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Question: A hydrated blue copper (II) sulfate salt with a formula \(\rm{YCuSO_4.XH_2O}\) is heated until it is...

A hydrated blue copper (II) sulfate salt with a formula YCuSO4.XH2O\rm{YCuSO_4.XH_2O} 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?
A. 1
B. 2
C. 4
D. 5
E. 10

Explanation

Solution

First calculate the difference between the mass of hydrated salt and anhydrous salt. This is equal to the mass of water of hydration. Then calculate the number of moles of anhydrous salt and the water of hydration. Then determine the ratio of the number of moles of anhydrous salt to the number of moles of water of hydration.

Complete answer:
The mass of hydrated copper (II) sulfate is 500 g.
The mass of anhydrous copper (II) sulfate is 320 g.
The difference between the mass of hydrated copper (II) sulfate and the mass of anhydrous copper (II) sulfate is equal to the mass of water of hydration.
Calculate the mass of water of hydration.
500 g-320 g=180 g
The molecular weight of water is 18 g/mol.
Divide mass of water of hydration with molecular weight of water to obtain the number of moles of water of hydration:
No. of moles of water of hydration = 180 g18 g/mol=10 mol\rm{\dfrac{180\, g}{18\, g/mol}=10\,mol}
The molecular weight of anhydrous copper(II) sulfate is 159.6 g\mol.
Divide the mass of anhydrous copper(II) sulfate with its molecular weight and calculate the number of moles of anhydrous copper(II) sulfate.
Number of moles of anhydrous copper(II) sulfate = 320 g159.6 g/mol=2 mol\rm{\dfrac{320\, g}{159.6\, g/mol}=2\,mol}
The ratio of the number of moles of anhydrous copper(II) sulfate to the number of moles of water of hydration is 2:10 or 1:5. This ratio is equal to Y:X. So Y=1, and X=5 .
Hence, the value of X in the formula of the hydrated salt is 5.
The formula of the hydrated salt is CuSO4.5H2O\rm{CuSO_4.5H_2O} . The hydrated salt is copper sulfate pentahydrate.

**Hence, the correct option is the option (D).

Note:**
Anhydrous copper sulphate is colourless or white. Hydrate copper sulphate is blue. Thus, copper sulphate can be used as an indicator to detect the present of water or moisture in the surroundings.