Question

When the value of rate constant \((k)\) is \(2.0 \, \mathrm{min^{-1}}\), then what will be half time of reaction \((t_{1/2})\) in seconds?

• A. 34.4
• B. 24.6
• C. 30.2
• D. 20.8

Hint:

For a first-order reaction, always use \(t_{1/2} = \frac{0.693}{k}\). If the answer is asked in seconds, first calculate using the given unit and then convert carefully.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The unit $\text{min}^{-1}$ indicates a first-order reaction. For first-order reactions, the half-life is independent of the initial concentration.
Step 2: Formula Application:
$t_{1/2} = \frac{0.693}{k}$
Step 3: Explanation:
$t_{1/2} = \frac{0.693}{2.0 \text{ min}^{-1}} = 0.3465$ minutes. To convert to seconds: $0.3465 \times 60 = 20.79$ seconds.
Step 4: Final Answer:
The half-life is approximately 20.8 seconds.