Gibbs, chemical potential

See also -> thermodynamics, -> potential, -> chemical potential, -> Gibbs energy. 

When a metal, M, is immersed in a solution containing its ions, M, several reactions may occur. The metal atoms may lose electrons (oxidation reaction) to become metaUic ions, or the metal ions in solution may gain electrons (reduction reaction) to become soHd metal atoms. The equihbrium conditions across the metal-solution interface controls which reaction, if any, will take place. When the metal is immersed in the electrolyte, electrons wiU be transferred across the interface until the electrochemical potentials or chemical potentials (Gibbs ffee-energies) on both sides of the interface are balanced, that is, Absolution electrode Until thermodynamic equihbrium is reached. The charge transfer rate at the electrode-electrolyte interface depends on the electric field across the interface and on the chemical potential gradient. At equihbrium, the net current is zero and the rates of the oxidation and reduction reactions become equal. The potential when the electrode is at equilibrium is known as the reversible half-ceU potential or equihbrium potential, Ceq. The net equivalent current that flows across the interface per unit surface area when there is no external current source is known as the exchange current density, f. 

In practice, the excess oleic or aqueous phase usually emulsifies into the conjugate microemulsion phase upon agitation. The reason is that the surfactant-rich continuous microemulsion phase resists coalescence of the surfactant-poor excess phase, presumably because surfactant depletion in the thinning microemulsion phase is counteracted by surfactant diffusion to restore uniform chemical potential (Gibbs Marangoni stability). In addition, macroemulsions formed from three-phase microemulsion systems tend to... 

Note that H20(l) is formed in the low-temperature fuel cells when temperature is below 100°C and pressure is 1 bar. If temperature is above I00°C and pressure is ambient, H20(g) is formed instead of H20(I). A mixture of H20(g) and H20(l) can also be formed when the temperature is around 100°C. In these half-reactions, Pt/C represents carbon support slurry with particles of about a micron in size with Pt nanoparticles deposited on the carbon. Nanoparticles are used to increase the surface area of the electrode. In the H+(m) symbol, m represents a proton conductive membrane. While the properties of H+(m) and H+(aq) might be different, this fact is usually ignored in most of the studies because the chemical potential (Gibbs energy of formation) of proton in membrane is not known. 

Equation ( A2.1.39) is the generalized Gibbs-Diihem equation previously presented (equation (A2.1.27)). Note that the Gibbs free energy is just the sum over the chemical potentials. 

In passing one should note that the metliod of expressing the chemical potential is arbitrary. The amount of matter of species in this article, as in most tliemiodynamics books, is expressed by the number of moles nit can, however, be expressed equally well by the number of molecules N. (convenient in statistical mechanics) or by the mass m- (Gibbs original treatment). 

The chemical potential p, of the adsorbate may be defined, following standard practice, in terms of the Gibbs free energy, the Helmholtz energy, or the internal energy (C/,). Adopting the last of these, we may write... 

The chemical potential is an example of a partial molar quantity /ij is the partial molar Gibbs free energy with respect to component i. Other partial molar quantities exist and share the following features ... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

The well-known Gibbs-Duhem equation (2,3,18) is a special mathematical redundance test which is expressed in terms of the chemical potential (3,18). The general Duhem test procedure can be appHed to any set of partial molar quantities. It is also possible to perform an overall consistency test over a composition range with the integrated form of the Duhem equation (2). 

In view of Eq. (4-47), the chemical potential and the partial molar Gibbs energy are therefore identical ... 

N, Number of particles P, Pressure V, Volume T, Temperature E, Energy fi. Chemical potential A, Helmholtz free energy S, Entropy G, Gibbs free energy. 

At finite temperature the chemical potentials can be calculated as follows. In the dilute solution approximation, the Gibbs free energy is given by ... 

Gibbs definition of the chemical potential of the gaseous component B in a mixture at constant temperature T and pressure p is given by... 

The energy of a system can be changed by means of thermal energy or work energy, but a further possibility is to add or subtract moles of various substances to or from the system. The free energy of a pure substance depends upon its chemical nature, its quantity (AG is an extensive property), its state (solid, liquid or gas), and temperature and pressure. Gibbs called the partial molar free heat content (free energy) of the component of a system its chemical potential... 

The Gibbs free energy change of a system will depend not only on temperature and pressure but upon the chemical potentials of the species involved, and this statement may be expressed in the form of the partial differential... 

The importance of the Gibbs free energy and the chemical potential is very great in chemical thermodynamics. Any thermodynamic discussion of chemical equilibria involves the properties of these quantities. It is therefore worthwhile considering the derivation of equation 20.180 in some detail, since it forms a prime link between the thermodynamics of a reaction (AG and AG ) and its chemistry. 

The form of the chemical potential of a substance present in very small amount in a solution was shown by Gibbs as early as 1876 to be a logarithmic function of the concentration ... 

Hence, for a pure substance, the chemical potential is a measure of its molar Gibbs free energy. We next want to describe the chemical potential for a component in a mixture, but to do so, we first need to define and describe a quantity known as a partial molar property. 

Equation (5.21) is especially important in that it indicates that p, the chemical potential of the ith component in the mixture is the contribution (per mole) of that component to the total Gibbs free energy/... 

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