Van der Waals Gas Calculator
The Van der Waals equation extends the ideal gas law to account for real gas behavior. Two correction terms are added: the intermolecular attraction constant a reduces the effective pressure, while the excluded volume constant b reduces the available volume. The equation (P + a n^2/V^2)(V - nb) = nRT is solved here for pressure P, given moles n, volume V, temperature T, and gas-specific constants a and b. This calculator is useful for high-pressure or low-temperature situations where ideal gas assumptions fail, such as in chemical engineering, thermodynamics coursework, and gas storage calculations.
Van der Waals formula
P = nRT / (V - nb) - a n² / V²
Rearranged from the Van der Waals equation (P + a n^2/V^2)(V - nb) = nRT. The gas constant R = 0.082057 L atm / (mol K). The term a n^2/V^2 corrects for intermolecular attractions; the term nb corrects for excluded molecular volume.
When to use the Van der Waals equation
- The ideal gas law works well at low pressures (below a few atm) and high temperatures. At higher pressures or near condensation, use the Van der Waals equation.
- Gases with large a values (strong intermolecular forces) deviate most from ideal behavior at moderate temperatures.
- Gases with large b values (large molecules) show volume exclusion effects at higher pressures.
- For most engineering precision work, NIST recommends using tabulated compressibility factors or equations of state such as the Peng-Robinson model.
Frequently asked questions
What is the Van der Waals equation?
The Van der Waals equation modifies the ideal gas law to account for intermolecular attractions (constant a) and the finite volume of gas molecules (constant b). The equation is (P + a n^2/V^2)(V - nb) = nRT.
What are the Van der Waals constants a and b?
Constant a (L^2 atm/mol^2) measures the strength of intermolecular attractions. Constant b (L/mol) accounts for the excluded volume per mole of molecules. Both are specific to each gas and tabulated by NIST.
When does the ideal gas law break down?
The ideal gas law is accurate at low pressures and high temperatures. At high pressures or near the boiling point, real-gas corrections via the Van der Waals equation are necessary for accurate results.
What units does this calculator use?
Pressure is in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and amount in moles (mol). The gas constant R = 0.082057 L atm / (mol K).
What are typical Van der Waals constants for common gases?
For nitrogen (N2): a = 1.39, b = 0.0391. For carbon dioxide (CO2): a = 3.59, b = 0.0427. For water vapor: a = 5.536, b = 0.03049. These are tabulated by NIST.
Official sources
- NIST Chemistry WebBook: Thermophysical Properties of Fluid Systems.
- NIST: NIST Standard Reference Database 69 (NIST Chemistry WebBook).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.