Oxidation-reduction equilibrium constants

Several types of reactions are commonly used in analytical procedures, either in preparing samples for analysis or during the analysis itself. The most important of these are precipitation reactions, acid-base reactions, complexation reactions, and oxidation-reduction reactions. In this section we review these reactions and their equilibrium constant expressions. 

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 now possible to calculate the equilibrium constants of oxidation-reduction reactions, and thus to determine whether such reactions can find application in quantitative analysis. Consider first the simple 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... 

The reduction of iodine by ferrocyanide is simple second-order with Aij (25 °C) = (1.3 + 0.3)x 10 l.mole sec This is the reverse of the oxidation of iodide by ferricyanide (p. 409), but the ratio k(forward)/k(back) does not agree well with the equilibrium constant determined potentiometrically. Addition of 1 strongly retards the reduction and 13 was discounted as a reactant, the mechanism suggested being... 

In the temperature range of400 to 700 °C the values of the equilibrium constants of the first two reactions are larger than the corresponding values for tungsten oxide reduction. Thus, for an equal moisture content in the hydrogen used, the reduction of molybdenum... 

Comproportionation equilibrium constants for Equation 9.3 between dications and neutral molecules of carotenoids were determined from the SEEPR measurements. It was confirmed that the oxidation of the carotenoids produced n-radical cations (Equations 9.1 and 9.3), dications (Equation 9.2), cations (Equation 9.4), and neutral ir-radicals (Equations 9.5 and 9.6) upon reduction of the cations. It was found that carotenoids with strong electron acceptor substituents like canthaxanthin exhibit large values of Kcom, on the order of 103, while carotenoids with electron donor substituents like (J-carotene exhibit Kcom, on the order of 1. Thus, upon oxidation 96% radical cations are formed for canthaxanthin, while 99.7% dications are formed for P-carotene. This is the reason that strong EPR signals in solution are observed during the electrochemical oxidation of canthaxanthin. 

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. 

As the equilibrium constant for the reduction of iron oxide is on the order of 0.1 (see Table 2.1), traces of water are already sufficient to oxidize a supported iron catalyst. 

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). 

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. 

The equilibrium constant is used for the first of these reactions since no electrons are involved in the equation, that is, no change of oxidation state is occurring. But since there are electrons in the second reaction, the Nernst equation which handles reduction reactions must be used. 

Table III also shows the values of the equilibrium constants, KVAp for the conversion of iron nitrosyl complexes into the corresponding nitro derivatives. Keq decreases downwards, meaning that the conversions are obtained at a lower pH for the complexes at the top of the table. Thus, NP can be fully converted into the nitro complex only at pHs greater than 10. The NO+ N02 conversion, together with the release of N02 from the coordination sphere, are key features in some enzymatic reactions leading to oxidation of nitrogen hydrides to nitrite (14). The above conversion and release must occur under physiological conditions with the hydroxylaminoreductase enzyme (HAO), in which the substrate is seemingly oxidized through two electron paths involving HNO and NO+ as intermediates. Evidently, the mechanistic requirements are closely related to the structure of the heme sites in HAO (69). No direct evidence of bound nitrite intermediates has been reported, however, and this was also the case for the reductive nitrosylation processes associated with ferri-heme chemistry (Fig. 4) (25).

Arsenic. The inorganic species arsenate [As(V)] and arsenite [As(III)] were measured in the depth profile of the lake over the seasonal cycle (Figure 6) (32). The relevant reduction and oxidation processes will be briefly considered. The equilibrium constants for the various reactions are calculated on the basis of the thermodynamic data given in refs. 66 and 67. According to the thermodynamic sequence, the reduction of As(V) to As(III) occurs in a p range similar to that of the reduction of Fe(OH)3(s) to Fe(II) (Figure 2). 

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