Identify the reactants and products in the chemical reaction. The reactants are aluminum sulfate \((\text{Al}_2(\text{SO}_4)_3)\) and silver nitrate \((\text{AgNO}_3)\). The products are silver sulfate \((\text{Ag}_2\text{SO}_4)\) and aluminum nitrate \((\text{Al}(\text{NO}_3)_3)\).
Write the unbalanced chemical equation using the chemical formulas of the reactants and products: \(\text{Al}_2(\text{SO}_4)_3 + \text{AgNO}_3 \rightarrow \text{Ag}_2\text{SO}_4 + \text{Al}(\text{NO}_3)_3\).
Balance the equation by ensuring the number of atoms of each element is the same on both sides. Start by balancing the aluminum atoms. There are 2 aluminum atoms in \(\text{Al}_2(\text{SO}_4)_3\), so you need 2 \(\text{Al}(\text{NO}_3)_3\) on the product side.
Next, balance the sulfate \((\text{SO}_4)\) ions. There are 3 sulfate ions in \(\text{Al}_2(\text{SO}_4)_3\), so you need 3 \(\text{Ag}_2\text{SO}_4\) on the product side.
Finally, balance the silver \((\text{Ag})\) and nitrate \((\text{NO}_3)\) ions. You need 6 \(\text{AgNO}_3\) to provide 6 silver atoms for 3 \(\text{Ag}_2\text{SO}_4\) and 6 nitrate ions for 2 \(\text{Al}(\text{NO}_3)_3\). The balanced equation is \(\text{Al}_2(\text{SO}_4)_3 + 6\text{AgNO}_3 \rightarrow 3\text{Ag}_2\text{SO}_4 + 2\text{Al}(\text{NO}_3)_3\).