Equilibrium electrode potential Nernst equation

The equilibrium electrode potential is given by the Nernst equation (cf. 3.2.17),... 

Equation (5.9) is the general Nernst equation giving the concentration dependence of the equilibrium cell voltage. It will be used in the next section of this chapter to derive the equilibrium electrode potential for metal/metal-ion and redox electrodes. 

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. 

Equilibrium electrode potential — is the value of -> electrode potential determined exclusively by a single redox system ox/red in the absence of current and under complete equilibration. The rates of ox to red reduction and of red to ox oxidation processes are equal under these circumstances (see exchange current density). The value of equilibrium e.p. is determined by the - Nernst equation. Equilibrium e.p. presents a - redox potential in its fundamental sense. See also - reversibility. 

The equilibrium electrode potential is the electrical potential of an electrode measured against a reference electrode when there is no current flowing through the electrode. It is also called open circuit potential (OCP). The equilibrium potential between a metal and a solution of its ions is given by the Nernst equation as follows ... 

In the given form, the Butler-Volmer equation is applicable rather broadly, for flat model electrodes, as well as for heterogeneous fuel cell electrodes. In the latter case, concentrations in Eq. (2.13) are local concentrations, established by mass transport and reaction in the random composite structure. At equilibrium,/f = 0, concentrations are uniform. These externally controlled equilibrium concentrations serve as the reference (superscript ref) for defining the equilibrium electrode potential via the Nernst equation. 

Redox reactions are usually described by a disguised form of equilibrium constant called the standard cell potential. It is directly proportional to the log of the Kl. A system of hypothetical half-cell potentials is based on the standard hydrogen electrode. The Nernst equation relates cell potentials to the log of activities involved and to the K°q. For a reaction to which a net change in oxidation states n applies. 

This is the famous Butler-Volmer equation. Incorporating the Nernst equation, which relates the equilibrium electrode potential to the standard equilibrium potential and to the equilibrium composition of the bulk electrolyte (concentrations with superscript b) via... 

The equilibrium electrode potential Eq depends of course on the actual concentrations c or the activities a = c/ of the dissolved species according to the Nernst equation (where / is the activity coefficient). For the discussed electrode reactions with T = 298 K and the definition pH =-log Ch... 

The Nernst equation (16) relates the equilibrium electrode potential eq (the electrical potential of the working electrode with respect to any convenient reference electrode) to the bulk solution concentrations [O] and [R] when the system is in equilibrium. As the bulk concentration [O] increases or the bulk concentration [R] decreases, the equilibrium potential becomes more positive. 

It must not be assumed that the protection potential is numerically equal to the equilibrium potential for the iron/ferrous-ion electrode (E ). The standard equilibrium potential (E ) for iron/ferrous-ion is -0-440V (vs. the standard hydrogen electrode). If the interfacial ferrous ion concentration when corrosion ceases is approximately 10 g ions/1 then, according to the Nernst equation, the equilibrium potential (E ) is given by ... 

It must be emphasised that standard electrode potential values relate to an equilibrium condition between the metal electrode and the solution. Potentials determined under, or calculated for, such conditions are often referred to as reversible electrode potentials , and it must be remembered that the Nernst equation is only strictly applicable under such conditions. 

The potential of the electrode surface is determined by the Nernst equation introduced in Sec. 1.3.3. In an equilibrium, the currents in anodic and cathodic directions are equal. If they are related to an electrode area, they are called exchange-current densities, j0 ... 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

Comparison with Eq. (2.10) shows that the measured potential is simply the difference between the equilibrium potentials of the two redox couples, each measured with respect to its own reference electrode. Admittedly, this is an obvious result, but it is useful to derive it from first principles. The corresponding Nernst equation is ... 

This important equation can be qualitatively interpreted in the following way. When the two components Ox and Red are present in solution at certain concentrations, the working electrode will spontaneously find its equilibrium potential (imposed by the Nernst equation) and there will be no overall current flow. In order for Ox to be reduced or Red oxidized, the system must be moved from equilibrium. This can be achieved by setting a potential different from that for equilibrium. The process of oxidation or reduction will be favoured depending on whether... 

ET much faster than transport (transport control). Electrochemical equilibrium is attained at the electrode surface at all times and defined by the electrode potential E. The concentrations Cox and Cred of oxidized and reduced forms of the redox couple, respectively, follow the Nernst equation (1) (reversible ET)... 

The Nernst equation defines the equilibrium potential of an electrode. A simplified thermodynamic derivation of this equation is given in the Sections 5.3 to 5.5. Here we will give the kinetic derivation of this equation. 

When Vf=Vb, the electrode reaction is in equilibrium and no change occurs overall. The potential at which the reaction is in equilibrium is the equilibrium potential. If we express it by Eeq (V), we get the following Nernst equation from Eqs (5.2) and (5.3) ... 

Unlike anions that specifically adsorb at electrodes, cations normally do not lose their solvation shell due to their smaller size and are electrostatically adsorbed at electrodes at potentials negative to the pzc. However, depending on the affinity with the foreign substrate, cations can be reduced to a lower oxidation state or even discharged completely to the corresponding metal atom at the sub-monolayer or monolayer level at potentials positive to the equilibrium Nernst potential for bulk deposition. This deposition of metal atoms on foreign metal electrodes at potential positive to that predicted by the Nernst equation for bulk deposition has been called underpotential deposition and has been extensively investigated in recent years. Detailed discussion of the... 

Figure 3.37 illustrates the Nernst diffusion layer in terms of concentration-distance profiles for a solution containing species O. As pointed out previously, the concentration of redox species in equilibrium at the electrode-solution interface is determined by the Nernst equation. Figure 3.37A illustrates the concentration-distance profile for O under the condition that its surface concentration has not been perturbed. Either the cell is at open circuit, or a potential has been applied that is sufficiently positive of Eq R not to alter measurably the surface concentrations of the 0,R couple. 

The Nernst Equation for the Concentration Dependence of Metal/Metal-Ion Potential. In the general case of a metal/metal-ion electrode, a metal M is in an equilibrium with its ions in the solution... 

The potential of this electrode is defined (Section 5.2) as the voltage of the cell Pt H2(l atm) H+(<2 = 1) MZ+ M, where the left-hand electrode, Et = 0, is the normal hydrogen reference electrode (described in Section 5.6). We will derive the Nernst equation on the basis of the electrochemical kinetics in Chapter 6. Here we will use a simplified approach and consider that Eq. (5.9) can be used to determine the potential E of the M/Mz+ electrode as a function of the activity of the products and reactants in the equilibrium equation (5.10). Since in reaction (5.10) there are two reactants, Mz+ and e, and only one product of reaction, M, Eq. (5.9) yields... 

In the previous section the mercury electrode has been described. If no redox pairs (e.g. Fe2+ and Fe3+) are in solution and if we exclude gas reactions, the mercury electrode is completely polarizable. Polarizable means If a potential is applied, a current flows only until the electric double layer has formed. No electrons are transferred from mercury to molecules in the solution and vice versa. The other extreme is a completely reversible electrode, for which the Agl electrode is an example. Each attempt to change the potential of an Agl electrode leads to a current because the equilibrium potential is fixed by the concentrations of Ag+ or I according to the Nernst equation. 

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