Colligative Properties

When a solute is added to a pure solvent (A), the mole fraction of A decreases. The mole fraction is the ratio of the number of moles of A to the total number of moles in the solution. This decrease in mole fraction leads to a reduction in A's chemical potential (μ_A).

The changes in μ_A also affect the solution's colligative properties. Colligative properties are properties of a solution that depend only on the number of solute particles present, not their identity. Examples include boiling point elevation and freezing point depression. Vapor pressure measures the pressure exerted by a vapor in equilibrium with its liquid or solid phase. A decrease in μ_A means the solution's vapor pressure is lower than pure A's. This suggests that A is less likely to transition from the liquid to the gas phase in the solution than in its pure form.

However, introducing a nonvolatile solid solute to a solvent has minimal impact on the overall vapor pressure of the solution. The vapor pressure is expressed as the product of A's mole fraction (X_A), its vapor pressure (P*_A), and the activity coefficient (𝛄_A). The activity coefficient measures the deviation of a component from its ideal behavior.

The change in vapor pressure (ΔP_A) is the difference between the vapor pressure of the solution and that of pure A. The expression of ΔP_A is obtained by replacing the term for the solution vapor pressure in the equation and assuming 𝛄_A to be unity in very dilute solutions. This assumption simplifies the equation, making it more practical to apply in these cases.

The equation can also be expressed using the mole fraction of a non-dissociating solute, which is a solute that does not break into ions when dissolved in a solvent. In summary, adding a solute to a solvent changes the solvent's mole fraction and μ value. These changes are reflected in the solution's colligative properties, such as vapor pressure, and can be modeled mathematically.