Question

Find the half-life of a first order reaction if $ K = 2.31 \times 10^5 \, \text{s}^{-1} $.

• A. \( 2.99 \times 10^{-6} \, \text{s} \)
• B. \( 1.17 \times 10^{-5} \, \text{s} \)
• C. \( 3.00 \times 10^{-5} \, \text{s} \)
• D. \( 1.00 \times 10^{-6} \, \text{s} \)

Hint:

For first-order reactions, remember that the half-life is independent of the initial concentration and only depends on the rate constant \( K \).

Answer 1

The Correct Option is C

For a first-order reaction, the half-life \( t_{1/2} \) is given by the equation: \[ t_{1/2} = \frac{\ln 2}{K} \] where \( K \) is the rate constant. Given that: \[ K = 2.31 \times 10^5 \, \text{s}^{-1} \] Substitute this value into the equation for \( t_{1/2} \): \[ t_{1/2} = \frac{\ln 2}{2.31 \times 10^5} = \frac{0.693}{2.31 \times 10^5} \approx 3.00 \times 10^{-5} \, \text{s} \]
Thus, the half-life of the reaction is \( 3.00 \times 10^{-5 \, \text{s}} \).