Van der Waals equation

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Corrected gas equation.

Key relation(P + a/V²)(V − b) = RT

(P + a/V²)(V − b) = RT per mole corrects for attraction (a) and finite molecular volume (b). It predicts a critical point.

Worked example

CO₂: a = 0.364 Pa·m⁶/mol², b = 4.27×10⁻⁵ m³/mol.

Common mistake

It's an approximation.

In more detail

The van der Waals equation (P + a n²/V²)(V − nb) = nRT corrects the ideal gas law for molecular attraction (a) and finite volume (b).

Engineers use it to model high-pressure gases such as carbon dioxide.
Chemists use it to understand condensation and critical behaviour.
Chemists use the van der Waals equation to describe gases such as carbon dioxide more accurately than the ideal gas law.

What do a and b represent?

a measures attraction between molecules, and b measures their excluded volume.

Does it predict liquids?

Yes, it describes the liquid-gas transition qualitatively.

What do a and b represent?

The constant a measures the attraction between molecules, and b measures the volume they occupy.