} = - {3 \over 5}{{d\left[ {B{r^ - }} \right]} \over {dt}}$$
2

### AIPMT 2009

For the reaction, N2 + 3H2 $$\to$$ 2NH3, if
$${{d\left[ {N{H_3}} \right]} \over {dt}}$$ = 2 $$\times$$ 10$$-$$4 mol L$$-$$1 s$$-$$1,
the value of $${{ - d\left[ {{H_2}} \right]} \over {dt}}$$ would be
A
4 $$\times$$ 10$$-$$4 mol L$$-$$1 s$$-$$1
B
6 $$\times$$ 10$$-$$4 mol L$$-$$1 s$$-$$1
C
1 $$\times$$ 10$$-$$4 mol L$$-$$1 s$$-$$1
D
3 $$\times$$ 10$$-$$4 mol L$$-$$1 s$$-$$1

## Explanation

N2 + 3H2 $$\to$$ 2NH3

$$- {1 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}} = {1 \over 2}{{d\left[ {N{H_3}} \right]} \over {dt}}$$

$$\Rightarrow$$ $$- {{d\left[ {{H_2}} \right]} \over {dt}} = {3 \over 2}{{d\left[ {N{H_3}} \right]} \over {dt}}$$

= $${3 \over 2} \times 2 \times {10^{ - 4}}$$

= $$3 \times {10^{ - 4}}$$ mol L$$-$$1 s$$-$$1
3

### 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+].
4

### 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 = $${{1000} \over {2.303}}K$$

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