Equilibrium constant redox

Environment and Life, RSC Publishing, p. i60 As this cytoplasmic (in cell) organic chemistry was reductive of necessity, because the ingredients were made of the oxides of carbon, it was inevitable that oxidizing compounds, which became oxygen, would be released. There followed in the environment an unavoidable and predictable sequence of the oxidation of minerals and non-metal elements in solution, limited by diffusion but generally following sequentially equilibrium constants, redox potentials. ... 

Unlike the reactions that we have already considered, the equilibrium position of a redox reaction is rarely expressed by an equilibrium constant. Since redox reactions involve the transfer of electrons from a reducing agent to an oxidizing agent, it is convenient to consider the thermodynamics of the reaction in terms of the electron. 

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

Balance the following redox reactions, and calculate the standard-state potential and the equilibrium constant for each. Assume that the [H3O+] is 1 M for acidic solutions, and that the [OH ] is 1 M for basic solutions. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

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... 

Redox reactions, like all reactions, eventually reach a state of equilibrium. It is possible to calculate the equilibrium constant for a redox reaction from the standard voltage. To do that, we start with the relation obtained in Chapter 17 ... 

It is of interest to consider the calculation of the equilibrium constant of the general redox reaction, viz. ... 

This equation may be employed to calculate the equilibrium constant of any redox reaction, provided the two standard potentials Ef and Ef are known from the value of K thus obtained, the feasibility of the reaction in analysis may be ascertained. 

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. 

The fact that we can calculate E° from standard potentials allows us to calculate equilibrium constants for any reaction that can be expressed as two half-reactions. The reaction does not need to be spontaneous nor does it have to be a redox reaction. Toolbox 12.3 summarizes the steps and Example 12.8 shows the steps in action. 

While these calculations provide information about the ultimate equilibrium conditions, redox reactions are often slow on human time scales, and sometimes even on geological time scales. Furthermore, the reactions in natural systems are complex and may be catalyzed or inhibited by the solids or trace constituents present. There is a dearth of information on the kinetics of redox reactions in such systems, but it is clear that many chemical species commonly found in environmental samples would not be present if equilibrium were attained. Furthermore, the conditions at equilibrium depend on the concentration of other species in the system, many of which are difficult or impossible to determine analytically. Morgan and Stone (1985) reviewed the kinetics of many environmentally important reactions and pointed out that determination of whether an equilibrium model is appropriate in a given situation depends on the relative time constants of the chemical reactions of interest and the physical processes governing the movement of material through the system. This point is discussed in some detail in Section 15.3.8. In the absence of detailed information with which to evaluate these time constants, chemical analysis for metals in each of their oxidation states, rather than equilibrium calculations, must be conducted to evaluate the current state of a system and the biological or geochemical importance of the metals it contains. 

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 ... 

The magnitude of this equilibrium constant indicates that the redox reaction goes essentially to completion. This reflects the fact that bromine is a potent oxidizing agent and copper is relatively easy to oxidize. 

C19-0023. Use values in Table 19-1 to calculate the equilibrium constant for the redox reaction... 

According to Eq. (3.21) and taking into account that the electrode potential differs by a constant term from the metal-solution Galvani potential, we thus have an expression for the equilibrium potential of this electrode and, at the same time, for the equilibrium potential, redox of this redox system ... 

The equilibrium constant K for (por)Fe(OH2) (por)Fe, which determines the molar fraction of the 5-coordinate redox-active Fe catalyst. This constant was estimated from analysis of the catalytic turnover frequencies in the presence of varying concentrations of an inhibitor, CN, which competes with both O2 and H2O for the 5-coordinate Fe porphyrin. 

The above important relationship now allows evaluation of the thermodynamic driving force of a redox reaction in terms of a measurable cell emf. Moreover, it is possible to utilize the relationship between the standard state potential and the standard state free energy to arrive at an expression for the equilibrium constant of a redox reaction in terms of the emf. Thus... 

In summary, certain equilibrium constants of complex formation, of solubility products and of redox potentials form a set of fixed values that must be looked at in the context of the compartment which contains the components and which controlled evolution in fair part, against a background of rising amounts of environmental oxidised elements. The other factors were the rates of synthesis as dictated by supply of energy and of reactants in the environment. 

Correlating Redox Potential with Equilibrium Constant for Atom Transfer. 242... 

The redox potential of CuIIL/CuIL couple is related to the equilibrium constant for electron transfer (KET) according to the equation ... 

The reaction has an associated equilibrium constant K, which is understood to carry Boltzman terms accounting for electrostatic effects of any surface complexa-tion reactions embedded within the redox reaction. The reaction s activity product at any point in the simulation is given by,... 

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). 

In equilibrium of redox reactions, the Fermi level of the electrode equals the Fermi level of the redox particles (ckm) = panodic reaction current equals, but in the opposite direction, the cathodic reaction current (io = io = io). It follows from the principle of micro-reversibility that the forward and backward reaction currents equal each other not only as a whole current but also as a differential current at constant energy level e io(e) = tS(e) = io(e). Referring to Eqns. 8-7 and 8-8, we then obtain the exchange reaction ciurent as shown in Eqn. 8-18 ... 

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. 

Secondly, if the volume of ceric ion is to be an acceptable measure of the quantity of ferrous material in solution, then the reaction needs to go to completion, that is, the equilibrium constant K of the redox reaction (e.g. equation (4.1)) must be high. 

The equilibrium constant of the redox reaction represented by equation (4.1) is given by the following ... 

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