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Van der Waals equation calculator

Estimate real-gas pressure or temperature with the van der Waals equation using total or molar volume and cited gas constants or custom parameters.

Calculator

Predicted pressure
249,434
Predicted temperature
300
Attraction constant a (Pa m⁶/mol²)
0.00000000
Excluded molar volume b (m³/mol)
0.00000000
Molar volume (m³/mol)
0.01000000
Ideal-gas pressure
249,434
Compressibility factor Z
1.00000000

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How this calculator works

The van der Waals model corrects ideal-gas pressure for molecular attraction and excluded volume. Constants are specific to each gas, and the molar volume must exceed b. The presets convert the cited table into SI units. The model is approximate and can fail near phase coexistence or dense states. Pressure or temperature is determined directly; this tool does not choose a phase from the cubic volume equation.

Formula

(P + a/Vm²)(Vm - b) = RT; P = RT/(Vm - b) - a/Vm²; Vm = V/n; Z = P Vm/(RT).

Worked example

With custom a = b = 0, 1 mol at 300 K in 0.01 m³ gives 249433.879 Pa, matching the ideal-gas law. With 2 mol in 0.01 m³ at 166289.252 Pa and zero corrections, temperature is 100 K.

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Frequently asked questions

What units do the custom constants use?

Use Pa m⁶/mol² for a and m³/mol for b. A table in bar L²/mol² and L/mol needs conversion.

Why must molar volume exceed b?

The available-volume term Vm - b must be positive. At or below b the gas-state formula is invalid.

Does the model predict condensation reliably?

It captures qualitative nonideal behaviour, but detailed phase equilibrium needs a suitable equation of state and phase-stability treatment.

Sources

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