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Which of the following compounds is used for water softening?
(A) \[{\text{C}}{{\text{a}}_{\text{3}}}{\left( {{\text{P}}{{\text{O}}_{\text{4}}}} \right)_{\text{2}}}\]
(B) \[{\text{N}}{{\text{a}}_{\text{3}}}{\text{P}}{{\text{O}}_{\text{4}}}\]
(C) \[{\text{N}}{{\text{a}}_6}{{\text{P}}_{\text{6}}}{{\text{O}}_{18}}\]
(D) \[{\text{N}}{{\text{a}}_{\text{2}}}{\text{HP}}{{\text{O}}_4}\]

Answer
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Hint: Hard water contains calcium and magnesium ions. In soft water, the concentration of calcium and magnesium cations is very low. During water softening, remove calcium and magnesium ions from hard water to make it soft water.

Complete answer:
The chemical formulae \[{\text{C}}{{\text{a}}_{\text{3}}}{\left( {{\text{P}}{{\text{O}}_{\text{4}}}} \right)_{\text{2}}}\], \[{\text{N}}{{\text{a}}_{\text{3}}}{\text{P}}{{\text{O}}_{\text{4}}}\] , \[{\text{N}}{{\text{a}}_{\text{2}}}{\text{HP}}{{\text{O}}_4}\] represents compounds calcium phosphate, sodium phosphate and disodium hydrogen phosphate. These compounds cannot remove calcium and magnesium cations from hard water. Hence, the options (A), (B) and (D) are incorrect options.
The compound with chemical formula \[{\text{N}}{{\text{a}}_6}{{\text{P}}_{\text{6}}}{{\text{O}}_{18}}\] is called Calgon. It is also called sodium hexametaphosphate. Hard water contains calcium and magnesium cations. The counterions are chlorides, sulphates and bicarbonate ions. These cations react with sodium hexametaphosphate (Calgon) to form salts. These salts contain inactive complex anions. These salts do not precipitate out in soap solution. Thus, sodium hexametaphosphate removes the hardness of water and makes water soft.

Hence, the correct option is the option (C) \[{\text{N}}{{\text{a}}_6}{{\text{P}}_{\text{6}}}{{\text{O}}_{18}}\].

Additional Information: Given below are some methods by which you can remove hardness of water.
In Clark’s process, we add slaked lime.
Another process involves addition of washing soda
Other processes include Calgon process and ion Exchange process
In the ion exchange process, we use ion exchange resins. Calcium and magnesium cations present in hard water are exchanged with protons present on the ion exchange resin.

Note: We can classify the hardness of water as temporary hardness and permanent hardness. We can remove temporary hardness by boiling and filtration. To remove permanent hardness, we need certain chemicals.