Translate the following statements into chemical equations and then balance them.
$(a)$ Hydrogen gas combines with nitrogen to form ammonia.
$(b)$ Hydrogen sulphide gas burns in air to give water and sulphur dioxide.
$(c)$ Barium chloride reacts with aluminium sulphate to give aluminium chloride and a precipitate of barium sulphate.
$(d)$ Potassium metal reacts with water to give potassium hydroxide and hydrogen gas.

(A) The reaction is $H_{2(g)} + N_{2(g)} \to NH_{3(g)}$. Balancing gives $3H_{2(g)} + N_{2(g)} \to 2NH_{3(g)}$.
$(b)$ The reaction is $H_{2}S_{(g)} + O_{2(g)} \to H_{2}O_{(l)} + SO_{2(g)}$. Balancing gives $2H_{2}S_{(g)} + 3O_{2(g)} \to 2H_{2}O_{(l)} + 2SO_{2(g)}$.
$(c)$ The reaction is $BaCl_{2(aq)} + Al_{2}(SO_{4})_{3(aq)} \to AlCl_{3(aq)} + BaSO_{4(s)}$. Balancing gives $3BaCl_{2(aq)} + Al_{2}(SO_{4})_{3(aq)} \to 2AlCl_{3(aq)} + 3BaSO_{4(s)}$.
$(d)$ The reaction is $K_{(s)} + H_{2}O_{(l)} \to KOH_{(aq)} + H_{2(g)}$. Balancing gives $2K_{(s)} + 2H_{2}O_{(l)} \to 2KOH_{(aq)} + H_{2(g)}$.