Question

A first-order reaction which is $30\%$ complete in $30$ minutes has a half-life period of:

• A. $24.2min$
• B. $58.2min$
• C. $102.2min$
• D. $120.2min$

Answer 1

The correct option is B $58.2min$

It is a 1st order reaction

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

but $k=\frac{0.693}{t_{\frac{1}{2}}}$

$\frac{0.693}{t_{1/2}}=\frac{2.303}{30}log\frac{100}{70}$

$t_{1/2}=58.2min$

Hence, the correct option is $B$