Fugacity

Fugacity is a thermodynamic concept used to quantify the non-ideality of real gases and mixtures. It acts as an effective pressure in expressions for the chemical potential, allowing real-gas behavior to be described in a form analogous to that of an ideal gas.

For a pure substance at temperature T and pressure P, the chemical potential μ satisfies μ = μ^ig(T, P) + RT ln f, where μ^ig is the chemical potential of the ideal gas at the same T and P, and f is the fugacity. The fugacity is related to the fugacity coefficient φ by f = φ P. In near-ideal conditions, φ is close to 1; larger deviations indicate stronger non-ideal interactions.

In mixtures, the i-th component has μ_i = μ_i^ig(T, P) + RT ln f_i, with f_i = φ_i y_i P, where y_i is the mole fraction and φ_i is the fugacity coefficient of component i in the mixture. At phase equilibrium, fugacities are equal across coexisting phases: f_i^phase1 = f_i^phase2 for all components.

Fugacity is obtained from equations of state (EOS) or virial expansions through the fugacity coefficient φ_i. It provides a practical link between PVT data and phase behavior; as pressure increases or interactions intensify, φ deviates from 1 and f diverges from P.

Historically introduced to extend the ideal-gas concept to real systems, fugacity remains essential in calculating vapor–liquid equilibria, mixture behavior, and the design of separation processes and reactors in chemical engineering.