QJEEM23Ch0f3a: JEE Main 2023 Chemistry - Class 12 JEEM23Ch0f3a Solution: A student has studied the decomposition of a gas AB 3 at 25 ∘…

Question

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A student has studied the decomposition of a gas AB $_{3}$ at 25 $^{\circ}$ 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

Accepted Answer

\begin{aligned} t_{1 / 2} \propto {(P_{o})}^{1 - n} \\ \frac{{(t_{1 / 2})}_{1}}{{(t_{1 / 2})}_{2}} = \frac{{(P_{o})}_{1}^{1 - n}}{{(P_{o_{2}})}_{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 \end{aligned}

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