Reduction equilibrium constants

When using logjoK against l/T graphs, in order to find the temperature at which reduction becomes energetically feasible it is necessary to determine the temperature at which the equilibrium constant for the reduction indicates a displacement of the reaction in favour of the metal. 

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. 

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

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... 

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. 

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 ... 

With a view to determining the equilibrium constant for the isomerisation, the rates of reduction of an equilibrium mixture of cis- and rra/i5-Co(NH3)4(OH2)N3 with Fe have been measured by Haim S . At Fe concentrations above 1.5 X 10 M the reaction with Fe is too rapid for equilibrium to be established between cis and trans isomers, and two rates are observed. For Fe concentrations below 1 X lO M, however, equilibrium between cis and trans forms is maintained and only one rate is observed. Detailed analysis of the rate data yields the individual rate coefficients for the reduction of the trans and cis isomers by Fe (24 l.mole sec and 0.355 l.mole .sec ) as well as the rate coefficient and equilibrium constant for the cw to trans isomerisation (1.42 x 10 sec and 0.22, respectively). All these results apply at perchlorate concentrations of 0.50 M and at 25 °C. Rate coefficients for the reduction of various azidoammine-cobalt(lll) complexes are collected in Table 12. Haim discusses the implications of these results on the basis that all these systems make use of azide bridges. The effect of substitution in Co(III) by a non-bridging ligand is remarkable in terms of reactivity towards Fe . The order of reactivity, trans-Co(NH3)4(OH2)N3 + > rra/is-Co(NH3)4(N3)2" > Co(NH3)sN3 +, is at va-... 

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... 

This expression for the equilibrium constant is found to contain the term V in the denominator. Since K must remain constant, an increase in V would cause % also to increase. Stated in an another form, the dissociation of AB is favoured by a reduction in the pressure. A pressure increase would bring down V, and to maintain the constant value of K, x must decrease. Thus, a pressure increase would tend to inhibit the dissociation of AB. As in the previous case, it will be of interest in this case also to examine the effects of some other factors on the equilibrium. It is left to the readers as an exercise to establish for this case the following results (i) the effect of the addition of either A or B is to suppress the degree of dissociation of AB (ii) the addition of an inert gas at constant volume does not alter the degree of dissociation of AB and (iii) the addition of an inert gas at constant pressure increases the degree of dissociation of AB. 

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... 

The data of Table 6.11 create a wealth of information on the free energies of inorganic reactions. Although reported as emfs, these data are readily transformed into free energies by the expression AG° = —n i it. Such free-energy data are of considerable utility in determining equilibrium properties and, in particular, the equilibrium constant for the overall cell reaction. The possibility of the reduction of ferric ion to ferrous ion by zinc as a reduct-ant is considered as an example. The reaction in which one would be interested might be executed in the cell... 

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. 

Reaction (1) is a reversible process, and it can be a source of superoxide if only its equilibrium is shifted to the right. The estimation of the equilibrium constant for this reaction in aqueous solution is impossible because the reduction potential of water-insoluble ubiquinone in water is of course undetectable. However, Reaction (1) occurs in the mitochondrial membrane and therefore, the data for the aqueous solutions are irrelevant for the measurement of its equilibrium. Some time back we studied Reaction (1) in aprotic media and found out that Ki is about 0.4 [23]. As the ubiquinone concentration in mitochondria is very high (it is about... 

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