Equilibrium constant for redox reaction

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. 

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... 

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... 

The fact that we can calculate E° from standard potentials allows us to calculate equilibrium constants for any reaction that can be expressed as two half-reactions. The reaction does not need to be spontaneous nor does it have to be a redox reaction. Toolbox 12.3 summarizes the steps and Example 12.8 shows the steps in action. 

Problems in this chapter include some brainbusters designed to bring together your knowledge of electrochemistry, chemical equilibrium, solubility, complex formation, and acid-base chemistry. They require you to find the equilibrium constant for a reaction that occurs in only one half-cell. The reaction of interest is not the net cell reaction and is not a redox reaction. Here is a good approach ... 

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). 

Rate constants for one-electron redox reactions depend upon the relative reduction potentials of the reactants. We have been able to derive the one-electron reduction potential of S03 by measuring the equilibrium constant for its reaction with chlorpromazine (C1PZ)... 

Under certain conditions, the ratio of lactate to pyruvate is an indicator of redox status. By rearranging the equation for the equilibrium constant for the reaction catalyzed by lactate dehydrogenase (EC 1.1.1.27), it can be seen that the ratio of lactate to pyruvate is proportional to the ratio of NADH to NADL... 

In either case, one may use cystine as a model for hair, since the literature [5-7] shows that the redox potential of cystine-type disulfides is virtually independent of the charge group about the disulfide bond. However, reduction potentials of mercaptans do vary with pH [6], Therefore, equilibrium constants for these reactions will also vary with pH. Patterson et al. 

Assuming equilibrium, this suggests that the difference in redox potential between thioglycolic acid and cysteine in keratin fibers increases with increasing pH above 6, and the equilibrium constant for this reaction increases similarly. 

When one wants to calculate the equilibrium constant of reaction (1.2.3) from the standard potentials of the system hexacyanoferrate(II/III) and 2H" /H2, it is essential that one writes this equation with the oxidized form of the system and hydrogen on the left side and the reduced form and protons on the right side. Only then does the sign convention hold true and Eq. (1.2.13) yields the equilibrium constant for the reaction when the tabulated standard potentials are used. Note also that the standard potential of the hydrogen electrode is 0 V for the reaction written as 2H+ - - 2e H2, or written as H+ - - e 1 2- Table 1.2.1 gives a compilation of standard potentials of electrode reactions. (Standard potentials are available from many different sources [2].) Although only single redox couples are listed, the standard potentials of each system always refer to the reaction ... 

A similar relationship is true for all equilibrium redox reactions. With knowledge of (Sn VSn ) and °(Ce VCe ), it is possible to calculate the equilibrium constant for the reaction. 

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

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... 

Balance the following redox reactions, and calculate the standard-state potential and the equilibrium constant for each. Assume that the [H3O+] is 1 M for acidic solutions, and that the [OH ] is 1 M for basic solutions. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

Redox reactions, like all reactions, eventually reach a state of equilibrium. It is possible to calculate the equilibrium constant for a redox reaction from the standard voltage. To do that, we start with the relation obtained in Chapter 17 ... 

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... 

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