Redox equilibria reduction half-reactions

One of the most useful applications of standard potentials is in the calculation of equilibrium constants from electrochemical data. The techniques that we develop here can be applied to any kind of reaction, including neutralization and precipitation reactions as well as redox reactions, provided that they can be expressed as the difference of two reduction half-reactions. 

The equilibrium constant for this reaction is actually the solubility product, Ksp, for silver chloride (Section 11.10). It does not matter that overall the reaction is not a redox reaction so long as it can be expressed as the differ- ence of two reduction half-reactions. Because silver chloride is almost insol-i uble, we expect K to be very small (and E° to be negative). 

In soil solutions the most important chemical elements that undergo redox reactions are C, N, O, S, Mn, and Fe. For contaminated soils the elements As, Se, Cr, Hg, and Pb could be added. Table 2.4 lists reduction half-reactions (most of which are heterogeneous) and their equilibrium constants at 298.15 K under 1 atm pressure for the six principal elements involved in soil redox phenomena. Although the reactions listed in the table are not full redox reactions, their equilibrium constants have thermodynamic significance and may he calculated with the help of Standard-State chemical potentials in the manner... 

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 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... 

This is a quantitative calculation, so it is appropriate to use the seven-step problem-solving strategy. We are asked to determine an equilibrium constant from standard reduction potentials. Visualizing the problem involves breaking the redox reaction into its two half-reactions ... 

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 ... 

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 ... 

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. 

Since tables of standard apparent reduction potentials and standard transformed Gibbs energies of formation contain the same basic information, there is a question as to whether this chapter is really needed. However, the consideration of standard apparent reduction potentials provides a more global view of the driving forces in redox reactions. There are two contributions to the apparent equilibrium constant for a biochemical redox reaction, namely the standard apparent reduction potentials of the two half-reactions. Therefore it is of interest to compare the standard apparent reduction potentials of various half reactions. 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

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. 

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... 

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... 

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... 

Analyze We are given a redox equation and asked to use standard reduction potentials to calculate the equilibrium constant, Plan can be calculated from E° using Equation 20.18. Thus, we must first determine E° from the values for its half-reactions. 

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 ... 

Electrode potential, E The energy, expressed as a voltage, of a redox couple at equilibrium. E is the potential of the electrode when measured relative to a standard (ultimately the SHE). E depends on temperature, activity and solvent. By convention, the half cell must first be written as a reduction, and the potential is then designated as positive if the reaction proceeds spontaneously with respect to the SHE. Otherwise, E is negative. 

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 ... 

Also known as the standard hydrogen electrode (SHE), it is a redox reference electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. The potential of the NHE is defined as zero and based oti equilibrium of the following redox half-cell reaction, typically on a Pt surface 2H+(aq) + 2e H2(g). The activities of both the reduced form and the oxidized form are maintained at unity. That implies that the pressure of hydrogen gas is 1 atm and the concentration of hydrogen ions in the solution is 1 M. 

The first step consists of identifying the two half-reduction couples that are facing each other and affixing to them the judicious stoichiometric coefficients in such a way that the equilibrium in electrons should be satisfied. This step is called the redox balance. In the given example, the two half-redox reactions are... 

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