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# nth Order Reaction - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:35 AM | #JEE Main

## Quick Facts

• nth Order Kinetics is considered one of the most asked concept.

• 13 Questions around this concept.

## Solve by difficulty

A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will be

$\mathrm{a^2 x}$ Half-life  $\mathrm{ t_{3 / 2}}$   =  constant confirms that the reaction is of

For a reaction:
$\mathrm{3A\rightarrow products}$
It is found that the rate of reaction doubles when the concentration of A is increased by four times. What is the order of the reaction?

## Concepts Covered - 1

nth Order Kinetics

nth order kinetics

The rates of the reaction is proportional to nth power of reactant

$\mathrm{\frac{d[A]}{dt}=-k[A]^{n}}$

$\Rightarrow \mathrm{\frac{d[A]}{[A]^{n}}=-k\ dt}$

$\Rightarrow \mathrm{\int_{A_0}^{[A]_t} \frac{d[A]}{[A]^{n}}=-k\ \int_0^t dt}$

$\Rightarrow \mathrm{\left [\frac{[A]^{1-n}}{1-n} \right ]_{[A]_0}^{[A]_t}= -k[t]_0^t}$

$\Rightarrow \mathrm{\frac{1}{(n-1)}\left [ \frac{1}{[A]_t^{(n-1)}}-\frac{1}{[A]_0^{(n-1)}} \right ] = k(t)}$

Half life for any nth order reaction

$\mathrm{t_\frac{1}{2}=\frac{1}{(k)(n-1)([A]_0^{n-1})}[2^{n-1}-1]}$

Thus for any general nth order reaction it is evident that,

$\mathrm{t_\frac{1}{2}\propto [A]_0^{1-n}}$

It is to be noted that the above formula is applicable for any general nth order reaction except n=1.

Can you think of the reason why this is not applicable for a first order reaction?

## Study it with Videos

nth Order Kinetics

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