Chemistry · General chemistry II · Worked example

Freezing and boiling points of antifreeze

25.0 g of ethylene glycol, C₂H₆O₂, is dissolved in 100.0 g of water. Find the freezing and boiling points of the solution. For water, Kf = 1.86 °C·kg/mol and Kb = 0.512 °C·kg/mol.

Δ T_{f} = i K_{f} m, Δ T_{b} = i K_{b} m

Moles of solute

Ethylene glycol’s molar mass is 2(12.01) + 6(1.008) + 2(16.00) = 62.07 g/mol. It is a nonelectrolyte, so i = 1.

n = \frac{25.0 g}{62.07 g/mol} = 0.4028 mol

Molality

Divide by kilograms of solvent, not by the solution’s mass or volume. Keep the extra digit, 4.028, for the next two steps and round only the reported temperatures.

m = \frac{0.4028 mol}{0.1000 kg} = 4.028 mol/kg

Freezing-point depression

The freezing point drops below 0.00 °C by ΔTf.

Δ T_{f} = (1) (1.86) (4.028) = 7.49 \circ C \Rightarrow T_{f} = - 7.49 \circ C

Boiling-point elevation

The boiling point rises above 100.00 °C by ΔTb.

Δ T_{b} = (1) (0.512) (4.028) = 2.06 \circ C \Rightarrow T_{b} = 102.06 \circ C

Result

The solution freezes at −7.49 °C and boils at 102.06 °C (at 1 atm, treating it as ideal).

Your turn

What is the freezing point of 0.100 m CaCl₂(aq), assuming ideal dissociation?

Show the answer and explanation

About −0.558 °C.

CaCl₂ gives three ions, so i = 3. ΔTf = 3 × 1.86 × 0.100 = 0.558 °C, so the solution freezes at −0.558 °C. The measured value is a little smaller in magnitude because of ion pairing.

Δ T_{f} = (3) (1.86) (0.100) = 0.558 \circ C

Keep exploring

Open the Colligative studio with this solution, switch to boiling-point elevation, then try i = 2 to see what an ionic solute would do.

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Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

Tro, Chemistry: A Molecular Approach, 4th ed., §13.5 Expressing Solution Concentration, pp. 585–592 (molality, p. 588)
Tro, Chemistry: A Molecular Approach, 4th ed., §13.6 Colligative Properties: Vapor Pressure Lowering, Freezing Point Depression, Boiling Point Elevation, and Osmotic Pressure, pp. 593–605 (volatile solutes, p. 597; osmotic pressure, pp. 603–604)
Tro, Chemistry: A Molecular Approach, 4th ed., §13.7 Colligative Properties of Strong Electrolyte Solutions, pp. 605–607
OpenStax Chemistry 2e — Colligative properties

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