Question

The rate constant for a first-order reaction is \( 0.0693 \, \text{min}^{-1} \). What is the half-life of the reaction?

• A. \( 10 \, \text{min} \)
• B. \( 15 \, \text{min} \)
• C. \( 5 \, \text{min} \)
• D. \( 20 \, \text{min}

Hint:

\textbf{Key Fact:} For first-order reactions, the half-life is independent of the initial concentration and depends only on the rate constant.

Answer 1

The Correct Option is A

• Formula for Half-Life of First-Order Reaction: For a first-order reaction, the half-life t_1/2 is given by t_1/2 = ln 2 / k, where k is the rate constant and ln 2 ≈ 0.693.
• Given Value: k = 0.0693 min^-1.
• Calculate Half-Life:
  t_1/2 = 0.693 / 0.0693 ≈ 10 min.
• Option Analysis:
  • (1) 10 min: Matches the calculated value. This is correct.
  • (2) 15 min: Too high.
  • (3) 5 min: Too low.
  • (4) 20 min: Too high.
• Conclusion: The half-life is (1) 10 min.