50 " mL of " water on titration with standard soap solution gave the following results: Lather factor `=0.4` mL, total hardness `(TH)=8.2mL`, permanent hardness (PH)`=2.5mL` and standard hard water (containing `0.2 g CaCO_3L^(-1))=19.9mL`. Calculate each type of hardness in ppm.

Explanation

To solve the problem of calculating the hardness of water in ppm based on the provided titration results, we will follow these steps:

### Step 1: Calculate the Strength of Calcium Carbonate (CaCO3)
The concentration of standard hard water is given as 0.2 g of CaCO3 per liter.

- **Equivalent weight of CaCO3**:
\[
\text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{n factor}} = \frac{100 \text{ g/mol}}{2} = 50 \text{ g/equiv}
...