What is vapor–liquid equilibrium (VLE)?

Vapor–liquid equilibrium (VLE) is the condition where a liquid mixture and its vapor phase coexist at equilibrium at a given temperature and pressure. At VLE, the composition of each phase is constant in time and related through thermodynamic relationships such as Raoult’s law or more advanced activity-coefficient models.

Which assumptions does this VLE calculator use?

This calculator assumes an ideal binary mixture that obeys Raoult’s law and ideal-gas behavior in the vapor phase. It uses Antoine equations for pure-component vapor pressures. Non-ideal systems, associating components, and electrolytes are not modeled.

Can I use this tool for design of distillation columns?

You can use the VLE calculator to build intuition, generate T–x–y or P–x–y diagrams, and perform simple flash calculations that are useful as a first step in distillation design. However, rigorous column design requires additional tools such as McCabe–Thiele or equilibrium-stage simulators and, for non-ideal mixtures, more advanced thermodynamic models.

Vapor–Liquid Equilibrium (VLE) Calculator

How this VLE calculator works

This tool models a binary vapor–liquid equilibrium (VLE) system assuming an ideal solution that follows Raoult’s law and ideal-gas behavior in the vapor phase. You can:

Generate T–x–y diagrams at constant pressure (isobaric VLE).
Generate P–x–y diagrams at constant temperature (isothermal VLE).
Perform a simple isothermal flash calculation (given overall composition, T, and P).

1. Raoult’s law and Antoine equation

For an ideal binary mixture of components 1 and 2, Raoult’s law states:

\( y_i P = x_i P_i^{sat}(T) \quad (i = 1,2) \)

with \( x_1 + x_2 = 1 \), \( y_1 + y_2 = 1 \).

The pure-component saturation pressures are computed with the Antoine equation:

\( \log_{10}\left(\frac{P_i^{sat}}{\text{mmHg}}\right) = A_i - \dfrac{B_i}{T + C_i} \)

where T is in °C and \( A_i, B_i, C_i \) are Antoine constants.

2. Bubble point and dew point at constant pressure (T–x–y)

At a given pressure \( P \), the bubble-point temperature for a liquid composition \( x_1 \) satisfies:

\( P = x_1 P_1^{sat}(T_b) + (1 - x_1) P_2^{sat}(T_b) \)

The corresponding vapor composition is:

\( y_1 = \dfrac{x_1 P_1^{sat}(T_b)}{P} \)

Similarly, the dew-point temperature for a vapor composition \( y_1 \) satisfies:

\( 1 = y_1 \dfrac{P}{P_1^{sat}(T_d)} + (1 - y_1) \dfrac{P}{P_2^{sat}(T_d)} \)

3. Bubble and dew pressure at constant temperature (P–x–y)

At a fixed temperature T, the bubble pressure for a liquid composition \( x_1 \) is:

\( P_b = x_1 P_1^{sat}(T) + (1 - x_1) P_2^{sat}(T) \)

The dew pressure for a vapor composition \( y_1 \) is:

\( \dfrac{1}{P_d} = \dfrac{y_1}{P_1^{sat}(T)} + \dfrac{1 - y_1}{P_2^{sat}(T)} \)

4. Isothermal flash calculation (Rachford–Rice)

For a feed with overall composition \( z_1 \) at given T and P, we first compute K-values \( K_i = P_i^{sat}(T) / P \). The vapor fraction \( \beta \) is found from the Rachford–Rice equation:

\( f(\beta) = \sum_{i=1}^{2} \dfrac{z_i (K_i - 1)}{1 + \beta (K_i - 1)} = 0 \)

Once \( \beta \) is known, phase compositions follow:

\( x_i = \dfrac{z_i}{1 + \beta (K_i - 1)}, \quad y_i = K_i x_i \)

How to use the VLE calculator

Select the calculation mode:
- T–x–y diagram for isobaric VLE vs. temperature.
- P–x–y diagram for isothermal VLE vs. pressure.
- Isothermal flash for a single equilibrium stage.
Choose a preset system (e.g., ethanol/water or benzene/toluene) or select “Custom components” and enter your own Antoine constants from a reliable data source.
Set operating conditions:
- For T–x–y: specify pressure P (kPa).
- For P–x–y: specify temperature T (°C).
- For flash: specify T, P, and overall composition \( z_1 \).
Click “Run calculation”. The tool will:
- Generate the requested diagram (T–x–y or P–x–y) with both liquid and vapor curves.
- For flash, report vapor fraction, liquid fraction, and phase compositions.
- Allow you to download the underlying data as CSV for further analysis.

Limitations and good practice

Assumes ideal solutions; non-ideal systems may require activity-coefficient models (e.g., NRTL, UNIQUAC).
Antoine constants are valid only over a certain temperature range; extrapolation can be inaccurate.
For design work, always cross-check with experimental data or a process simulator.

FAQ

Can this calculator handle azeotropes?

Azeotropes can appear even under Raoult’s law if the pure-component vapor-pressure curves intersect in a certain way, but most real azeotropes are strongly non-ideal. This tool does not include activity coefficients, so it cannot reliably predict azeotropic behavior for non-ideal mixtures.

Where can I find Antoine constants?

Antoine constants are tabulated in chemical engineering handbooks, the NIST Chemistry WebBook, and many physical property databases. Make sure you use a consistent unit convention (here: T in °C, P in mmHg) and the correct temperature range.