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Ron and Hermione begin with 1.50 g of the hydrate copper(II)sulfate ∙ x-hydrate (CuSO4 ∙ xH2O), where x is an integer. Part of their practical exam is to determine this integer x. They are working in pairs, though Hermione is doing most of the work. This should be discouraged! After dehydration they find that they are left with 0.96 g of the an-hydrate CuSO4. What is the unknown integer x. Round the answer to the nearest integer.

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Answer:

  • The unknown integer X in the formula is 5.

Explanation:

1) Data:

a) Mass of CuSO₄ ∙ XH₂O = 1.50 g

b) Mass of CuSOâ‚„ = 0.96

c) X = ?

2) Additional needed data:

a) Molar Mass of CuSOâ‚„ = 159,609 g/mol

b) Molar mass of Hâ‚‚O = 18,01528 g/mol

3) Chemical principles and formulae used:

a) Law of conservation of mass

b) Molar mass = mass in grams / number of moles = m / n

4) Solution:

a) Law of conservation of mass:

  • Mass of CuSOâ‚„ ∙ XHâ‚‚O = mass of CuSOâ‚„ + mass of Hâ‚‚O

  • 1.50g = 0.96g + mass of Hâ‚‚O ⇒ mass of Hâ‚‚O = 1.50g - 0.96g = 0.54g

b) Moles

  • n = m / molar mass

  • CuSOâ‚„: n = 0.96g / 159.609 g/mol = 0.0060 mol

  • Hâ‚‚O: 0.54g / 18.01528 g/mol = 0.030 mol

c) Proportion:

Divide both mole amounts by the least of the two numbers, i.e. 0.0060

  • CuSOâ‚„:  0.0060 / 0.0060 = 1

  • Hâ‚‚O: 0.030 mol / 0.0060 = 5

Then, the ratio of CuSOâ‚„ to Hâ‚‚O is 1 : 5 and the chemical formula is:

  • CuSOâ‚„ . 5Hâ‚‚O.

Hence, the value of X is 5.

Answer:

CuSO4*5H2O

X = 5

Explanation:

Step 1: Data given

Mass of the copper(II)sulfate hydrate = 1.50 grams

After dehydration they find that they are left with 0.96 g of the an-hydrate CuSO4.

Step 2: Calculate mass of water

Mass of water = mass of hydrate - mass of anhydrate

Mass water = 1.50 grams - 0.96 grams

Mass water = 0.54 grams

Step 3: Calculate moles of water

Moles H2O = mass / molar mass

Moles H2O = 0.54 grams / 18.02 g/mol

Moles H2O = 0.030 moles

Step 4: Calculate moles of CuSO4

Moles CuSO4 = 0.96 grams / 159.61 g/mol

Moles CuSO4 = 0.0060 moles

Step 5: Calculate mol ratio

We divide by the smallest amount of moles

H2O : 0.030 / 0.060 = 5

CuSO4: 0.0060 / 0.0060 = 1

For 1 mol CuSO4 we have 5 moles of H2O

CuSO4*5H2O

X = 5

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