How would you explain the following observations?
$(i)$ $BeO$ is almost insoluble but $BeSO_4$ is soluble in water,
$(ii)$ $BaO$ is soluble but $BaSO_4$ is insoluble in water,
$(iii)$ $LiI$ is more soluble than $KI$ in ethanol.

(A) $(i)$ $BeO$ is almost insoluble in water because $Be^{2+}$ and $O^{2-}$ are both small ions,leading to high lattice energy that hydration energy cannot overcome. $BeSO_4$ is soluble because the large $SO_4^{2-}$ anion reduces the lattice energy.
$(ii)$ $BaO$ is soluble because $Ba^{2+}$ and $O^{2-}$ have a size mismatch,resulting in lower lattice energy. $BaSO_4$ is insoluble because both $Ba^{2+}$ and $SO_4^{2-}$ are large,leading to high lattice energy due to favorable packing.
$(iii)$ $LiI$ is more soluble than $KI$ in ethanol due to the higher covalent character of $LiI$ caused by the high polarising power of the small $Li^+$ ion,which makes it more compatible with the organic solvent ethanol.