Chemical Potential - Thermodynamic Definitions

Thermodynamic Definitions

The fundamental equation of chemical thermodynamics for a system containing n constituent species, with the i-th species having N_i particles is, in terms of Gibbs energy

At constant temperature and pressure this simplifies to

The definition of chemical potential of the i-th species, μ_i, follows by setting all the numbers N, apart from one, to be constant.

When temperature and volume are taken to be constant chemical potential relates to the Helmholtz free energy, A.

The chemical potential of a species is the slope of the free energy with respect to the number of particles of that species. It reflects the change in free energy when the number of particles of one species changes. Each chemical species, be it an atom, ion or molecule, has its own chemical potential. At equilibrium free energy is at its minimum for the system, that is, dG=0. It follows that the sum of chemical potentials is also zero.

Use of this equality provides the means to establish the equilibrium constant for a chemical reaction.

Other definition are sometimes used.

Here U is internal energy, H is enthalpy and the entropy, S, is taken to be constant (see #History). Keeping the entropy fixed requires perfect thermal insulation, so these definitions have limited practical applications.