75 % of a first order reaction was completed in 32 min . When was 50 % of the reaction completed ?

Options

A. 24 min
B. 16 min
C. 8 min
D. 4 min

Answer

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

### Step-by-Step Solution:

1. **Understand the Reaction Completion**:
- We know that in a first-order reaction, the time taken to reach a certain percentage completion can be related to the half-life of the reaction.
- If 75% of the reaction is completed, then 25% of the reactant remains.

2. **Relate Completion to Half-Life**:
- For a first-order reaction, the relationship between the percentage completion and half-life can be understood as follows:
- 50% completion means 1 half-life has passed.
- 75% completion means that 25% of the reactant remains, which corresponds to 2 half-lives (since after 1 half-life, 50% remains, and after 2 half-lives, 25% remains).

3. **Calculate the Time for Half-Lives**:
- Given that 75% completion occurs in 32 minutes (which corresponds to 2 half-lives), we can calculate the duration of one half-life:
\[ \text{Time for 2 half-lives} = 32 \text{ minutes} \]
\[ \text{Time for 1 half-life} = \frac{32}{2} = 16 \text{ minutes} \]

4. **Determine the Time for 50% Completion**:
- Since 50% completion corresponds to 1 half-life, we can conclude that:
\[ \text{Time for 50% completion} = 16 \text{ minutes} \]

### Final Answer:
Thus, 50% of the reaction was completed in **16 minutes**.

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