1

AIPMT 2011 Mains

The unit of rate constant for a zero order reaction is
A
mol L$-$1 s$-$1
B
L mol$-$1 s$-$1
C
L2 mol$-$2 s$-$1
D
s$-$1

Explanation

Rate = K[A]0

Unit of k = mol L–1 sec–1
2

AIPMT 2011 Mains

The rate of the reaction :   2N2O5 $\to$ 4NO2 + O2
can be written in three ways.

${{ - d\left[ {{N_2}{O_5}} \right]} \over {dt}} = k\left[ {{N_2}{O_5}} \right]$

${{d\left[ {N{O_2}} \right]} \over {dt}} = k'\left[ {{N_2}{O_5}} \right];\,\,$ ${{d\left[ {{O_2}} \right]} \over {dt}} = k''\left[ {{N_2}{O_5}} \right]$

The relationship between k and k' and between k and k'' are
A
$k' = 2k ; k'' = k$
B
$k' = 2k ; k'' = k/2$
C
$k' = 2k ; k'' = 2k$
D
$k' = k ; k'' = k$

Explanation

Rate of disappearance of reactants = Rate of appearance of products

$- {1 \over 2}$${{ - d\left[ {{N_2}{O_5}} \right]} \over {dt}} = {1 \over 4}$${{d\left[ {N{O_2}} \right]} \over {dt}}$ = ${{d\left[ {{O_2}} \right]} \over {dt}}$

$\Rightarrow$ ${1 \over 2}$$k\left[ {{N_2}{O_5}} \right] = {1 \over 4}$$k'\left[ {{N_2}{O_5}} \right]$ = $k''\left[ {{N_2}{O_5}} \right]$

$\Rightarrow$ ${k \over 2} = {{k'} \over 4} = k''$

$\Rightarrow$ $k' = 2k ; k'' = k/2$
3

AIPMT 2011 Prelims

Which one of the following statements for the order of a reaction is incorrect?
A
Order can be determined only experimentally.
B
Order is not influenced by stoichiometric coefficient of the reactants.
C
Order of a reaction is sum of power to the concentration terms of reactants to express the rate of reaction.
D
Order of reaction is always whole number.

Explanation

Order of a reaction is not always whole number. It can be zero, or fractional also.
4

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