For a first order reaction, time taken for half of the reaction to complete is `t_(1)and 3/4` of the reaction to complete is `t_(2)`. How are `t_(1)and t_(2) related?

Explanation

To find the relationship between \( t_1 \) (the time taken for half of the reaction to complete) and \( t_2 \) (the time taken for three-quarters of the reaction to complete) for a first-order reaction, we can use the integrated rate law for first-order reactions.

### Step-by-step Solution:

1. **Understanding the First-Order Reaction**:
For a first-order reaction, the time taken to complete a certain fraction of the reaction can be expressed using the formula:
\[
t = \frac{2.303}{k} \log \left( \frac{A}{A - X} \right)
...