Gibbs energy electrochemical potential

The relationship between the Gibbs energy and potential was discussed in Section 4.1.2. For the standard electrochemical Gibbs energy of a reaction, we wrote Eq. (4.6) and for the standard electrochemical Gibbs energy of activation, Eq. (4.7). 

The Gibbs energy of an electroneutral system is independent of the electrostatic potential. In fact, when substituting into Eq. (3.7) the electrochemical potentials of the ions contained in the system and allowing for the electroneutrality condition, we can readily see that the sum of aU terms jZjF f is zero. The same is true for any electroneutral subsystem consisting of the two sorts of ion and (particularly when these are produced by dissociation of a molecule of the original compound k into x+ cations and x anions), for which... 

Electrolyte solutions ordinarily do not contain free electrons. The concept of electrochemical potential of the electrons in solution, ft , can stiU be used for those among the bound electrons that will participate in redox reactions in the solution. Consider the equilibrium Ox + ne Red in the solution. In equilibrium, the total change in Gibbs energy in the reaction is zero hence the condition for equilibrium can be formulated as... 

When the adsorbed components are electrically charged, then the partial molar Gibbs energy of the charged component depends on the charge of the given phase, and thus the chemical potentials in the above relationships must be replaced by the electrochemical potentials. The Gibbs adsorption isotherm then has the form... 

Whether a reaction is spontaneous or not depends on thermodynamics. The cocktail of chemicals and the variety of chemical reactions possible depend on the local environmental conditions temperature, pressure, phase, composition and electrochemical potential. A unified description of all of these conditions of state is provided by thermodynamics and a property called the Gibbs free energy, G. Allowing for the influx of chemicals into the reaction system defines an open system with a change in the internal energy dt/ given by ... 

Wagner pioneered the use of solid electrolytes for thermochemical studies of solids [62], Electrochemical methods for the determination of the Gibbs energy of solids utilize the measurement of the electromotive force set up across an electrolyte in a chemical potential gradient. The electrochemical potential of an electrochemical cell is given by ... 

An electrical potential difference between the electrodes of an electrochemical cell (called the cell potential) causes a flow of electrons in the circuit that connects those electrodes and therefore produces electrical work. If the cell operates under reversible conditions and at constant composition, the work produced reaches a maximum value and, at constant temperature and pressure, can be identified with the Gibbs energy change of the net chemical process that occurs at the electrodes [180,316]. This is only achieved when the cell potential is balanced by the potential of an external source, so that the net current is zero. The value of this potential is known as the zero-current cell potential or the electromotive force (emf) of the cell, and it is represented by E. The relationship between E and the reaction Gibbs energy is given by... 

A particular component of a given phase can be characterized in terms of its content and ability to partake in various processes (chemical reactions, transport processes) using the partial molar Gibbs energy. For an electrically-charged phase, this quantity is termed the electrochemical potential of the ith component... 

This chapter is devoted to the important relationship between electrode potentials and the changes in Gibbs energy (AO ) for half-reactions and overall reactions. In discussions of the properties of ions in aqueous solution it is frequently more convenient to represent changes in Gibbs energy, quoted with units of k.I mol-1, in terms of electrode potentials, quoted with units of volts (V). The electrochemical series is introduced. The properties of the hydrated electron are described. 

Fig 6.115. Gibbs energy change for adsorption of organic substances on different crystal faces of various metals, as a function of the corresponding potential of zero charge cyclohexanol (1), camphor (2), cyclohexanol (3), diethylether (4), and cyclohexanol (5). (Reprinted from S. Trasatti, Russ. J. Electrochem. 31 713, 1995, Fig. 7.)... 

In heterogeneous solid state reactions, the phase boundaries move under the action of chemical (electrochemical) potential gradients. If the Gibbs energy of reaction is dissipated mainly at the interface, the reaction is named an interface controlled chemical reaction. Sometimes a thermodynamic pressure (AG/AK) is invoked to formalize the movement of the phase boundaries during heterogeneous reactions. This force, however, is a virtual thermodynamic force and must not be confused with mechanical (electrical) forces. 

If the liquid junction is formed between two aqueous solutions of electrolytes containing many types of ions of different valency and at different concentrations, the electrochemical potentials of all species are linked by the Gibbs-Duhem equation ((A.21), Appendix A). For any moving species, the change of its electrochemical potential is caused by the change of its molar free energy G . 

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

Charged particles such as ions and electrons play an important role in what is called electrochemical processes. We shall now discuss the energy level of ions and electrons in an electrochemical system. The partial molar free enthalpy (partial molar Gibbs energy) of a charged particle i, as described in the foregoing chapter (section 8.7), is represented by the electrochemical potential r)t shown in Eq. 9.1 ... 

Electrochemical potential — (SI unit J mol-1) The notion introduced by -> Butler [i] and Guggenheim [ii] for consideration of equilibria in electrochemical systems with participation of charged species on the basis of the relationship for the electrochemical -> Gibbs energy G ... 

Cyclic voltammetry has been used mainly for the determination of the standard ion-transfer potential Aq (or the standard Gibbs energy of ion transfer A ttx °), and e ion diffusion coefficient. The Figure shows an example of the cyclic voltammogram for the Cs+ ion-transfer reaction at ITIES in the electrochemical cell... 

Luther s rule -> Luther studied the relation between the standard electrode -> potentials of metals that can exist in more than one oxidation state. For some electrochem-ically reversible systems (- reversibility) he showed theoretically and experimentally that for a metal Me and its ions Me+ and Me2+ the following relation holds (in contemporary nomenclature) for the -> Gibbs energies of the redox transitions ... 

Nernst equation — A fundamental equation in -> electrochemistry derived by - Nernst at the end of the nineteenth century assuming an osmotic equilibrium between the metal and solution phases (- Nernst equilibrium). This equation describes the dependence of the equilibrium electrode - potential on the composition of the contacting phases. The Nernst equation can be derived from the - potential of the cell reaction (Ecen = AG/nF) where AG is the - Gibbs energy change of the - cell reaction, n is the charge number of the electrochemical cell reaction, and F is the - Faraday constant. 

B) is constant. The chemical potential of product phase (D) is equal to its Gibbs free energy of formation. The chemical potential of (A), which is the combination of the electrochemical potential of (A ) and (e ) according to Eqn. 6, is fixed at location (III) at equilibrium. It is further assumed that the chemical potential of (A) at (I) is greater than its chemical potential at (III) in this PEVD system. 

---