1. BeO has higher lattice enthalpy than hydration enthalpy and hence is insoluble in water. BeSO4 on the contrary, is soluble because the lattice enthalpy is less due to bigger sulphate ion.
2. In barium oxide, BaO, due to larger size of barium ion the lattice enthalpy is less than hydration enthalpy and hence it is soluble in water. On the other hand, in BaSO4 due to larger size of barium as well as sulphate ion, the magnitude of hydration enthalpy is much smaller than the lattice enthalpy and hence it is insoluble in water.
3. In Kl the chemical bond is ionic in character. On the other hand, due to small size of lithium ion and its high polarising power, the bond in Li is predominantly covalent in character. Hence, Li is more soluble than Kl in ethanol.