The half-life of a first order reaction is 25 minutes. Its rate constant is:

\(2.8 × 10^{-2} min^{-1}\)

The correct answer is option 4. \(2.8 × 10^{-2} min^{-1}\).

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

\[ t_{1/2} = \frac{0.693}{k} \]

Given that the half-life (\(t_{1/2}\)) of the reaction is 25 minutes, we can rearrange the equation to solve for the rate constant (\(k\)):

\[ k = \frac{0.693}{t_{1/2}} \]

Substituting the given value of \(t_{1/2}\) into the equation, we get:

\[ k = \frac{0.693}{25\, \text{min}} \]

\[ k \approx 0.02772 \, \text{min}^{-1} \]

Rounding to the appropriate number of significant figures, we get:

\[ k \approx 2.8 \times 10^{-2} \, \text{min}^{-1} \]

So, the correct answer is: (4) \(2.8 \times 10^{-2} \, \text{min}^{-1}\)