Question

The half-life period of a first order chemical reaction is 6.93 minutes.
The time required for 99% completion of reaction will be (log 2 = 0.301)

• A. 230.3 min
• B. 23.03 min
• C. 46.06 min
• D. 460.6 min

Answer 1

The correct option is C

46.06 min

$k=\frac{0.693}{t_{\frac{1}{2}}}$ (first order)

$=\frac{0.693}{6.93}=0.1mi{n}^{-1}$

Now, for first order reaction,
$\left[A\right]=[A{]}_0{e}^{-kt}\to kt$

$=2.303log\frac{[A{]}_o}{\left[A\right]}$

Now,$kt=2.303log\frac{[A{]}_o}{\frac{\left[A\right].}{100}}$

$\Rightarrow kt=2.303log\left[100\right]$

$\Rightarrow kt=2.303\times 2\Rightarrow t=\frac{4.606}{k}$

$\Rightarrow t=\frac{4.606}{0.1}=46.06min$