If 75% of first order reaction is completed in 32 min, then 50% of the reaction would be complete in:

Options

A. 16min
B. 24min
C. 10min
D. 40min

Answer

To solve the problem of how long it takes for 50% of a first-order reaction to complete when 75% of the reaction is completed in 32 minutes, we can follow these steps:

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

### Step 2: Set up the equation for the completion of 75%
Given that 75% of the reaction is completed in 32 minutes, we can express this relationship mathematically:
\[ t_{75\%} = 2 \times T_{1/2} \]
Where:
- \( t_{75\%} = 32 \) minutes
- \( T_{1/2} \) is the half-life we need to find.

### Step 3: Solve for the half-life (T1/2)
Substituting the known value into the equation:
\[ 32 \text{ minutes} = 2 \times T_{1/2} \]

Now, divide both sides by 2:
\[ T_{1/2} = \frac{32 \text{ minutes}}{2} = 16 \text{ minutes} \]

### Step 4: Determine the time for 50% completion
Since we have found that the half-life \( T_{1/2} \) is 16 minutes, this means that it takes 16 minutes for 50% of the reaction to be completed.

### Final Answer
Thus, the time required for 50% of the reaction to complete is **16 minutes**.

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