A `50 mL` sample of hard water containing `Ca^(2+)` and `Mg^(2+)` ions is titrated with `50 mL. 0.005 M EDTA` solution at `pH=10`, using eriochrome balck`-T` indicator to reach equivalence point.
In a equal amount of hard water sample, `Mg^(2+)` ions are precipitated as `Mg(OH)_(2)` by adding suitable amount of `NaOH`. the solution, after precipitation of `Mg(OH)_(2)`, is stirred and then titrated with `EDTA` solution using calcon as indicator, and it requires `10 mL` of above `EDTA` solution to reach equivalence point.
a. Calculate the strength of `Ca^(2+)` and `Mg^(2+)` ions present in hard water.
b. Calculate the hardness due to `Ca^(2+)` ions in p p m of `CaCO_(3)`.
c. Calculate the hardness due to `Mg^(2+)` ions in p p m of `CaCO_(3)`.
d. Calculate the total hardness of water in p p m of `CaCO_(3)`.

Explanation

To solve the problem step by step, we will break down the information provided and use stoichiometric calculations to find the required values.

### Given Information:
1. **Volume of hard water sample**: 50 mL
2. **Molarity of EDTA solution**: 0.005 M
3. **Volume of EDTA used in first titration (with Eriochrome Black-T)**: 50 mL
4. **Volume of EDTA used in second titration (with Calcon)**: 10 mL
5. **pH of the solution**: 10
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