Balanced Chemical Equation: [ \text{Fe}_2(\text{SO}_4)_3(\text{aq}) + 3\text{K}_2\text{S}(\text{aq}) \rightarrow \text{Fe}_2\text{S}_3(\text{s}) + 3\text{K}_2\text{SO}_4(\text{aq}) ]
Complete Ionic Equation: In the complete ionic equation, we represent all the ions that are present in the solution. The spectator ions (ions that do not participate in the reaction) are omitted. [ 2\text{Fe}^{3+}(\text{aq}) + 6\text{SO}_4^{2-}(\text{aq}) + 6\text{K}^+(\text{aq}) \rightarrow \text{Fe}_2\text{S}_3(\text{s}) + 6\text{K}^+(\text{aq}) + 6\text{SO}_4^{2-}(\text{aq}) ]
Net Ionic Equation: The net ionic equation includes only the species that actively participate in the reaction. We cancel out the spectator ions. [ \text{Fe}^{3+}(\text{aq}) + 3\text{SO}_4^{2-}(\text{aq}) \rightarrow \text{Fe}_2\text{S}_3(\text{s}) ]
So, the net ionic equation for the given reaction is: [ \text{Fe}^{3+}(\text{aq}) + 3\text{SO}_4^{2-}(\text{aq}) \rightarrow \text{Fe}_2\text{S}_3(\text{s}) ]