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What is the formula of the hydrated salt of barium chloride if 36.6 g of the hydrated salt, on strong heating, gives 5.4 g of Hâ‚‚O?

(1) BaClâ‚‚·7Hâ‚‚O
(2) BaClâ‚‚·2Hâ‚‚O
(3) BaClâ‚‚·3Hâ‚‚O
(4) BaClâ‚‚·5Hâ‚‚O

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:

  1. Find the Mass of Anhydrous Barium Chloride (BaClâ‚‚):

    • 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 BaClâ‚‚ is 36.6 g - 5.4 g = 31.2 g.
  2. Calculate the Moles of Anhydrous BaClâ‚‚:

    • The molar mass of BaClâ‚‚ (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 BaClâ‚‚ = [tex]\frac{31.2 \text{ g}}{208.23 \text{ g/mol}} \approx 0.15 \text{ moles}[/tex]
  3. Calculate the Moles of Water Lost:

    • The molar mass of water (Hâ‚‚O) is 18.02 g/mol.
    • Moles of Hâ‚‚O = [tex]\frac{5.4 \text{ g}}{18.02 \text{ g/mol}} \approx 0.30 \text{ moles}[/tex]
  4. Determine the Mole Ratio:

    • The mole ratio of water to anhydrous BaClâ‚‚ is:
      [tex]\frac{0.30 \text{ moles of Hâ‚‚O}}{0.15 \text{ moles of BaClâ‚‚}} = 2[/tex]

    This means there are 2 moles of water per mole of BaClâ‚‚.

  5. 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): BaClâ‚‚·2Hâ‚‚O.

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Rewritten by : Jeany