Step 1: Understanding solubility trends. The precipitation of metal sulphates depends on their solubility product constant (\( K_{sp} \)). The lower the \( K_{sp} \) value, the less soluble the compound is, meaning it will precipitate first.
Step 2: Solubility of sulphates. The solubility order of alkaline earth metal sulphates (\({M}^{2+} {SO}_4^{2-}\)) decreases down the group: \[ {MgSO}_4>{CaSO}_4>{SrSO}_4>{BaSO}_4 \] Since barium sulphate (\({BaSO}_4\)) has the lowest solubility, it will precipitate first.