Mg(NO$$_3$$)$$_2$$.XH$$_2$$O and Ba(NO$$_3$$)$$_2$$.YH$$_2$$O, represent formula of the crystalline forms of nitrate salts. Sum of X and Y is _______

The standard crystalline hydrated form of magnesium nitrate is a hexahydrate: $$Mg(NO_3)_2·6H_2O.$$
Therefore, X = 6.

Barium nitrate typically crystallizes as an anhydrous salt directly from aqueous solutions under ordinary laboratory conditions because its lattice energy outweighs its hydration energy.

Therefore, it contains no water of crystallization: $$Ba(NO_3)_2$$ (or $$Ba(NO_3)_2·0H_2O$$).
Therefore, Y = 0.

Final Calculation

To find the required sum of the water molecules of crystallization:

X + Y = 6 + 0 = 6