`75%` of the first order reaction completed in 3 min. `50%` of the reaction was completed in

Options

A. 24 min
B. 8 min
C. 1.5 min
D. 4 min

Answer

To solve the problem of determining the time taken for 50% completion of a first-order reaction when 75% completion occurs in 3 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**: For a first-order reaction, the relationship between the time taken for different percentages of completion is given by:
\[ T_{75\%} = 2 \times T_{50\%} \]
This means that the time taken to reach 75% completion is twice the time taken to reach 50% completion.

2. **Given Data**: We know from the problem that:
\[ T_{75\%} = 3 \text{ minutes} \]

3. **Setting Up the Equation**: Using the relationship from step 1, we can express the time for 50% completion as:
\[ T_{50\%} = \frac{T_{75\%}}{2} \]

4. **Substituting the Known Value**: Now, substituting the value of \( T_{75\%} \):
\[ T_{50\%} = \frac{3 \text{ minutes}}{2} = 1.5 \text{ minutes} \]

5. **Conclusion**: Therefore, the time taken for 50% of the reaction to be completed is:
\[ T_{50\%} = 1.5 \text{ minutes} \]

### Final Answer:
The time taken for 50% of the reaction to be completed is **1.5 minutes**.

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