Q21 / 90 · JEE Main 2021 (18 Mar Shift 2) · Chemistry

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 : $\ln 2 = 0.69, \ln 10 = 2.3$ ]

Correct answer: 10

Solution

$\frac{t_{99.9 %}}{t_{50 %}} = \frac{\frac{1}{K} \ln \frac{100}{0.1}}{\frac{1}{K} \ln 2}$

$= \frac{\ln 1000}{\ln 2} \times t_{50 %}$

$= \frac{3 \ln 10}{\ln 2} \times 1$

$= \frac{3 \times 2.3}{0.69} = 10$

Hence, the correct answer is 10.