How can the permanent hardness of water be removed? 

Na₂CO₃

The correct answer is option 1. Na₂CO₃.

The permanent hardness of water, which is mainly due to the presence of calcium and magnesium ions, can be removed by using sodium carbonate \((Na_2CO_3)\). Sodium carbonate reacts with calcium and magnesium ions to form insoluble carbonates, which can then be removed through precipitation. The chemical equation for the reaction is:

\[ \text{Ca(HCO3)2 (aq) + Na2CO3 (aq) → CaCO3 (s) + 2NaHCO3 (aq)} \]

\[ \text{Mg(HCO3)2 (aq) + Na2CO3 (aq) → MgCO3 (s) + 2NaHCO3 (aq)} \]

The formed calcium carbonate \((CaCO_3)\) and magnesium carbonate \((MgCO_3)\) are insoluble and can be separated from the water, thus reducing the hardness.