Question 11 of 50intermediate🔧 ApplyNumerical2 marks

Calculate the mass of ascorbic acid (Vitamin C, C6H8O6) to be dissolved in 75 g of acetic acid to lower its melting point by 1.5°C. Kf = 3.9 K kg mol-1.

Correct Answer

The mass of ascorbic acid required is 5.07 g.

Exercise: Intext Questions | Q: 1.11 | (Page 23)
For More Understanding

Explanation

This is a straightforward application of the freezing point depression formula. The question provides all necessary values: ΔTf = 1.5°C, Kf = 3.9 K kg mol⁻¹, and mass of solvent (acetic acid) = 75 g. The molar mass of ascorbic acid (C₆H₈O₆) must be calculated from its molecular formula. Since ascorbic acid is a non-electrolyte in acetic acid, the van't Hoff factor i = 1, so no correction for dissociation is needed.

Solution Steps

  1. Step 1: Calculate molar mass of ascorbic acid (C₆H₈O₆) = (6×126 \times 12) + (8×18 \times 1) + (6×166 \times 16) = 72 + 8 + 96 = 176 g mol⁻¹

  2. Step 2: Using the formula for depression in freezing point: ΔTf = Kf × m, where m is molality

  3. Step 3: Calculate molality: m = ΔTf / Kf = 1.5 / 3.9 = 0.3846 mol kg⁻¹

  4. Step 4: Convert mass of solvent to kg: 75 g = 0.075 kg

  5. Step 5: Calculate moles of ascorbic acid: moles = molality × mass of solvent (kg) = 0.3846×0.0750.3846 \times 0.075 = 0.02885 mol

  6. Step 6: Calculate mass of ascorbic acid: mass = moles × molar mass = 0.02885×1760.02885 \times 176 = 5.07 g

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