Oxidation-reduction potentials equilibrium relations

That oxidation-reduction potentials are related to equilibrium constants may be used to underscore the fact that they apply to (theoretically) reversible reactions. The oxidized member of any couple will reduce some of the reduced member of any other couple, provided a reaction mechanism exists. The potentials of the two couples permit an estimation only of the possible extent of the reaction nothing can be predicted about the rate, or indeed, whether the reaction will occur at all. In determining the extent of any reaction, actual concentrations of all reagents must be considered, since the actual equilibrium is important, not the equilibrium of an ideal 1 M solution that might be calculated from AE or AFo values. 

The general equation relating the equilibrium constant for a reaction involving the transfer of n electrons and standard oxidation-reduction potentials is... 

From Nernst s equation related to individual equilibrium potentials we may deduce that the oxidizing power of hydrogen peroxide, which is higher with a more positive reduction potential of the system (lb), grows with increasing concentration of the hydrogen ions in the solution. On the other hand the... 

Since the corrosion of iron in copper sulfate solution involves an oxidation and reduction reactions with exchange of electrons, the reaction must involve an electrochemical potential difference, related to the equilibrium constant. This relationship may be written as ... 

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. 

Note Try to avoid learning some ariritrary rule such as the best oxidizing agent is on the bottom left. That will not serve you well if the list of potentials is presented with the most positive first, which is the usual convention. Standard reduction potentials also can be combined to calculate cell potentials. Cell potentials can then be related to the position of equilibrium for redox reactions, a skill we will practice shortly. 

We have seen that a positive standard cell potential corresponds to a spontaneous oxidation-reduction reaction. And we know (from Chapter 17) that the spontaneity of a reaction is determined by the sign of AG°. Therefore, ceii 2nd AG° must be related. We also know from Section 17.9 that AG° for a reaction is related to the equilibrium constant (K) for the reaction. Since and AG° are related, then E n and K must also be related. 

In the mixed potential theory (MPT) model, both partial reactions occur randomly on the surface, both with respect to time and space. However, given the catalytic nature of the reductant oxidation reaction, it may be contended that such a reaction would tend to favor active sites on the surface, especially at the onset of deposition, and especially on an insulator surface catalyzed with Pd nuclei. Since each reaction strives to reach its own equilibrium potential and impose this on the surface, a situation is achieved in which a compromise potential, known as the mixed potential (.Emp), is assumed by the surface. Spiro [27] has argued the mixed potential should more correctly be termed the mixture potential , since it is the potential adopted by the complete electroless solution which comprises a mixture of reducing agent and metal ions, along with other constituents. However, the term mixed potential is deeply entrenched in the literature relating to several systems, not just electroless deposition. 

First reported in 1986 (181), the complex [Os(NH3)5(acetone)]2+ and related aldehyde and ketone complexes (177) were the first examples of linkage isomerizations on Os(III/II). In acetone solution, a detailed electrochemical and chemical investigation revealed that the substi-tutionally inert complex, [Os(NH3)5(Tj2-acetone)]2+, is in facile equilibrium with the rj1 form, the former being favored by 21 kJ mol-1. Upon oxidation, the Os—C bond is ruptured, but the Os—O bond remains intact, even in good donor solvents such as dma. Reduction of the i71-acetone-Os(III) species occurs at a potential of 750 mV negative of that of the 172 form in acetone. Subsequent tj1 - 172 isomerization of the ketone occurs with a specific rate of 6 x 103 sec-1 at 20 2°C. 

The equilibrium redox potential, the free energy change per mole electron for a given reduction, represents the oxidizing intensity of the couple at equilibrium. It is conveniently expressed for many applications in terms of the parameter, pE, as proposed by Jorgensen (8) and popularized by Sillen (14). This parameter is defined by the relation,... 

As the potential is increased, there is a point at which no equilibrium state is reached, but instead, an appreciable steady current flows which will obey Ohm s law over a reasonable range of applied potential. The potential at which this steady current is observed is called the decomposition potential because it is accompanied by chemical reaction (electrolysis) at the electrode surfaces. These electrode reactions are quite generally the oxidation (anode) and reduction (cathode) of ionic or molecular species present in the solution. If the reactions at the electrodes are reversible, then the decomposition potential Ed is related by the Nernst equation to the free energy changes of the electrode reactions... 

One of the first questions one might ask about forming a metal complex is how strong is the metal ion to ligand binding In other words, what is the equilibrium constant for complex formation A consideration of thermodynamics allows us to quantify this aspect of complex formation and relate it to the electrode potential at which the complex reduces or oxidizes. This will not be the same as the electrode potential of the simple solvated metal ion and will depend on the relative values of the equilibrium constants for forming the oxidized and reduced forms of the complex. The basic thermodynamic equations which are needed here show the relationships between the standard free energy (AG ) of the reaction and the equilibrium constant (K), the heat of reaction, or standard enthalpy (A// ), the standard entropy (AS ) and the standard electrode potential (E for standard reduction of the complex (equations 5.1-5.3). 

Electrochemical detection is based on the electrical signal arising between two electrodes immersed in a sample solution. Electroanalytical techniques fall into two main categories, potentiometric and Faradaic techniques. Potentiometry is the measurement of a potential difference between two electrodes under equilibrium conditions (i.e., no current flow). The potential is then related to concentration of the analyte species. Faradaic processes are based on the oxidation or reduction of the analyte, where a specific potential waveform is applied and the current is used to extract information about the sample. Many different techniques have been developed to gain quantitative and... 

There is clear evidence that adsorbate and alloyed metal atoms on platinum surface promote CO electro-oxidation. The reduced overpotential is primarily a result of the promotion of the activation of water. The subsequent kinetics are determined by the details of a Langmuir-Hinshelwood reaction between the adsorbed oxidant (OH) and adsorbed CO. Evidence is also presented that relates this promotion (or poisoning) of CO electro-oxidation to tolerate CO in hydrogen feeds in the hydrogen electro-oxidation reaction. An alternative mechanism that may operate at low potentials [79,113] may be that the reduction in CO adsorption energy on platinum induced by Ru [86,113,114] results in a higher equilibrium concentration of nonpoisoned sites. The relative importance of these mechanisms is a function... 

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 rate of the reduction and oxidation processes is related to the magnitude of the overlap of the appropriate electronic states for the corresponding reaction. As can be seen in Figure 1.1(a), when the potential applied at the working electrode corresponds to the equilibrium potential, the overlap of occupied states on the electrode with (empty) states of species A is the same as that of empty states on the electrode with occupied states of species B. This reflects the fact that the rates of oxidation and reduction are the same and so a dynamic equilibrium is established. 

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