`50%` of a reaction is completed in 16 minutes. What fraction of the reaction would occur in 32 minutes ? Given that reaction follow first order reaction.

Answer

To solve the problem step by step, we will use the properties of first-order reactions and the concept of half-life.

### Step-by-Step Solution:

1. **Understand the Half-Life Concept**:
For a first-order reaction, the half-life (t₁/₂) is constant and does not depend on the concentration of the reactant. In this case, we are given that the half-life is 16 minutes.

2. **Calculate the Reaction Completion at 16 Minutes**:
Since the half-life is 16 minutes, after 16 minutes, 50% of the reactant (A) has been converted into product (P). This means that the fraction of the reaction completed after 16 minutes is:
\[ \text{Fraction completed} = \frac{1}{2} = 0.5 \]

3. **Determine the Reaction Completion at 32 Minutes**:
After another 16 minutes (totaling 32 minutes), we will again apply the half-life concept. At this point, we start with the remaining amount of reactant after the first 16 minutes. Since 50% of A has reacted, 50% remains.

Now, we apply the half-life again to the remaining 50%:
\[ \text{Fraction reacted in the next 16 minutes} = \frac{1}{2} \times \text{(remaining A)} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

4. **Calculate the Total Fraction Reacted in 32 Minutes**:
To find the total fraction of the reaction that has occurred in 32 minutes, we add the fractions from both intervals:
\[ \text{Total fraction reacted} = \text{Fraction reacted in first 16 minutes} + \text{Fraction reacted in next 16 minutes} \]
\[ = \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]

5. **Final Answer**:
Therefore, the fraction of the reaction that would occur in 32 minutes is:
\[ \frac{3}{4} \]