Question

For a first order reaction with rate constant of 230 s\(^{-1}\), the half-life is:

• A. \( 3.45 \times 10^{-2} \, \text{s} \)
• B. \( 3.01 \times 10^{-2} \, \text{s} \)
• C. \( 3.45 \times 10^{-3} \, \text{s} \)
• D. \( 3.01 \times 10^{-3} \, \text{s} \)

Hint:

For first-order reactions, remember the half-life formula \( t_{1/2} = \frac{0.693}{k} \). This is crucial when calculating half-life from the rate constant.

Answer 1

The Correct Option is D

The half-life of a first-order reaction is given by the formula: \[ t_{1/2} = \frac{0.693}{k} \] where \( t_{1/2} \) is the half-life and \( k \) is the rate constant. Given \( k = 230 \, \text{s}^{-1} \), substituting this into the equation: \[ t_{1/2} = \frac{0.693}{230} = 3.01 \times 10^{-3} \, \text{s} \] Thus, the half-life is \( 3.01 \times 10^{-3} \, \text{s} \).