(i) Solutions of barium chloride and sodium sulphate in water react to give insoluble barium sulphate and the solution of sodium chloride.

(ii) Sodium hydroxide solution (in water) reacts with hydrochloric acid solution (in water) to produce sodium chloride solution and water.

Here are the balanced chemical equations with state symbols:

(i) Barium chloride (aqueous) + Sodium sulphate (aqueous) → Barium sulphate (solid) + Sodium chloride (aqueous) \[ \text{BaCl}_2(aq) + \text{Na}_2\text{SO}_4(aq) \rightarrow \text{BaSO}_4(s) + 2\text{NaCl}(aq) \] (ii) Sodium hydroxide solution (aqueous) + Hydrochloric acid solution (aqueous) → Sodium chloride solution (aqueous) + Water (liquid) \[ \text{NaOH}(aq) + \text{HCl}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l) \] These equations include the state symbols, indicating the physical states of the reactants and products.