The Reagent which is commercially known as ‘calgon’ that is used to remove the permanent hardness of water in Calgon’s method. Find out the number of moles of calgon required to remove 12 moles of `Ca^(2+)` ion present in hard water.

Explanation

To solve the problem of determining the number of moles of Calgon required to remove 12 moles of \( \text{Ca}^{2+} \) ions present in hard water, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Chemical Formula of Calgon**:
The chemical formula for Calgon is \( \text{Na}_6\text{P}_6\text{O}_{18} \).

2. **Understand the Reaction**:
Calgon reacts with calcium ions (\( \text{Ca}^{2+} \)) to remove hardness from water. The relevant reaction can be summarized as follows:
\[ 3 \text{Ca}^{2+} + \text{Na}_6\text{P}_6\text{O}_{18} \rightarrow 3 \text{Ca}(\text{Na}_2\text{P}_6\text{O}_{18}) + 6 \text{Na}^{+} \]
This indicates that 1 mole of Calgon reacts with 3 moles of \( \text{Ca}^{2+} \).

3. **Calculate the Moles of Calgon Required**:
From the reaction, we can see that:
- 1 mole of Calgon removes 3 moles of \( \text{Ca}^{2+} \).
- Therefore, to find out how many moles of Calgon are needed for 12 moles of \( \text{Ca}^{2+} \), we can set up a proportion:
\[ \text{Moles of Calgon} = \frac{\text{Moles of } \text{Ca}^{2+}}{3} \]
Substituting the given value:
\[ \text{Moles of Calgon} = \frac{12 \text{ moles of } \text{Ca}^{2+}}{3} = 4 \text{ moles of Calgon} \]

4. **Conclusion**:
Thus, the number of moles of Calgon required to remove 12 moles of \( \text{Ca}^{2+} \) ions is **4 moles**.