Q.(i) Among the alkaline earth metals BeO is insoluble in water but other oxides are soluble. Why?

(i) BeO is covalent and insoluble due to Be2+'s very high polarising power; other Group 2 oxides are more ionic and soluble. (ii) Graham's Law: rate of diffusion is inversely proportional to the square root of molar mass.

(i) Why BeO is insoluble while other alkaline earth oxides are soluble:

Down Group 2 (Be, Mg, Ca, Sr, Ba), the ionic radius of M2+ increases steadily while the charge stays +2, so the charge-to-size ratio (and hence the polarising power, by Fajans' rules) decreases down the group. Be2+ is the smallest, most highly charged-density cation in the group, so it strongly polarises the oxide ion's electron cloud, pulling electron density towards itself and giving BeO substantial covalent character — covalent oxides do not readily dissociate into ions in water, so BeO is essentially insoluble (and in fact somewhat amphoteric, like a covalent oxide).

For MgO, CaO, SrO, and BaO, the larger, less polarising M2+ ions form oxides that are progressively more purely ionic. In ionic solids, solubility in water is governed by the balance between lattice energy (energy to break the ionic lattice, decreasing down the group as the ions get larger and interact less strongly) and hydration energy (also decreasing down the group, but less steeply); down the group, lattice energy falls off faster than hydration energy, so the oxides/hydroxides become progressively more soluble from Mg to Ba. This is why only BeO stands out as essentially insoluble/covalent while the rest are increasingly soluble ionic oxides.

(ii) Diffusion Law (Graham's Law): …