Identify the elements and polyatomic ions involved in the reaction: aluminum (Al), sulfate (SO4), potassium (K), phosphate (PO4), and the compounds Al2(SO4)3, K3PO4, AlPO4, and K2SO4.
Write down the unbalanced chemical equation: \(\mathrm{Al_2(SO_4)_3 (aq) + K_3PO_4 (aq) \rightarrow AlPO_4 (s) + K_2SO_4 (aq)}\).
Balance the aluminum (Al) atoms first. Since there are 2 Al atoms in \(\mathrm{Al_2(SO_4)_3}\), place a coefficient of 2 in front of \(\mathrm{AlPO_4}\) to balance Al: \(\mathrm{Al_2(SO_4)_3 + K_3PO_4 \rightarrow 2 AlPO_4 + K_2SO_4}\).
Balance the phosphate (PO4) groups next. There are 2 phosphate groups on the product side (from \(2 \times \mathrm{AlPO_4}\)), so place a coefficient of 2 in front of \(\mathrm{K_3PO_4}\) on the reactant side: \(\mathrm{Al_2(SO_4)_3 + 2 K_3PO_4 \rightarrow 2 AlPO_4 + K_2SO_4}\).
Finally, balance the sulfate (SO4) and potassium (K) ions. There are 3 sulfate groups in \(\mathrm{Al_2(SO_4)_3}\), so place a coefficient of 3 in front of \(\mathrm{K_2SO_4}\) on the product side to balance sulfate and potassium atoms: \(\mathrm{Al_2(SO_4)_3 + 2 K_3PO_4 \rightarrow 2 AlPO_4 + 3 K_2SO_4}\).