The half-life of a substance in a first-order reaction is 15 minutes. The rate constant is:

4.62 × 10^–2 min^–1

The correct answer is option 2. \(4.62 \times 10^{-2}\, \ min^{-1}\)

In a first-order reaction, the half-life (\(t_{1/2}\)) is related to the rate constant (\(k\)) by the equation:

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

Given that the half-life of the substance is 15 minutes, we can use this equation to find the rate constant.

\(15 \, \text{minutes} = \frac{0.693}{k} \)

Rearranging the equation to solve for \(k\):

\(k = \frac{0.693}{15 \, \text{minutes}} \)

\(k \approx 0.0462 \, \text{min}^{-1} \)

Among the given options, the closest rate constant value is (2) \(4.62 \times 10^{-2} \, \text{min}^{-1}\).