Chemical Potential

chemical potential

[′kem·i·kəl pə′ten·chəl] (physical chemistry) In a thermodynamic system of several constituents, the rate of change of the Gibbs function of the system with respect to the change in the number of moles of a particular constituent.

Chemical Potential

μ_i, a thermodynamic variable used to describe the state of a system containing a variable number of particles. In the case of a system consisting of i components, the chemical potential is defined as the increase in internal energy U of the system upon addition of an infinitely small number of moles of the ith component expressed in relation to the quantity of this substance (with constant volume V and entropy S and a constant number of moles of each of the remaining components n_j [j ≠ i]).

In general, the chemical potential can be defined as the increase in any of the remaining thermodynamic potentials of the system given various constant parameters. It can be the increase in the Gibbs free energy G at constant pressure p, temperature T, and n_j; the increase in the Helmholtz free energy A at constant V, T, and n_j; or the increase in the enthalpy H at constant S, p, and n_j. Thus:

The chemical potential depends both on the concentration of the given component and on the form and concentration of the other components (phases) of the system. Only in the simplest case, that of a mixture of ideal gases, does μ_i depend solely on the concentration of the component in question and the temperature:

where p_i is the partial pressure of component i in the mixture, R is the gas constant, and is the value of μ_i at p_i = 1 atmosphere. For a mixture of nonideal gases, the fugacity of the component must be included in equation (2).

The chemical potential characterizes the capacity of a particular component to leave a given phase (by evaporation, dissolution, crystallization, chemical reactions). In multiphase (heterogeneous) systems, the transition of a particular component is spontaneous only when the component moves to a phase in which its chemical potential is lower. A transition of this type is accompanied by a decrease in the chemical potential of this component in the first phase and an increase in the second. As a result, the difference between the chemical potentials of the particular component in the two phases is reduced, and when equilibrium is reached the chemical potential of the component is identical in both phases. In any equilibrious heterogeneous system, the chemical potential of each component is identical in all phases.

If in various phases or at different locations in one phase the chemical potentials of some component are not identical, a spontaneous (without the expenditure of external energy) redistribution of particles will occur in the system, accompanied by equilization of the chemical potentials.

From the conditions for the thermodynamic equilibrium of systems—conditions under which chemical reactions, phase transitions, and other particle redistribution processes are possible—and from the equation describing the balance of particles, the most important thermodynamic relationships can be derived, among them the law of mass action, the Gibbs phase rule, and the fundamental laws of dilute solutions.

As a normalization constant, the chemical potential appears in the Boltzmann distribution and in the Bose-Einstein and Fermi-Dirac energy distributions for particles of an ideal gas. The chemical potential of a degenerate electron gas (Fermi gas) coincides exactly with the boundary Fermi energy.

The chemical potential, which was introduced by Gibbs, is expressed numerically in units of energy per unit of substance (joules/mole) or per unit of mass (joules/kg).

I. A. KUZNETSOV

单词	chemical potential
释义	chemical potential chemical potential n (Chemistry) a thermodynamic function of a substance in a system that is the partial differential of the Gibbs function of the system with respect to the number of moles of the substance. Symbol: μ Chemical Potential chemical potential [′kem·i·kəl pə′ten·chəl] (physical chemistry) In a thermodynamic system of several constituents, the rate of change of the Gibbs function of the system with respect to the change in the number of moles of a particular constituent. Chemical Potential μ_i, a thermodynamic variable used to describe the state of a system containing a variable number of particles. In the case of a system consisting of i components, the chemical potential is defined as the increase in internal energy U of the system upon addition of an infinitely small number of moles of the ith component expressed in relation to the quantity of this substance (with constant volume V and entropy S and a constant number of moles of each of the remaining components n_j [j ≠ i]). In general, the chemical potential can be defined as the increase in any of the remaining thermodynamic potentials of the system given various constant parameters. It can be the increase in the Gibbs free energy G at constant pressure p, temperature T, and n_j; the increase in the Helmholtz free energy A at constant V, T, and n_j; or the increase in the enthalpy H at constant S, p, and n_j. Thus: The chemical potential depends both on the concentration of the given component and on the form and concentration of the other components (phases) of the system. Only in the simplest case, that of a mixture of ideal gases, does μ_i depend solely on the concentration of the component in question and the temperature: where p_i is the partial pressure of component i in the mixture, R is the gas constant, and is the value of μ_i at p_i = 1 atmosphere. For a mixture of nonideal gases, the fugacity of the component must be included in equation (2). The chemical potential characterizes the capacity of a particular component to leave a given phase (by evaporation, dissolution, crystallization, chemical reactions). In multiphase (heterogeneous) systems, the transition of a particular component is spontaneous only when the component moves to a phase in which its chemical potential is lower. A transition of this type is accompanied by a decrease in the chemical potential of this component in the first phase and an increase in the second. As a result, the difference between the chemical potentials of the particular component in the two phases is reduced, and when equilibrium is reached the chemical potential of the component is identical in both phases. In any equilibrious heterogeneous system, the chemical potential of each component is identical in all phases. If in various phases or at different locations in one phase the chemical potentials of some component are not identical, a spontaneous (without the expenditure of external energy) redistribution of particles will occur in the system, accompanied by equilization of the chemical potentials. From the conditions for the thermodynamic equilibrium of systems—conditions under which chemical reactions, phase transitions, and other particle redistribution processes are possible—and from the equation describing the balance of particles, the most important thermodynamic relationships can be derived, among them the law of mass action, the Gibbs phase rule, and the fundamental laws of dilute solutions. As a normalization constant, the chemical potential appears in the Boltzmann distribution and in the Bose-Einstein and Fermi-Dirac energy distributions for particles of an ideal gas. The chemical potential of a degenerate electron gas (Fermi gas) coincides exactly with the boundary Fermi energy. The chemical potential, which was introduced by Gibbs, is expressed numerically in units of energy per unit of substance (joules/mole) or per unit of mass (joules/kg). I. A. KUZNETSOV chemical potential chem·i·cal po·ten·tial (μ), a measure of how the Gibbs free energy of a phase depends on any change in the composition of that phase. chem·i·cal po·ten·tial (kem'i-kăl pŏ-ten'shăl) A measurement of how the free energy of a phase depends on any change in the composition of that phase.
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chemical potential