(i) Due to high lattice enthalpy and covalent nature, BeO is insoluble in water. In case of ionic BeSO4, the hydration enthalpy is much more than its lattice enthalpy. Hence, it is water soluble.
(ii) Oxide ion has smaller size than sulphate ion. BaO has smaller lattice energy than BaSO4 as bigger cation stablizes bigger anion to greater extent than smaller cation stabilizes bigger anion. Hence, BaO is water soluble and BaSO4 is water insoluble.
(iii) As per Fajan rules, smaller Li+ ion polarizes bigger I− to a greater extent than K+ ion. Hence, LiI is more covalent than KI and hence, more soluble in organic solvents such as ethanol.