Equilibrium constants of redox reactions

Table 8.6 Apparent equilibrium constants of redox reactions at 298.15 K, pH 7, and ionic strength 0.25 M...

This provides the useful conversion between standard potentials and equilibrium constants of redox reactions. 

The equilibrium constant of redox reactions is generally expressed in terms of the appropriate electrode potentials (Topics C5, C8), but for the above reaction ... 

Unlike the reactions that we have already considered, the equilibrium position of a redox reaction is rarely expressed by an equilibrium constant. Since redox reactions involve the transfer of electrons from a reducing agent to an oxidizing agent, it is convenient to consider the thermodynamics of the reaction in terms of the electron. 

It is evident that the abrupt change of the potential in the neighbourhood of the equivalence point is dependent upon the standard potentials of the two oxidation-reduction systems that are involved, and therefore upon the equilibrium constant of the reaction it is independent of the concentrations unless these are extremely small. The change in redox potential for a number of typical oxidation-reduction systems is exhibited graphically in Fig. 10.15. For the MnO, Mn2+ system and others which are dependent upon the pH of the... 

The quantitative relationship between %° and AG° allows the calculation of equilibrium constants for redox reactions. For a cell at equilibrium... 

We will use standard electrode potentials throughout the rest of this text to calculate cell potentials and equilibrium constants for redox reactions as well as to calculate data for redox titration curves. You should be aware that such calculations sometimes lead to results that are significantly different from those you would obtain in the laboratory. There are two main sources of these differences (1) the necessity of using concentrations in place of activities in the Nernst equation and (2) failure to take into account other equilibria such as dissociation, association, complex formation, and solvolysis. Measurement of electrode potentials can allow us to investigate these equilibria and determine their equilibrium constants, however. 

However, based strictly on the standard reduction potentials of the two redox couples involved, the equilibrium constant of the reaction as written would be exceedingly small. To further complicate matters, the rates of disappearance of 02 in the presence of Fe(II)TMPyP, as monitored by RRDE techniques, and the rates of disappearance of 02 in the presence of Fe(III)TMPyP, as measured by spectrophotometric methods [52], yielded very similar values. The most likely resolution of this seeming quandary invokes formation of a macrocycle-dioxygen adduct as a short-lived, albeit yet to be detected, intermediate. 

The redox reaction of the pyridine coenzyme with an alcohol involves both a change from a cationic to a neutral species and the reversible loss of a proton, as shown in Fig. 3. Therefore, the external equilibrium constant of these reactions depends on solvent polarity, pH, and the structure of the substrate... 

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... 

Potential on Concentration Concentration Cells The Nernst Equation Ion-Selective Electrodes Calculation of Equilibrium Constants for Redox Reactions... 

Since many disciplines now use pe as much as Eh to express electron activity in a system, it is worthwhile to discuss the relationships between these two variables (Lindsay, 1979). Eive decades ago the Swedish chemist Lars Gunnar Sillen suggested that the electrons (e ) can be considered as any other reactant or product in chemical reactions. Sillen and Martell (1964) tabulated equilibrium constants for redox reactions in terms of both E° (standard electrode potentials) and log K (equilibrium activity constants), and encouraged the use of log K to calculate pe values for redox systems. Like pH, the electron activity in a reaction can be defined as... 

The concept of formal potentials has been developed for the mathematical treatment of redox titrations, because it was quickly realized that the standard potentials cannot be used to explain potentiometric titration curves. Generally, formal potentials are experimentally determined using equations similar to Eq. (1.2.24) because it is easy to control the overall concentrations of species in the two redox states. For calculating formal potentials it would be necessary to know the standard potential, all equilibrium constants of side reactions , and the concentrations of all solution constituents. In many cases this is still impossible as many equilibrium constants and the underlying chemical equilibria are still unknown. It is the great advantage of the concept of formal potentials to enable a quantitative description of the redox... 

The free energy of solvation of the proton is the common reference for the equilibrium constant of both reactions 3 and 4. The reverse of reaction 4 is reaction 1, defining the redox potential of the XVX" couple (Equation 13.2). Expressing the equilibrium constant of reaction 3 in terms of the pK of XH, Hess law requires that... 

The equilibrium constant of this reaction is about 10 °. This reaction results from the superimposition of the following half-redox equilibria ... 

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

It is of interest to consider the calculation of the equilibrium constant of the general redox reaction, viz. ... 

This equation may be employed to calculate the equilibrium constant of any redox reaction, provided the two standard potentials Ef and Ef are known from the value of K thus obtained, the feasibility of the reaction in analysis may be ascertained. 

While these calculations provide information about the ultimate equilibrium conditions, redox reactions are often slow on human time scales, and sometimes even on geological time scales. Furthermore, the reactions in natural systems are complex and may be catalyzed or inhibited by the solids or trace constituents present. There is a dearth of information on the kinetics of redox reactions in such systems, but it is clear that many chemical species commonly found in environmental samples would not be present if equilibrium were attained. Furthermore, the conditions at equilibrium depend on the concentration of other species in the system, many of which are difficult or impossible to determine analytically. Morgan and Stone (1985) reviewed the kinetics of many environmentally important reactions and pointed out that determination of whether an equilibrium model is appropriate in a given situation depends on the relative time constants of the chemical reactions of interest and the physical processes governing the movement of material through the system. This point is discussed in some detail in Section 15.3.8. In the absence of detailed information with which to evaluate these time constants, chemical analysis for metals in each of their oxidation states, rather than equilibrium calculations, must be conducted to evaluate the current state of a system and the biological or geochemical importance of the metals it contains. 

The above important relationship now allows evaluation of the thermodynamic driving force of a redox reaction in terms of a measurable cell emf. Moreover, it is possible to utilize the relationship between the standard state potential and the standard state free energy to arrive at an expression for the equilibrium constant of a redox reaction in terms of the emf. Thus... 

Since k2/k 2 corresponds to the equilibrium constant of the redox reaction (redox potential), Eq. (9.12) suggests that the dissolution reaction may depend both on the tendency to bind the reductant to the Fe(III)(hydr)oxide surface and (even if the electron transfer is not overall rate determining), on the redox equilibrium (see Fig. 9.4b). 

In equilibrium of redox reactions, the Fermi level of the electrode equals the Fermi level of the redox particles (ckm) = panodic reaction current equals, but in the opposite direction, the cathodic reaction current (io = io = io). It follows from the principle of micro-reversibility that the forward and backward reaction currents equal each other not only as a whole current but also as a differential current at constant energy level e io(e) = tS(e) = io(e). Referring to Eqns. 8-7 and 8-8, we then obtain the exchange reaction ciurent as shown in Eqn. 8-18 ... 

To be aware that the redox reagents must be chosen with care for complete oxidation or reduction of the analyte, the equilibrium constant of the redox reaction, OX -E REDi RED] -E OX2, must exceed about 10, so the separation between E for the two couples must exceed about 0.35 V for a one-electron couple. 

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