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.

(N/A) $(i)$ $BeO$ is almost insoluble in water because $Be^{2+}$ is a small cation with high charge density,leading to very high lattice energy that hydration energy cannot overcome. In $BeSO_4$,the large $SO_4^{2-}$ anion reduces the lattice energy,making it soluble.
$(ii)$ $BaO$ is soluble because $Ba^{2+}$ and $O^{2-}$ have a size mismatch,resulting in lower lattice energy that is easily overcome by hydration energy. In $BaSO_4$,both $Ba^{2+}$ and $SO_4^{2-}$ are large,leading to high lattice energy,making it insoluble.
$(iii)$ $LiI$ is more soluble than $KI$ in ethanol due to the higher polarising power of the small $Li^+$ ion,which imparts greater covalent character to $LiI$ compared to $KI$,facilitating its dissolution in organic solvents like ethanol.