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. 398.8mm
• D. 400 min

Answer 1

Answer: (C)

For first order reaction, $t=\frac{2.303}{k}\log \frac{a}{a-x}$ For 1st case, $a=100,x=50andt=120min$ $k=\frac{2.303}{120}\log \frac{100}{100-50}$ $=\frac{2.303}{120}\log 2$ $=\frac{2.303}{120}\times 0.3010$ $k=0.005775{\min }^{-1}$ For the Und case $t=\frac{2.303}{0.005775}\log \frac{100}{100-90}$ $=\frac{2.303}{0.005775}\log 10$ $=398.78-398.8min$