Question

In a first order reaction, if the time taken for completion of $50$ percent of the reaction is $t$ seconds, then the time required for completion of $99.9$ percent of the reaction is

• A. $10t$
• B. $5t$
• C. $100t$
• D. $2t$

Answer 1

The correct option is A $10t$

We know that for a first order reaction, the time taken for completion of $50\%$ is $t=\frac{0.693}{k}\Rightarrow k=\frac{0.693}{t}$
When $99.9\%$ is completed, then $0.1\%$ or $\frac{1}{1000}$ of the reactant will be left.
The rate equation of first order reaction is
$k{t}^{\prime }=2.303\log \frac{A_0}{A_t}\Rightarrow \frac{0.693}{t}\times t^{\prime }=2.303\log \frac{a}{a/1000}\Rightarrow \frac{0.693}{t}\times t^{\prime }=2.303\times 3\Rightarrow t^{\prime }=10t$