Depression of Freezing Point

When a solute is dissolved in a solvent, one of the most striking changes is that the resulting solution freezes at a lower temperature than the pure solvent. This phenomenon, known as the depression of freezing point (or freezing point depression), is a colligative property — meaning it depends only on the number of solute particles dissolved, not on their chemical identity. Whether you dissolve sugar, salt, or urea in water, the same number of moles of particles will produce the same drop in freezing point. The physical explanation lies in thermodynamics. At the freezing point of a pure solvent, the chemical potential of the liquid and solid phases are equal. When a solute is added, it lowers the chemical potential of the liquid phase (by increasing the entropy of mixing) without significantly affecting the solid phase. This imbalance means the solid phase can only become stable at a lower temperature, where equilibrium is re-established. In simpler terms, solute particles disrupt the ordered crystal lattice formation, so more kinetic energy must be removed — i.e., the temperature must drop further — before freezing can occur. Freezing point depression has enormous practical importance. Antifreeze mixtures in car radiators, road de-icing salts, and the preservation of biological tissues all exploit this colligative property. Understanding the quantitative relationship between solute concentration and the freezing point change — captured by the cryoscopic constant, $K_f$ — allows chemists and engineers to design solutions for precise thermal applications.

Key takeaways

What is a Colligative Property?
The Role of Molality
The Cryoscopic Constant, K_f
The van 't Hoff Factor, i
Antifreeze: A Real-World Application

What is a Colligative Property?

Colligative properties depend on the ratio of solute particles to solvent particles (concentration), not on what those particles are. Freezing point depression, boiling point elevation, osmotic pressure, and vapour pressure lowering are all colligative properties. This means 1 mol of glucose and 1 mol of urea dissolved separately in 1 kg of water each produce identical freezing point depressions.

The Role of Molality

Freezing point depression calculations use molality (m) — moles of solute per kilogram of solvent — rather than molarity. Molality is temperature-independent because it is based on mass, not volume. The formula is: m = (moles of solute) ÷ (kilograms of solvent). For example, dissolving 0.5 mol of glucose in 500 g (0.5 kg) of water gives m = 0.5 ÷ 0.5 = 1.00 mol kg⁻¹.

The Cryoscopic Constant, K_f

Each solvent has a characteristic cryoscopic constant, $K_f$ , which represents how much the freezing point drops per molal unit of solute. For water, $K_f = 1.86\ \text{°C kg mol}^{-1}$ . This value is derived from thermodynamic properties of the solvent: $K_f = \frac{R T_f^2 M}{\Delta H_{fus} \times 1000}$ , where $T_f$ is the freezing point of the pure solvent in Kelvin, $M$ is the molar mass of the solvent in g mol⁻¹, and $\Delta H_{fus}$ is the enthalpy of fusion per gram. For benzene, $K_f = 5.12\ \text{°C kg mol}^{-1}$ ; for camphor, $K_f = 37.7\ \text{°C kg mol}^{-1}$ — making camphor useful for molecular mass determination.

The van 't Hoff Factor, i

For electrolytes that dissociate into ions, the actual number of particles in solution is greater than the formula units dissolved. The van 't Hoff factor $i$ accounts for this. For a non-electrolyte like glucose, $i = 1$ . For NaCl, which dissociates as $\ce{NaCl -> Na^+ + Cl^-}$ , the ideal $i = 2$ . For $\ce{CaCl2 -> Ca^{2+} + 2Cl^-}$ , $i = 3$ . In reality, ion-pairing in concentrated solutions causes $i$ to be slightly less than the ideal integer value, but for dilute solutions the ideal value is a good approximation.

Antifreeze: A Real-World Application

Ethylene glycol ( $\ce{HOCH2CH2OH}$ , molar mass 62.07 g mol⁻¹) is the active component in most automotive antifreeze. Because it is a molecular (non-electrolyte) compound, $i = 1$ . A 50/50 mixture by volume of ethylene glycol and water (roughly 9.0 mol kg⁻¹) lowers the freezing point by approximately $\Delta T_f = 1.86 \times 9.0 \approx 16.7\ \text{°C}$ , giving a freeze point near $-16.7\ \text{°C}$ . Road salt (\ce{NaCl}) with $i = 2$ is even more effective per mole: 1 mol kg⁻¹ of NaCl depresses the freezing point by $1.86 \times 2 = 3.72\ \text{°C}$ .

The Key Equation

\Delta T_f = i \cdot K_f \cdot m

\Delta T_f — Freezing point depression (°C (or K)): The magnitude of the decrease in freezing point relative to the pure solvent. Always a positive value; the actual new freezing point is T_f(pure) − ΔT_f.
i — van 't Hoff factor (dimensionless): Number of particles produced per formula unit of solute when dissolved. i = 1 for non-electrolytes; i = 2 for NaCl; i = 3 for CaCl₂ (ideal, dilute solutions).
K_f — Cryoscopic constant (°C kg mol⁻¹): A solvent-specific constant reflecting its thermodynamic properties. Water: 1.86; Benzene: 5.12; Acetic acid: 3.90; Camphor: 37.7 °C kg mol⁻¹.
m — Molality (mol kg⁻¹): Moles of solute dissolved per kilogram of solvent (not solution). m = n(solute) / mass(solvent in kg).

Worked Example

Problem. A car radiator contains a solution made by dissolving 1.20 kg of ethylene glycol (\ce{HOCH2CH2OH}, M = 62.07 g mol⁻¹) in 4.00 kg of water. (a) Calculate the molality of the solution. (b) Calculate the freezing point depression. (c) State the new freezing point of the coolant.

\Delta T_f = 1 \times 1.86 \times 4.83 = 8.99\ ^\circ\text{C};\quad T_f = -8.99\ ^\circ\text{C}

Answer. The freezing point of the coolant is approximately −9.0 °C.

Figure

Diagram

Origins · 1 minFrançois-Marie Raoult and how this was discovered

François-Marie Raoult

1830–1901 · French

Raoult is best known for Raoult's Law governing vapour pressure lowering, but he was equally pioneering in systematic studies of freezing point depression. Between 1878 and 1882, he measured the freezing point depressions of hundreds of solutions in various solvents and established the quantitative relationship between solute concentration and ΔT_f, laying the groundwork for the concept of the cryoscopic constant. His careful, reproducible measurements helped establish colligative properties as a field and provided early evidence for the ionic dissociation theory when he noticed that electrolyte solutions produced anomalously large depressions. Raoult worked mostly without laboratory assistants and often funded his own research. He declined academic positions in Paris to remain in Grenoble, where he could carry out his meticulous experimental work undisturbed.

Boiling Point Elevation — Boiling point elevation is the complementary colligative property: solutes raise the boiling point of a solvent by the analogous equation ΔT_b = i·K_b·m, using the ebullioscopic constant K_b instead of K_f.
Osmotic Pressure — Osmotic pressure (π = iMRT) is another colligative property depending on particle count. It shares the same theoretical foundation as freezing point depression and is especially important in biological and medical contexts.
Molality and Concentration Units — Freezing point depression calculations require molality (mol kg⁻¹). Understanding why molality is preferred over molarity for colligative properties is essential to applying the ΔT_f formula correctly.
van 't Hoff Factor and Electrolyte Dissociation — The van 't Hoff factor i directly multiplies the freezing point depression for electrolytes. Understanding ionic dissociation (e.g., NaCl → Na⁺ + Cl⁻) is critical for correctly calculating ΔT_f for salts and other strong electrolytes.