100 mL sample of hard water is titrated with 500 " mL of " 0.001 M EDTA solution at `pH=10`, using eriochrome black-T indicator to reach equivalence point. An equal another amount of hard water sample is boiled for 30 min. After filtration and cooling, the same sample is titrated with 200 " mL of " 0.011 M EDTA solution at `pH=10` using Mg-EDTA complex solution and erichrome black-T indicator to reach equivalence point.
(i). Calculate the total hardness of water sample (temporary`+`permanent) in ppm of `CaCO_3`.
(ii). Calculate the permanent hardness of water sample in ppm of `CaCO_3`.
(iii). Calculate the temporary hardness of water sample in ppm of `CaCO_3`

Explanation

To solve the problem of calculating the total hardness, permanent hardness, and temporary hardness of the hard water sample, we will follow these steps:

### Step 1: Calculate Total Hardness
The total hardness of the water sample can be calculated using the first titration data. We have a 100 mL sample of hard water titrated with 500 mL of 0.001 M EDTA solution.

1. **Calculate moles of EDTA used:**
\[
\text{Moles of EDTA} = \text{Molarity} \times \text{Volume (L)} = 0.001 \, \text{mol/L} \times 0.500 \, \text{L} = 0.0005 \, \text{mol}
...