Equilibrium constant of oxidation-reduction reactions

Here the subscripts 1 and 2 refer to the individual redox systems. The equilibrium constant of such a reaction (Section 1.13), expressed with concentrations is 

This equilibrium constant is related to the standard free energy change, AG , of this reaction  

MnOj + 8H+ + 5Fe2 + Mn2++5Fe3++ 4H20 For this reaction 

Using this example we can show the correlation between standard oxidation-reduction potentials without applying the thermodynamical concepts mentioned above. The oxidation-reduction potential of the system 

If the reaction reaches equilibrium, the oxidation-reduction potentials of both systems are equal  

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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 ... 

The oxidation reactions already described have been discussed in terms of equilibria. From the equilibrium values it can be seen that some compounds, such as acetaldehyde, are oxidized by DPN or TPN quantitatively, whereas, at the same pH values, malate, lactate and ethanol react to a very slight extent. The equilibrium constants of oxidation-reduction reactions have been used to evaluate a property of members... 

The values E°, pe° and are different forms to express equilibrium constants of individual oxidation-reduction reactions. The first one is measured in volts of electric voltage, and the rest of them are dimensionless values. As a rule, as equilibrium constants of oxidation-reduction... 

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. 

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. 

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. 

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... 

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... 

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. 

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). 

One reaction that occurs in producing steel from iron ore is the reduction of iron(II) oxide by carbon monoxide to give iron metal and carbon dioxide. The equilibrium constant Kp for the reaction at 1000 K is 0.259. 

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) ... 

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. 

The equilibrium constant of reaction (1), K = [Cu ][Cu ]/[Cu ], is of the order of 10 thus, only vanishingly small concentrations of aquo-copper(I) species can exist at equilibrium. However, in the absence of catalysts for the disproportionation—such as glass surfaces, mercury, red copper(I) oxide (7), or alkali (311)—equilibrium is only slowly attained. Metastable solutions of aquocopper(I) complexes may be generated by reducing copper(II) salts with europium(II) (113), chromium(II), vanadium(II) (113, 274), or tin(II) chloride in acid solution (264). The employment of chromium(II) as reducing agent is best (113), since in most other cases further reduction to copper metal is competitive with the initial reduction (274). 

The work described in the foregoing sections is of a preliminary nature. Nevertheless, it offers hope that experimental scales of free hydrogen ion concentration (pcn or pmn) in seawater may be feasible. One need not know pmn or pan to derive meaningful equilibrium data, such as acid-base ratios and solubilities, provided that suitable apparent equilibrium constants are chosen (7). In these cases, the unit selected for the acidity scale disappears by cancellation. Nevertheless, the acidity of seawater is a parameter of broader impact. It plays a role, for example, in the kinetics of organic oxidation-reduction reactions and in a variety of quasi-equilibrium processes of a biological nature. The concentration of free hydrogen ions is clearly understood, and its role in these complex interactions is more clearly defined than that of a quantity whose unit purports to involve the concept of a single-ion activity. 

As you know, oxidation-reduction reactions can involve molecules, ions, free atoms, or combinations of all three. To make it easier to discuss redox reactions without constantly specilying the kind of particle involved, chemists use the term species. In chemistry, a species is any kind of chemical unit involved in a process. For example, a solution of sugar in water contains two major species. In the equilibrium equation NH3 + H2O NH/ + OH , there are four species the two molecules NH3 and H2O and the two ions NH/ and OH. ... 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

For the pH values of leachate in these experiments (6.5 to 7.5), the As(V) species in reactions 6 and 7 predominate. Arsenate concentrations were below detection limits throughout the experiments however, after reactive organic carbon concentrations in the core decreased to the level where reduction of O2 was incomplete, geochemical modeling predicted oxidation of As(lll) to As(V). Because As(V) was not detected in core effluent, it was not possible to derive equilibrium constants for these adsorption reactions on this core material, and the equilibrium constants listed in Dzombak and Morel (1990) were used in the model. For reaction 6, the Log Kas(v)i was 23.51 and for reaction 7, the Log Kas(v)2 was 10.58. Arsenite adsorption was modeled by ... 

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... 

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