Why does adding a solute lower the vapor pressure of a solution?

When a nonvolatile solute dissolves in a volatile solvent, solute particles occupy the liquid surface, reducing the number of solvent particles available to vaporize. Since the condensation rate remains unchanged, dynamic equilibrium is reestablished at a lower vapor pressure with fewer solvent molecules in the gaseous state.

What is Raoult's law and how does it apply to vapor pressure?

Raoult's law states that the partial pressure of a solution equals the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent. For a solution with 3.5 mol water and 1.5 mol glycerol at 25°C, the mole fraction is 0.70, yielding a vapor pressure of 16.7 torr compared to pure water's 23.8 torr.

How is vapor pressure lowering calculated from the mole fraction of solute?

Vapor pressure lowering (ΔP) is directly proportional to the mole fraction of the solute. Using the equation derived from Raoult's law, if the solute mole fraction is 0.3 and pure water's vapor pressure is 23.8 torr, the pressure lowering equals 7.14 torr, demonstrating this colligative property.

What distinguishes colligative properties from other solution properties?

Colligative properties depend only on the concentration or number of solute particles, not their type. Vapor pressure lowering is a colligative property, meaning any nonvolatile solute at the same concentration produces identical pressure reduction, unlike properties such as pH that depend on solute identity.

What role does dynamic equilibrium play in vapor pressure lowering?

In a pure solvent, dynamic equilibrium occurs when vaporization and condensation rates are equal. In a solution, the reduced solvent surface area decreases vaporization rate. Condensation rate remains constant, so equilibrium reestablishes at lower vapor pressure with fewer solvent molecules in the vapor phase.

Why must a solute be nonvolatile for vapor pressure lowering to occur?

A nonvolatile solute has negligible vapor pressure and cannot escape into the gas phase. This ensures that only solvent molecules contribute to the solution's vapor pressure. If the solute were volatile, it would add its own partial pressure, complicating the relationship and preventing the simple lowering effect observed with nonvolatile solutes.

How does entropy explain vapor pressure lowering in solutions?

The more dispersed nature of matter in a solution, compared to separate solvent and solute phases, stabilizes solvent molecules and hinders their vaporization. This entropy effect results in lower vapor pressure and correspondingly higher boiling point, reflecting the thermodynamic stabilization of the solution state.

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Vapor Pressure Lowering

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Some properties of a solution depend on the type of solute. An aqueous solution of hydrochloric acid turns a pH paper red, while a sodium hydroxide solution turns it blue.

Other properties of a solution depend only on the concentration or the number of particles of the solute rather than the type of solute. These are called colligative properties.

One such property is the vapor pressure of a solution. The vapor pressure of a liquid is the pressure of the gas above the liquid resulting from evaporation when the liquid and the gas are in a dynamic equilibrium in a closed container.

The vapor pressure of the solution is always less than that of the pure solvent.

Consider a solution made when a non-volatile solute, that is one with no measurable vapor pressure, is added to a volatile solvent.

In a pure solvent, the entire surface of the liquid is solvent particles. Some of these particles escape into the gaseous state to create vapor, while some of the gas molecules above condense back into a liquid state.

When the rate of vaporization equals the rate of condensation, a dynamic equilibrium is reached.

In a solution, the liquid surface has both solute and solvent particles. So, a smaller number of the surface solvent particles can vaporize.

The rate of condensation decreases to re-establish the dynamic equilibrium with the diminished rate of vaporization, now with a lower concentration of solvent particles in the gaseous state.

The vapor pressure of a solution can be calculated by Raoult’s law, which states that the partial pressure of a solution is equal to the mole fraction of the solvent, X, multiplied by the vapor pressure of the pure solvent, Pº.

For example, a solution contains 1.5 mol of a non-volatile solute such as glycerol and 3.5 mol of water at 25 °C. The mole fraction of the solvent is 0.70 and the vapor pressure of pure water is 23.8 torr.

The vapor pressure of the solution can be calculated using Raoult’s law to be 16.7 torr, 70% of the vapor pressure of the pure solvent.

An equation for vapor pressure lowering, ΔP, can also be derived from Raoult’s Law. Since the mole fraction of the solvent is equal to one minus the mole fraction of the solute, it can be substituted into Raoult’s Law.

This can be used to create an equation where vapor pressure lowering is directly proportional to the mole fraction of the solute.

Recalling the previous example, the mole fraction of the solute is 1 minus the mole fraction of the solvent. Plugging in the value, the mole fraction of the solute is 0.3.

Given that the vapor pressure of pure water is 23.8 torr, the lowering of vapor pressure is calculated to be 7.14 torr.

Adding ΔP and the vapor pressure of the solution, the vapor pressure of the pure solvent is obtained

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The equilibrium vapor pressure of a liquid is the pressure exerted by its gaseous phase when vaporization and condensation are occurring at equal rate…