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Answer :
To determine the formula of the hydrated salt of barium chloride, we need to find the number of water molecules associated with each barium chloride molecule. Here's how you can determine it step by step:
Find the Mass of Anhydrous Barium Chloride (BaCl₂):
- The total mass of the hydrated salt is given as 36.6 g.
- The mass of water lost upon heating is 5.4 g.
- Therefore, the mass of anhydrous BaCl₂ is 36.6 g - 5.4 g = 31.2 g.
Calculate the Moles of Anhydrous BaCl₂:
- The molar mass of BaCl₂ (where barium = 137.33 g/mol and chlorine = 35.45 g/mol) is:
[tex]137.33 + 2 \times 35.45 = 208.23 \text{ g/mol}[/tex] - Moles of BaCl₂ = [tex]\frac{31.2 \text{ g}}{208.23 \text{ g/mol}} \approx 0.15 \text{ moles}[/tex]
- The molar mass of BaCl₂ (where barium = 137.33 g/mol and chlorine = 35.45 g/mol) is:
Calculate the Moles of Water Lost:
- The molar mass of water (H₂O) is 18.02 g/mol.
- Moles of H₂O = [tex]\frac{5.4 \text{ g}}{18.02 \text{ g/mol}} \approx 0.30 \text{ moles}[/tex]
Determine the Mole Ratio:
- The mole ratio of water to anhydrous BaCl₂ is:
[tex]\frac{0.30 \text{ moles of H₂O}}{0.15 \text{ moles of BaCl₂}} = 2[/tex]
This means there are 2 moles of water per mole of BaCl₂.
- The mole ratio of water to anhydrous BaCl₂ is:
Conclusion:
- The formula of the hydrated barium chloride is [tex]\text{BaCl}_2 \cdot 2\text{H}_2\text{O}[/tex].
Based on the calculations, the correct answer is option (2): BaCl₂·2H₂O.
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