Vapour Pressure of Solutions of Solids in Liquids — Core Principles

Core Principles

When a non-volatile solid is dissolved in a volatile liquid, the vapour pressure of the resulting solution is always lower than that of the pure solvent at the same temperature. This phenomenon occurs because the solute particles occupy a portion of the liquid's surface, reducing the number of solvent molecules that can escape into the vapour phase.

Raoult's Law quantifies this observation, stating that the partial vapour pressure of the solvent in the solution ($P_A$) is directly proportional to its mole fraction ($x_A$) in the solution, given by $P_A = x_A P_A^0$, where $P_A^0$ is the vapour pressure of the pure solvent.

The difference, $P_A^0 - P_A$, is the lowering of vapour pressure. The relative lowering of vapour pressure, $rac{P_A^0 - P_A}{P_A^0}$, is equal to the mole fraction of the solute ($x_B$). This property is colligative, meaning it depends only on the number of solute particles, not their identity.

This principle is crucial for determining the molar mass of unknown non-volatile solutes and forms the basis for understanding other colligative properties.

Important Differences

vs Pure Solvent vs. Solution with Non-volatile Solute

Aspect	This Topic	Pure Solvent vs. Solution with Non-volatile Solute
Surface Area for Evaporation	Entire surface available for solvent molecules to escape.	Portion of surface occupied by non-volatile solute particles, reducing available area for solvent escape.
Rate of Evaporation	Higher rate of solvent molecule escape.	Lower rate of solvent molecule escape due to reduced surface exposure.
Vapour Pressure	Higher vapour pressure ($P_A^0$).	Lower vapour pressure ($P_A < P_A^0$). The extent of lowering depends on solute concentration.
Boiling Point	Lower boiling point (boils when $P_A^0$ equals external pressure).	Higher boiling point (requires higher temperature for $P_A$ to equal external pressure, known as boiling point elevation).
Freezing Point	Higher freezing point.	Lower freezing point (known as freezing point depression).
Raoult's Law	Not applicable in this context (it's a reference point).	Obeys Raoult's Law: $P_A = x_A P_A^0$ (for ideal solutions).

The fundamental difference between a pure solvent and a solution containing a non-volatile solute lies in their vapour pressures and, consequently, other colligative properties. The presence of non-volatile solute particles at the liquid surface in a solution hinders the escape of solvent molecules, leading to a reduced rate of evaporation and thus a lower vapour pressure compared to the pure solvent. This lowering of vapour pressure is a direct cause for the elevation of the boiling point and depression of the freezing point of the solution, all of which are colligative properties dependent on the number of solute particles.