Redox systems half-cells

36 REDOX SYSTEMS (HALF-CELLS) Although all oxidation-reduction reactions are based on the transfer of electrons, this cannot always be seen immediately from the reaction equations. These processes can be better understood if they are split into two separate steps, the oxidation of one substance and the reduction of another one. Let us look into the examples quoted in the previous section. 

In these steps it is necessary to write down the exact number of electrons which are released or taken up in order to balance the charges. It is easy to see from these steps what actually happens if the reaction proceeds the electrons released by Sn2+ are taken up by Fe3+. It can also be seen that equation (i) is 

In general therefore, each oxidation-reduction reaction can be regarded as the sum of an oxidation and a reduction step. It has to be emphasized that these individual steps cannot proceed alone each oxidation step must be accompanied by a reduction and vice versa. These individual reduction or oxidation steps, which involve the release or uptake of electrons are often called half-cell reactions (or simply half-cells) because from combinations of them galvanic cells (batteries) can be built up. The latter aspect of oxidation-reduction reactions 

All the oxidation-reduction reactions used in examples (a) to (e) proceed in one definite direction e.g. Fe3+ can be reduced by Sn2+, but the opposite process, the oxidation of Fe2+ by Sn4+ will not take place. That is why the single arrow was used in all the reactions, including the half-cell processes as well. If however we examine one half-cell reaction on its own, we can say that normally it is reversible. Thus, while Fe3+ can be reduced (e.g. by Sn2+) to Fe2+, it is also true that with a suitable agent (e.g. MnO ) Fe2+ can be oxidized to Fe3+. It is quite logical to express these half-cell reactions as chemical equilibria, which also involve electrons, as 

The substances which are involved in such an equilibrium form a redox system. Thus, we can speak about the iron(III)-iron(II) or about the tin(IV)-tin(II) or the permanganate-manganese(II) system and so on. In a redox system therefore, an oxidized and a reduced form of a substance are in equilibrium, in which electrons (and in some cases protons) are exchanged. For practical purposes we will classify these redox systems in two categories. 

---

Each half-reaction possesses its own redox system and from these two systems the cell reaction or redox reaction is built up. 

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). 

Fig. 22.6. Redox potentials (mV) of various half-cell reactions during mixing of fluid from a subsea hydrothermal vent with seawater, as a function of the temperature of the mixture. Since the model is calculated assuming 02(aq) and H2(aq) remain in equilibrium, the potential for electron acceptance by dioxygen is the same as that for donation by dihydrogen. Dotted line shows currently recognized upper temperature limit (121 °C) for microbial life in hydrothermal systems. A redox reaction is favored thermodynamically when the redox potential for the electron-donating half-cell reaction falls below that of the accepting half-reaction.

The standard electrode potential of an element is defined as its electrical potential when it is in contact with a molar solution of its ions. For redox systems, the standard redox potential is that developed by a solution containing molar concentrations of both ionic forms. Any half-cell will be able to oxidize (i.e. accept electrons from) any other half-cell which has a lower electrode potential (Table 4.1). 

Redox half-reactions are often written for brevity as, for example, Li+ + e - Li. with the state symbols omitted. The electrode system represented by the half-reaction may also be written as Li+ /Li. The standard redox potentials for ion-ion redox systems can be determined by setting up the relevant half-cell and measuring the potential at 298 K relative to a standard hydrogen electrode. For example, the standard redox potential for the half-reactions... 

If a complete reaction implies a value of 10, which systems are suitable for redox titrations of this type, i.e. what is the relationship between o,r of the two half cells and K ... 

Many redox systems are suitable for use as volumetric reagents for quantitative analysis provided that (i) both states within the oxidized and reduced forms of the redox-active titrant comprise a fast nemstian couple, (ii) all redox states are soluble in the solutions employed, and (iii) the separation between the standard electrode potential for each of the constituent half cells is 0.35/n V (where n is the number of electrons in the titrant couple). 

The reduction-oxidation potential (typically expressed in volts) of a compound or molecular entity measured with an inert metallic electrode under standard conditions against a standard reference half-cell. Any oxidation-reduction reaction, or redox reaction, can be divided into two half-reactions, one in which a chemical species undergoes oxidation and one in which another chemical species undergoes reduction. In biological systems the standard redox potential is defined at pH 7.0 versus the hydrogen electrode and partial pressure of dihydrogen of 1 bar. 

Iron has two common valence states, 2+ and 3-r, hence oxidation-reduction (redox) reactions in the Fe-02-H20 system must be taken into account. A redox reaction involves transfer of electrons between reacting species. Such a reaction can be divided into two half cell reactions, one describing gain of electrons and the other, their loss. For example, the reduction of Fe to Fe " by hydrogen gas. 

A ubiquitous characteristic of vanadium chemistry is the fact that vanadium and many of its complexes readily enter into redox reactions. Adjustment of pH, concentration, and even temperature have often been employed in order to extend or maintain system integrity of a specific oxidation state. On the other hand, deliberate attempts to use redox properties, particularly in catalytic reactions, have been highly successful. Vanadium redox has also been successfully utilized in development of a redox battery. This battery employs the V(V)/V(IV) and V(III)AT(II) redox couples in 2.5 M sulfuric acid as the positive and negative half-cell electrolytes, respectively. Scheme 12.2 gives a representation of the battery. The vanadium components in both redox cells are prepared from vanadium pentoxide. There are two charge-discharge reactions occurring in the vanadium redox cells, as indicated in Equation 12.1 and Equation 12.2. The thermodynamics of the redox reactions involved have been extensively studied [8],... 

Chlorostannate and chloroferrate [110] systems have been characterized but these metals are of little use for electrodeposition and hence no concerted studies have been made of their electrochemical properties. The electrochemical windows of the Lewis acidic mixtures of FeCh and SnCh have been characterized with ChCl (both in a 2 1 molar ratio) and it was found that the potential windows were similar to those predicted from the standard aqueous reduction potentials [110]. The ferric chloride system was studied by Katayama et al. for battery application [111], The redox reaction between divalent and trivalent iron species in binary and ternary molten salt systems consisting of 1-ethyl-3-methylimidazolium chloride ([EMIMJC1) with iron chlorides, FeCb and FeCl j, was investigated as possible half-cell reactions for novel rechargeable redox batteries. A reversible one-electron redox reaction was observed on a platinum electrode at 130 °C. 

Redox equilibrium — An equilibrium system may involve one or more - redox reactions taking place in solution. Such reactions may be written as a combination of individual half reactions (- half-cell reactions), for example... 

A number of half-cell redox reactions pertinent in soil-water systems are given in Tables 5.4 and 5.5. Note that at 25°C, pe = 16.9 Eh and Eh = 0.059 pe. Graphically, the relationship between pe and Eh is shown in Figure 5.3. 

In order to balance oxidation-reduction equations, we must therefore find out how many electrons are released by the reducing agent and taken up by the oxidizing agent. This can easily be done if the half-cell reaction equations of the redox systems involved are known. In the above example, if we write up the two half-cell equations ... 

Remember that when redox systems are at equilibrium, the electrode potentials of all half-reactions are identical. This generality applies whether the reactions take place directly in solution or indirectly in a galvanic cell. 

Figure 2.30 Energy-level scheme and cell half-cell reactions for a semiconductor I redox system I metal electrochemical photovoltaic cell.

The splitting of redox reaetions into two half cell reactions by introducing the symbol e is highly useful. It should be noted that the e notation does not in any way refer to solvated electrons. When calculating the equilibrium composition of a chemical system, both e , and can be chosen as components and they can be treated numerically in a similar way equilibrium constants, mass balances, etc. may be defined for both. However, while represents the hydrated proton in aqueous solution, the above equations use only the activity of e , and never the concentration of e . Concentration to activity conversions (or activity coefficients) are never needed for the electron cf. Appendix B, Example B.3). 

The electrons provided in the light reaction, however, may also be directly exported from the cells and used to reduce a variety of extracellular substrates. This electron export is effected by surface enzymes (called transplasmamembrane reductases) spanning the plasmamembrane from the inside surface to the outside. They transfer electrons from an internal electron donor [chiefly NADH and NADPH see Crane et al. (1985)] to an external electron acceptor. Direct reduction of extracellular compounds by transplasmamembrane electron transport proteins is prevalent in all cells thus far examined (Fig. 2.2). Although the function of this redox system is still subject to speculation, in phytoplankton it shows considerable activity, relative to other biochemical processes. A host of membrane-impermeable substrates, including ferricyanide, cytochrome c, and copper complexes, are reduced directly at the cells surface by electrons originating from within the cell. In phytoplankton, where the source of electrons is the light reactions of photosynthesis, the other half-redox reaction is the evolution of ()2 from H20. In heterotrophs, the electrons originate in the respiration of reduced substances. 

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 ... 

FIGURE 20.3 Expenmental apparatus used to measure the standard reduction potential of the indicated redox couples (a) the ethanol/acetaldehyde couple, (b) the fumarate/ succinate couple. Part (a) shows a sample/reference half-cell pair for measurement of the standard reduction potential of the ethanol/acetaldehyde couple. Because electrons flow toward the reference half-cell and away from the sample half-cell, the standard reduction potential is negative, specifically -0.197 V. In contrast, the fumarate/succinate couple (b) accepts electrons from the reference half-cell that is, reduction occurs spontaneously in the system, and the reduction potential is thus positive. For each halfcell, a half-cell reaction describes the reaction taking place. For the fumarate/succinate half-cell coupled to a H /H2 reference half-cell (b), the reaction taking place is indeed the reduction of fumarate. 

---