Equilibrium constants standard redox potentials

The equilibrium constant, K, for this reaction at 25°C is 4.2x10- The standard redox potentials for the following two reactions ... 

While the redox titration method is potentiometric, the spectroelectrochemistry method is potentiostatic [99]. In this method, the protein solution is introduced into an optically transparent thin layer electrochemical cell. The potential of the transparent electrode is held constant until the ratio of the oxidized to reduced forms of the protein attains equilibrium, according to the Nemst equation. The oxidation-reduction state of the protein is determined by directly measuring the spectra through the tranparent electrode. In this method, as in the redox titration method, the spectral characterization of redox species is required. A series of potentials are sequentially potentiostated so that different oxidized/reduced ratios are obtained. The data is then adjusted to the Nemst equation in order to calculate the standard redox potential of the proteic species. Errors in redox potentials estimated with this method may be in the order of 3 mV. 

The parameter R is the gas constant, T is the temperature, F is the Faraday constant and n is the number of electrons consumed in the electron transfer step (Eq. 2). The standard potential, Eq of the redox couple O/R is defined as the reduction potential of O when the activity coefficients for both O and R are equal to one. Once Fq is known, the electrode potential can be used to measure concentrations in solutions or to calculate equilibrium constants, for redox equilibria (Eq. 3) involving two or more redox couples as shown in Eq. 4. 

Example 8.13. Chlorine Redox Equilibria Summarize in a pc-pH diagram the information contained in the equilibrium constants, I — 0, 25°C, of the following three reactions involving Cl2(aq), Cl, OCl, and HOCl. [For convenience, in addition to the equilibrium constant, the standard redox potential. 

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. 

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

From the equilibrium constant with glutathione and the standard redox potential of the GSSG/GSH pair, the redox potential of DsbA can be calculated. The redox potential of DsbA is —120 mV, making it the most oxidizing disulfide bond known. For comparison, the redox potential of thioredoxin is —270 mV, and therefore much more reducing. 

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... 

After that the equilibrium constants are calculated from the values of conventional standard redox potentials. 

A converse exists to the calculation of equilibrium constants from the halfreduction potentials It is the possibility to obtain the unknown redox potentials of some couples. In order to achieve it, a redox equilibrium between two couples is investigated. The equilibrium constant is determined, if the standard redox potential of one of both couples is already known. The value of the other (unknown) is immediately deduced. This strategy is, of course, of great importance in physical and analytical chemistries. It is in this way that the standard potentials of slow electrochemical systems (see electrochemistry), in particular, those of organic redox couples, have been determined. 

As we ve already noted, it is rarely realistic to use standard redox potentials to calculate equilibrium constants since the standard conditions often do not prevail. It is more judicious to use apparent standard potentials and formal potentials when they are known. In this case, the calculated equilibrium constants are no longer the thermodynamic ones, but the apparent ones. They are given by the relation... 

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. 

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. 

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... 

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 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. 

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 photoelectrolysis of H2O can be performed in cells being very similar to those applied for the production of electricity. They differ only insofar as no additional redox couple is used in a photoelectrolysis cell. The energy scheme of corresponding systems, semiconductor/liquid/Pt, is illustrated in Fig. 9, the upper scheme for an n-type, the lower for a p-type electrode. In the case of an n-type electrode the hole created by light excitation must react with H2O resulting in 02-formation whereas at the counter electrode H2 is produced. The electrolyte can be described by two redox potentials, E°(H20/H2) and E (H20/02) which differ by 1.23 eV. At equilibrium (left side of Fig. 9) the electrochemical potential (Fermi level) is constant in the whole system and it occurs in the electrolyte somewhere between the two standard energies E°(H20/H2) and E°(H20/02). The exact position depends on the relative concentrations of H2 and O2. Illuminating the n-type electrode the electrons are driven toward the bulk of the semiconductor and reach the counter electrode via the external circuit at which they are consumed for Hj-evolution whereas the holes are dir tly... 

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... 

In addition, electrode reactions are frequently characterized by an irreversible, i.e., slow, electron transfer. Therefore, overpotentials have to be applied in preparative-scale electrolyses to a smaller or larger extent. This means not only a higher energy consumption but also a loss in selectivity as other functions within the molecule can already be attacked. In the case of indirect electrolyses, no overpotentials are encountered as long as reversible redox systems are used as mediators. It is very exciting that not only overpotentials can be eliminated but frequently redox catalysts can be applied with potentials which are 600 mV or in some cases even up to 1 Volt lower than the electrode potentials of the substrates. These so-called redox reactions opposite to the standard potential gradient can take place in two different ways. In the first place, a thermodynamically unfavorable electron-transfer equilibrium (Eq. (3)) may be followed by a fast and irreversible step (Eq. (4)) which will shift the electron-transfer equilibrium to the product side. In this case the reaction rate (Eq. (5)) is not only controlled by the equilibrium constant K, i.e., by the standard potential difference be-... 

The approach in the previous section was facilitated by the assumption that none of the intermediates has a substantial interfacial concentration compared with the stable reactants O and R. This is justified if the reactions proceed in such a potential range that equilibrium constants Ka, KaKi, K0K)Ky, etc. are much larger than unity and equilibrium constants like KR, KRK2, KRK2KY, etc. are much smaller than unity. As K0KX — exp [(F/RT) ( - °)] and KYK2KR = exp [(F/RT) (E — E%)], this implies that E2 >E°X, i.e. the standard potential of the redox couple O/Y should be much smaller than that of the redox couple Y/R. 

If the rate of electron transfer is low (or the scan rate is too high), electron transfer will not be able to adjust the surface concentrations of -Fc and -Fc+ to values that are at equilibrium with the applied potential (quasireversible or totally irreversible case, see Chap. 3). In this case, the anodic peak and the cathodic peaks will not be at the same potential that is, AEpk will be greater than zero volts. Kinetic information about the surface-bound redox couple can be obtained from such quasireversible or irreversible voltammograms. For example, methods for obtaining the standard heterogeneous rate constant (see Chap. 2) for the surface-confined redox couple have been developed [41,42]. 

FIGURE 18.7 The relationship between the equilibrium constant K for a redox reaction with n = 2 and the standard cell potential E°. Note that K is plotted on a logarithmic scale. 

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. 

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 extent of deposition of a metal M introduced as M"+ on a Cu catalyst (or on a metal of lower standard potential) depends on the redox reaction equilibrium constant ... 

Continued cycling to steady state would populate many of the species, leading to the result shown in Fig. 13.19. Here there are four redox couples accessed (R /0 , RpOb, Rf /Of, and Rf /Of, whose distinct standard potentials are related by the equilibrium constants around the cube faces [43]. This will result in a set of overlapping waves on the i-E curves, and corresponding mass changes on the AM-E curves, which will be practically... 

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