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The freezing point constant for water is -1.86 °C m⁻¹. If 5.00 g Na₂SO₄ is dissolved in 45.0 g H₂O, the freezing point is changed by -3.82 °C. Calculate the van't Hoff factor for Na₂SO₄.

1. 2.05
2. 2.63
3. 3.11
4. 0.381

Correct answer: 3.11

Solution

The van't Hoff factor (i) is calculated using the formula ΔTf = i × Kf × m. Here, ΔTf = -3.82 °C, Kf = -1.86 °C m⁻¹, and m (molality) = moles of solute / kg of solvent. Moles of Na₂SO₄ = 5.00 g / 142 g/mol = 0.0352 mol, and solvent mass = 45.0 g = 0.045 kg. Thus, m = 0.0352 / 0.045 = 0.782 m. Substituting, i = ΔTf / (Kf × m) = 3.82 / (1.86 × 0.782) ≈ 3.11.

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