Question

Thermal decomposition of a compound is of first order. If $50\%$ sample of the compound is decomposed in $120$ minute, how long will it take for $90\%$ of the compound to decompose?

Answer 1

Half life of reaction $=120$ min
We know that,
$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{120}=5.77\times {10}^{-3}{min}^{-1}$
Applying first order reaction equation,
$t=\frac{2.303}{k}{\log }_{10}\frac{a}{a-x}$
If $a=100$, $x=90$ or $(a-x)=10$,
So, $t=\frac{2.303}{5.77\times {10}^{-3}}{\log }_{10}10=\frac{2.303}{5.77\times {10}^{-3}}=399min$.