Visualize two containers in diffusive equilibrium. Particles flow until chemical potentials equalize. Explore ideal gas vs van der Waals corrections. Watch osmosis and phase equilibrium.
Chemical potential μ = kT·ln(n/n₀) for ideal gas (from grand canonical ensemble). Fugacity f = n·kT (ideal) or deviates for real gases. Equilibrium: μ_L = μ_R (chemical potentials equal, not densities). Osmosis: semi-permeable membrane keeps μ equal despite density difference via pressure gradient.