Equilibrium Constants and Reduction Potentials

Appendix Five Equilibrium Constants and Reduction Potentials... 

These conventions are arbitrary, but you must use them if you wish to use tabulated values of equilibrium constants, standard reduction potentials, and free energies. 

From the equilibrium constant, a reduction potential of 0.84 V at this pH was derived. From this, and the pK. of HS03 of 7.2 [61], = 0.63 V was derived for the S03 "/ S03" couple. This value was called into question in a subsequent pulse radiolysis study, this time involving equilibrium with C102"/C102 [62]. In this study, =0.76 V was derived, a value which appeared to reconcile some differences observed in derived reduction potentials for several phenols. In both studies there are potential problems, since the rate constants for the reactions of the radicals with HS03"/S03 " are not exceedingly fast k 3-5 x 10 L mol" s" ). This means that the equilibrium is not established rapidly, allowing the... 

For the limit of very fast kinetics, the RPV response is analogous to that of the E mechanism but shifted toward more positive potentials (in the case of a reduction process), the shift magnitude being dependent on the value of the equilibrium constant. This can be observed clearly in Fig. 4.27 by comparing the curve for (k + 2)f2 > 105 and for the E mechanism (empty points). From Eq. (4.245) it can be inferred that the mid-potential value CinidR[.y only depends on the equilibrium constant, and is independent of geometric and kinetic parameters and coincident with. E1 [80]. 

Oxidation-Reduction Systems in Analytical Chemistry.—An examination of the calculation just made shows that the very small equilibrium constant, and hence the virtually complete interaction of one system with the other, is due to the large difference in the standard potentials of the two systems. The system with the more negative standard potential as recorded in Table LIII, e.g., Pt Fe++, in the case con-... 

When the pH is specified, each biochemical half reaction makes an independent contribution to the apparent equilibrium constant K for the reaction written in terms of reactants rather than species. The studies of electochemical cells have played an important role in the development of biochemical thermodynamics, as indicated by the outstanding studies by W. Mansfield Clarke (1). The main source of tables of ° values for biochemical half reactions has been those of Segel (2). Although standard apparent reduction potentials ° can be measured for some half reactions of biochemical interest, their direct determination is usually not feasible because of the lack of reversibility of the electrode reactions. However, standard apparent reduction potentials can be calculated from for oxidoreductase reactions. Goldberg and coworkers (3) have compiled and evaluated the experimental determinations of apparent equilibrium constants and standard transformed enthalpies of oxidoreductase reactions, and their tables have made it possible to calculate ° values for about 60 half reactions as functions of pH and ionic strength at 298.15 K (4-8). 

Table 8.3. Equilibrium Constants and Standard Electrode Potentials for Some Reduction Half-Reactions...

Numerous applications of standard electrode potentials have been made in various aspects of electrochemistry and analytical chemistry, as well as in thermodynamics. Some of these applications will be considered here, and others will be mentioned later. Just as standard potentials which cannot be determined directly can be calculated from equilibrium constant and free energy data, so the procedure can be reversed and electrode potentials used for the evaluation, for example, of equilibrium constants which do not permit of direct experimental study. Some of the results are of analjrtical interest, as may be shown by the following illustration. Stannous salts have been employed for the reduction of ferric ions to ferrous ions in acid solution, and it is of interest to know how far this process goes toward completion. Although the solutions undoubtedly contain complex ions, particularly those involving tin, the reaction may be represented, approximately, by... 

Hess measured the apparent equilibrium constant for reduction of cytochrome by ferroeyanide as a function of pH 185), and found that the actual reduction step did not involve a proton and was entirely independent of pH. The free energy of reduction, and hence the reduction potential, change with pH only because the ratio of amounts of state III and IV changes with pH. The observed decrease of cytochrome reduction potential of 60 mV per pH unit above pH 8 is exactly what would be calculated from the simple Nernst equation. 

The one-electron reduction potential of interest is then calculated from the equilibrium constant and the one-electron reduction potential of the redox reference couple using Nemst s equation (AE° = 0.0591 log K). While electrochemical techniques often yield irreversible oxidation potentials, pulse radiolysis usually yields thermodynamically correct one-electron reduction potenticils, provided the reactions are fast... 

Analyze We are going to have to combine what we know about equilibrium constants and electrochemistry to obtain reduction potentials. 

The first work on measuring the rate constant of the protolytic reaction by the polarographic method was published in 1947 (R. Brdiehka). Later several other electrochemical methods were developed for measuring rates of fest ion reactions. For the electrochemical determination of the reaction rate constant, it is necessary for the chemical equilibrium to exist in the system and for at least one of the reactants to participate in the electrode process. The reaction rate of electron transfer on the electrode increases exponentially with an increase in its potential E when E > Eg, where Egq is the equilibrium oxidation or reduction potential of the reactant on the electrode. The current strength is... 

Potentiometry measures the difference in potential between two electrodes immersed in a solution. One of the electrodes probes the solution, while the other serves as a reference. The reference electrode has a constant and reproducible potential which is independent of its environmenL The potential of the probe electrode is the potential at the interface between the solid and liquid phases, where the oxidation and reduction reactions occur. For example, at the interface between a conducting wire and a redox system, there is an exchange of electrons between the wire and the compounds being oxidized and reduced. Equilibrium is achieved when the rates of oxidation and reduction are equal, and the composition of the solution surrounding the electrode is constant. The equilibrium potential is then given by the Nemst Law ... 

Preparation and chemistry of chromium compounds can be found ia several standard reference books and advanced texts (7,11,12,14). Standard reduction potentials for select chromium species are given ia Table 2 whereas Table 3 is a summary of hydrolysis, complex formation, or other equilibrium constants for oxidation states II, III, and VI. 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

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. 

In addition to defined standard conditions and a reference potential, tabulated half-reactions have a defined reference direction. As the double arrow in the previous equation indicates, E ° values for half-reactions refer to electrode equilibria. Just as the value of an equilibrium constant depends on the direction in which the equilibrium reaction is written, the values of S ° depend on whether electrons are reactants or products. For half-reactions, the conventional reference direction is reduction, with electrons always appearing as reactants. Thus, each tabulated E ° value for a half-reaction is a standard reduction potential. 

Equations and provide a method for calculating equilibrium constants from tables of standard reduction potentials. Example illustrates the technique. 

---