🧪 Fractional Distillation — VLE & the McCabe-Thiele Method

Watch a McCabe-Thiele staircase construction show how each theoretical plate enriches vapor in the more volatile component, and see why fractional distillation beats a single simple-distillation pass.

ChemistryInteractive
McCabe-Thiele x-y diagram: equilibrium curve, y=x diagonal, and the staircase construction · Right strip: pot composition · Press Play to animate

How it Works

When a binary liquid mixture of components A (more volatile, lower boiling) and B (less volatile, higher boiling) boils, the vapor above it is always richer in A than the liquid it came from. This is vapor-liquid equilibrium (VLE), governed by Raoult's law and summarized by the relative volatility α. Plotting vapor mole fraction y against liquid mole fraction x traces an equilibrium curve that bows above the y=x diagonal — the larger α is, the more the curve bows, and the easier separation becomes.

A single boil-and-condense step is simple distillation: one equilibrium jump from x to y. Fractional distillation repeats this jump many times inside a column of theoretical plates, each one an idealized vaporization-condensation stage. The McCabe-Thiele staircase construction visualizes this: starting on the diagonal at the liquid composition, step up to the equilibrium curve (one vaporization), then across to the diagonal (that vapor condensing to become the next stage's liquid). Each full step is one plate, and the final height reached is the achievable distillate purity. Meanwhile, as the more volatile component is preferentially removed, the composition remaining in the pot drifts toward B — a slow depletion known as Rayleigh distillation.

Relative volatility: α = (y_A/x_A) / (y_B/x_B) = (y_A/x_A) / ((1−y_A)/(1−x_A))
Equilibrium curve: y = α·x / (1 + (α−1)·x)
McCabe-Thiele step: (x, x) → (x, y_eq(x)) → (y_eq(x), y_eq(x))
Rayleigh distillation: ln(L₀/L) = ∫ dx / (y*(x) − x), x from x_W to x₀

Frequently Asked Questions

What is vapor-liquid equilibrium and why is vapor always richer in the more volatile component?

Vapor-liquid equilibrium (VLE) describes the composition of vapor that forms above a boiling liquid mixture at equilibrium. Because the more volatile component A has a higher vapor pressure, Raoult's law predicts that the vapor phase is always enriched in A relative to the liquid it boiled from: y_A > x_A whenever A is more volatile than B.

What is relative volatility α and how is it defined?

Relative volatility α = (y_A/x_A) / (y_B/x_B) compares how much more readily component A vaporizes relative to B. A larger α means the equilibrium curve bows further above the y=x diagonal, so a given liquid composition produces a much richer vapor, making separation easier with fewer theoretical plates.

What does a theoretical plate represent?

A theoretical plate is an idealized stage where vapor and liquid reach full equilibrium before the vapor moves on and the liquid falls back. Each plate corresponds to one vaporization-condensation cycle, and each cycle enriches the vapor further in the more volatile component.

Why do more theoretical plates give better separation?

Every plate performs one equilibrium enrichment step. Stacking plates in a fractionating column repeats this enrichment multiple times before the vapor exits at the top, so a column with more plates can reach a much higher purity distillate than a single boiling flask.

What does the McCabe-Thiele staircase construction show and how do you read it?

The McCabe-Thiele method draws steps between the equilibrium curve and the y=x diagonal on an x-y diagram. Starting from the liquid composition, a vertical line rises to the equilibrium curve (one vaporization step), then a horizontal line moves to the diagonal (that vapor condensing into the next stage's liquid). Each full step is one theoretical plate; the number of steps needed to reach a target purity is the number of plates required.

What is the difference between simple distillation and fractional distillation?

Simple (single-stage) distillation performs only one vaporization-condensation step, giving modest enrichment limited by the equilibrium curve at that composition. Fractional distillation uses a packed or plated column that provides many theoretical plates, repeating the enrichment step over and over to reach a much higher final purity.

What is an azeotrope and why does it limit distillation?

An azeotrope is a composition where the vapor has exactly the same composition as the liquid (y = x on the equilibrium curve), so no amount of additional equilibrium stages can separate the mixture further by ordinary distillation. Ethanol-water is the classic example, forming an azeotrope near 95.6% ethanol by mass — which is why distilled spirits cannot exceed that purity through distillation alone.

What causes real vapor-liquid equilibrium curves to deviate from the ideal, constant-α model?

Ideal Raoult's law behavior with constant relative volatility only holds for chemically similar liquids, such as benzene-toluene. Mixtures with strong intermolecular interactions, like ethanol and water, show non-ideal behavior where α itself varies with composition, which is what produces azeotropes and curves that cross the y=x diagonal.

What are real-world applications of fractional distillation?

Fractional distillation is used in petroleum refining towers that separate crude oil into gasoline, kerosene, diesel and other fractions by boiling point, in alcohol and spirit production, in industrial separation of chemical mixtures, and in cryogenic air separation plants that split liquid air into nitrogen and oxygen.

About this simulation

Written by MySimulator Team · Reviewed by MySimulator Editorial Review

Last updated: 11 July 2026

This simulator draws a live McCabe-Thiele diagram for an idealized binary liquid mixture. Drag the relative volatility slider and watch the blue equilibrium curve bow further above the diagonal — the signature of a component that vaporizes much more readily than its partner. Press Play and the amber staircase climbs step by step, one theoretical plate at a time, each step landing a little higher on the diagonal to show exactly how a fractionating column enriches vapor far beyond what a single boil-and-condense pass could achieve. As the animation loops, the pot composition slowly drifts toward the less volatile component, a slow depletion known as Rayleigh distillation.

🔬 What it shows

A McCabe-Thiele x-y diagram with the equilibrium curve, the y=x diagonal, and an animated staircase construction that steps from the pot's liquid composition up to the equilibrium curve and across to the diagonal, once per theoretical plate. A side panel shows the boiling pot's liquid color-coded by its current composition.

🎮 How to use

Adjust relative volatility α, the number of theoretical plates, and the initial pot composition x₀, or pick a mixture preset. Press Play to animate the staircase construction and watch the pot composition deplete over repeated distillation cycles; press Reset to return to the starting charge.

💡 Did you know?

Benzene and toluene form a nearly ideal pair with constant relative volatility, which is why textbooks use it as the classic McCabe-Thiele example. Ethanol and water, by contrast, are non-ideal and form an azeotrope near 95.6% ethanol — no number of theoretical plates can push ordinary distillation past that point.

Frequently asked questions

What does the x₀ slider control?

x₀ sets the starting liquid mole fraction of the more volatile component A in the distillation pot, the point on the diagonal where the McCabe-Thiele staircase begins its first step upward toward the equilibrium curve.

Why does the equilibrium curve bow above the diagonal, and what happens if α is close to 1?

The curve bows above y=x because the more volatile component always concentrates in the vapor. As α approaches 1, the two components vaporize almost equally readily, so the curve hugs the diagonal and even many theoretical plates barely improve purity — a sign the mixture is nearly impossible to separate by ordinary distillation.

What is Rayleigh distillation and why does the pot composition decrease over time?

As vapor is continuously drawn off the top of the column, it always carries away more of the volatile component than the pot currently holds. This selective removal steadily depletes the volatile component from the remaining liquid, a process described by the Rayleigh distillation equation and visualized here as the pot's composition drifting down each animation cycle.

What do the mixture presets represent?

Benzene-toluene and the generic high- and low-volatility pairs are idealized systems with constant relative volatility, ideal for the McCabe-Thiele method. The ethanol-water preset approximates the low end of its volatility range but is marked non-ideal because its real relative volatility shrinks toward 1 near the azeotrope, which this simplified constant-α model does not capture.

How is distillate purity for N plates compared to a single simple-distillation pass?

The stats panel computes the vapor composition reachable after one plate (simple distillation) and after the full N-plate staircase, then reports the difference in percentage points. This purity gain grows quickly with additional plates, especially at lower relative volatility, which is exactly why industrial columns use many plates rather than one boiling flask.

What are the limitations of this idealized simulation?

The model assumes constant relative volatility, ignores reflux ratio, plate efficiency below 100%, and heat and mass transfer effects, and cannot reproduce a real azeotrope where the curve crosses the diagonal. It is intended to build intuition for the McCabe-Thiele method and Rayleigh depletion, not to replace rigorous process design calculations.