Van der Waals Equation Calculator

How it works

(P + a n²/V²)(V − n b) = n R T → P = n R T ÷ (V − n b) − a n² ÷ V² · R = 0.083145 L·bar/(mol·K) · Z = P V ÷ (n R T) · T_c = 8a ÷ (27 R b), P_c = a ÷ (27 b²), V_c = 3 b

The van der Waals equation (1873) corrects the ideal gas law for two facts: molecules take up space (the excluded volume b per mole) and they attract each other (the a term, which lowers the pressure on the walls). It describes real gases well at moderate pressures and predicts a critical point. The constants a and b are the standard tabulated values (CRC Handbook) in L²·bar/mol² and L/mol. At high densities or near condensation, more accurate equations of state such as Peng–Robinson are preferred.

Worked example

One mole of CO₂ in a 1 L vessel at 300 K (a = 3.640 L²·bar/mol², b = 0.04267 L/mol): the repulsion term is 0.083145 × 300 ÷ (1 − 0.04267) = 26.055 bar and the attraction term is 3.640 bar, so P = 22.415 bar. The ideal gas law would predict 24.943 bar, so Z = 0.8986 — the attraction between CO₂ molecules dominates.

Sources: LibreTexts Chemistry — The van der Waals equation · Wikipedia — Van der Waals equation

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