How does the McCabe–Thiele method count theoretical stages?

Draw the equilibrium curve and the diagonal on a y–x diagram. The rectifying line is y = R/(R+1)·x + x_D/(R+1), the q-line is y = q/(q−1)·x − z_F/(q−1), and the stripping line joins (x_B, x_B) to their intersection. Starting at (x_D, x_D), step horizontally to the equilibrium curve (the liquid leaving stage 1), then vertically to the operating line, and repeat until x ≤ x_B. The number of steps is the number of theoretical stages including the reboiler, and the step that crosses the intersection is the optimal feed stage. The calculator draws this automatically and reports fractional stages too.

What are the minimum reflux ratio and the Fenske equation?

As the reflux ratio falls, the operating line moves toward the equilibrium curve; when they meet on the q-line (the pinch) infinitely many stages are needed, and that reflux ratio is R_min = (x_D − y*)/(y* − x*). At the other extreme, total reflux needs the fewest stages, given by the Fenske equation N_min = ln[(x_D/(1−x_D))·((1−x_B)/x_B)]/ln α — about 6.43 for x_D = 0.95, x_B = 0.05 and α = 2.5. Practical columns usually run at 1.2–2 times R_min.

How do I use the Antoine equation to find the boiling point at altitude?

The Antoine equation log₁₀P = A − B/(C + t) relates vapor pressure (mmHg) to temperature (°C). A liquid boils when its vapor pressure equals the surrounding pressure, so solving t = B/(A − log₁₀P) − C gives the boiling point at that pressure. The calculator converts altitude to pressure with the International Standard Atmosphere: at 3650 m the pressure is about 484 mmHg and water boils at roughly 87.9 °C. Each constant set is accurate only within its temperature range, and out-of-range results are flagged.

Why can't ordinary distillation produce pure ethanol from ethanol–water?

Ethanol–water is strongly non-ideal and forms a minimum-boiling azeotrope at 78.2 °C and about 95.6 wt% ethanol at 1 atm, where vapor and liquid have the same composition. Beyond that point the vapor is no longer richer in ethanol, so plain distillation stops enriching; azeotropic or extractive distillation, molecular sieves or membranes are needed. This calculator implements only the ideal Raoult model and warns about water, alcohol and acid pairs rather than inventing activity coefficients.

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🍾Distillation Calculator - Antoine Vapor Pressure, T-x-y Diagram & McCabe-Thiele

Distillation separates liquids by their difference in volatility, and this calculator covers the whole chain from pure-component vapor pressure to column design. (1) Vapor pressure and boiling point: Antoine constants (log₁₀P/mmHg = A − B/(C + t/°C), standard values from Lange's Handbook and the Yaws compilation) for 20 common liquids — water, methanol, ethanol, acetone, benzene, toluene, hexane, ethyl acetate, dichloromethane, acetonitrile and more — each checked against its literature normal boiling point to within 1%. Get the vapor pressure at any temperature, the boiling point at any pressure or altitude (at 3650 m the standard pressure is about 484 mmHg and water boils near 87.9 °C), and ΔHvap from two points with the Clausius–Clapeyron equation (water at 25 °C and 100 °C gives about 42.7 kJ/mol). (2) Ideal binary mixtures: bubble and dew points by Raoult's law with T–x–y, P–x–y and y–x diagrams; benzene–toluene at 1 atm and x = 0.5 boils at 92.1 °C with y = 0.714 and α ≈ 2.49. (3) McCabe–Thiele: enter feed composition z_F, feed condition q, distillate x_D, bottoms x_B and the reflux ratio (or a multiple of R_min) to draw the operating lines, q-line and stage-by-stage staircase, with the number of theoretical stages, optimal feed stage, minimum reflux from the pinch, Fenske minimum stages (N_min = 6.43 for x_D = 0.95, x_B = 0.05, α = 2.5) and a Gilliland estimate. (4) Simple batch distillation with the Rayleigh equation. Non-ideal pairs and the ethanol–water azeotrope are flagged.

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How to use Vapor–Liquid Equilibrium & Distillation

1Choose vapor pressure, binary VLE, McCabe–Thiele or batch distillation
2Pick the liquids (or a constant relative volatility α) and enter temperature, pressure, compositions, feed condition and reflux ratio
3Read vapor pressures, bubble and dew points, phase diagrams, stage count, minimum reflux and Fenske results; export charts or CSV

FAQ

How does the McCabe–Thiele method count theoretical stages?: Draw the equilibrium curve and the diagonal on a y–x diagram. The rectifying line is y = R/(R+1)·x + x_D/(R+1), the q-line is y = q/(q−1)·x − z_F/(q−1), and the stripping line joins (x_B, x_B) to their intersection. Starting at (x_D, x_D), step horizontally to the equilibrium curve (the liquid leaving stage 1), then vertically to the operating line, and repeat until x ≤ x_B. The number of steps is the number of theoretical stages including the reboiler, and the step that crosses the intersection is the optimal feed stage. The calculator draws this automatically and reports fractional stages too.
What are the minimum reflux ratio and the Fenske equation?: As the reflux ratio falls, the operating line moves toward the equilibrium curve; when they meet on the q-line (the pinch) infinitely many stages are needed, and that reflux ratio is R_min = (x_D − y*)/(y* − x*). At the other extreme, total reflux needs the fewest stages, given by the Fenske equation N_min = ln[(x_D/(1−x_D))·((1−x_B)/x_B)]/ln α — about 6.43 for x_D = 0.95, x_B = 0.05 and α = 2.5. Practical columns usually run at 1.2–2 times R_min.
How do I use the Antoine equation to find the boiling point at altitude?: The Antoine equation log₁₀P = A − B/(C + t) relates vapor pressure (mmHg) to temperature (°C). A liquid boils when its vapor pressure equals the surrounding pressure, so solving t = B/(A − log₁₀P) − C gives the boiling point at that pressure. The calculator converts altitude to pressure with the International Standard Atmosphere: at 3650 m the pressure is about 484 mmHg and water boils at roughly 87.9 °C. Each constant set is accurate only within its temperature range, and out-of-range results are flagged.
Why can't ordinary distillation produce pure ethanol from ethanol–water?: Ethanol–water is strongly non-ideal and forms a minimum-boiling azeotrope at 78.2 °C and about 95.6 wt% ethanol at 1 atm, where vapor and liquid have the same composition. Beyond that point the vapor is no longer richer in ethanol, so plain distillation stops enriching; azeotropic or extractive distillation, molecular sieves or membranes are needed. This calculator implements only the ideal Raoult model and warns about water, alcohol and acid pairs rather than inventing activity coefficients.

Features

Antoine constants for 20 common liquids, each checked against its normal boiling point
Vapor pressure at any temperature; boiling point at any pressure or altitude
ΔHvap from two points (Clausius–Clapeyron) and from the Antoine slope
Raoult's law bubble and dew points with T–x–y, P–x–y and y–x diagrams
McCabe–Thiele construction: operating lines, q-line, staircase, stage count and optimal feed stage
Minimum reflux from the pinch, Fenske N_min, total-reflux stepping and Gilliland estimate
Rayleigh batch distillation: liquid remaining and average distillate composition
Non-ideality and ethanol–water azeotrope warnings; PNG, SVG and CSV export

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