1

### AIPMT 2010 Prelims

During the kinetic study of the reaction, 2A + B $\to$ C + D, following results were obtained
Run [A]/mol L$-$1 [B]/mol L$-$1 Initial rate of formation
of D/mol L$-$1 min$-$1
I. 0.1 0.1 6.0$\times$10$-$3
II. 0.3 0.2 7.2$\times$10$-$2
III. 0.3 0.4 2.88$\times$10$-$1
IV. 0.4 0.1 2.40$\times$10$-$2

Based on the above data which one of the following is correct?
A
Rate = k[A]2[B]
B
Rate = k[A][B]
C
Rate = k[A]2[B]2
D
Rate = k[A][B]2

## Explanation

Rate = k[A]x [B]y

For the given situations

(I) rate = k(0.1)x (0.1)y = 6.0$\times$10$-$3

(II) rate = k(0.2)x (0.3)y = 7.2$\times$10$-$2

(III) rate = k(0.3)x (0.4)y = 2.88$\times$10$-$1

(IV) rate = k(0.4)x (0.1)y = 2.40$\times$10$-$2

Dividing eq. (I) by eq. (IV) we get

${\left( {{{0.1} \over {0.4}}} \right)^x}{\left( {{{0.1} \over {0.1}}} \right)^y} = {{6.0 \times {{10}^{ - 3}}} \over {2.4 \times {{10}^{ - 2}}}}$

$\Rightarrow$ ${\left( {{1 \over 4}} \right)^x} = {\left( {{1 \over 4}} \right)^1}$

$\Rightarrow$ x = 1

On dividing eq. (II) by eq. (III) we get

${\left( {{{0.3} \over {0.3}}} \right)^x}{\left( {{{0.2} \over {0.4}}} \right)^y} = {{7.2 \times {{10}^{ - 2}}} \over {2.88 \times {{10}^{ - 1}}}}$

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

$\Rightarrow$ y = 2

$\therefore$ Rate = k[A][B]2
2

### AIPMT 2010 Mains

The rate of the reaction, 2NO + Cl2 $\to$ 2NOCl is given by the rate equation rate = k[NO]2[Cl2]. The value of the rate constant can be increased by
A
increasing the temperature
B
increasing the concentration of NO
C
increasing the concentration of the Cl2
D
doing all of these.

## Explanation

The value of rate constant can be increased by increasing the temperature and is independent of the initial concerntration of the reactants.
3

### AIPMT 2010 Prelims

For the reaction N2O5(g) $\to$  2NO2(g) + 1/2O2(g)
the value of rate of disappearance of N2O5 is given as 6.25 $\times$ 10$-$3 mol L$-$1 s$-$1. The rate of formation of NO2 and O2 is given respectively as
A
6.25 $\times$ 10$-$3 mol L$-$1 s$-$1 and
6.25 $\times$ 10$-$3 mol L$-$1 s$-$1
B
1.25 $\times$ 10$-$2 mol L$-$1 s$-$1 and
3.125 $\times$ 10$-$3 mol L$-$1 s$-$1
C
6.25 $\times$ 10$-$3 mol L$-$1 s$-$1 and
3.125 $\times$ 10$-$3 mol L$-$1 s$-$1
D
1.25 $\times$ 10$-$2 mol L$-$1 s$-$1 and
6.25 $\times$ 10$-$3 mol L$-$1 s$-$1

## Explanation

N2O5(g) $\to$  2NO2(g) + 1/2O2(g)

$- {{d\left[ {{N_2}{O_5}} \right]} \over {dt}} = {1 \over 2}{{d\left[ {N{O_2}} \right]} \over {dt}} = 2{{d\left[ {{O_2}} \right]} \over {dt}}$

$\Rightarrow$ ${{d\left[ {N{O_2}} \right]} \over {dt}} = - 2{{d\left[ {{N_2}{O_5}} \right]} \over {dt}}$

= 2 $\times$ 6.25 $\times$ 10 mol l-1 sec-1

= 1.25 $\times$ 10$-$2 mol L$-$1 s$-$1

${{d\left[ {{O_2}} \right]} \over {dt}} = - {1 \over 2}{{d\left[ {{N_2}{O_5}} \right]} \over {dt}}$

= ${{6.25 \times {{10}^{ - 3}}} \over 2}$

= 3.125 $\times$ 10$-$3 mol L$-$1 s$-$1
4

### AIPMT 2009

Half-life period of a first order reaction is 1386 seconds. The specific rate constant of the reaction is
A
0.5 $\times$ 10$-$2 s$-$1
B
0.5 $\times$ 10$-$3 s$-$1
C
5.0 $\times$ 10$-$2 s$-$1
D
5.0 $\times$ 10$-$3 s$-$1.

## Explanation

Specific rate constant

k = ${{0.693} \over {{t_{1/2}}}}$

= ${{0.693} \over {1386}}$

= 0.5 $\times$ 10-3 sec-1