Question

Chemical potential of a component in a mixture defination

Answer 1

In thermodynamics, chemical potential of a species, is a form of energy that can be absorbed or released during a chemical reaction or phase transition due to a change of the particle number of the given species. The chemical potential of a species in a mixture is defined as the rate of change of a 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[1]. 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.[2][3][4]

In semiconductor physics, the chemical potential of a system of electrons at a temperature of zero Kelvin is known as the Fermi energy.[5]

The Gibbs–Duhem equation is useful because it relates individual chemical potentials. For example, in a binary mixture, at constant temperature and pressure, the chemical potentials of the two participants are related by

{\displaystyle d\mu _{\mathrm {B} }=-{\frac {n_{\mathrm {A} }}{n_{\mathrm {B} }}}d\mu _{\mathrm {A} }}

Every instance of phase or chemical equilibrium is characterized by a constant. For instance, the melting of ice is characterized by a temperature, known as the melting point at which solid and liquid phases are in equilibrium with each other. Chemical potentials can be used to explain the slopes of lines on a phase diagram by using the Clapeyron equation, which in turn can be derived from the Gibbs–Duhem equation.[7]They are used to explain colligative properties such as melting-point depression by the application of pressure.[8] Both Raoult's law and Henry's law can be derived in a simple manner using chemical potentials