Question

Which of the following represents the expression for the 3/4th life of a 1st-order reaction?

• A. \( t_{1/4} = \frac{2.303}{k} \log\left( \frac{1}{3} \right) \)
• B. \( t_{1/4} = \frac{2.303}{k} \log\left( \frac{4}{3} \right) \)
• C. \( t_{1/4} = \frac{0.693}{k} \)
• D. \( t_{1/4} = \frac{2.303}{k} \log\left( \frac{2}{3} \right) \)

Hint:

For first-order reactions, the half-life and quarter-life are related by logarithmic expressions that depend on the rate constant.

Answer 1

The Correct Option is B

Step 1: For a first-order reaction, the half-life \( t_{1/2} \) is given by \( t_{1/2} = \frac{0.693}{k} \). To find the expression for \( t_{1/4} \), we use the following relationship for first-order reactions: \[ t_{1/4} = \frac{2.303}{k} \log\left( \frac{4}{3} \right) \]
Conclusion: The correct expression for the 3/4th life of a first-order reaction is given by option (B).