Concept of colligative properties of solutions
Colligative properties are properties of dilute solutions that depend only on the number of particles of a non-volatile solute and do not depend on its chemical nature. The decisive role is played by the number of particles in the solution, rather than their individual characteristics. Colligative properties include the lowering of the saturated vapor pressure of the solvent over the solution, elevation of the boiling point, depression of the freezing point, and osmotic pressure.
The theoretical basis of all quantitative relationships is Le Chatelier's principle: when a solute is added, the equilibrium between the liquid and gaseous phases of the solvent shifts, which leads to a change in the physical constants of the solution.
Raoult's first law
The vapor pressure of a solvent over a solution of a non-volatile substance is always lower than over the pure solvent at the same temperature. The explanation is based on the dynamic equilibrium of evaporation ⇌ condensation. When a non-volatile substance is added to the solvent, part of the solvent molecules is bound by the solvation process and leaves the equilibrium. According to Le Chatelier's principle, the equilibrium shifts toward the liquid phase—condensation predominates, so the vapor pressure decreases.
Quantitatively, the vapor pressure lowering is proportional to the mole fraction of the solute. It is the mole fraction that is used in the first formulation of Raoult's law.
Raoult's second law: boiling and freezing
The second law describes the change in phase transition temperatures:
- Boiling point elevation of the solution compared to the pure solvent: ΔTb = i · E · m.
- Freezing point depression of the solution: ΔTf = i · K · m.
Here m is the molal concentration (moles of solute per 1 kg of solvent). Molality is used because, unlike molarity which changes due to thermal expansion of the solution, it is temperature-independent.
E is the ebullioscopic constant, K is the cryoscopic constant. These are tabulated characteristics of the solvent: for water, cyclohexane, naphthalene, and benzene they are known and depend only on the nature of the solvent.
Van 't Hoff's isotonic coefficient
The isotonic coefficient i accounts for the dissociation of the solute and effectively shows into how many particles a formula unit breaks down in solution.
- For non-electrolytes (glucose, sucrose, urea, amino acids), i = 1.
- For strong electrolytes, i is equal to the number of ions into which the formula unit dissociates: NaCl → 2 (Na⁺ + Cl⁻), K₂SO₄ → 3 (2K⁺ + SO₄²⁻), AlCl₃ → 4.
- For weak electrolytes, i takes a fractional value and depends on the degree of dissociation.
The larger i is, the more pronounced the colligative effects are at the same molality.
Third law: osmotic pressure (van 't Hoff's law)
When two solutions of different concentrations are separated by a semipermeable membrane, the solvent spontaneously passes into the more concentrated solution. The pressure that must be applied to stop this transition is called osmotic pressure.
Van 't Hoff's equation: π = i · C · R · T, where C is the molar concentration (this is the only colligative law using molarity), R is the universal gas constant, and T is the absolute temperature in kelvins. Osmosis forms the basis of plant cell turgor, renal function, and infusion therapy.
Practical examples
- Salting water for pasta: salt raises the boiling point, so it is more rational to salt the water after it has already boiled to avoid wasting extra energy on heating.
- Salting icy roads: salt brine freezes at a significantly lower temperature than pure water, so ice melts even at sub-zero ambient temperatures.
- Plant sap in winter: a high concentration of sugars in the cell sap of trees lowers the freezing point, protecting tissues from ice destruction during frosts.
Key points
- Colligative properties depend only on the number of solute particles, not on their nature.
- Raoult's first law: the vapor pressure of the solvent over a solution is lower than over the pure solvent; the mole fraction is used.
- Raoult's second law relates the boiling and freezing ΔT to molality through constants E and K.
- Molality is preferred over molarity because it does not depend on temperature.
- The isotonic coefficient i reflects dissociation: for non-electrolytes i = 1, for strong electrolytes it equals the number of ions.
- Van 't Hoff's law describes osmotic pressure: π = i·C·R·T, the only law using molar concentration.
- Le Chatelier's principle underlies all colligative relationships.
- Everyday illustrations: salt on roads, boiling salted water, frost resistance of plant saps.