A first-order reaction is 50% completed in 30 minutes at 27°C. Its rate constant is:

2.31 × 10^–2 min^–1

Given:
t½ = 30 minutes
To determine the rate constant (k) of a first-order reaction, we can use the equation:
t½ = \(\frac{0.693}{k}\)
Substituting the given value of t½ into the equation:
30 = \(\frac{0.693}{k}\)
To solve for k, we rearrange the equation:
k = \(\frac{0.693}{30}\)
Evaluating this expression:
k ≈ 0.0231 min\(^{-1}\)
Therefore, the rate constant of the first-order reaction is approximately 0.0231 min\(^{-1}\).
Among the given options:
(1) 2.31 × 10\(^{-2}\) min\(^{-1}\)
(2) 3.21 × 10\(^{-3}\) min\(^{-1}\)
(3) 4.75 × 10\(^{-2}\) min\(^{-4}\)
(4) 1.33 × 10\(^{-3}\) min\(^{-1}\)
Option (1) 2.31 × 10\(^{-2}\) min\(^{-1}\) matches the calculated rate constant. Thus, the correct answer is an option (1).