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Chemical Engineering
Vapor-Liquid Equilibrium Simulator — Raoult's Law
When an ideal binary mixture is in equilibrium between its liquid and its vapour, what composition does each phase have and at what temperature? From Raoult's law and the Antoine equation this tool computes the bubble point, dew point, equilibrium compositions and relative volatility in real time, and lets you see on the T-x-y and y-x diagrams exactly why distillation can separate components.
Parameters
Binary system (light-heavy)
Sets the Antoine constants. Component 1 is the lighter (more volatile) component
Liquid-phase light fraction x₁
Input composition for the bubble-point calculation
Vapour-phase light fraction y₁
Input composition for the dew-point calculation
Total pressure P
kPa
Operating pressure of the system. 101.3 kPa is standard atmospheric
Results
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Bubble point T_b (°C)
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Equil. vapour y₁ (with x₁)
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Dew point T_d (°C)
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Equil. liquid x₁ (with y₁)
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Relative volatility α
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Enrichment y₁ − x₁
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Boiling-point diagram (T-x-y) — operating points and tie line
The lower curve is the bubble-point line, the upper one the dew-point line, and the region between them is the two-phase zone. The pulsing dots are the current operating points and the horizontal line is the tie line linking the equilibrium liquid and vapour.
T-x-y diagram — bubble and dew curves
y-x equilibrium diagram — equilibrium curve and diagonal
Raoult's law. The partial pressure p_i of each component is its liquid mole fraction x_i times the pure-component vapour pressure P_i^sat. The temperature at which the partial pressures sum to the total pressure is the bubble point.
The pure-component vapour pressure follows the Antoine equation (T in °C, P^sat in mmHg, constants A, B, C component-specific). The equilibrium vapour composition y₁ comes directly from Raoult's law.
$$\alpha=\frac{P_1^{sat}}{P_2^{sat}}$$
Relative volatility α is the ratio of the light and heavy pure-component vapour pressures. The vapour is always richer in the more volatile component, and the further α is from 1 the easier the separation by distillation.
What is Vapor-Liquid Equilibrium and Raoult's Law?
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"Vapor-liquid equilibrium" comes up all the time in chemical engineering. Basically it's the steady state where a liquid and its vapour sit together, right?
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Yes, that picture is fine. Put a benzene-toluene mixture in a closed vessel at a fixed temperature and a vapour builds up above the liquid surface. When the rates of evaporation and condensation just balance and neither the liquid nor the vapour composition changes any more, that is vapor-liquid equilibrium. The real question is: "if the liquid is 50:50, what ratio is the vapour above it?" and "at what temperature does it start to boil?" Raoult's law answers exactly that.
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Raoult's law — that's something like p = x·P, isn't it? What does that equation actually say?
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Roughly: "the pressure each component contributes to the vapour (its partial pressure) is set by how much of it is in the liquid (the mole fraction x) times the vapour pressure P^sat it would have on its own as a pure liquid." That is p_i = x_i·P_i^sat. If benzene makes up half the liquid, its partial pressure is half the pure-benzene vapour pressure. The total pressure is the sum of the benzene and toluene partial pressures. For an ideal mixture that is all you need to solve the equilibrium.
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The pure-component vapour pressure P^sat changes with temperature. How do you get that?
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That's where the Antoine equation comes in: log₁₀P^sat = A − B/(C+T), with A, B and C constants fitted to experiment for each component. Plug in a temperature T and you get the pure-component vapour pressure. This tool uses it to find, for a fixed liquid composition x₁, the temperature T that satisfies Σx_i·P_i^sat = P — it searches with bisection. That temperature is the boiling point, the bubble point. Drag the x₁ slider and the bubble point moves smoothly between the boiling point of benzene (about 80°C) and toluene (about 110°C).
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I see. So why is the equilibrium vapour always biased toward the lighter component? The result cards always show y₁ above x₁.
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Good question. The light component — benzene here — has a higher vapour pressure than toluene at the same temperature. So in y₁ = x₁·P1^sat/P the P1^sat is large and y₁ gets pushed above x₁. The vapour is always richer in the more volatile component. That is the heart of distillation: vaporise once and condense, and the benzene is more concentrated. Repeat that stage after stage and a 50:50 feed yields 99% benzene. On the y-x diagram below, the equilibrium curve sitting well above the y=x diagonal is exactly "one vaporisation's worth of enrichment."
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There's also that number called relative volatility α. What is it good for?
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Think of α as the "ease-of-separation meter." It is α = P1^sat/P2^sat, the ratio of the two vapour pressures. If α is 2 or 3 the equilibrium curve bulges far from the diagonal and you can separate the mixture in few stages. If α is around 1.1 the curve hugs the diagonal and you need dozens of stages. In practice engineers say "a system with α below about 1.05 cannot be done by ordinary distillation — consider extractive distillation or another route." When α reaches exactly 1 you have an azeotrope, and simple distillation can never make it pure. Switch systems and watch how α changes.
Frequently Asked Questions
Raoult's law states that, in an ideal solution, the partial pressure p_i of each component equals its liquid mole fraction x_i multiplied by the vapour pressure P_i^sat it would have as a pure liquid (p_i = x_i·P_i^sat). The total pressure P is the sum of the partial pressures. This tool uses the Antoine equation to get the pure-component vapour pressure as a function of temperature and then computes bubble points, dew points and equilibrium compositions for mixtures such as benzene-toluene. For components that are chemically similar, this simple ideal model is accurate enough for practical work.
The bubble point is the temperature at which the first bubble appears when a liquid of a given composition is heated; it is set by the condition that the sum of the partial pressures equals the total pressure, Σx_i·P_i^sat = P. The dew point is the temperature at which the first droplet appears when a vapour of a given composition is cooled, set by Σy_i/P_i^sat = 1/P. At the same total pressure the two temperatures coincide only if the liquid and vapour compositions are equal. On a T-x-y diagram the lower curve is the bubble point and the upper one the dew point, and the region between them is the two-phase coexistence zone.
Relative volatility α is the ratio of the pure-component vapour pressures of the light and heavy components, α = P1^sat/P2^sat, and it measures how easy the separation by distillation is. The further α is from 1, the more the equilibrium vapour is enriched in the light component, so a single vaporise-condense step changes the composition a lot and a high purity can be reached with few stages. Mixtures with α close to 1 (components with close boiling points) are hard to separate and need many column stages or a high reflux ratio. When α equals exactly 1 an azeotrope forms and ordinary distillation cannot separate the mixture.
The light component has a higher pure-component vapour pressure than the heavy one at the same temperature. Raoult's law gives the equilibrium vapour composition as y_1 = x_1·P1^sat/P, and the larger P1^sat is, the more y_1 exceeds x_1. So the vapour phase is always richer in the more volatile component. This enrichment of the light component at every vaporisation is exactly the principle of distillation: by repeating vaporisation and condensation stage after stage, the distillate ends up far purer than the feed. On the y-x diagram in this tool, the equilibrium curve lying above the y=x diagonal at every point is this enrichment made visible.
Real-World Applications
Distillation column design: The distillation columns of oil refineries and petrochemical plants cannot be designed without vapor-liquid equilibrium calculations. Splitting crude oil into light naphtha, kerosene and gas oil, or separating benzene from toluene, both rest on the same "enrichment of the light component at every vaporisation" that this tool shows. Designers solve the vapor-liquid equilibrium at each stage to fix the required number of theoretical stages and the reflux ratio. Because relative volatility α directly sets the separation difficulty, the first thing checked in an early design study is α.
Solvent recovery and purification: Recovering and reusing solvents used in painting, printing or semiconductor manufacturing also relies heavily on purification by distillation. Hydrocarbon solvents such as toluene and hexane tend to form mixtures with chemically similar components and show nearly ideal equilibrium, so calculations based on Raoult's law work well. From the target recovery rate and purity, the column operating conditions are set with this kind of equilibrium calculation.
The basis of process simulators: Commercial process simulators such as Aspen Plus and Pro/II carry out huge numbers of vapor-liquid equilibrium calculations internally. For ideal solutions they use Raoult's law; for non-ideal systems they switch to activity-coefficient models (NRTL, UNIQUAC) or equations of state. The ideal model in this tool is the starting point for understanding those advanced models, and it can also serve as a sanity check that estimates whether a simulation result is reasonable.
Education and concept building: In chemical-engineering education, being able to "read" a T-x-y diagram and a y-x equilibrium diagram is a basic skill. The two-phase region between the bubble and dew curves, reading liquid and vapour compositions off a tie line, the gap between the equilibrium curve and the diagonal showing the separating power — experiencing these as pictures rather than just equations is what leads on to stage counting by the McCabe-Thiele method and the understanding of distillation column design.
Common Misconceptions and Pitfalls
The biggest pitfall is assuming Raoult's law applies to every mixture. Raoult's law holds only for ideal solutions — mixtures where the molecules are similar in size and type and the interaction between unlike molecules is about the same as between like ones. The benzene-toluene and pentane-hexane systems in this tool are exactly such near-ideal cases, but a system like ethanol-water, where hydrogen bonding is involved, deviates strongly from ideality and forms an azeotrope (the point where α reaches 1 and distillation can no longer separate the mixture). Non-ideal systems require the modified Raoult's law with an activity coefficient γ, p_i = γ_i·x_i·P_i^sat, and the results of this tool cannot be applied directly.
Next, confusing the bubble point with the dew point. Even for the same numerical composition, the temperature you get depends entirely on whether you read it as a liquid composition x₁ or a vapour composition y₁. The temperature at which an x₁=0.5 liquid produces a bubble (bubble point) and the temperature at which a y₁=0.5 vapour forms dew (dew point) are different things. That is why this tool provides separate input sliders for the bubble point (x₁) and the dew point (y₁). On the T-x-y diagram, too, remember to read the lower curve (bubble point) against the liquid-composition axis and the upper curve (dew point) against the vapour-composition axis.
Finally, "raising the total pressure always makes separation easier" is not true. Changing the pressure of course changes the bubble- and dew-point temperatures, but the relative volatility α also changes through its temperature dependence. As a general trend, raising the pressure (and hence the temperature) brings α closer to 1 and makes separation harder. Vacuum distillation, on the other hand, lets heat-sensitive materials be handled at low temperature and has the benefit of gaining α. Choosing the pressure means balancing separation difficulty, operating temperature, equipment cost and the availability of cooling water or heat sources; moving the total pressure P in this tool while watching α gives a feel for that sensitivity.
How to Use
Enter liquid mole fraction x₁ (0–1) for component 1 using the slider or numerical input x1LiqNum
Set total system pressure in bar via pressTotalNum; typical range 1–10 bar for light hydrocarbons
Click Calculate to solve Raoult's Law: y₁ = x₁·P₁ˢᵃᵗ / P_total and determine bubble point T_b and dew point T_d
Read equilibrium vapour composition y₁, relative volatility α = K₁/K₂, and enrichment (y₁ − x₁) for separation assessment
Worked Example
For a binary ethane–propane mixture at 5 bar: x₁(ethane) = 0.40, saturation pressures P₁ˢᵃᵗ = 18.5 bar, P₂ˢᵃᵗ = 8.9 bar. Raoult's Law yields K₁ = 18.5/5 = 3.7, K₂ = 8.9/5 = 1.78, relative volatility α = 3.7/1.78 = 2.08. Bubble point T_b ≈ −20°C; vapour enriches to y₁ ≈ 0.62. Enrichment = 0.62 − 0.40 = 0.22, confirming ethane preferentially vaporizes.
Practical Notes
Raoult's Law assumes ideal liquid mixtures; deviations occur for polar pairs (methanol–water) or asymmetric molecular sizes—use activity coefficient models (NRTL, Wilson) for γᵢ > 1.5