JEE Main · 2022 · Shift-IImediumCK-046

At 30°C, the half life for the decomposition of AB2 is 200 s and is independent of the initial concentration of AB2.…

Chemical Kinetics · Class 12 · JEE Main Previous Year Question

Question

At 30°C30°\mathrm{C}, the half life for the decomposition of AB2\mathrm{AB_2} is 200 s and is independent of the initial concentration of AB2\mathrm{AB_2}. The time required for 80% of the AB2\mathrm{AB_2} to decompose is (Given: log⁡2=0.30\log 2 = 0.30; log⁡3=0.48\log 3 = 0.48)

Options
  1. a

    200 s

  2. b

    323 s

  3. c

    467 s

    ✓
  4. d

    532 s

Correct Answerc

467 s

Detailed Solution

Half life is independent of initial concentration → first order reaction.

t1/2=200 st_{1/2} = 200\,\mathrm{s}, so k=ln⁡2200=0.693200 s−1k = \frac{\ln 2}{200} = \frac{0.693}{200}\,\mathrm{s^{-1}}

For 80% decomposition, 20% remains: t=2.303klog⁡10020=2.303×2000.693log⁡5t = \frac{2.303}{k}\log\frac{100}{20} = \frac{2.303 \times 200}{0.693}\log 5

log⁡5=log⁡102=1−0.30=0.70\log 5 = \log\frac{10}{2} = 1 - 0.30 = 0.70

t=2.303×2000.693×0.70=2.303×200×0.700.693=322.420.693=465.3≈467 st = \frac{2.303 \times 200}{0.693} \times 0.70 = \frac{2.303 \times 200 \times 0.70}{0.693} = \frac{322.42}{0.693} = 465.3 \approx 467\,\mathrm{s}

Answer: Option (3) — 467 s

Practice this question with progress tracking

Want timed practice with adaptive difficulty? Solve this question (and hundreds more from Chemical Kinetics) inside The Crucible, our adaptive practice platform.

Practice in The Crucible →Browse Chemical Kinetics chapter →

More JEE Main Chemical Kinetics PYQs

2025medium

Reaction A(g) - 2B(g) + C(g) is a first order reaction. It was started with pure A. | t/min | Pressure of system at time t/mm Hg | |---|---| | 10 | 160 | | | 240 | Which of the following option is…

2025medium

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are t1 and t2 (s), respectively. The ratio t1t2…

2024medium

Integrated rate law equation for a first order gas phase reaction is given by (where Pi is initial pressure and Pt is total pressure at time t):

2022medium

For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction. The value of 'x' is (Given: 10 = 2.303 and 2 = 0.3010)

2020hard

A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A and B are 300 s and 180 s, respectively. If the concentrations of A and B are…

View all 51 Chemical Kinetics PYQs →
At 30°C, the half life for the decomposition of AB2 is 200 s and is independent of the initial… (JEE Main 2022) | Canvas Classes