Nernst equation redox electrodes

The redox (electrode) potential for ion-ion redox systems at any concentration and temperature is given by the Nernst equation in the form... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

In agreement with the theory of electrolysis, treated in Sections 3.1 and 3.2, the parts of the residual current and the limiting current are clearly shown by the nature of the polarographic waves because for the cathodic reduction of Cd2+ and Zn2+ at the dme we have to deal with rapid electron transfer and limited diffusion of the cations from the solution towards the electrode surface and of the metal amalgam formed thereon towards the inside of the Hg drop, we may conclude that the half-wave potential, Eh, is constant [cf., Fig. 3.13 (a ] and agrees with the redox potential of the amalgam, i.e., -0.3521V for Cd2+ + 2e - Cd(Hg) and -0.7628 V for Zn2+ + 2e -> Zn(Hg) (ref. 10). The Nernst equation is... 

Analogously to eqn. 3.72 for stationary electrodes and a reversible redox couple of soluble ox and red, Kies derived for chronopotentiometry at a dme via insertion in the Nernst equation... 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

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 ... 

Equation 13 0.059, [ox] E — Eq + log n [red] This is the well known Nernst equation. Eo is the potential of the electrode when [ox] = [red]. This potential E0 is called the standard electrode potential (sep) which is a characteristic for a particular redox couple. Table 2-1 gives the sep of a number of redox couples. 

We consider again the redox reaction Ox + ze = Red with a solution initially containing only the oxidized form Ox. The electrode is initially subjected to an electrode potential Ei where no reaction takes place. For the sake of simplicity, it is assumed that the diffusion coefficients of species Ox and Red are equal, i.e., D = D0x = DKeA. Now, the potential E is linearly increased or decreased with E(t) = Ei vt (v is a potential scan rate, and signs + and represent anodic scan and cathodic scan, respectively.) Under the assumption that the redox couple is reversible, the surface concentrations of Ox and Red, i.e., cs0x and 4ed, respectively, are always determined by the electrode potential through the Nernst equation... 

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)... 

A redox couple that is wholly in solution can be analysed without recourse to a redox electrode - indeed, in the example given here, analysis with an iron rod would complicate the situation since the Fe " ", Fe " " system itself obeys the Nernst equation (equation (3.8)). 

Analyses using inert electrodes are experimentally identical to those using redox electrodes but are less useful in practice since we usually want to know how much metal is in solution, and use of the Nernst equation (equation (3.8)), e.g. for the case of Fe and Fe " ", will merely tell us the ratio of the respective redox states in solution. 

Dynamic electrochemistry is seen to alter the ratio of a(0) to a(R) for the redox couple at the surface of the working electrode (i.e. at the electrode solution interface). Note that this alteration occurs during electrolysis, such that the electrode potential Eq,r can shift according to the Nernst equation. 

Nernst Equation for Concentration Dependence of RedOx Potential. Equation (5.9) applied to the general RedOx electrode (5.16) yields... 

Potentiometry is a method of obtaining chemical information by measuring the potential of an indicator electrode under zero current flow. It is based on the Nernst equation, which expresses the electrode potential as a function of the activity (or activities) of the chemical species in solution. The information obtained varies with indicator electrode, from the activity (concentration) of a chemical species to the redox potential in the solution. The potential of the indicator electrode is measured against a reference electrode using a high inptit-impedance mV/pH me-... 

Redox Electrodes If a platinum electrode is immersed in a solution containing the oxidized and reduced forms (Ox, Red) of a redox reaction Ox+ne <=> Red, its potential is given by the Nernst equation (Section 5.2.1) ... 

The redox equilibrium Hg2+ + 2e Hg(/) is established rapidly at the surface of the Hg electrode, so the Nernst equation for the cell can be written in the form... 

Redox chemistry at the two surfaces of the 02 sensor. The voltage difference between the two electrodes is governed by the Nernst equation AV - (RT/2F) ln P0j(left)/P0 (right)), where R is the gas constant, r is the sensor temperature, and F is the Faraday constant. 

In the Figure 3.18 example, after imposing Ej across the electrode-solution interface, the potential is scanned negatively toward the standard redox potential of the O/R couple. The ratios of O and R that must exist at the electrode surface (Cr/Cq) at several potentials during the scan are given in each figure. These values are dictated by the Nernst equation for a reversible system (see Table 3.1). Since the solution initially contained only O, the R required to satisfy the Nernst equation is obtained from O by reduction, causing cathodic current. 

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. 

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. 

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. 

It is important to note that the electrode potential is related to activity and not to concentration. This is because the partitioning equilibria are governed by the chemical (or electrochemical) potentials, which must be expressed in activities. The multiplier in front of the logarithmic term is known as the Nernst slope . At 25°C it has a value of 59.16mV/z/. Why did we switch from n to z when deriving the Nernst equation in thermodynamic terms Symbol n is typically used for the number of electrons, that is, for redox reactions, whereas symbol z describes the number of charges per ion. Symbol z is more appropriate when we talk about transfer of any charged species, especially ions across the interface, such as in ion-selective potentiometric sensors. For example, consider the redox reaction Fe3+ + e = Fe2+ at the Pt electrode. Here, the n = 1. However, if the ferric ion is transferred to the ion-selective membrane, z = 3 for the ferrous ion, z = 2. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

The dynamics of the system are described by k°, with its units being s 1 for an adsorbed reactant. A redox couple with a large k° will establish the equilibrium concentrations given by the Nernst equation on a short timescale. Kinetically facile systems of this type require high-speed electrochemical techniques to successfully probe the electrode dynamics. The largest k° values that have been reliably measured are of the order of 106 s-1 and are associated with mechanistically simple reactions, i.e. there are no coupled chemical kinetics or significant structural differences between the oxidized and reduced forms. 

Measurements can be done using the technique of redox potentiometry. In experiments of this type, mitochondria are incubated anaerobically in the presence of a reference electrode [for example, a hydrogen electrode (Chap. 10)] and a platinum electrode and with secondary redox mediators. These mediators form redox pairs with Ea values intermediate between the reference electrode and the electron-transport-chain component of interest they permit rapid equilibration of electrons between the electrode and the electron-transport-chain component. The experimental system is allowed to reach equilibrium at a particular E value. This value can then be changed by addition of a reducing agent (such as reduced ascorbate or NADH), and the relationship between E and the levels of oxidized and reduced electron-transport-chain components is measured. The 0 values can then be calculated using the Nernst equation (Chap. 10) ... 

Half-cell reaction — The redox reaction (- electrode reaction) proceeding in a half-cell. The half-cell reaction changes the ratio of the activities of the reduced and oxidized forms. When the half-cell reaction is electrochemically reversible (see reversibility), the -> Nernst equation will describe the dependence of the -> electrode potential on the ratio of the activities of the reduced and oxidized forms. 

A measure of the oxidation/reduction capability of a solution (liquid or solid) measured with an -> inert electrode. For -> electrochemically reversible systems it is defined by the - Nernst equation. For -> electrochemically irreversible systems it is a conditional measuring quantity, i.e., depending on the experimental conditions. See also -> potential, - redox potential. 

Peters equation — Obsolete term for the - Nernst equation in the special case that the oxidized and reduced forms of a redox pair are both dissolved in a solution and a reversible potential is established at an inert metal electrode. Initially Nernst derived his equation for the system metal/metal ions, and it was Peters in the laboratory of -> Ostwald, F. W. who published the equation for the above described case [i]. The equation is also sometimes referred to as Peters-Nernst equation [ii]. 

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. 

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