Question

The half-life of a first-order reaction with a rate constant (\( k \)) of 3 min\(^{-1}\) is:

• A. \( 0.693 \) min
• B. \( 2.31 \) min
• C. \( 6.93 \) min
• D. \( 0.231 \) min

Hint:

For first-order reactions, half-life is independent of initial concentration and is calculated as \( t_{1/2} = \frac{0.693}{k} \).

Answer 1

The Correct Option is D

Step 1: The half-life (\( t_{1/2} \)) of a first-order reaction is given by the formula: \[ t_{1/2} = \frac{0.693}{k} \] Step 2: Substituting \( k = 3 \) min\(^{-1}\): \[ t_{1/2} = \frac{0.693}{3} = 0.231 \text{ min} \]