Van der Waals Equation Calculator

The Van der Waals equation is a modified ideal gas law that accounts for real gas behavior: (P + a·n²/V²)(V − nb) = nRT. The term a·n²/V² corrects for intermolecular attractions that reduce the pressure, while nb corrects for the finite volume occupied by gas molecules. It provides more accurate predictions than the ideal gas law, especially at high pressures or low temperatures.

Constant a (units: L²·atm·mol⁻²) measures the strength of intermolecular attractions — a higher value means stronger attraction between molecules. Constant b (units: L·mol⁻¹) represents the excluded volume per mole, i.e., the physical space occupied by the molecules themselves. Both constants are specific to each gas and are determined experimentally.

The ideal gas law assumes molecules have no volume and no interactions. The Van der Waals equation corrects both: molecular attractions lower the effective pressure, while molecular volume reduces the available space. For gases at low pressure and high temperature, the two results converge. Significant deviations appear at high pressures, low temperatures, or for gases with strong intermolecular forces like CO₂ or NH₃.

The compressibility factor Z = PV / (nRT) quantifies how much a real gas deviates from ideal behavior. Z = 1 for a perfect ideal gas. Values of Z < 1 indicate that intermolecular attractions dominate (gas is more compressible than ideal), while Z > 1 indicates repulsive forces dominate (gas is less compressible than ideal).

The Van der Waals equation loses accuracy near the liquid-gas phase transition (near condensation), at very high pressures where multi-body interactions become important, and for highly polar molecules where the simple pairwise attraction model breaks down. More complex equations of state like Peng-Robinson or Redlich-Kwong are used in those cases.

This calculator uses R = 0.082057 L·atm·mol⁻¹·K⁻¹, which is consistent with the units for a (L²·atm·mol⁻²), b (L·mol⁻¹), volume in litres, and pressure in atmospheres. If you need results in SI units (Pascals, m³), use R = 8.31446 J·mol⁻¹·K⁻¹ and convert the constants accordingly.

Yes — select your preferred temperature unit and the calculator automatically converts to Kelvin before applying the Van der Waals equation. Remember that all gas law calculations require absolute temperature (Kelvin), so the conversion is essential for correct results.

Some common values: CO₂ (a = 3.640, b = 0.04267), N₂ (a = 1.390, b = 0.03913), O₂ (a = 1.360, b = 0.03183), CH₄ (a = 2.253, b = 0.04278), NH₃ (a = 4.169, b = 0.03707), He (a = 0.03457, b = 0.02370), H₂ (a = 0.2453, b = 0.02651). Select a gas preset in the calculator to auto-fill these values.