A student has studied the decomposition of a gas $\mathrm{AB}_{3}$ at $25^{\circ} \mathrm{C}$. He obtained the following data. | $\mathrm{p}(\mathrm{mm} \mathrm{Hg})$ | 50 | 100 | 200 | 400 | | Relative $t_{1/2}(\mathrm{~s})$ | 4 | 2 | 1 | 0.5 | The order of the reaction is

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Chemical Kinetics

A student has studied the decomposition of a gas

AB_{3}

2 5^{\circ} C

. He obtained the following data.

$p (mm Hg)$	50	100	200	400
Relative $t_{1/2} (s)$	4	2	1	0.5

The order of the reaction is

Answer: (B)

For a reaction of order

n

the half-life depends on initial pressure as

t_{1/2} \propto P_{0}^{1 - n}

. The data show each doubling of pressure halving the half-life: from

50

100

mm Hg the half-life falls from

4

2

s. Hence

t_{1/2} \propto P_{0}^{- 1}

, so

1 - n = - 1

. Solving gives

n = 2

, so the decomposition of

A B_{3}

is second order.

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Single correct option