For a reaction A `to` Products, starting with initial concentrations of `5xx10^(-3)` M and `25xx10^(-4)`M, half-lives are found to be 1.0 and 8.0 hour respectively. If we start with an initial concentration of `1.25xx10^(-3)` M, what will be the half-life of the reaction ?

Explanation

To find the half-life of the reaction when starting with an initial concentration of \(1.25 \times 10^{-3}\) M, we can use the relationship between half-life and concentration for reactions of different orders.

### Step-by-Step Solution:

1. **Identify Given Data:**
- For concentration \(A_1 = 5 \times 10^{-3}\) M, half-life \(T_{1/2} = 1.0\) hour.
- For concentration \(A_2 = 2.5 \times 10^{-3}\) M (which is \(25 \times 10^{-4}\) M), half-life \(T_{1/2} = 8.0\) hours.
- We need to find the half-life \(T_{1/2}\) for concentration \(A_3 = 1.25 \times 10^{-3}\) M.
...