Phase equilibrium
fᶫᵢ = fᵛᵢyᵢφᵛᵢP = xᵢγᵢPˢᵃᵗᵢAt low pressure, φᵛᵢ ≈ 1 and the Poynting correction is neglected.Explore binary vapour–liquid equilibrium with ideal, activity-coefficient, and Peng–Robinson models.
NRTL
Lever rule · phase amounts
Phase equilibrium
fᶫᵢ = fᵛᵢyᵢφᵛᵢP = xᵢγᵢPˢᵃᵗᵢAt low pressure, φᵛᵢ ≈ 1 and the Poynting correction is neglected.Modified Raoult law
P = Σ xᵢγᵢPˢᵃᵗᵢyᵢ = xᵢγᵢPˢᵃᵗᵢ / PIdeal Raoult law is recovered when γ₁ = γ₂ = 1.Ideal binary P–x–y
Pᵇᵘᵇ = x₁Pˢᵃᵗ₁ + x₂Pˢᵃᵗ₂1/Pᵈᵉʷ = y₁/Pˢᵃᵗ₁ + y₂/Pˢᵃᵗ₂Antoine vapour pressure
ln(Pˢᵃᵗ/bar) = A − B/(T + C)The valid temperature interval depends on the selected compound.Activity models
Gᴱ/RT → ln γᵢγᵢ = f(x₁, x₂, model parameters)NRTL and Wilson describe liquid-phase non-ideality.van der Waals EOS
P = RT/(V − b) − a/V²aᵢ = 27R²T²cᵢ/(64Pᶜᵢ)bᵢ = RTᶜᵢ/(8Pᶜᵢ); mixture a uses kᵢⱼ.Peng–Robinson EOS
P = RT/(V − b) − aα/[V(V + b) + b(V − b)]Kᵢ = yᵢ/xᵢ = φᶫᵢ/φᵛᵢaα and b use critical properties and acentric factors; mixture a includes the binary interaction parameter kᵢⱼ.T–x–y holds pressure constant and solves the bubble temperature. P–x–y holds temperature constant and solves the bubble pressure. The plotted dew curve uses the corresponding equilibrium vapour composition y₁.
Equilibrium data
| x₁ liquid | y₁ vapour | Temperature (°C) |
|---|---|---|
| 0.000 | 0.0000 | 100.003 |
| 0.025 | 0.2302 | 93.482 |
| 0.050 | 0.3597 | 89.185 |
| 0.075 | 0.4421 | 86.157 |
| 0.100 | 0.4985 | 83.932 |
| 0.125 | 0.5392 | 82.252 |
| 0.150 | 0.5698 | 80.957 |
| 0.175 | 0.5934 | 79.945 |
| 0.200 | 0.6120 | 79.145 |
| 0.225 | 0.6269 | 78.508 |
| 0.250 | 0.6391 | 77.996 |
| 0.275 | 0.6492 | 77.584 |
| 0.300 | 0.6576 | 77.249 |
| 0.325 | 0.6648 | 76.976 |
| 0.350 | 0.6709 | 76.752 |
| 0.375 | 0.6763 | 76.566 |
| 0.400 | 0.6810 | 76.411 |
| 0.425 | 0.6853 | 76.280 |
| 0.450 | 0.6893 | 76.168 |
| 0.475 | 0.6930 | 76.070 |
| 0.500 | 0.6966 | 75.984 |
| 0.525 | 0.7002 | 75.907 |
| 0.550 | 0.7038 | 75.837 |
| 0.575 | 0.7076 | 75.773 |
| 0.600 | 0.7117 | 75.715 |
| 0.625 | 0.7161 | 75.661 |
| 0.650 | 0.7210 | 75.613 |
| 0.675 | 0.7265 | 75.572 |
| 0.700 | 0.7327 | 75.540 |
| 0.725 | 0.7399 | 75.518 |
| 0.750 | 0.7482 | 75.512 |
| 0.775 | 0.7578 | 75.524 |
| 0.800 | 0.7691 | 75.562 |
| 0.825 | 0.7824 | 75.632 |
| 0.850 | 0.7982 | 75.744 |
| 0.875 | 0.8171 | 75.910 |
| 0.900 | 0.8400 | 76.147 |
| 0.925 | 0.8678 | 76.475 |
| 0.950 | 0.9021 | 76.921 |
| 0.975 | 0.9451 | 77.524 |
| 1.000 | 1.0000 | 78.337 |
Raoult, NRTL and Wilson use the Koretsky Antoine coefficients and are intended for subcritical, low-pressure liquid mixtures. van der Waals and Peng–Robinson calculate fugacities in both phases; Peng–Robinson is generally the better starting point for light gases or elevated pressure. These diagrams are educational simulations; validate interaction parameters and phase stability before process-design use.