Phase equilibria is the study of when and how a mixture splits into two or more distinct physical phases, liquid and vapour most commonly in chemical engineering, and exactly what composition each resulting phase settles into once that split happens. Getting that prediction right is a genuinely practical question, not an academic one: it's what actually tells an engineer whether a given process can be handled with a simple holding tank, or whether it genuinely requires a full distillation column to separate its components.
A mixture's components don't split into phases in equal proportion to how they started
When a liquid mixture partially vaporises, the resulting vapour phase and the remaining liquid phase don't generally carry the same relative proportions of each component the original mixture had; a more volatile component tends to concentrate more heavily in the vapour phase, while a less volatile one tends to stay concentrated in the liquid. Phase equilibria calculations predict exactly how strongly that split happens for a given mixture at a given temperature and pressure, using each component's relative volatility as the key figure driving how effectively the phases can actually be separated from each other.
How strongly that split happens determines what equipment can actually achieve real separation
If a mixture's components split very unevenly between phases, even a single vaporisation step can achieve a genuinely useful separation, sometimes needing nothing more elaborate than a simple flash tank. If the components instead split only weakly between phases, a single step won't separate them meaningfully at all, and achieving real separation requires a distillation column that repeats the vaporise-and-condense cycle many times over, stacked stages that progressively concentrate the more volatile component further with each pass. Which of these a given separation actually needs is decided directly by the underlying phase equilibrium behaviour, not by guesswork or convention.
What we're still unsure about
That relative volatility governs how strongly a mixture's components split between liquid and vapour phases, and that this directly determines the separation equipment a process actually needs, are well established, thoroughly confirmed principles of chemical engineering thermodynamics. What's more genuinely a matter of ongoing predictive difficulty is exactly how accurately phase behaviour can be predicted for mixtures with strong, complicated interactions between dissimilar molecules, since some mixtures depart considerably from simpler idealised models, and engineers continue to rely on a mix of measured data and increasingly sophisticated models to predict phase behaviour for exactly these more difficult, non-ideal mixtures, rather than one universal formula covering every case reliably.
This sits inside Thermodynamics & Phase Equilibria, one of eight topics in Chemical Engineering, one of four domains in Engineering, one of seventeen subjects the app can quiz you on.