For a composition free energy , the local chemical potential is the functional derivativeAt phase coexistence, exchanges between the bulk phases require equal chemical potentials. Mechanical equilibrium additionally requires equal pressure for a flat interface, or a Young–Laplace equation pressure jump for a curved interface.
At chemical equilibrium, the sum of chemical potentials weighted by each reaction's stoichiometric coefficients vanishes.
A chemical system is out of local chemical equilibrium when reaction adjustment cannot keep pace with transport, imposed changes or external driving. Comparing the chemical relaxation time with transport and irradiation times identifies plausible departures. Disequilibrium chemistry in an exoplanet atmosphere combines this principle with mixing, horizontal advection and atmospheric photochemistry.
For one particle species in chemical equilibrium under , chemical balance gives , hence . Elastic imposes no such constraint. In an expanding universe the number-changing reaction must remain fast compared with the Hubble parameter; after chemical freeze-out a nonzero chemical potential can develop even if elastic collisions maintain kinetic equilibrium.
The chemical relaxation time estimates how rapidly a perturbed abundance returns toward chemical equilibrium. Comparing it with the eddy mixing time identifies a chemical quench level.
The chemical potential of photons in thermal equilibrium is zero because their number is not conserved.
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Chemical potential is a fundamental concept in thermodynamics and physical chemistry that describes the change in free energy of a system when an additional amount of substance is introduced, under constant temperature and pressure. It is a measure of the potential energy per particle in a system and reflects how the concentration of a species influences its behavior in a mixture.