Question

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

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

Answer 1

The correct option is C $398.8min$

The molecule decomposes $50$% in $120min$. Thus, the half life period $t_{1/2}=120min$

The rate constant

$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{\text{120 min}}=\text{0.005775 min}$
Time it will take to decompose $90$%

$t=\frac{2.303}{k}log\frac{a}{a-x}$

$t=\frac{2.303}{\text{0.005775 min}}log\frac{100}{100-90}$

$t=\text{398.8 min}$