A first order reaction is found to have rate constant, $k = 3.0 × 10^{-1}\, s^{-1}$. The half life of the reaction will be:

2.31 s

The correct answer is Option (3) → 2.31 s

For a first-order reaction, the relationship between the half-life ($t_{1/2}$) and the rate constant ($k$) is given by the formula:

$t_{1/2} = \frac{\ln(2)}{k} \approx \frac{0.693}{k}$

Given:

• Rate constant ($k$) = $3.0 \times 10^{-1} \text{ s}^{-1} = 0.3 \text{ s}^{-1}$

Calculation:

$t_{1/2} = \frac{0.693}{0.3}$

$t_{1/2} = 2.31 \text{ s}$

Conclusion:

The half-life of the reaction is 2.31 s.