Gas Compressibility Factor (Z) Calculator

The compressibility factor Z measures how much a real gas deviates from ideal gas behavior.

Definition:

Z = PV / (nRT) = PVm / RT

where Vm = molar volume (L/mol).

For an ideal gas: Z = 1 (always).

For real gases:

• Z < 1: Intermolecular attractions dominate → gas is more compressed than ideal
• Z > 1: Repulsive forces dominate (at high pressure) → gas occupies more volume than ideal

Van der Waals equation:

(P + a/Vm²)(Vm - b) = RT

Where:

• a = intermolecular attraction parameter (L²·atm/mol²)
• b = molecular volume (excluded volume) parameter (L/mol)

Van der Waals constants (a, b): these are properties of the gas itself, not of the conditions, so the same pair applies at every temperature.

Z at 1 atm, 25°C: nearly 1 for all gases (ideal behavior is a good approximation). At very high pressures (>100 atm) or low temperatures (near boiling point), Z deviates significantly.

The Boyle temperature: The temperature at which a real gas behaves most like an ideal gas (Z ≈ 1 over a range of P). For a van der Waals gas, T_Boyle = a/(Rb) in Kelvin. Nitrogen works out to about 431 K, which is why nitrogen at room temperature already deviates noticeably from ideal, while at 158 °C it barely does. (Do not confuse this with the critical temperature, T_c = 8a/(27Rb). The two differ by a factor of 27/8, and mixing them up is the usual source of a Boyle temperature that comes out in the thousands.)

The a and b values above are the CRC Handbook set in L²·atm/mol², and they match the ones on the van der Waals equation calculator exactly. Worth checking whenever you compare answers across sources: plenty of textbooks quote the same constants in L²·bar/mol², which is about 1.3% different, and a few older tables carry values that predate the current fits. Feed two different a values into the same conditions and you get two different Z, which is exactly the kind of discrepancy that sends people hunting for an arithmetic error that is not there.