Freezing Point Depression
Freezing point depression is the decrease in the freezing (solidification) point of a solvent caused by dissolving a solute, because the solute particles disrupt the formation of the ordered solid lattice. The magnitude of depression depends on the number of solute particles per unit mass of solvent, not their chemical nature. Practical applications include road de-icing with salt, antifreeze in vehicle radiators, and the preservation of biological samples in cryoprotective solutions.
Key Formula
ΔTf = i × Kf × m
LaTeX: \Delta T_f = i \cdot K_f \cdot m
| Symbol | Meaning | Unit |
|---|---|---|
| ΔTf | Depression in freezing point | °C or K |
| i | van't Hoff factor | dimensionless |
| Kf | Cryoscopic constant of the solvent | K·kg/mol |
| m | Molality of solution | mol/kg |
Worked Example
Problem
What mass of NaCl must be dissolved in 1.00 kg of water to lower the freezing point by 3.72 °C? Kf(water) = 1.86 K·kg/mol. NaCl dissociates completely into Na⁺ and Cl⁻ (i = 2).
Solution
Step 1 – Rearrange formula: m = ΔTf ÷ (i × Kf) = 3.72 ÷ (2 × 1.86) = 3.72 ÷ 3.72 = 1.00 mol/kg. Step 2 – Moles of NaCl = 1.00 mol/kg × 1.00 kg = 1.00 mol. Step 3 – Mass = 1.00 mol × 58.44 g/mol = 58.44 g.
Answer
58.44 g of NaCl is required
Cryoscopic Constants (Kf) for Common Solvents
| Solvent | Normal FP (°C) | Kf (K·kg/mol) | Common Use |
|---|---|---|---|
| Water | 0.00 | 1.86 | Biological & food chemistry |
| Benzene | 5.50 | 5.12 | Molar mass determination |
| Acetic acid | 16.60 | 3.90 | Organic solvents |
| Cyclohexane | 6.50 | 20.20 | Polymer chemistry |
| Camphor | 179.50 | 37.70 | Micro-cryoscopy |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Colligative Properties
Colligative properties are physical properties of solutions that depend only on the number of solute particles dissolved, not on the chemical identity of those particles. These properties include boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. They are widely used in industries such as food preservation, antifreeze formulation, and clinical medicine to control solution behaviour.
Boiling Point Elevation
Boiling point elevation is the phenomenon by which the boiling point of a solution is higher than that of the pure solvent, due to the presence of dissolved solute particles lowering the vapour pressure of the solvent. The increase in boiling point is directly proportional to the molal concentration of solute particles. This principle is exploited in automotive antifreeze formulations and in certain cooking techniques to raise the boiling temperature of water.
Osmotic Pressure
Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane separating the solution from the solvent. It arises because solvent molecules move spontaneously from a region of lower solute concentration (higher solvent chemical potential) to higher concentration by osmosis. Osmotic pressure is critical in biological systems — it maintains cell turgor, governs kidney function, and is the basis of reverse osmosis water purification.
From Old French "frésir" (to freeze) and Latin "depressio" (a pressing down). Systematic study began with Raoult in 1878; Jacobus van't Hoff derived the theoretical framework in 1887.