Nernst equation redox systems

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. 

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

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

A classification of electrodes has already been given in Section 1.3.1. The function of the indicator electrode is to indicate by means of its potential the concentration of an ion or the ratio of the concentrations of two ions belonging to the same redox system. Under non-faradaic conditions, the relationship between the potential and these concentrations is given by the Nemst or the more extended Nernst-Van t Hoff equation, as explained below. As a single potential between an electrode and a solution cannot be measured in the absolute sense but only in a relative manner, a reference electrode is needed its function is merely to possess preferably a constant potential or at any rate a known potential under the prevailing experimental conditions. Often both electrodes cannot be placed in the same solution, so that a second solution... 

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. 

The first two terms on the right-hand side of this equation express the proper overpotential of the electrode reaction rjr (also called the activation overpotential) while the last term, r)c, is the EMF of the concentration cell without transport, if the components of the redox system in one cell compartment have concentrations (cOx)x=0 and (cRed)x=0 and, in the other compartment, Cqx and cRcd. The overpotential given by this expression includes the excess work carried out as a result of concentration changes at the electrode. This type of overpotential was called the concentration overpotential by Nernst. The expression for a concentration cell without transport can be used here under the assumption that a sufficiently high concentration of the indifferent electrolyte suppresses migration. 

Many natural waters, including most waters at low temperature, do not achieve redox equilibrium (e.g., Lindberg and Runnells, 1984 see Chapter 7). In this case, no single value of pe or Eh can be used to represent the redox state. Instead, there is a distinct value for each redox couple in the system. Applying the Nernst equation to Reaction 3.46 gives a pe or Eh representing the hydrolysis of water. Under disequilibrium conditions, this value differs from those calculated from reactions such as,... 

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)). 

The course of electron transfer reactions (redox reactions, see p. 14) also follows the law of mass action. For a single redox system (see p.32), the Nernst equation applies (top). The electron transfer potential of a redox system (i. e., its tendency to give off or take up electrons) is given by its redox potential E (in standard conditions, E° or E° ). The lower the... 

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. 

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) ... 

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. 

Open-circuit potential (OCP) — This is the - potential of the - working electrode relative to the - reference electrode when no potential or - current is being applied to the - cell [i]. In case of a reversible electrode system (- reversibility) the OCP is also referred to as the - equilibrium potential. Otherwise it is called the - rest potential, or the - corrosion potential, depending on the studied system. The OCP is measured using high-input - impedance voltmeters, or potentiometers, as in - potentiometry. OCP s of - electrodes of the first, the second, and the third kind, of - redox electrodes and of - ion-selective membrane electrodes are defined by the - Nernst equation. The - corrosion po-... 

Inhomogeneous redox systems The forms of Nernst equation quoted in Section 1.41(a), (b), and (c) are, strictly speaking, valid only for homogeneous redox systems, where there is no change in the number of molecules (or ions) when the substance is reduced or oxidized. For inhomogeneous systems, where this is not the case, general equations would be too complex to quote, but the... 

The model can be further tested by varying the concentration of one of the species as illustrated in Fig. 6.9. In this case, the Fermi level of the redox system is shifted according to the Nernst equation. One can easily prove by using Eqs. (6.37), (6.38) and (640) that in this case and >red are equal at = Ep,redox. 

The half cell reactions for hydrogen and oxygen form a starting point from which to consider redox systems in water. The Nernst equation for the reduction of oxygen may be written in terms of pH ... 

The Nernst equation is applicable only if the redox reaction is reversible. Not all reactions are completely reversible in natural systems activities of reacting components may be too low or equilibrium may be reached very slowly. In a sediment, the biotic microenvironment may create a redox potential that is different from the surrounding macroenvironment. For this reason, measurements of Eh in natural systems must be cautiously evaluated and not used strictly for calculations of chemical equilibria. Calculations of redox equilibria are in some cases valuable, in the sense that they will give information about the direction of chemical reactions. 

Third, the Fe(III) and Fe(II) activities in each system at each time are calculated by the procedure outlined below, and an ORP calculated using the Nernst equation (Eh ). Eh is then compared to Eh, the Eh recorded by the redox electrodes (corrected to SHE). The solubility product for the precipitated solid ferric hydroxide phase is also calculated for each data point using the pH and computed values of Fe " or one of its hydrolysis species. 

Construct a coulomctric titration curve of 100.0 ml, of a I M 1 IjSOj solution containing Fe(ll) titrated with Ce(lV) generated from 0.075 M Ce(lll). T he titration is monitored by potentiometry. The initial amount of Te(II) present is 0.0.5182 mmol. A constant current of 20.0 mA is used, bind the time corresponding to the equivalence point. Then, for about ten values of time before the equivalence point, use the stoichiometry of the reaction to calculate the amount ofFe produced and the amount of Fe remaining. Use the Nernst equation to find the system potential. Find the equivalence point potential in the usual manner for a redox titration. Fur about ten times after the equivalence point, calculate the amount of Ce produced from the electrolysis and the amount of Cc remaining. Plot the curve of system potential versus electrolysis time. 

One of the main advantages of the optically transparent thin-layer spectroelectrochemical technique (OTTLSET) is that the oxidized and reduced forms of the analyte adsorbed on the electrode and in the bulk solution can be quickly adjusted to an equilibrium state when the appropriate potential is applied to the thin-layer cell, thereby providing a simple method for measuring the kinetics of a redox system. The formal potential E° and the electron transfer number n can be obtained from the Nernst equation by monitoring the absorbance changes in situ as a function of potential. Other thermodynamic parameters, such as AH, AS, and AG, can also be obtained. Most redox proteins do not undergo direct redox reactions on a bare metal electrode surface. However, they can undergo indirect electron transfer processes in the presence of a mediator or a promoter the determination of their thermodynamic parameters can then... 

Principles Redox Protein Systems. In most cases, redox proteins undergo extremely slow electron transfer reactions at electrodes. Therefore, the thermodynamic parameters cannot be determined directly from the equations described above. One method for resolving this problem is to add a mediator, M, to the solution. The mediator shuttles electrons between the electrode and the protein and thereby accelerates the electrochemical reaction of the protein. A reversible or quasi-reversible electron transfer reaction of the redox protein, P, is then achieved indirectly through the mediator as shown in Scheme I. The Nernst equation is... 

The quantitative capability of the Nernst equation to predict the activity of chemical species is valid only under equilibrium conditions. Most of the redox couples are not in equilibrium, except in highly reduced soils steady-state condition may result in pseudoequilibrium conditions. In soils, redox equilibrium is probably never reached because of the continuous addition of electron donors and acceptors. Biological systems add and remove electrons continuously. Thus, redox potential measurements cannot be used to accurately predict the activity of specific reductant and oxidant of the system. 

It is worth noticing that, according to the Nernst equation, that is related to the equilibrium between cadmium oxide (Cd ) and reduced cadmium, the amount of cadmium oxide (Cd ) remaining in solution at the potential of our system set by the couple (H2/H ), should be theoretically higher than lOOOOppm (Fig. 18.36). From our results, it is obvious that the cadmium concentration in solution is decreased to ppm or even ppb level. Cadmium can then be deposited at a potential more positive than that proposed by the Nernst equation. This phenomenon has already been reported in the past with other metals and has been called underpotential deposition [236]. In fact, when cadmium is reduced, it does not build cadmium-cadmium bonds, but cadmium-nickel bonds. Therefore, the Nernst equation with standard redox potentials (Cd/Cd ) and (H2/H ) does not well represent underpotential cadmium deposition. According to Kolb [237], the potential shift observed in the underpotential deposition of a metallic ion (M +) onto a metal... 

The equilibrium potentials set up by the iron and chromium redox systems at the inert electrodes depend on the concentration ratios of the divalent and trivalent [M +] ions (M stands for iron and chromium, respectively), according to the Nernst equation ... 

In LSV and CV, a redox system may show a Nernstian, quasireversible or totally irreversible behavior depending on the scan rate employed, since V determine the time available for the electrodesolution interphase to attain the equilibrium condition dictated by the Nernst equation. Such a dependence is usually rationalized by the following dimensionless parameter, comparing the standard heterogeneous rate constant with the scan rate v ... 

---