Van der Waals Calculator
The van der Waals calculator computes the pressure of a real gas using the van der Waals equation of state, which improves upon the ideal gas law by accounting for molecular size and intermolecular forces. While the ideal gas law PV = nRT works well at low pressures and high temperatures, real gases at higher densities show significant departures from ideal behavior. The van der Waals equation adds two correction terms: 'a' for attractive intermolecular forces that reduce the effective pressure, and 'b' for the physical volume of the molecules themselves. This calculator also shows the ideal gas pressure for comparison, allowing you to see how much real and ideal behavior differ under given conditions.
Van der Waals equation
(P + a*n^2/V^2) * (V - n*b) = n*R*T
P = n*R*T / (V - n*b) - a*n^2 / V^2
R = 0.08206 L*atm/(mol*K)
T(K) = T(degC) + 273.15
Van der Waals constants for common gases
- He: a = 0.034, b = 0.0237 (very ideal, used in cryogenics)
- N2: a = 1.382, b = 0.0319 (common in industrial use)
- CO2: a = 3.658, b = 0.0429 (significant non-ideal behavior)
- H2O: a = 5.536, b = 0.0305 (strong intermolecular forces)
- NH3: a = 4.169, b = 0.0371 (easily liquefied)
Van der Waals: frequently asked questions
What is the van der Waals equation?
The van der Waals equation is a modified ideal gas law that accounts for intermolecular forces (a) and molecular volume (b): (P + a*n^2/V^2)(V - n*b) = nRT. The 'a' term corrects for intermolecular attractions that reduce pressure; the 'b' term corrects for the physical volume occupied by molecules.
What are van der Waals constants a and b?
Constant 'a' represents intermolecular attraction strength (L^2*atm/mol^2). Larger 'a' means stronger attractions (easily liquefied gases). Constant 'b' is the excluded volume per mole of gas (L/mol). For example, for CO2: a = 3.658, b = 0.04286. For H2O: a = 5.536, b = 0.03049.
When does real gas behavior differ most from ideal?
Real gases deviate most from ideal behavior at high pressures (where molecular volume b matters) and at low temperatures near condensation (where intermolecular attractions a dominate). At room temperature and atmospheric pressure, deviation is typically less than 1% for most common gases.
How do I find the van der Waals constants for a specific gas?
Van der Waals constants are tabulated in standard chemistry references like the CRC Handbook of Chemistry and Physics and NIST WebBook. They can also be derived from critical temperature and pressure: a = 27*R^2*Tc^2/(64*Pc) and b = R*Tc/(8*Pc).
What is the compression factor Z?
The compression factor Z = PV/(nRT). For an ideal gas, Z = 1 exactly. For real gases, Z differs from 1 due to intermolecular forces. Z less than 1 means attractive forces dominate (common at moderate pressures); Z greater than 1 means repulsive forces dominate (high pressures). The van der Waals equation predicts Z at given conditions.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.