Question

What is rate constant of a first order reaction having half life \(138.6 \text{ minute}\)?

• A. \(5.0 \text{ minute}^{-1}\)
• B. \(0.54 \text{ minute}^{-1}\)
• C. \(0.25 \text{ minute}^{-1}\)
• D. \(0.005 \text{ minute}^{-1}\)

Hint:

First order: \(t_{1/2} = 0.693/k\) → directly use for quick calculation.

Answer 1

The Correct Option is D

Concept:
For first order reaction: \[ t_{1/2} = \frac{0.693}{k} \]

Step 1: Rearrange formula. \[ k = \frac{0.693}{t_{1/2}} \]

Step 2: Substitute values. \[ k = \frac{0.693}{138.6} \]

Step 3: Calculate. \[ k = 0.005 \text{ minute}^{-1} \]

Step 4: Conclusion. \[ \text{Rate constant = } 0.005 \text{ minute}^{-1} \]