Question

In a first order reaction, time required for completion of $99.9\%$ is $x$ times of half-life $(f_{1/2})$ of the reaction, $x$ is

• A. $2$
• B. $4$
• C. $5$
• D. $10$

Answer 1

Answer: (D)

When reaction is completed $99.9$
${\left[R\right]}_n={\left[R\right]}_0-0.999{\left[R\right]}_0$
$k=\frac{2.303}{t}log\frac{{\left[R\right]}_0}{\left[R\right]}=\frac{2.303}{t}log\frac{{\left[R\right]}_0}{{\left[R\right]}_0-0.999{\left[R\right]}_0}$
$=\frac{2.303}{t}log10^3\Rightarrow t=6.909k$
For half-life of the reaction,$t_{12}=0.693/k$
$\frac{t}{t12}log10^3\Rightarrow t=6.909/k$