Ideal and Non-ideal Solution Behavior

Core Idea

Ideal solutions follow Raoult's law and require no heat of mixing. Real solutions exhibit deviations quantified by activity coefficients γᵢ; fugacity f̄ᵢ = γᵢ xᵢ fᵢ replaces partial pressure. Common models (Wilson, NRTL, UNIQUAC) predict liquid-liquid and vapor-liquid equilibrium based on component interactions, critical for distillation and extraction design.

Explainer

From partial molar properties, you know that the chemical potential of component i in a mixture is μᵢ = μᵢ° + RT ln(aᵢ), where aᵢ is the activity — a dimensionless measure of how "active" the component is compared to a reference state. The key question is how activity relates to composition. The answer depends on whether the solution is ideal.

An ideal solution is one where every molecule experiences the same intermolecular forces regardless of its neighbors. This means mixing is purely entropic — there is no enthalpy of mixing (ΔH_mix = 0) and the volume doesn't change on mixing (ΔV_mix = 0). Under these conditions, Raoult's law holds: the partial pressure of component i above the solution equals its mole fraction times its pure-component saturation pressure, pᵢ = xᵢ Pᵢˢᵃᵗ. Activity coefficients γᵢ are all equal to 1. Ideal behavior is a reasonable approximation for mixtures of chemically similar species (e.g., benzene + toluene, or isotopes), but most engineering systems deviate significantly.

Real solutions have non-unity activity coefficients. If molecules of different species repel each other more than like molecules do (weaker cross-interactions), the vapor pressure exceeds the Raoult's law prediction — a positive deviation (γᵢ > 1). The liquid molecules prefer to escape into the vapor. If cross-interactions are stronger than like-interactions (e.g., hydrogen bonding between different species), vapor pressures fall below Raoult's law — negative deviation (γᵢ < 1). The activity coefficient captures this departure: the fugacity in the liquid phase is f̄ᵢ = γᵢ xᵢ fᵢ, where fᵢ is the pure-component fugacity.

The engineering consequences are large. Azeotropes occur when the vapor and liquid compositions become equal — no further separation is possible by simple distillation. For a positive-deviation binary mixture, the total vapor pressure has a maximum above what Raoult's law predicts; at that composition, the mixture boils at a temperature lower than either pure component (minimum-boiling azeotrope). The ethanol-water system at 95.6 mol% ethanol (78.1°C at 1 atm) is the canonical example — this is why absolute alcohol cannot be made by distillation alone. Negative-deviation systems form maximum-boiling azeotropes (the HCl-water azeotrope at 20.2% HCl, 108.6°C). Activity coefficient models like Wilson, NRTL, and UNIQUAC fit experimental phase equilibrium data and extrapolate to other conditions, making them the workhorses of distillation design software.