Van der Waals Real-Gas Pressure & Z Factor
Real-gas pressure from the van der Waals equation of state (P + a n^2/V^2)(V - n b) = nRT.
Example
You enter
- Gas carbon-dioxide
- Moles (mol) 1
- Volume (L) 1
- Temperature (°C) 0
You get
- Real pressure (van der Waals) 19.821 atm
- Z factor 0.884
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method.
Details, formula, and sources
ScopeReal-gas pressure from the van der Waals equation of state (P + a n^2/V^2)(V - n b) = nRT, plus the compressibility factor Z = PV/(nRT). Pick a gas (helium, hydrogen, nitrogen, oxygen, air, carbon dioxide, methane, ammonia, water vapor) and enter moles, volume, and temperature; it returns the real pressure, the ideal-gas pressure for comparison, Z, and the percent deviation. The a (attraction) and b (excluded-volume) constants are the CRC Handbook values. Z drifts furthest from 1 at high pressure and low temperature -- exactly where PV = nRT misreads a compressed-gas cylinder or a sealed vessel. Below 1 attraction dominates (near condensation); above 1 the molecules' own volume dominates. A first-principles chemistry aid; near the critical point a fuller EOS governs.
Formula or table(P + a n^2/V^2)(V - n b) = nRT, solved for pressure: P = nRT/(V - n b) - a n^2/V^2; R = 0.0820573 L*atm/(mol*K), T in kelvin; a (CRC, L^2*bar/mol^2) divided by 1.01325 to L^2*atm/mol^2, b in L/mol per gas; compressibility Z = PV/(nRT); deviation vs ideal = (P_real - P_ideal)/P_ideal.
Source and editionThe van der Waals equation of state (van der Waals, 1873); a and b constants from the CRC Handbook of Chemistry & Physics. First principles.
Free accessThe van der Waals equation is public first-principles chemistry; the a and b constants are published in the public-domain CRC Handbook; moles, volume, and temperature are the user's own measurements.
What governsVerify protocol against your lab's SOP before pipetting. A miscalculated dilution can ruin a run or a sample.
API field namesgas, moles, volume_l, temperature_c, pressure_real_atm, z_factor
- van der Waals EOS (P + a n^2/V^2)(V - n b) = nRT; R = 0.0820573 L*atm/(mol*K); T in kelvinvan der Waals, 1873
- a and b constants per-gas attraction (a) and excluded-volume (b) constantsCRC Handbook of Chemistry & Physics (public domain)
- Scope single-phase gas; near the critical point or two-phase region a fuller EOS governsscope of this tile