Equilibrium constant Oxidation-reduction potentials

Equilibrium considerations other than those of binding are those of oxidation/reduction potentials to which we drew attention in Section 1.14 considering the elements in the sea. Inside cells certain oxidation/reductions also equilibrate rapidly, especially those of transition metal ions with thiols and -S-S- bonds, while most non-metal oxidation/reduction changes between C/H/N/O compounds are slow and kinetically controlled (see Chapter 2). In the case of fast redox reactions oxidation/reduction potentials are fixed constants. 

Quantitative structure-chemical reactivity relationships (QSRR). Chemical reactivities involve the formation and/or cleavage of chemical bonds. Examples of chemical reactivity data are equilibrium constants, rate constants, polarographic half wave potentials and oxidation-reduction potentials. 

From such examples it becomes apparent that the greater the difference between the standard oxidation-reduction potentials, the higher the value of the equilibrium constant, that is the reactions become the more complete. In practice, a difference of 0-3 V for n = 1 secures a value for K greater than 10s, which means that in practical terms the reaction will take place quantitatively. If, on the other hand, the difference of standard potentials, as defined by equations (i) and (v) is negative, the reaction is not feasible in fact it will proceed in the opposite direction. 

Another method of evaluating standard oxidation-reduction potentials is to make use of chemical determinations of equilibrium constants. ... 

Standard Oxidation-reduction Potentials and Equilibrium Constants 655 Constants of Radioactive Disintegration 665-8... 

Reactions that take place consecutive to the electrode process can be studied polarographioally only in those cases in which the electrode process is reversible. In these cases the wave-heights and the wave-shape remain unaffected by the chemical processes. However, the half-wave potentials are shifted relative to the equilibrium oxidation-reduction potential, determined e.g. potentiometrically. Hence, whereas in all above examples, limiting currents were measured to determine the rate constant, it is the shifts of half-wave potentials which are measured here. First- and second-order chemical reactions will be discussed in the following. 

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

Standard Oxidation-reduction Potentials and Equilibrium Constants (The values apply to temperature 25°C, with standard concentration for aqueous solutions 1 M and standard pressure of gases 1 atm.)... 

To determine an oxidation-reduction potential for one half-reaction (or couple), the potential for the other couple must be known as well as the equilibrium constant of the over-all reaction. Oxidation-reduction potentials are thus seen to be arbitrary, relative values. The evaluation of potentials is made with reference to an accepted standard the primary reference half-reaction is ... 

If the oxidation-reduction potentials of two systems are known, the equilibrium constant for a reaction between them may be calculated. Such calculations are valid even in cases in which the systems do not react directly with each other and in cases in which direct measurements may be obscured by side reactions. The oxidation of ethanol (1 M) by... 

AFo is the standard free energy of the reaction, and must not be confused with the constant F, usually written in bold type to minimize confusion. In the example of the alcohol dehydrogenase reaction at pH 7.0, AFo may be evaluated from oxidation-reduction potentials without first calculating the equilibrium constant. 

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. 

From the equilibrium constants of (1.69), (1.70) and (1.71), we obtain the stability fields of iron minerals on logfo -pH diagram at constant temperature, pressure and S (Fig. 1.29) and on Eh (oxidation-reduction potential)-pH diagram. 

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... 

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). 

Perhaps the most fundamental fimctional property of a heme prosthetic group at the active site of a heme protein is the relative stability of the reduced and oxidized states of the heme iron. A number of structural characteristics of the heme binding environment provided by the apo-protein have been identified as contributing to the regulation of this equilibrium and have been reviewed elsewhere 82-84). Although a comprehensive discussion of these factors is not possible in the space available here, they can be summarized briefly. The two most significant influences of the reduction potential of the heme iron appear to be the dielectric constant of the heme environment 81, 83) and the chemical... 

Because of the bulk of comparable material available, it has been possible to use half-wave potentials for some types of linear free energy relationships that have not been used in connection with rate and equilibrium constants. For example, it has been shown (7, 777) that the effects of substituents on quinone rings on their reactivity towards oxidation-reduction reactions, can be approximately expressed by Hammett substituent constants a. The susceptibility of the reactivity of a cyclic system to substitution in various positions can be expressed quantitatively (7). The numbers on formulae XIII—XV give the reaction constants Qn, r for the given position (values in brackets only very approximate) ... 

Standard half-cell potentials can be used to compute standard cell potentials, standard Gibbs free energy changes, and equilibrium constants for oxidation-reduction reactions. 

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. 

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