1. Tardigrade
  2. Question
  3. Chemistry
  4. A first order reaction takes 40 min for 30 % decomposition. What will be t1/2?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A first order reaction takes $40$ min for $30\%$ decomposition. What will be $t_{1/2}$?

Chemical Kinetics

Solution:

$30\%$ decomposition means $X = 30\%$ of $R_{0} $ or $R=R_{0}-0.3R_{0}$ $=0.7R_{0}$
For first order, $k=\frac{2.303}{t} log$ $\frac{\left[R_{0}\right]}{\left[R\right]}$
$=\frac{2.303}{40} log$ $\frac{10}{7} min^{-1}$ $=8.918\times10^{-3}$ $min.^{-1}$
$t_{1/ 2}$ $=\frac{0.693}{k}$ $=\frac{0.693}{8.918\times10^{-3} min.^{-1}}$ $=77.7 \, min.$