Question 4 of 50intermediate🔧 ApplyNumerical2 marks

Calculate the mass of urea (NH2CONH2) required in making 2.5 kg of 0.25 molal aqueous solution.

Correct Answer

The mass of urea required is approximately 37 g (or 36.95 g).

Exercise: Intext Questions | Q: 1.4 | (Page 5)
For More Understanding

Explanation

This question tests understanding of molality, which is defined as moles of solute per kilogram of solvent. The key is recognizing that in a molal solution, the mass of solvent is different from the total mass of solution. Students must use the relationship: Molality = Moles of solute / Mass of solvent (in kg), and solve for the unknown mass of urea.

Solution Steps

  1. Step 1: Calculate molar mass of urea (NH₂CONH₂) = 2(14) + 4(1) + 12 + 16 = 60 g mol⁻¹

  2. Step 2: Let mass of urea = w g. Then mass of water (solvent) = (2500 - w) g = (2500 - w)/1000 kg

  3. Step 3: Apply molality formula: Molality = Moles of solute / Mass of solvent in kg

  4. Step 4: Substitute values: 0.25 = (w/60) ÷ [(2500-w)/1000]

  5. Step 5: Solve: 0.25×600.25 \times 60 × (2500 - w) = w × 1000 → 15(2500 - w) = 1000w → 37500 - 15w = 1000w → 1015w = 37500

  6. Step 6: Calculate: w = 37500/1015 = 36.95 g ≈\approx 37 g

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