Question

A first order reaction takes $40$ min for $30\%$ decompsoition. The value of $t_{1/2}$will be:

• A. $97.7$min
• B. $77.7$min
• C. $80.5$min
• D. $70.7$min

Answer 1

Answer: (B)

$77.7$min

$k=\frac{2.303}{t}log\frac{a}{a-x}$

$=\frac{2.303}{40}log\frac{a}{a-0.30a}$

$=\frac{2.303}{40}log\frac{10}{7}=8.918\times {10}^{-3}mi{n}^{-1}$

$\Rightarrow t_{1/2}=\frac{0.693}{k}$

or $=\frac{0.693}{8.918\times {10}^{-3}}$

$=77.7$min