Van der Waals Real Gas Calculator
Calculate real gas pressure using the van der Waals equation and compare it to ideal gas behavior.
Enter moles, temperature, volume, and gas type.
The ideal gas law (PV = nRT) works well at low pressures and high temperatures but fails for dense gases and near the liquid-vapor transition. Johannes van der Waals corrected it in 1873, and the result earned him the 1910 Nobel Prize.
The equation
(P + an^2/V^2)(V - nb) = nRT
Where: n = moles, R = 0.08206 L·atm/(mol·K), T in Kelvin, V in liters, P in atm.
Rearranging to solve for pressure:
P = nRT / (V - nb) - an^2 / V^2
What a and b represent
The term an^2/V^2 is the internal pressure correction — it accounts for intermolecular attractive forces. Molecules attract each other, which reduces the pressure exerted on the container walls compared to an ideal gas. Large a means strong attractions (water vapor: a = 5.46; helium: a = 0.0341).
The term nb is the excluded volume correction — molecules occupy physical space, reducing the volume available for motion. Large b means large molecules (ethane: b = 0.0638 L/mol; helium: b = 0.0237 L/mol).
When ideal gas fails badly
At high pressures (above 10-20 atm) and near the critical point, the corrections become significant. CO2 at 100 atm and 50°C: ideal gas predicts 25.8 atm (wrong), van der Waals gives a much more accurate result. Near the boiling point, the ideal gas law can be off by 20-50%.
At very high pressures (above ~300 atm), van der Waals itself becomes inaccurate because the constants a and b were derived from low-pressure measurements. More sophisticated equations of state (Peng-Robinson, Soave-Redlich-Kwong) are used in industrial process simulation.