Freezing Point Depression Calculator

Freezing point depression is a colligative property, which means it depends on the number of solute particles rather than on what those particles are.

Formula:

ΔTf = Kf × m × i

T_new = T_freeze − ΔTf

Where:

• ΔTf = freezing point depression (°C or K)
• Kf = cryoscopic constant of solvent
• m = molality (mol solute / kg solvent)
• i = van’t Hoff factor (number of particles per formula unit)

Van’t Hoff factor i:

• Non-electrolytes (glucose, sucrose): i = 1
• NaCl (→ Na⁺ + Cl⁻): ideal i = 2, actual ≈ 1.8 at typical concentrations
• CaCl₂ (→ Ca²⁺ + 2Cl⁻): ideal i = 3, actual ≈ 2.5
• MgSO₄ (→ Mg²⁺ + SO₄²⁻): ideal i = 2, actual ≈ 1.4 (ion pairing)

Kf values for common solvents:

Practical applications:

• Road salt (NaCl): 1 mol NaCl in 1 kg water lowers freezing point by ~3.4°C (i ≈ 1.8)
• Antifreeze (ethylene glycol): a 50/50 mix by volume protects to about −37°C
• Cryoscopy: measuring molar mass of unknown compounds by measuring ΔTf → Molar mass M = (Kf × mass_solute × 1000) / (ΔTf × mass_solvent_g)

Worked example: finding a molar mass by cryoscopy

Dissolve 1.20 g of an unknown non-electrolyte in 25.0 g of camphor, and the melting point drops by 13.6 °C. Camphor’s Kf is 37.7.

• m = ΔTf ÷ (Kf × i) = 13.6 ÷ 37.7 = 0.361 mol/kg
• moles of solute = 0.361 × 0.0250 kg = 0.00902 mol
• M = 1.20 g ÷ 0.00902 mol = 133 g/mol

Camphor is the traditional solvent for this because its Kf is so large. Run the same sample in water and the freezing point moves by only 0.67 °C, which is hard to read off an ordinary thermometer.

Why the measured drop always comes up a little short

The formula assumes every ion wanders off independently. In a real solution the oppositely charged ones spend part of their time paired, so 1 molal NaCl behaves more like 1.8 molal than 2. The gap widens with concentration and with charge. Magnesium sulfate is nominally i = 2 and measures nearer 1.4, because a doubly charged pair holds together far more readily than a singly charged one.

Use the ideal integer for homework. For anything you plan to rely on, measure it, or look up the value at the concentration you are actually working at.