A student has studied the decomposition of a gas $A{B}_{3}$ at $25^{\circ}C$. He obtained the following data $p(mmHg)$ $50$ $100$ $200$ $400$ Relative ${t}_{\frac{1}{2}}(s)$ $4$ $2$ $1$ $0.5$ The order of the reaction is

JEE Main 2023 — Chemistry Physical Chemistry

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A student has studied the decomposition of a gas $A{B}_{3}$ at $25^{\circ}C$ . He obtained the following data

$p(mmHg)$	$50$	$100$	$200$	$400$
Relative ${t}_{\frac{1}{2}}(s)$	$4$	$2$	$1$	$0.5$

The order of the reaction is

Official previous-year question

Held on 24 Jan 2023 · Verified 6 Jul 2026.

Options

A
$0.5$
B
$2$
C
$1$
D
$0$ (zero)

Did you get this right?

Solution

By observing the data given, by doubling the pressure, half-life is reduced to half. This result is following second order kinetics. Mathematically it can be proved as follows,

The half-life and initial pressure of ${n}^{\mathrm{th}}$ order reaction can be related as follows,

${t}_{\frac{1}{2}}\propto {({P}_{o})}^{1-n}$

$\frac{{({t}_{\frac{1}{2}})}_{1}}{{({t}_{\frac{1}{2}})}_{2}}=\frac{{({P}_{0})}_{1}^{1-n}}{{({P}_{0})}_{2}^{1-n}}$

$\Rightarrow (\frac{4}{2})={(\frac{50}{100})}^{1-n}$

$\Rightarrow 2={(\frac{1}{2})}^{1-n}$

$\Rightarrow 2={(2)}^{n-1}$

$\Rightarrow n-1=1$

$\Rightarrow n=2$

Hence, the order of the reaction is second order.

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Solution

By observing the data given, by doubling the pressure, half-life is reduced to half. This result is following second order kinetics. Mathematically it can be proved as follows,

The half-life and initial pressure of ${n}^{\mathrm{th}}$ order reaction can be related as follows,

${t}_{\frac{1}{2}}\propto {({P}_{o})}^{1-n}$

$\frac{{({t}_{\frac{1}{2}})}_{1}}{{({t}_{\frac{1}{2}})}_{2}}=\frac{{({P}_{0})}_{1}^{1-n}}{{({P}_{0})}_{2}^{1-n}}$

$\Rightarrow (\frac{4}{2})={(\frac{50}{100})}^{1-n}$

$\Rightarrow 2={(\frac{1}{2})}^{1-n}$

$\Rightarrow 2={(2)}^{n-1}$

$\Rightarrow n-1=1$

$\Rightarrow n=2$

Hence, the order of the reaction is second order.

JEE Main 2023 — Chemistry Physical Chemistry

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JEE Main 2023 — Chemistry Physical Chemistry

Options

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Solution

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JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

Keep practicing Physical Chemistry