The Phase Diagram
The T-xy diagram is the chemical engineer's map of vapor-liquid equilibrium. At any point on the diagram, you know the temperature, the composition of the liquid phase, and the composition of the vapor phase in equilibrium with it. Below the bubble-point curve, everything is liquid; above the dew-point curve, everything is vapor; between them lies the two-phase region where both phases coexist. Every distillation column operates within this lens-shaped region, separating mixtures by exploiting the composition difference between coexisting phases.
Bubble & Dew Points
The bubble-point temperature is the temperature at which the first tiny vapor bubble forms when a liquid is heated at constant pressure. Mathematically, it satisfies Σx_iP_i^sat(T) = P. The dew-point temperature is where the first liquid droplet condenses from a cooling vapor: Σy_i/K_i(T) = 1. The gap between these curves determines how effective a single equilibrium stage is — wider gaps mean greater enrichment per stage and easier separation.
Relative Volatility & Separation
The shape of the T-xy envelope encodes the ease of separation. When the two components have very different boiling points (wide envelope), relative volatility α is large and few distillation stages suffice. When boiling points are close (narrow envelope), α approaches 1 and separation becomes energy-intensive, requiring many stages and high reflux ratios. The simulation shows how adjusting the boiling points changes the envelope width and the resulting equilibrium compositions.
Pressure Effects
System pressure shifts the entire diagram vertically. Higher pressure raises boiling temperatures and generally narrows the VLE envelope because the ratio of vapor pressures P_A^sat/P_B^sat decreases as temperature increases (components become more similar in volatility). This is why vacuum distillation is preferred for close-boiling mixtures — reducing pressure increases relative volatility, widening the phase envelope and improving separation efficiency at the cost of larger column diameter to handle the increased vapor volume.