`75%` of a first-order reaction was completed in `32` minutes, when was `50%` of the reaction completed ?

Options

A. `24` minute
B. `16` minute
C. `8` minute
D. `48` minute

Explanation

To solve the problem of determining when 50% of a first-order reaction was completed given that 75% was completed in 32 minutes, we can follow these steps:

### Step 1: Understand the relationship between completion percentages and time in first-order reactions.
For a first-order reaction, the time taken to reach a certain percentage completion can be related to the half-life of the reaction. Specifically, for a first-order reaction:
- The time taken to reach 75% completion (T75%) is equal to 2 times the half-life (T1/2).

### Step 2: Use the given information.
We are given that T75% = 32 minutes.

### Step 3: Relate T75% to T1/2.
Using the relationship from Step 1:
\[ T75\% = 2 \times T_{1/2} \]
Substituting the known value:
\[ 32 \text{ minutes} = 2 \times T_{1/2} \]

### Step 4: Solve for T1/2.
To find T1/2, we can rearrange the equation:
\[ T_{1/2} = \frac{32 \text{ minutes}}{2} \]
\[ T_{1/2} = 16 \text{ minutes} \]

### Step 5: Conclusion.
Thus, the time taken for 50% of the reaction to be completed (T1/2) is 16 minutes.

### Final Answer:
The time when 50% of the reaction was completed is **16 minutes**.

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