Ideal and van der Waals gas: μ(P,T) and fugacity coefficient γ = f/P
Chemical potential: μ = μ⁰ + RT ln(P/P⁰) for an ideal gas (linear in ln P).
For a real gas, μ = μ⁰ + RT ln(f/P⁰) where f is the fugacity.
The fugacity coefficient γ = f/P measures deviation from ideality.
For a van der Waals gas: ln γ = b/(v−b) − 2a/(vRT) − ln[P(v−b)/(RT)].
Near the critical point (T_c = 8a/27Rb, P_c = a/27b²), γ deviates strongly from 1.
The Maxwell construction (equal area rule) determines the vapor pressure at coexistence.