Redox equilibria oxidation half-reactions

In an electrochemical cell a redox reaction occurs in two halves (see Topic B4). Electrons are liberated by the oxidation half reaction at one electrode and pass through an electrical circuit to another electrode where they are used for the reduction. The cell potential E is the potential difference between the two electrodes required to balance the thermodynamic tendency for reaction, so that the cell is in equilibrium and no electrical current flows. E is related to the molar Gibbs free energy change in the overall reaction (see Topic B3) according to... 

The oxidation or reduction of a substrate suffering from sluggish electron transfer kinetics at the electrode surface is mediated by a redox system that can exchange electrons rapidly with the electrode and the substrate. The situation is clear when the half-wave potential of the mediator is equal to or more positive than that of the substrate (for oxidations, and vice versa for reductions). The mediated reaction path is favored over direct electrochemistry of the substrate at the electrode because, by the diffusion/reaction layer of the redox mediator, the electron transfer step takes place in a three-dimensional reaction zone rather than at the surface Mediation can also occur when the half-wave potential of the mediator is on the thermodynamically less favorable side, in cases where the redox equilibrium between mediator and substrate is disturbed by an irreversible follow-up reaction of the latter. The requirement of sufficiently fast electron transfer reactions of the mediator is usually fulfilled by such revemible redox couples PjQ in which bond and solvate... 

The curves relative to the half-reactions intersect at the point corresponding to the formation of the so-called activated complex. The height of the energy barrier of the two redox processes (oxidation, /z0x reduction, hRed) is inversely proportional to the respective reaction rates. Since in this case h0x = hRed, it is immediately apparent that these conditions identify the equilibrium conditions. 

REDOX HALF-REACTIONS. Electron transfer reactions involve oxidation (or loss of electrons) of one component and reduction (or gain of electrons) by a second component. Therefore, a complete redox reaction can be treated as the sum of two half-reactions such that the stoichiometry and electric charge is balanced across a chemical equilibrium. For each such half-reaction, there is an associated standard potential E°. The hydrogen ion-hydrogen gas couple is ... 

In redox electrodes an inert metal conductor acts as a source or sink for electrons. The components of the half-reaction are the two oxidation states of a constituent of the electrolytic phase. Examples of this type of system include the ferric/ferrous electrode where the active components are cations, the ferricyanide/ferrocyanide electrode where they are anionic complexes, the hydrogen electrode, the chlorine electrode, etc. In the gaseous electrodes equilibrium exists between electrons in the metal, ions in solution and dissolved gas molecules. For the half-reaction... 

When a biochemical half-reaction involves the production or consumption of hydrogen ions, the electrode potential depends on the pH. When reactants are weak acids or bases, the pH dependence may be complicated, but this dependence can be calculated if the pKs of both the oxidized and reduced reactants are known. Standard apparent reduction potentials E ° have been determined for a number of oxidation-reduction reactions of biochemical interest at various pH values, but the E ° values for many more biochemical reactions can be calculated from ArG ° values of reactants from the measured apparent equilibrium constants K. Some biochemical redox reactions can be studied potentiometrically, but often reversibility cannot be obtained. Therefore a great deal of the information on reduction potentials in this chapter has come from measurements of apparent equilibrium constants. 

The firm thermodynamic status of log KR for reduction half-reactions permits the use of these parameters in the normal way (see Section 1.2 and Special Topic 1) to evaluate equilibrium activities of oxidized and reduced species and to compare the stabilities of reactants and products in redox reactions. As an example of a stability comparison, consider the possible reduction of N(V) to N(0) through the oxidation of C(0) to C(IV) in a soil solution.13 The reduction half-reaction for denitrification is implicit in Eq. 2.20 that for C oxidation is... 

The present view is that cytochrome a is the acceptor of electrons from cytochrome c, but that a simple linear electron-transfer sequence from cytochrome a to Cua and then to the cytochrome 03/Cub centre is unlikely. Instead the sequence shown in equation (63) holds, where cytochrome a is in rapid equilibrium with Cua. These views depend largely upon pre-steady-state kinetics of the redox half reactions of the enzyme with its two substrates, ferrocytochrome c and O2. However, these conclusions are not in accord with kinetic studies under conditions when both substrates are bound to the enzyme, and which show maximal rates of electron transfer from cytochrome c to O2. In particular some of the cytochrome c is oxidized at a faster rate than a metal centre in the oxidase. In contrast, at high ionic strength conditions, where the cytochrome c and the cytochrome oxidase are mainly dissociated, oxidation of cytochrome c occurs only slowly following the complete oxidation of the oxidase. These results for the fast oxidation of cytochrome c have been interpreted in terms of direct electron transfer from cytochrome c to the bridged peroxo intermediate involving 03 and Cub, or to a two-electron transfer to O2 from cytochromes a and 03 during the initial phase of the reaction. 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

The pe of a surface water at pH 7, in equilibrium with atmospheric oxygen, is calculated to be 13.6 it decreases to approximately 4 in an environment where both oxidized and reduced iron are present and drops to approximately — 4 where sulfide or methane are being produced, pe can be calculated from the measured concentrations of products and reactants in a redox half-reaction. A scale equivalent to pe is the Eh scale, which is expressed in volts and is based on the determination of electron activity using electrochemical methods. Eh is related to pe by the following equation,... 

We can generalize Equation 19-6 by stating that at equilibrium, the electrode potentials for all half-reactions in an oxidation/reduction system are equal. This generalization applies regardless of the number of half-reactions present in the system because interactions among all must take place until the electrode potentials are identical. For example, if we have four oxidation/reduction systems in a solution, interaction among all four takes place until the potentials of all four redox couples are equal. 

M Note that the product ab is the total number of electrons gained in the reduction (and lost in the oxidation) represented by the balanced redox equation. Thus, if a = h, it is not necessary to multiply the half-reactions by a and b.lia = b = n, the equilibrium constant is determined from... 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

One can spot dismutation by calculating the oxidation number of the three species involved. The oxidation degree of iodine is 0 in I2, -I in 1 and -i-V in 103 . This equilibrium is not a redox half-reaction, but an overall reaction which is the balance of the two redox half-reactions corresponding to the IO37I2 and 12/r couples. 

Ideally, the two extreme states of this material should correspond to the C0O2/UC0O2 couple. To express the Nernst law In this material In a simplified manner, one can consider only the equilibrium of lithium ions which keep their oxidation number -i-l. This implies that the insertion material is a sufficiently good electronic conductor for the Insertion limit to be ruled by the ionic insertion sites. The redox half-reaction can then be written ... 

The net reaction is the oxidation of Ce(III) to Ce(IV) by bromate. In the bistable regime there is a state, where essentially no reaction occurs, which coexists with a state in which a percentage of Ce(III) is oxidized to Ce(IV). In this system we measured [6] at the same time the optical density which gives concentrations of Ce(IV) by Beer s law, and hence also the concentration of Ce(III) by conservation, and the emf of a Pt electrode which at equilibrium follows the Nernst equation (10.1). The experiment consisted of the measurement of the emf of the Ce(III)/Ge(IV) half reaction at a redox (Pt-Ag/AgGl) electrode imder equilibrium and stationary non-equilibrium conditions. The apparatus is shown in Fig. 10.1, but in these experiments the parts 4 7 were not present. From these measurements we determined that there exists a non-Nernstian contribution in a non-equilibrium stationary state as shown in Table 10.2. The concentration of [Ce(III)]ss in the stationary state is obtained... 

Bromate ions are strong oxidizing agents. During the course of the reaction, they are reduced into bromide ions according to the half-redox equilibrium... 

As an illustrative example for calculating the redox equilibrium between a NAC and a naturally occurring reductant, we consider the reduction of nitrobenzene at 25 °C in a 5 mM aqueous H2S solution buffered at pH 7.0. We assume that nitrobenzene (NB) is reduced to aniline (AN) and that hydrogen sulfide is oxidized to elemental sulfur (S(s)). From Figure 3 we get the EgCw) values for the two half-reactions ... 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Most redox reactions in vitro reach equilibrium only extremely slowly with half times of the order of months or years, even though they may be highly favoured thermodynamically. This is illustrated by the persistence of N2 in oxic systems even though its oxidation to NOs is strongly favoured (Table 4.1). However, microbes in soil and water are capable of catalysing particular reactions from which they obtain energy for metabolism. The half times of such microbially catalysed reactions are of the order of hours or days. 

As a consequence when the difference between equilibrium potentials of the two half redox reactions is low, the modifying metal, during the preparation of a bimetallic catalyst by direct redox reaction, will be deposited selectively on specific sites of the parent metal (i.e. sites that are highly oxidizable such as comers, edges, etc.). However, the equilibrium potentials are defined by Nemst s law which provides facilities to fit the potential values by changing the concentrations of the oxidized and reduced forms (eqs 2 and 2 ) and so induces selective deposition of the modifier on the parent catalyst. 

The reduction potential is an electrochemical concept. Consider a substance that can exist in an oxidized form X and a reduced form X . Such a pair is called a redox couple. The reduction potential of this couple can be determined by measuring the electromotive force generated by a sample half-cell connected to a standard reference half-cell (Figure 18.6). The sample half-cell consists of an electrode immersed in a solution of 1 M oxidant (X) and 1 M reductant (X ). The standard reference half-cell consists of an electrode immersed in a 1 M H+ solution that is in equilibrium with H2 gas at 1 atmosphere pressure. The electrodes are connected to a voltmeter, and an agar bridge establishes electrical continuity between the half-cells. Electrons then flow from one half-cell to the other. If the reaction proceeds in the direction... 

The silver-silver chloride electrode is an example of a metal electrode that participates as a member of a redox couple. The silver-silver chloride electrode consists of a silver wire or rod coated with AgCl(s) that is immersed in a chloride solution of constant activity this sets the half-cell potential. The Ag/AgCl electrode is itself considered a potentiometric electrode, as its phase boundary potential is governed by an oxidation-reduction electron transfer equilibrium reaction that occurs at the surface of the silver ... 

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