In a first order reaction, the concentration of the reactant decreases from 0.6 M to 0.3 M in 30 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

Options

A. 50 min
B. 30 min
C. 15 min
D. 60 min

Explanation

To solve the problem, we need to analyze the first-order reaction and use the information provided to find the time taken for the concentration to change from 0.1 M to 0.025 M.

### Step-by-Step Solution:

1. **Identify the Initial and Final Concentrations:**
- Initial concentration (C1) = 0.1 M
- Final concentration (C2) = 0.025 M

2. **Determine the Half-Life of the Reaction:**
- We know from the question that the concentration decreases from 0.6 M to 0.3 M in 30 minutes. This represents a 50% reduction in concentration, which corresponds to one half-life (t₁/₂).
- Therefore, the half-life (t₁/₂) = 30 minutes.

3. **Calculate the Number of Half-Lives Required:**
- From 0.1 M to 0.05 M is one half-life (30 minutes).
- From 0.05 M to 0.025 M is another half-life (30 minutes).
- Thus, the total change from 0.1 M to 0.025 M involves 2 half-lives.

4. **Calculate the Total Time Taken:**
- Total time = Number of half-lives × Duration of each half-life
- Total time = 2 × 30 minutes = 60 minutes.

### Final Answer:
The time taken for the concentration to change from 0.1 M to 0.025 M is **60 minutes**.

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