Question

The rate constant of a first-order reaction is \( 2 \times 10^{-3} \, \text{s}^{-1} \). What is the half-life of the reaction?

• A. 0.347 s
• B. 1.4 s
• C. 0.693 s
• D. 2.0 s

Hint:

For first-order reactions, the half-life is independent of the initial concentration, unlike zero-order and second-order reactions.

Answer 1

The Correct Option is A

For a first-order reaction, the half-life is given by the equation: \[ t_{\frac{1}{2}} = \frac{0.693}{k} \] Where: - \( k = 2 \times 10^{-3} \, \text{s}^{-1} \) is the rate constant. Substitute the values: \[ t_{\frac{1}{2}} = \frac{0.693}{2 \times 10^{-3}} = 346.5 \, \text{s} \] Thus, the half-life of the reaction is approximately 0.347 s.