Redox equations

ENZYME KINETIC EQUATIONS REDOX-ACTIVE AMINO ACIDS TOPAQUINONE REDOX POTENTIAL Redox reactions,... 

Platinum electrodes in conjunction with a reference electrode can be used to measure E values in environmental samples. However, these values cannot be considered definitive since they may represent a composite response of several redox couples and the actual response of the electrode can be limiting. A more direct approach is to measure the proportion of the oxidized and reduced components in a system and calculate Fh using the Nemst equation. Redox indicators [listed below with °(W)] may also be used as probes to assess redox status. Comparable to acid-base indicators, the color of these compounds changes when oxidized or reduced. With the exception of resomfin which is pink, the oxidized form of these compounds is blue while the reduced counterpart is yellow or colorless. 

For more complicated redox reactions, a general fonn of the Nemst equation may be derived by analogy with A2.4.113. If we consider a stoichiometric reaction of the following type ... 

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

For a simple electron transfer reaction containing low concentrations of a redox couple in an excess of electrolyte, the potential established at an inert electrode under equilibrium conditions will be governed by the Nemst equation and the electrode will take up the equilibrium potential for the couple 0/R. In temis of... 

Using the electron transfer definition, many more reactions can be identified as redox (reduction-oxidation) reactions. An example is the displacement of a metal from its salt by a more reactive metal. Consider the reaction between zinc and a solution of copper(If) sulphate, which can be represented by the equation... 

The change in the redox potential is given quantitatively by the Nernst equation ... 

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

Thus under standard conditions chloride ions are not oxidised to chlorine by dichromate(Vr) ions. However, it is necessary to emphasise that changes in the concentration of the dichromate(VI) and chloride ions alters their redox potentials as indicated by the Nernst equation. Hence, when concentrated hydrochloric acid is added to solid potassium dichromate and the mixture warmed, chlorine is liberated. 

Table 11.29 Equations for the Redox Determinations of the Elements with Equivalent Weights...

Equations for the principal methods for the redox determinations of the elements are given in Table 11.29. Volumetric factors in redox titrations for the common titrants are given in Table 11.28. 

Techniques responding to the absolute amount of analyte are called total analysis techniques. Historically, most early analytical methods used total analysis techniques, hence they are often referred to as classical techniques. Mass, volume, and charge are the most common signals for total analysis techniques, and the corresponding techniques are gravimetry (Chapter 8), titrimetry (Chapter 9), and coulometry (Chapter 11). With a few exceptions, the signal in a total analysis technique results from one or more chemical reactions involving the analyte. These reactions may involve any combination of precipitation, acid-base, complexation, or redox chemistry. The stoichiometry of each reaction, however, must be known to solve equation 3.1 for the moles of analyte. 

Redox reactions, such as that shown in equation 6.22, can be divided into separate half-reactions that individually describe the oxidation and the reduction processes. 

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

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... 

Although this treatment of buffers was based on acid-base chemistry, the idea of a buffer is general and can be extended to equilibria involving complexation or redox reactions. For example, the Nernst equation for a solution containing Fe + and Fe + is similar in form to the Henderson-Hasselbalch equation. 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

You will recall from Chapter 6 that the Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. Consider, for example, a titration in which the analyte in a reduced state, Ared) is titrated with a titrant in an oxidized state, Tox- The titration reaction is... 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

Coulometric Titrations Controlled-current coulometric methods commonly are called coulometric titrations because of their similarity to conventional titrations. We already have noted, in discussing the controlled-current coulometric determination of Fe +, that the oxidation of Fe + by Ce + is identical to the reaction used in a redox titration. Other similarities between the two techniques also exist. Combining equations 11.23 and 11.24 and solving for the moles of analyte gives... 

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. 

Electrochemical Reversibility and Determination of m In deriving a relationship between 1/2 and the standard-state potential for a redox couple (11.41), we noted that the redox reaction must be reversible. How can we tell if a redox reaction is reversible from its voltammogram For a reversible reaction, equation 11.40 describes the voltammogram. 

Aqueous solutions of sodium sulfite are alkaline and have a pH of ca 9.8 at 1 wt %. The solutions are oxidized readily by air. The redox potential is a function of pH, as would be expected from the foUowing equation ... 

Ox and Red are general symbols for oxidation and reduction media respectively, and n and (n-z) indicate their numerical charge (see Section 2.2.2). Where there is no electrochemical redox reaction [Eq. (2-9)], the corrosion rate according to Eq. (2-4) is zero because of Eq. (2-8). This is roughly the case with passive metals whose surface films are electrical insulators (e.g., A1 and Ti). Equation (2-8) does not take into account the possibility of electrons being diverted through a conductor. In this case the equilibrium... 

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