If the half-life (t1/2) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is cl…

Question

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

1. A. 2 minutes
2. B. 4 minutes
3. C. 5 minutes
4. D. 10 minutes (Correct answer)

Correct Answer

Option D — 10 minutes

Detailed Solution & Explanation

The correct answer is 10 minutes.

Key Points

• First order: $t=\dfrac{2.303}{k}\log\dfrac{A_0}{A_t}$, and $k=\dfrac{0.693}{t_{1/2}}$.
• For 99.9% completion, $\dfrac{A_0}{A_t}=1000$, so $t=\dfrac{2.303}{k}\log1000=\dfrac{2.303\times3}{k}$.
• This equals $\approx 10\,t_{1/2}=10\times1=10$ minutes.