Question

The thermal decomposition of a molecule shows first order kinetics. The molecule decomposes 50% in 120 min. How much time it will take to decompose 90%?

• A. 300 min
• B. 360 min
• C. 398.8 min
• D. 400 min

Answer 1

Answer: (C)

For first order reaction,
$ t = \frac{2.303}{k} \, log \, \frac{a}{a-x}$
For Ist case,
$$ a = 100, x = 50 and t = 120 min
$ k = \frac{2.303}{120} \, log \, \frac{100}{100-50}$
$ = \frac{2.303}{120} \, log \, 2$
$ = \frac{2.303}{120} \times 0.3010$
$ k = 0.00578 \, min^{-1}$
For the Ilnd case
$ t = \frac{2.303}{0.00578} \, log \, \frac{100}{100-90}$
$ = \frac{2.303}{0.00578} \, log \, 10$
$ = 398.4 \approx 398.8 \, min$