Question

If $99\%$ of a first order reaction was completed in $32$ minutes then, when $99.9\%$ of the reaction will complete:

• A. $50\text{min}$
• B. $46\text{min}$
• C. $48\text{min}$
• D. $49\text{min}$

Answer 1

The correct option is C $48\text{min}$

For a first order reaction,
$k=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$
Where, $a=\text{Initial concentration of reactant}$
$a-x=\text{concentration left after time t}$
According to the question,
$k=\frac{2.303}{32}log\left(\frac{100}{1}\right)$
$\Rightarrow k=\frac{2.303}{16}{\text{min}}^{-1}$
Therefore, when $99.9\%$ reaction will complete,
$t=\frac{2.303\times 16}{2.303}log\left(\frac{100}{0.1}\right)=48\text{min}$