AIPMT 2010 Prelims

For the reaction N₂O_5(g) $$ \to $$ 2NO_2(g) + 1/2O_2(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

6.25 $$ \times $$ 10^$$-$$3 mol L^$$-$$1 s^$$-$$1 and
6.25 $$ \times $$ 10^$$-$$3 mol L^$$-$$1 s^$$-$$1

1.25 $$ \times $$ 10^$$-$$2 mol L^$$-$$1 s^$$-$$1 and
3.125 $$ \times $$ 10^$$-$$3 mol L^$$-$$1 s^$$-$$1

6.25 $$ \times $$ 10^$$-$$3 mol L^$$-$$1 s^$$-$$1 and
3.125 $$ \times $$ 10^$$-$$3 mol L^$$-$$1 s^$$-$$1

1.25 $$ \times $$ 10^$$-$$2 mol L^$$-$$1 s^$$-$$1 and
6.25 $$ \times $$ 10^$$-$$3 mol L^$$-$$1 s^$$-$$1

Explanation

N₂O_5(g) $$ \to $$ 2NO_2(g) + 1/2O_2(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

MCQ (Single Correct Answer)

AIPMT 2009

Half-life period of a first order reaction is 1386 seconds. The specific rate constant of the reaction is

0.5 $$ \times $$ 10^$$-$$2 s^$$-$$1

0.5 $$ \times $$ 10^$$-$$3 s^$$-$$1

5.0 $$ \times $$ 10^$$-$$2 s^$$-$$1

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

MCQ (Single Correct Answer)

AIPMT 2009

For the reaction A + B $$ \to $$ products, it is observed that

(i) on doubling the initial concentration of A only, the rate of reaction is also doubled and
(ii) on doubling the initial concentration of both A and B, there is a change by a factor of 8 in the rate of the reaction.

The rate of this reaction is given by

rate = k[A]² [B]²

rate = k[A] [B]²

rate = k[A] [B]

rate = k[A]² [B]

Explanation

R = k[A]^m[B]ⁿ ... (i)

2R = k[2A]^m[B]ⁿ ... (ii)

8R = k[2A]^m[2B]ⁿ ... (iii)

from (i), (ii) and (iii), m = 1, n = 2

So, rate = k[A][B]²

MCQ (Single Correct Answer)

AIPMT 2009

In the reaction,
BrO$$_{3(aq)}^ - $$ + 5Br$$_{(aq)}^ - $$ + 6H⁺ $$ \to $$ 3Br_2(l) + 3H₂O_(l).
The rate of appearance of bromine (Br₂) is related to rate of disappearance of bromide ions as

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

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

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

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

Explanation

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

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