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Difficulty: MediumWater of Crystallization, Deliquescence, Efflorescence, and Hygroscopy

A 24.4 g24.4\text{ g} sample of hydrated barium chloride, BaCl2⋅xH2O\text{BaCl}_2 \cdot x\text{H}_2\text{O}, was heated strongly in a crucible to constant mass. The residue of anhydrous barium chloride obtained weighed 20.8 g20.8\text{ g}. What is the value of xx? [Ba=137,Cl=35.5,H=1,O=16][\text{Ba} = 137, \text{Cl} = 35.5, \text{H} = 1, \text{O} = 16]

  1. 2Answer
  2. B
    1
  3. C
    4
  4. D
    5

Answer

The value of xx is 2, giving the formula BaCl2⋅2H2O\text{BaCl}_2 \cdot 2\text{H}_2\text{O}.
Heating the hydrated salt removes all water of crystallization, leaving 20.8 g20.8\text{ g} of anhydrous BaCl2\text{BaCl}_2 (0.10 mol0.10\text{ mol}) and releasing 3.6 g3.6\text{ g} of water vapor (0.20 mol0.20\text{ mol}). The ratio of moles of water to moles of anhydrous salt is 0.200.10=2\frac{0.20}{0.10} = 2, so x=2x = 2.

Step-by-Step Solution

1
Calculate the mass of water of crystallization lost during heating.
Mass of H2O=24.4 g−20.8 g=3.6 g\text{Mass of H}_2\text{O} = 24.4\text{ g} - 20.8\text{ g} = 3.6\text{ g}
Heating drives off all water of crystallization, leaving only anhydrous salt.
2
Determine the molar masses of anhydrous BaCl2\text{BaCl}_2 and H2O\text{H}_2\text{O}.
Molar mass of BaCl2=137+2(35.5)=208 g/mol\text{Molar mass of BaCl}_2 = 137 + 2(35.5) = 208\text{ g/mol}; Molar mass of H2O=2(1)+16=18 g/mol\text{Molar mass of H}_2\text{O} = 2(1) + 16 = 18\text{ g/mol}
Molar masses are needed to convert mass quantities into mole quantities.
3
Calculate the number of moles of anhydrous BaCl2\text{BaCl}_2 and water.
Moles of BaCl2=20.8 g208 g/mol=0.10 mol\text{Moles of BaCl}_2 = \frac{20.8\text{ g}}{208\text{ g/mol}} = 0.10\text{ mol}; Moles of H2O=3.6 g18 g/mol=0.20 mol\text{Moles of H}_2\text{O} = \frac{3.6\text{ g}}{18\text{ g/mol}} = 0.20\text{ mol}
The stoichiometric coefficient xx represents the mole ratio of water molecules per mole of salt.
4
Find the mole ratio x=Moles of H2OMoles of BaCl2x = \frac{\text{Moles of H}_2\text{O}}{\text{Moles of BaCl}_2}.
x=0.20 mol0.10 mol=2x = \frac{0.20\text{ mol}}{0.10\text{ mol}} = 2
Simplifying the mole ratio determines the integer coefficient xx in the hydrated salt formula.

Key Concept

Determination of Water of Crystallization by Stoichiometric Gravimetric Heating
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Topics

Water of Crystallization, Deliquescence, Efflorescence, and Hygroscopy

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