Question

A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is ________ min. (Round off to the Nearest Integer). [Use : ln 2 = 0.69; ln 10 = 2.3]

Hint:

A useful shortcut for first-order reactions: $t_{99.9%} \approx 10 \times t_{1/2}$.

Answer 1

Correct Answer: 10

Step 1: For 1st order, $k = 0.69 / 1 = 0.69 \text{ min}^{-1}$.
Step 2: $t = \frac{1}{k} \ln \frac{100}{100-99.9} = \frac{1}{0.69} \ln(1000) = \frac{3 \ln 10}{0.69}$.
Step 3: $t = \frac{3 \times 2.3}{0.69} = \frac{6.9}{0.69} = 10 \text{ min}$.