A hydrated blue copper (II) sulfate salt with a formula $YCu{SO}_4\cdot X{H}_{2}O$ is heated until it is completely white in colour. The student who performed the dehydration of this salt took note of the mass of the sample before and after heating and recorded it as follows:
Mass of hydrated salt $=500$ g
Mass of dehydrated salt $=320$ g
What is the value of $X$ in the formula of the hydrated salt?

The correct option is E 5
Mass of hydrated salt $=500$ g
Mass of dehydrated salt $=320$ g
Mass of water $=500-320=180g$
The molar mass of water is 18 g/mol.
Number of moles of water $\frac{180}{18}=10$ mol
The molar mass of anhydrous copper sulphate is 159.6 g/mol.
The number of moles of anhydrous copper sulphate $=\frac{320}{159.6}=2$.
2 Moles of anhydrous copper sulphate corresponds to 10 moles of water.
1 mole of anhydrous copper sulphate corresponds to $\frac{10}{2}=5$ moles of water.
Hence, the value of $X$ is 5.