Question

The rate constant for a first-order reaction whose half-life is 480 seconds is:

• A. \( 2.88 \times 10^{-3} \, \text{s}^{-1} \)
• B. \( 2.72 \times 10^{-3} \, \text{s}^{-1} \)
• C. \( 1.44 \times 10^{-3} \, \text{s}^{-1} \)
• D. \( 1.44 \, \text{s}^{-1} \)

Hint:

For first-order reactions, the rate constant is inversely related to the half-life. Use the formula \( k = \frac{0.693}{t_{1/2}} \) to quickly calculate the rate constant.

Answer 1

The Correct Option is C

For a first-order reaction, the rate constant \( k \) is inversely proportional to the half-life \( t_{1/2} \), as defined by the equation:\[k = \frac{0.693}{t_{1/2}}.\]Given \( t_{1/2} = 480 \, \text{s} \), the rate constant is calculated as:\[k = \frac{0.693}{480}.\]The simplified result is:\[k = 1.44 \times 10^{-3} \, \text{s}^{-1}.\]This calculated rate constant is specific to first-order reactions and is directly determined by the half-life. Final Answer:\[\boxed{1.44 \times 10^{-3} \, \text{s}^{-1}}.\]