Question

In a first-order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is:

• A. 7.5 minutes
• B. 15 minutes
• C. 30 minutes
• D. 60 minutes

Hint:

For a first-order reaction, the half-life is independent of the initial concentration.

Answer 1

The Correct Option is C

Step 1: First-Order Reaction Half-Life Analysis
For a first-order reaction, the half-life (\( t_{1/2} \)) is constant: \[t_{1/2} = \frac{0.693}{k}\] Initial concentration is \( 0.8 M \). After one half-life (15 minutes), the concentration becomes \( 0.4 M \). After a second half-life (another 15 minutes), the concentration reduces to \( 0.2 M \). A third half-life (another 15 minutes) will reduce it further.
Step 2: Calculating Time to Reach \( 0.025 M \)
To reduce the concentration from \( 0.1 M \) to \( 0.025 M \), two half-lives are required.
Total time = \( 2 \times 15 \) minutes = 30 minutes.
Final Answer: 30 minutes.