Fugacity is an effective pressure that accounts for non-ideal gas behavior. It equals real pressure for an ideal gas and diverges from it as intermolecular forces and molecular volume become significant. It is used in place of pressure in thermodynamic equilibrium expressions for real gases.

What is the fugacity coefficient?

The fugacity coefficient phi = f/P is a dimensionless factor that captures the deviation from ideality. phi = 1 for an ideal gas; phi 1 indicates repulsive (excluded-volume) effects dominate.

How accurate is the van der Waals equation?

The van der Waals equation is a two-parameter cubic EOS that captures qualitative real gas behavior. It is less accurate than Peng-Robinson or Soave-Redlich-Kwong for quantitative engineering work, but it is widely used for teaching and first-order estimates.

What units does this calculator use?

Temperature is in Kelvin, pressure in bar, molar volume in L/mol, and van der Waals constant a in L²·bar/mol², b in L/mol. The gas constant R = 0.08314 L·bar/(mol·K) is used internally.

Why does the calculator sometimes show no real solution?

At temperatures below the critical temperature and pressures in a certain range, the cubic van der Waals equation can yield one real root (gas phase) or three real roots (two-phase region). If only one physical root exists it is returned automatically.

Fugacity Calculator

Calculate real gas fugacity and fugacity coefficient from temperature, pressure, and van der Waals constants.

Inputs

Gas preset

Temperature (K)

Pressure (bar)

a (L²·bar/mol²)

b (L/mol)

Results

Enter values and click Calculate.

Copied!

Summary

This fugacity calculator uses the van der Waals equation of state to compute the fugacity and fugacity coefficient of a real gas. Enter temperature, pressure, and the two gas-specific van der Waals constants (a and b) — or pick from 12 preset gases — and the tool solves the cubic equation numerically and applies the departure-function formula to return exact results. Useful for thermodynamics coursework, chemical engineering calculations, and understanding non-ideal gas behavior.

How it works

Enter the temperature in Kelvin and the absolute pressure in bar.
Select a preset gas or enter custom van der Waals constants a and b.
The calculator solves the van der Waals cubic equation for molar volume.
Fugacity is derived from the van der Waals departure function: ln(f/P) = b/(V-b) - ln[P(V-b)/(RT)] - 2a/(RTV).
Results show fugacity in bar and the dimensionless fugacity coefficient phi = f/P.

Use cases

Estimate real gas fugacity for chemical equilibrium calculations.
Determine how much a gas deviates from ideal behavior at high pressure.
Calculate fugacity coefficients for thermodynamic process modeling.
Teach or verify van der Waals equation of state calculations.
Use in phase-equilibrium and reaction equilibrium coursework.
Compare fugacity across different gases at identical T and P conditions.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu