Question

The half-life of a first-order reaction is 1386 seconds. What is the specific rate constant of this reaction?

• A. \(0.5 \times 10^{-3} \, \text{s}^{-1}\)
• B. \(5.0 \times 10^{-3} \, \text{s}^{-1}\)
• C. \(0.5 \times 10^{-2} \, \text{s}^{-1}\)
• D. \(5.0 \times 10^{-2} \, \text{s}^{-1}\)

Hint:

In first-order reactions, half-life is independent of concentration. Always use \( t_{1/2} = \frac{0.693}{k} \) to find the rate constant when half-life is given.

Answer 1

The Correct Option is A

For a first-order reaction, the relationship between the half-life and the rate constant is: \[ t_{1/2} = \frac{0.693}{k} \] Given: \[ t_{1/2} = 1386 \, \text{seconds} \] Now solve for \( k \): \[ k = \frac{0.693}{1386} \approx 0.0005 \, \text{s}^{-1} \] Expressed in scientific notation: \[ k = 0.5 \times 10^{-3} \, \text{s}^{-1} \] This matches option (1).