Final answer:
BaSO4 is insoluble in water primarily due to its low solubility product (Ksp) for the combination of Ba2+ and SO42- ions, not just lattice energy based on ionic size. The solubility rules highlight that most sulfate salts are soluble with exceptions like BaSO4, implying factors other than lattice energy play a significant role.
Step-by-step explanation:
The reason MgSO4 is soluble while BaSO4 is insoluble in water is related to the solubility rules and the ionic sizes involved in their structures. While it is true that solubility often has an inverse relationship with lattice energy, there are other factors to consider.
Solubility rules indicate that most sulfate salts are soluble, with the important exceptions of BaSO4, PbSO4, and SrSO4. This is due to the particular combination of ions that form a compound with low solubility, not just lattice energy considerations alone.
In the case of BaSO4, its insolubility is due to the low solubility product (Ksp) for the specific combination of Ba2+ and SO42- ions in water. It's not only the lattice energy, determined by ionic size, that affects solubility, but also the nature of the specific ions and their interaction with water molecules.
Thus, despite Ba2+ having a larger ionic size and potentially a lower lattice energy compared to Mg2+, BaSO4 is still insoluble because of other overriding factors dictated by the solubility rules.