Question

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

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

Answer 1

Answer: (A)

$77.7\, min$.

Answer 2

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