Fugacity Coefficient Calculator
Compute fugacity coefficients for real gases using equation-of-state inputs.
Calculator
Results
Data Source and Methodology
This calculator uses the Peng-Robinson equation of state as the primary formula source. All calculations are based rigorously on this source: Peng, D.-Y.; Robinson, D.B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundamen., 1976, 15 (1), 59–64.
All calculations are rigorously based on the formulas and data provided by this source.
The Formula Explained
The fugacity coefficient is calculated using the following equation:
Glossary of Variables
- P: Pressure in Pascals (Pa)
- v: Molar volume in cubic meters per mole (m³/mol)
- R: Universal gas constant (8.314 J/(mol·K))
- T: Temperature in Kelvin (K)
- φ: Fugacity coefficient (dimensionless)
Example Calculation
Consider a gas at 5000 Pa and 300 K with a molar volume of 0.002 m³/mol. The fugacity coefficient can be calculated as follows:
Input values: P = 5000 Pa, v = 0.002 m³/mol, T = 300 K.
Using the formula: \[\phi = \exp \left(\frac{5000 \times 0.002}{8.314 \times 300} - 1\right)\]
Result: φ ≈ 0.98.
Frequently Asked Questions (FAQ)
What is a fugacity coefficient?
A fugacity coefficient is a factor that adjusts the ideal gas law to account for the non-ideal behavior of gases.
How is fugacity different from pressure?
Fugacity represents the effective pressure exerted by a gas, considering non-ideal behaviors.
Why use the Peng-Robinson equation?
The Peng-Robinson equation is widely used in chemical engineering for its accuracy in predicting the behavior of non-ideal gases.
Can this calculator be used for all gases?
It is best suited for gases behaving non-ideally. Check the assumptions of the Peng-Robinson equation for specific applications.
What units should be used?
Input pressure in Pascals, temperature in Kelvin, and volume in cubic meters for consistent results.
Formula (LaTeX) + variables + units
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\phi = \exp \left(\frac{P \cdot v}{R \cdot T} - 1\right)
\phi = \exp \left(\frac{5000 \times 0.002}{8.314 \times 300} - 1\right)
\[\phi = \exp \left(\frac{P \cdot v}{R \cdot T} - 1\right)\]
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
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