For a first order reactions, the half -life is 10 mins. How much time in minutes will it take to reduce the concentration of reactant to 25% of its original concentration ?

Answer

To solve the problem, we need to determine how much time it will take for the concentration of a reactant in a first-order reaction to reduce to 25% of its original concentration, given that the half-life (t₁/₂) is 10 minutes.

### Step-by-Step Solution:

1. **Understand the concept of half-life**:
- The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration.
- For a first-order reaction, each half-life is constant.

2. **Calculate the first half-life**:
- Initially, the concentration of the reactant (A) is 100%.
- After the first half-life (10 minutes), the concentration will be:
\[ A = 100\% \rightarrow 50\% \]

3. **Calculate the second half-life**:
- After the second half-life (another 10 minutes), the concentration will decrease from 50% to:
\[ A = 50\% \rightarrow 25\% \]

4. **Total time taken**:
- Since it takes two half-lives to reduce the concentration from 100% to 25%, the total time taken will be:
\[ \text{Total time} = 10 \text{ minutes} + 10 \text{ minutes} = 20 \text{ minutes} \]

### Final Answer:
The time required to reduce the concentration of the reactant to 25% of its original concentration is **20 minutes**.

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