1

AIPMT 2011 Mains

The half-life of a substance in a certain enzyme-catalysed reaction is 138 s. The time required for the concentration of the substance to fall from 1.28 mg L$-$1 to 0.04 mg L$-$1 is
A
414 s
B
552 s
C
690 s
D
276 s

Explanation

We know, $N = {N_0}{\left( {{1 \over 2}} \right)^n}$

Give N0(original amount) = 1.28 mg L–1

N (amount of substance left after time T) = 0.04 mg L–1

$\therefore$ ${{0.04} \over {1.28}} = {\left( {{1 \over 2}} \right)^n}$

$\Rightarrow$ ${1 \over {32}} = {\left( {{1 \over 2}} \right)^n}$

$\Rightarrow$ n = 5

$\therefore$ Time required = 5 × t1/2 = 5 × 138 = 690 s
2

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
3

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]$ = $k''\left[ {{N_2}{O_5}} \right]$

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

$\Rightarrow$ $k' = 2k ; k'' = k/2$
4

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.