Question

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

• A. $77.7min$.
• B. $52.5min$.
• C. $46.2min$.
• D. $22.7min$.

Answer 1

Answer: (A)

$30\%$ decomposition means $X=30\%$ of $R_0$ or $R=R_0-0.3R_0$ $=0.7R_0$
For first order, $k=\frac{2.303}{t}log$ $\frac{\left[R_0\right]}{\left[R\right]}$
$=\frac{2.303}{40}log$ $\frac{10}{7}mi{n}^{-1}$ $=8.918\times 10^{-3}$ $min{.}^{-1}$
$t_{1/2}$ $=\frac{0.693}{k}$ $=\frac{0.693}{8.918\times 10^{-3}min{.}^{-1}}$ $=77.7min.$