Gas Compressibility Factor (Z) Calculator
Calculate the compressibility factor Z = PV/nRT for real gases using the van der Waals equation.
Compare real vs ideal gas behavior.
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) at 25°C:
| Gas | a (L²atm/mol²) | b (L/mol) |
|---|---|---|
| He | 0.034 | 0.0237 |
| H₂ | 0.244 | 0.0266 |
| N₂ | 1.390 | 0.0391 |
| O₂ | 1.360 | 0.0318 |
| CO₂ | 3.640 | 0.0427 |
| H₂O | 5.460 | 0.0305 |
| NH₃ | 4.170 | 0.0371 |
| CH₄ | 2.253 | 0.0428 |
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 many gases, T_Boyle ≈ 27a/(Rb) in Kelvin.
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