Question

7. A certain hydrate of potassium aluminum sulfate has the formula
KAl(SO4)2-XH2O. When a sample weighing 5.459 g is heated to remove all the
water, 2.583 g of anhydrous salt remains. What is the mass % of water in the
hydrate? Determine the value of x.

Answer 1

the percent of water in the hydrate = 52.68 %

x = 16

Explanation:

The chemical formula for the potassium aluminium sulfate is KAl(SO₄)₂ · xH₂O.

mass of water = mass of hydrated salt - mass of anhydrous salt

mass of water = 5.459 - 2.583 = 2.876 g

Knowing that the molar mass of KAl(SO₄)₂ · xH₂O is 258 + 18x g/mole, we devise the following reasoning:

if in        258 + 18x g of  KAl(SO₄)₂ · xH₂O there are 18x g of water

then in  5.459 g of  KAl(SO₄)₂ · xH₂O there are 2.876 g of water

(5.459 × 18x) / 2.876 = 258 + 18x

34.166x = 258 + 18x

34.166x - 18x = 258

16.166x = 258

x = 258 / 16.166

x = 16

The chemical formula of the potassium aluminium sulfate hydrate is  KAl(SO₄)₂ · 16 H₂O.

the percent of water in the hydrate = (mass of water / mass of the hydrate) × 100

the percent of water in the hydrate = (2.876 / 5.459) × 100

the percent of water in the hydrate = 52.68 %

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