Question

What is the half-life of a first order reaction if time required to decrease concentration of reactant from 1.0 M to 0.25 M is 10 hour?

• A. 12 hour
• B. 4 hour
• C. 5 hour
• D. 10 hour

Hint:

For first order reactions, each half-life reduces concentration to half. Two half-lives reduce to \(1/4\)th.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Concentration drops from 1.0 M to 0.25 M in 10 hours for a first order reaction.

Step 2: Key Formula or Approach:
After \(n\) half-lives, \(\frac{[A]}{[A]_0} = \left(\frac{1}{2}\right)^n\).

Step 3: Detailed Explanation:
\(\frac{0.25}{1.0} = \frac{1}{4} = \left(\frac{1}{2}\right)^2\), so \(n = 2\) half-lives.
Total time = \(n \times t_{1/2} = 2t_{1/2} = 10\) h \(\Rightarrow t_{1/2} = 5\) h.

Step 4: Final Answer:
Option (C) is correct.