A sample of hard water contains `0.05mol` of `CaC1_(2)`, per litre, What is the minimum concentration of `Na_(2)SO_(4)`, which must be added for removing `Ca^(2+)` ions from this water sample? `K_(sp)` for `CaSO_(4)` is `2.4 xx 10^(-5) at 25^(@)C`.

Explanation

To solve the problem, we need to determine the minimum concentration of \( \text{Na}_2\text{SO}_4 \) required to remove \( \text{Ca}^{2+} \) ions from hard water containing \( 0.05 \, \text{mol/L} \) of \( \text{CaCl}_2 \). The solubility product constant \( K_{sp} \) for \( \text{CaSO}_4 \) is given as \( 2.4 \times 10^{-5} \).

### Step-by-Step Solution:

1. **Identify the concentration of \( \text{Ca}^{2+} \):**
Since \( \text{CaCl}_2 \) dissociates completely in water, the concentration of \( \text{Ca}^{2+} \) ions is equal to the concentration of \( \text{CaCl}_2 \):
\[
[\text{Ca}^{2+}] = 0.05 \, \text{mol/L}
...