Below are the balanced equations for removal of temporary & permanent hardness in water by addition of washing soda:
Permanent Hard Water:
Washing sodaNa2CO3+Calcium sulphateCaSO4⟶Calcium carbonateCaCO3↓+Na2SO4
Temporary Hard Water:
Washing sodaNa2CO3+Calcium bicarbonateCa(HCO3)2⟶Calcium carbonateCaCO3↓+2NaHCO3