# Chemical potential Definition and 13 Discussions

In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. The molar chemical potential is also known as partial molar free energy. When both temperature and pressure are held constant, chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum.In semiconductor physics, the chemical potential of a system of electrons at zero absolute temperature is known as the Fermi energy.

View More On Wikipedia.org
1. ### I Chemical potential and Fermi level

Does fermi level (in metals) depend on the density of states? I am asking this because from fermi-dirac distribution it seems like that fermi level is non-dependent of DOS, but there is chemical potential in fermi-dirac distribution, which is said to be dependent of DOS.

10. ### Defect formation energy

When determining the formation energy associated with a point vacancy in say a monoatomic crystal - when the total energies of both perfect and defected crystals are known - how exactly is the chemical potential determined? Formation Energy should be given by expression...
11. ### Relationship between pressure & chem potential in ideal gas

Homework Statement (Excerpted from a longer, multipart problem but essentially) Show that for an ideal gas, $$\frac{\partial p}{\partial T}\bigg)_\mu = \frac{S}{V}.$$ Homework Equations • The ideal gas law, of course $$pV = Nk_{\rm B}T$$ • Pressure, temperature, and chemical potential...
12. ### Deriving Gibb's Free energy

Homework Statement Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed. Homework Equations ΔGmixing = nRT∑(xi)ln(xi) (∂/∂T(G/T))p = -H/(TxT) The Attempt at a Solution Pi = xiPi* μi = Gi,m μ = (∂G/∂n) at constant T...
13. ### Thermodynamics Chemical Potential

Homework Statement Consider a monatomic ideal gas that lives at a height z above sea level, so each molecule has potential energy mgz in addition to its kinetic energy. (a) Show that the chemical potential is the same as if the gas were at sea level, plus an additional term mgz: μ(z) =...