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 -

Options

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

Answer

To solve the problem, we need to determine the time taken for the concentration of a reactant in a first-order reaction to change from 0.1 M to 0.025 M. We know that the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes.

### Step-by-Step Solution:

1. **Understanding First-Order Reactions**:
In a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. The half-life (T_half) of a first-order reaction is constant and does not depend on the initial concentration.

2. **Calculate the Half-Life (T_half)**:
From the information given, the concentration decreases from 0.8 M to 0.4 M in 15 minutes. This represents one half-life because 0.4 M is half of 0.8 M.
\[ T_{half} = 15 \text{ minutes} \]

3. **Determine the Time for the Next Half-Life**:
Now, we need to find the time taken for the concentration to change from 0.1 M to 0.025 M.
- Starting from 0.1 M, the first half-life will take it to 0.05 M (15 minutes).
- The next half-life will take it from 0.05 M to 0.025 M (another 15 minutes).

4. **Calculate Total Time**:
Therefore, the total time taken for the concentration to change from 0.1 M to 0.025 M is:
\[ \text{Total Time} = 15 \text{ minutes} + 15 \text{ minutes} = 30 \text{ minutes} \]

### Final Answer:
The time taken for the concentration to change from 0.1 M to 0.025 M is **30 minutes**.

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