Question
Chemistry Question on Chemical Kinetics
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
398.8 min
Explanation
Solution
For first order reaction, \hspace25mm t = \frac{2.303}{k} \, log \, \frac{a}{a-x} For Ist case, \hspace10mm a = 100, x = 50 and t = 120 min \hspace20mm k = \frac{2.303}{120} \, log \, \frac{100}{100-50} \hspace20mm = \frac{2.303}{120} \, log \, 2 \hspace20mm = \frac{2.303}{120} \times 0.3010 \hspace20mm k = 0.00578 \, min^{-1} For the Ilnd case \hspace20mm t = \frac{2.303}{0.00578} \, log \, \frac{100}{100-90} \hspace20mm = \frac{2.303}{0.00578} \, log \, 10 \hspace20mm = 398.4 \approx 398.8 \, min