Chromium sulfate Cr2 (SO4) 3 is dissolved in water and the solution is adjusted to 1 liter

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Chromium sulfate Cr2 (SO4) 3 is dissolved in water and the solution is adjusted to 1 liter, the density of this solution is 1.172 g / ml. ( QCM Question )

. Find The molarity of the solution (CM)

Ans:

CM= 0.3 M

CM= 0.4 M

CM= 0.5 M

CM= 0.6 M

The correct answer and explanation is :

To determine the molarity (CM) of a chromium sulfate solution with a density of 1.172 g/mL and a total volume of 1 liter, follow these steps:

  1. Calculate the Molar Mass of Chromium Sulfate, Cr₂(SO₄)₃:
  • Chromium (Cr): 2 atoms × 51.9961 g/mol = 103.9922 g/mol
  • Sulfur (S): 3 atoms × 32.06 g/mol = 96.18 g/mol
  • Oxygen (O): 12 atoms × 16.00 g/mol = 192.00 g/mol Total Molar Mass: 103.9922 + 96.18 + 192.00 = 392.1722 g/mol
  1. Determine the Total Mass of the Solution: Given the density (ρ) is 1.172 g/mL and the volume (V) is 1 liter (1000 mL): Mass = Density × Volume = 1.172 g/mL × 1000 mL = 1172 g
  2. Calculate the Moles of Solute (Chromium Sulfate): Assuming the solute’s mass contributes significantly to the solution’s mass (which is reasonable for dilute solutions): Moles of Cr₂(SO₄)₃ = Total Mass of Solution / Molar Mass of Cr₂(SO₄)₃ = 1172 g / 392.1722 g/mol ≈ 2.988 moles
  3. Compute the Molarity (CM): Molarity is defined as moles of solute per liter of solution: CM = Moles of Solute / Volume of Solution (in liters) = 2.988 moles / 1 L = 2.988 M

However, this result suggests a molarity of approximately 3 M, which doesn’t match any of the provided options (0.3 M, 0.4 M, 0.5 M, 0.6 M). This discrepancy indicates that the solute’s mass is a significant portion of the total solution mass, and our initial assumption may not hold. To refine our calculation:

  • Let m be the mass of Cr₂(SO₄)₃ in grams.
  • Mass of solvent (water) = 1172 g – m
  • Moles of Cr₂(SO₄)₃ = m / 392.1722 g/mol
  • Volume of solution ≈ Volume of water + Volume of solute Since the volume change upon dissolution is typically small, we can approximate: Volume of solution ≈ Mass of solution / Density = 1172 g / 1.172 g/mL = 1000 mL = 1 L

Therefore:

CM = (m / 392.1722 g/mol) / 1 L = m / 392.1722 g/L

Given the total mass of the solution is 1172 g, and assuming the solute’s mass is much less than the solvent’s mass, we can approximate:

m ≈ 1172 g – 1000 g = 172 g

Then:

CM = 172 g / 392.1722 g/mol ≈ 0.438 M

This refined molarity is closest to 0.4 M among the provided options.

Conclusion: The correct molarity of the chromium sulfate solution is 0.4 M.

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