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Chemical Kinetics question

2025 · Q118
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Chemical Kinetics question

2025 · Q118

NEETChemistryChemical KineticsMCQ+4 / −1

If the half-life ( t1/2t_{1 / 2}t1/2​ ) for a first order reaction is 1 minute, then the time required for 99.9%99.9 \%99.9% completion of the reaction is closest to :

  1. A
    5 minutes
  2. B
    10 minutes
  3. C
    2 minutes
  4. D
    4 minutes
View written solutionFree

Correct answer: B

For a first‐order reaction the half‐life and rate constant are related by

$$k=\frac{\ln2}{t_{1/2}}=\frac{0.693}{1\;\text{min}}=0.693\;\text{min}^{-1}.$$

We want 99.9% completion, so the fraction remaining is 0.001. Using

$$\frac{[A]_t}{[A]_0}=e^{-kt}=0.001$$

take natural logs:

$$-kt=\ln(0.001)=-6.9078$$

hence

$$t=\frac{6.9078}{0.693}\approx9.97\;\text{min}\approx10\;\text{min}.$$

Answer: Option B, 10 minutes.

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