1

### AIPMT 2006

Consider the reaction :  N2(g) + 3H2(g) $\to$ 2NH3(g)

The equality relationship between ${{d\left[ {N{H_3}} \right]} \over {dt}}$ and $- {{d\left[ {{H_2}} \right]} \over {dt}}$ is
A
${{d\left[ {N{H_3}} \right]} \over {dt}} = - {{d\left[ {{H_2}} \right]} \over {dt}}$
B
${{d\left[ {N{H_3}} \right]} \over {dt}} = - {1 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}}$
C
$+ {{d\left[ {N{H_3}} \right]} \over {dt}} = - {2 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}}$
D
$+ {{d\left[ {N{H_3}} \right]} \over {dt}} = - {3 \over 2}{{d\left[ {{H_2}} \right]} \over {dt}}$

## Explanation

N2(g) + 3H2(g) $\to$ 2NH3(g)

Rate = ${{ - d\left[ {{N_2}} \right]} \over {dt}} = - {1 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}} = {1 \over 2}{{d\left[ {N{H_3}} \right]} \over {dt}}$

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

### AIPMT 2005

For a first order reaction A $\to$ B the reaction rate a reactant concentration of 0.01 M is found to be 2.0 $\times$ 10$-$5 mol L$-$1 s$-$1. The half-life period of the reaction is
A
30 s
B
220 s
C
300 s
D
347 s

## Explanation

Given [A] = 0.01 M

Rate = 2.0 × 10–5 mol L–1 S–1

For a first order reaction

Rate = k[A]

k = ${{2 \times {{10}^{ - 5}}} \over {0.01}} = 2 \times {10^{ - 3}}$

$\Rightarrow$ ${t_{1/2}} = {{0.693} \over {2 \times {{10}^{ - 3}}}} = 347\,\sec$
3

### AIPMT 2005

The rate of reaction between two reactions A and B decreases by a factor of 4 if the concentration of reactant B is doubled. The order of this reaction with respect to reactant B is
A
2
B
$-$2
C
1
D
$-$1

## Explanation

A + B $\to$ Product

Rate $\propto$ [A]x [B]y .......(1)

The rate of the reaction decreases by a factor of 4 if the concentration of reactant B is doubled.

${r \over 4}$ $\propto$ [A]x [2B]y ......(2)

From equation (1) and (2), we get

${\left( {{1 \over 2}} \right)^y} = 4$

$\Rightarrow$ y = -2

$\therefore$ Order of this reaction with respect to reactant B is -2.
4

### AIPMT 2004

The rate of a first order reaction is 1.5 $\times$ 10$-$2 mol L$-$1 min$-$1 at 0.5 M concentration of the reactant. The half-life of the reaction is
A
0.383 min
B
23.1 min
C
8.73 min
D
7.53 min

## Explanation

For a first order reaction, A $\to$ products

Rate(r) = k[A]

$\Rightarrow$ k = ${r \over {\left[ A \right]}}$

$\Rightarrow$ k = ${{1.5 \times {{10}^{ - 2}}} \over {0.5}} = 3 \times {10^{ - 2}}$

So, ${t_{1/2}} = {{0.693} \over {3 \times {{10}^{ - 2}}}}$ = 23.1 min