Question

The ratio of the time taken for 99.9$\%$ reaction and half life of the reaction is

• A. 100
• B. 49.95
• C. 10
• D. 1000

Answer 1

The correct option is C 10

For 99.9$\%$completion
$R=\left[R_0\right]-\frac{99.9}{100}\left[R_0\right]=0T\left(99.9\%\right)=\frac{2.303}{k}log\frac{\left[R_0\right]}{0.001\left[R_0\right]}=\frac{2.303}{k}log{10}^3=\frac{2.303\times k}{k}...\left(i\right)\Rightarrow t_{\frac{1}{2}}=\frac{2.303}{k}log\frac{\left[R_0\right]}{0.001\left[R_0\right]}=\frac{2.303log2}{k}=\frac{2.303\times 0.3010}{k}...\left(ii\right)$
Dividing Eq. (i) by Eq. (ii) we get
$\frac{t\left(99.9\%\right)}{t_{\frac{1}{2}}}=\frac{3}{0.3010}=10$