A reaction proceeds by first order, 75% of this reactin was completed in 32 min. The time required for 50% completion is

Options

A. 8 min
B. 16 min
C. 20 min
D. 24 min

Explanation

To solve the problem, we need to determine the time required for 50% completion of a first-order reaction, given that 75% of the reaction is completed in 32 minutes.

### Step-by-Step Solution:

1. **Understanding First-Order Reactions**:
In a first-order reaction, the time taken to reach a certain percentage completion is related to the time taken to reach half completion. Specifically, the time taken to complete 75% of the reaction is twice the time taken to complete 50%.

2. **Given Information**:
- Time for 75% completion, \( t_{75\%} = 32 \) minutes.
- We need to find the time for 50% completion, \( t_{50\%} \).

3. **Relationship Between Completion Times**:
From the properties of first-order reactions:
\[ t_{75\%} = 2 \times t_{50\%} \]

4. **Substituting the Known Value**:
We can substitute the known value of \( t_{75\%} \):
\[ 32 \text{ minutes} = 2 \times t_{50\%} \]

5. **Solving for \( t_{50\%} \)**:
To find \( t_{50\%} \), we rearrange the equation:
\[ t_{50\%} = \frac{32 \text{ minutes}}{2} = 16 \text{ minutes} \]

6. **Conclusion**:
The time required for 50% completion of the reaction is **16 minutes**.