Raoult’s Law for Ideal Solutions

Raoult’s law is a fundamental principle in physical chemistry that describes the vapor pressure of an ideal solution. An ideal solution is one where the intermolecular forces between different chemical species are the same as those between identical species. The law is expressed mathematically as [latex]P_i = P_i^* x_i[/latex]. Here, [latex]P_i[/latex] represents the partial vapor pressure of component ‘i’ above the solution, [latex]P_i^*[/latex] is the vapor pressure of the pure component ‘i’ at the same temperature, and [latex]x_i[/latex] is the mole fraction of component ‘i’ in the liquid phase.

This relationship implies that dissolving a non-volatile solute ([latex]P_{solute}^* = 0[/latex]) in a solvent will lower the solvent’s vapor pressure because its mole fraction [latex]x_{solvent}[/latex] becomes less than 1. For a solution with multiple volatile components, the total vapor pressure above the solution can be calculated by summing the partial pressures of each component, according to Dalton’s Law of Partial Pressures: [latex]P_{total} = \sum_i P_i = \sum_i P_i^* x_i[/latex]. This principle is the theoretical basis for fractional distillation, a process that separates liquids with different boiling points. The component with the higher pure vapor pressure ([latex]P_i^*[/latex]) will be more concentrated in the vapor phase than in the liquid phase, allowing for its separation.