JEE Main · 2023 · Shift-IImediumCK-075

A student has studied the decomposition of a gas AB3 at 25°C. He obtained the following data: | p\,(mm\,Hg) | Relative…

Chemical Kinetics · Class 12 · JEE Main Previous Year Question

Question

A student has studied the decomposition of a gas AB3\mathrm{AB_3} at 25°C25°\mathrm{C}. He obtained the following data:

| p(mmHg)p\,(\mathrm{mm\,Hg}) | Relative t1/2(s)t_{1/2}\,(\mathrm{s}) | |:---:|:---:| | 50 | 4 | | 100 | 2 | | 200 | 1 | | 400 | 0.5 |

The order of the reaction is

Options
  1. a

    0.5

  2. b

    2

  3. c

    1

  4. d

    0 (zero)

Correct Answerb

2

Detailed Solution

For an nnth order reaction: t1/2P01nt_{1/2} \propto P_0^{1-n}

From the data: when pressure doubles (50→100), t1/2t_{1/2} halves (4→2). So t1/2P01t_{1/2} \propto P_0^{-1}, meaning 1n=1n=21-n = -1 \Rightarrow n = 2.

Verification: 100→200 (×2): t1/2t_{1/2} goes 2→1 (÷2) ✓; 200→400 (×2): t1/2t_{1/2} goes 1→0.5 (÷2) ✓

Answer: Option (2) — 2 (second order)

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