Question

Determine the specific rate constant of the reaction. If the half-life period of a first-order reaction is 1402 s, then the rate constant is:

• A. \( 4.94 \times 10^{-3} \, \text{s}^{-1} \)
• B. \( 0.49 \times 10^{-3} \, \text{s}^{-1} \)
• C. \( 0.49 \times 10^{-4} \, \text{s}^{-1} \)
• D. \( 4.94 \times 10^{-5} \, \text{s}^{-1} \)

Hint:

For a first-order reaction, the rate constant \( k \) can be calculated using the half-life formula \( t_{1/2} = \frac{0.693}{k} \).

Answer 1

The Correct Option is B

For a first-order reaction, the half-life \( t_{1/2} \) is related to the rate constant \( k \) by the formula: \[ t_{1/2} = \frac{0.693}{k} \] Given that the half-life \( t_{1/2} = 1402 \, \text{s} \), we can solve for \( k \): \[ k = \frac{0.693}{t_{1/2}} = \frac{0.693}{1402 \, \text{s}} = 0.49 \times 10^{-3} \, \text{s}^{-1} \] Thus, the rate constant \( k \) is \( 0.49 \times 10^{-3} \, \text{s}^{-1} \). Therefore, the correct answer is option (B).