75% of a first order reaction is completed in 32 minutes. 50% of the reaction would have been completed in

Options

A. 24 mins
B. 16 mins
C. 18 mins
D. 23 mins

Explanation

To solve the problem of determining the time taken for 50% completion of a first-order reaction when 75% completion takes 32 minutes, we can use the properties of first-order kinetics.

### Step-by-Step Solution:

1. **Understanding First-Order Kinetics**:
For a first-order reaction, the time taken to reach a certain percentage completion can be related to the half-life of the reaction. The relationship is such that:
\[ T_{75\%} = 2 \times T_{50\%} \]
This means that the time taken to reach 75% completion is twice the time taken to reach 50% completion.

2. **Given Data**:
- Time taken for 75% completion, \( T_{75\%} = 32 \) minutes.

3. **Using the Relationship**:
From the relationship derived from first-order kinetics:
\[ T_{75\%} = 2 \times T_{50\%} \]
We can rearrange this to find \( T_{50\%} \):
\[ T_{50\%} = \frac{T_{75\%}}{2} \]

4. **Substituting the Known Value**:
Now substitute the value of \( T_{75\%} \):
\[ T_{50\%} = \frac{32 \text{ minutes}}{2} = 16 \text{ minutes} \]

5. **Conclusion**:
Therefore, the time taken for 50% completion of the reaction is **16 minutes**.

### Final Answer:
The time taken for 50% of the reaction to be completed is **16 minutes**.

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