Translate the following statements into chemical equations and then balance them.
$(a)$ Barium chloride reacts with aluminium sulphate to give aluminium chloride and a precipitate of barium sulphate.
$(b)$ Potassium metal reacts with water to give potassium hydroxide and hydrogen gas.

(N/A) The unbalanced equation is: $BaCl_{2} + Al_{2}(SO_{4})_{3} \longrightarrow AlCl_{3} + BaSO_{4}$.
To balance,we ensure the number of atoms of each element is equal on both sides: $3BaCl_{2}(aq) + Al_{2}(SO_{4})_{3}(aq) \longrightarrow 2AlCl_{3}(aq) + 3BaSO_{4}(s)$.
$(b)$ The unbalanced equation is: $K + H_{2}O \longrightarrow KOH + H_{2}$.
To balance,we ensure the number of atoms of each element is equal on both sides: $2K(s) + 2H_{2}O(l) \longrightarrow 2KOH(aq) + H_{2}(g)$.