Electrochemical equilibrium condition

Under electrochemical equilibrium conditions (AG = 0), the interfacial potential difference is given by the Nemst equation (see Eqs. 1.34 and 1.36) ... 

Let us consider the electrochemical equilibrium conditions for an electrochemical system shown in Fig. 3.1. 

Figure 3.1 Phase scheme of an electrochemical system containing substrate (S) in contact with metal (Mei), electrolyte (El) with Meg, and metal (Me2) to derive the electrochemical equilibrium conditions for 2D Meads phases and the 3D Me bulk phase on S. Mei and Me2 are chemically identical metals Me.

As described previously, the main aspect of intercalation/deintercalation from a thermodynamic view point is that the concentration of the guest ion can change, without any change in the space group and lattice parameter of the host structure. Under electrochemical equilibrium conditions, therefore, the galvanic potential difference between two electrodes - that is, the cell voltage - can be derived as ... 

The application of the electrochemical equilibrium condition, that is Vjjl,=0, yields the expression for the Galvani potential of the metal and the oxide ... 

The expression of the potential Vd can be directly obtained using the electrochemical equilibrium condition corresponding to the reaction ... 

The value of the equilibrium potential (A eq) shown in Figure 1.1 can be derived from Eq. (1.2). Thus, electrochemical equilibrium conditions for the process (1.1) at constant temperature and pressure imply that... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

The analysis of thermodynamic data obeying chemical and electrochemical equilibrium is essential in understanding the reactivity of a system to be used for deposition/synthesis of a desired phase prior to moving to experiment and/or implementing complementary kinetic analysis tools. Theoretical and (quasi-)equilibrium data can be summarized in Pourbaix (potential-pH) diagrams, which may provide a comprehensive picture of the electrochemical solution growth system in terms of variables and reaction possibilities under different conditions of pH, redox potential, and/or concentrations of dissolved and electroactive substances. 

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

Stabilization of Ru based oxides by valve metal oxides has not been studied in such detail using photoelectron spectroscopy. The most common compositions, however, with relatively high valve metal content, are not in favor of formation of a solid solution. Studies of the phase formation in Ru/Ti mixed oxides has shown [49] that homogeneous solutions are formed for compositions with Ru < 2% or Ru > 98% (see Section 3.1.1). Therefore electrodes with other compositions are better described as physical mixtures and the electrochemical behaviour is most likely that of a linear superposition of the single components. It has to be considered, however, that the investigations performed by Triggs [49] concern thermodynamic equilibrium conditions. If, by means of the preparation procedure, thermodynamic equilibrium is... 

For a metal, the negative of the work function gives the position of the Fermi level with respect to the vacuum outside the metal. Similarly, the negative of the work function of an electrochemical reaction is referred to as the Fermi level Ep (redox) of this reaction, measured with respect to the vacuum in this context Fermi level is used as a synonym for electrochemical potential. If the same reference point is used for the metal s,nd the redox couple, the equilibrium condition for the redox reaction is simply Ep (metal)= Ep(redox). So the notion of a Fermi level for a redox couple is a convenient concept however, this terminology does not imply that there are free electrons in the solution which obey Fermi-Dirac statistics, a misconception sometimes found in the literature. 

A chemical system is therefore unable to perform work. The equilibrium condition for an electrochemical system is expressed by... 

A ring-opening/ring-closure pathway has also been proposed to explain the conversion of 4-phenylfuroxan to the 3-phenyl tautomer under electrochemical oxidation conditions <86IZV1691>. The factors influencing both the equilibrium constants and the equilibration rates have been dis-... 

In analogy with the previous discussion, the adsorption isotherms for both, the pairing ion and the counter ion are obtained from the equilibrium condition for the corresponding electrochemical potentials according to the scheme ... 

Exchange Current Density. Let us now return to our electrochemical cell shown in Figure 3.8. This cell is a combination of two half-cells, with the oxidation reaction occurring at the anode and the reduction reaction occurring at the cathode resulting in a net flow of electrons from the anode to the cathode. Equilibrium conditions dictate that the rate of oxidation and reduction, roxid and rred, be equal, where both rates can be obtained from Faraday s Law ... 

This question is easy to answer There is always an equilibrium condition at the base of the discussion of any kinetic process. Nemst s equation is the electrochemical version of the well-known thermodynamic equation, AG = AG°+/KTln 0 /aKacam which forms a basic part of the treatment of equilibrium in chemical reactions and which is deduced and discussed in every thermodynamics text. Indeed, one can deduce Nemst s equation from it For at equilibrium ... 

At the same time, it is the position of the Fredox level that determines the thermodynamic properties of a semiconductor-solution interface. In particular, proceeding from the equilibrium condition F = Fredox, one may write the condition of an electrochemical reaction in the following form (Gerischer, 1977c) ... 

It is important to recognize that the Nernst equation is valid only at the equilibrium condition, determined by specifying i, = 0. Most electrochemical techniques (chronoamperometry, chronocoulometry, voltammetry, etc.) involve nonequilibrium conditions and therefore cannot be expected to exhibit a Nernstian response unless the rates are very fast and equilibrium is quickly reestablished at the surface. 

Since natural waters are generally in a dynamic rather than an equilibrium condition, even the concept of a single oxidation-reduction potential characteristic of the aqueous system cannot be maintained. At best, measurement can reveal an Eh value applicable to a particular system or systems in partial chemical equilibrium and then only if the systems are electrochemically reversible at the electrode surface at a rate that is rapid compared with the electron drain or supply by way of the measuring electrode. Electrochemical reversibility can be characterized... 

When a chemical change involving charge species is produced in an electrochemical system, under equilibrium conditions the following condition holds ... 

Double Potential Pulse Electrochemical Techniques combine the faradaic currents at two successive potential pulses recovering then the initial equilibrium conditions (in the case of a DME the two successive potentials are applied to the same drop). 

There has recently been much activity in developing molecular spectroscopic probes of electrochemical interfaces, as for other types of heterogeneous systems. The ultimate objectives of these efforts include not only the characterization of adsorbate molecular structure interactions under equilibrium conditions, but also the extraction of mechanistic and kinetic information from spectral detection of reactive adsorbates. 

Apart from the ease of precise control in an electrochemical path to synthesis, there is the unique feature of being able to force the electrode reaction to take place against its own AG. This is because the principal rule of chemical equilibria is AG = 0, but in electrochemical equilibria, the equilibrium condition is AG = -nFEKV Thus, if the cell potential is exactly rev, the chemical reaction in the cell is at equilibrium and nothing happens. However (in contrast to what can be done chemically), moving the potential of the working electrode in a more negative direction than its reversible potential stimulates the reaction to take off in a cathodic direction at a fixed rate i.e., it acts to reduce the reactant ... 

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