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
$k=\frac{2.303}{120}log\frac{100}{100-50}$
$=\frac{2.303}{120}log2$
$=\frac{2.303}{120}\times 0.3010$
$k=0.00578mi{n}^{-1}$
For the Ilnd case
$t=\frac{2.303}{0.00578}log\frac{100}{100-90}$
$=\frac{2.303}{0.00578}log10$
$=398.4\approx 398.8min$