Redox equilibria Nernst equation

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

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. 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

Many natural waters, including most waters at low temperature, do not achieve redox equilibrium (e.g., Lindberg and Runnells, 1984 see Chapter 7). In this case, no single value of pe or Eh can be used to represent the redox state. Instead, there is a distinct value for each redox couple in the system. Applying the Nernst equation to Reaction 3.46 gives a pe or Eh representing the hydrolysis of water. Under disequilibrium conditions, this value differs from those calculated from reactions such as,... 

Comparison with Eq. (2.10) shows that the measured potential is simply the difference between the equilibrium potentials of the two redox couples, each measured with respect to its own reference electrode. Admittedly, this is an obvious result, but it is useful to derive it from first principles. The corresponding Nernst equation is ... 

ET much faster than transport (transport control). Electrochemical equilibrium is attained at the electrode surface at all times and defined by the electrode potential E. The concentrations Cox and Cred of oxidized and reduced forms of the redox couple, respectively, follow the Nernst equation (1) (reversible ET)... 

The redox equilibrium Hg2+ + 2e Hg(/) is established rapidly at the surface of the Hg electrode, so the Nernst equation for the cell can be written in the form... 

Figure 3.37 illustrates the Nernst diffusion layer in terms of concentration-distance profiles for a solution containing species O. As pointed out previously, the concentration of redox species in equilibrium at the electrode-solution interface is determined by the Nernst equation. Figure 3.37A illustrates the concentration-distance profile for O under the condition that its surface concentration has not been perturbed. Either the cell is at open circuit, or a potential has been applied that is sufficiently positive of Eq R not to alter measurably the surface concentrations of the 0,R couple. 

Ksp, limits the concentrations in solution so that the actual redox potential is not the value calculated, which represents the values when [Ag+] = 1 M and tn = 1 M. If we use the concentrations established by the solubility equilibrium and the Nernst equation, we can calculate the actual redox potential ... 

Equation (5.9) is the general Nernst equation giving the concentration dependence of the equilibrium cell voltage. It will be used in the next section of this chapter to derive the equilibrium electrode potential for metal/metal-ion and redox electrodes. 

In the previous section the mercury electrode has been described. If no redox pairs (e.g. Fe2+ and Fe3+) are in solution and if we exclude gas reactions, the mercury electrode is completely polarizable. Polarizable means If a potential is applied, a current flows only until the electric double layer has formed. No electrons are transferred from mercury to molecules in the solution and vice versa. The other extreme is a completely reversible electrode, for which the Agl electrode is an example. Each attempt to change the potential of an Agl electrode leads to a current because the equilibrium potential is fixed by the concentrations of Ag+ or I according to the Nernst equation. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

The dynamics of the system are described by k°, with its units being s 1 for an adsorbed reactant. A redox couple with a large k° will establish the equilibrium concentrations given by the Nernst equation on a short timescale. Kinetically facile systems of this type require high-speed electrochemical techniques to successfully probe the electrode dynamics. The largest k° values that have been reliably measured are of the order of 106 s-1 and are associated with mechanistically simple reactions, i.e. there are no coupled chemical kinetics or significant structural differences between the oxidized and reduced forms. 

Measurements can be done using the technique of redox potentiometry. In experiments of this type, mitochondria are incubated anaerobically in the presence of a reference electrode [for example, a hydrogen electrode (Chap. 10)] and a platinum electrode and with secondary redox mediators. These mediators form redox pairs with Ea values intermediate between the reference electrode and the electron-transport-chain component of interest they permit rapid equilibration of electrons between the electrode and the electron-transport-chain component. The experimental system is allowed to reach equilibrium at a particular E value. This value can then be changed by addition of a reducing agent (such as reduced ascorbate or NADH), and the relationship between E and the levels of oxidized and reduced electron-transport-chain components is measured. The 0 values can then be calculated using the Nernst equation (Chap. 10) ... 

Equilibrium electrode potential — is the value of -> electrode potential determined exclusively by a single redox system ox/red in the absence of current and under complete equilibration. The rates of ox to red reduction and of red to ox oxidation processes are equal under these circumstances (see exchange current density). The value of equilibrium e.p. is determined by the - Nernst equation. Equilibrium e.p. presents a - redox potential in its fundamental sense. See also - reversibility. 

Open-circuit potential (OCP) — This is the - potential of the - working electrode relative to the - reference electrode when no potential or - current is being applied to the - cell [i]. In case of a reversible electrode system (- reversibility) the OCP is also referred to as the - equilibrium potential. Otherwise it is called the - rest potential, or the - corrosion potential, depending on the studied system. The OCP is measured using high-input - impedance voltmeters, or potentiometers, as in - potentiometry. OCP s of - electrodes of the first, the second, and the third kind, of - redox electrodes and of - ion-selective membrane electrodes are defined by the - Nernst equation. The - corrosion po-... 

Because the potential of an electrochemical cell depends on the concentrations of the participating ions, the observed potential can be used as a sensitive method for measuring ion concentrations in solution. We have already mentioned the ion-selective electrodes that work by this principle. Another application of the relationship between cell potential and concentration is the determination of equilibrium constants for reactions that are not redox reactions. For example, consider a modified version of the silver concentration cell shown in Fig. 11.11. If the 0.10 M AgN03 solution in the left-hand compartment is replaced by 1.0 M NaCl and an excess of solid AgCl is added to the cell, the observed cell potential can be used to determine the concentration of Ag+ in equilibrium with the AgCl(s). In other words, at 25°C we can write the Nernst equation as... 

Fig. 3.1. A, The respiratory chain. Q and c stand for ubiquinone and cytochrome c, respectively. Auxiliary enzymes that reduce ubiquinone include succinate dehydrogenase (Complex II), a-glycerophosphate dehydrogenase and the electron-transferring flavoprotein (ETF) of fatty acid oxidation. Auxiliary enzymes that reduce cytochrome c include sulphite oxidase. B, Thermodynamic view of the respiratory chain in the resting state (State 4). Approximate values are calculated according to the Nernst equation using oxidoreduction states from work by Muraoka and Slater, (NAD, Q, cytochromes c c, and a oxidation of succinate [6]), and Wilson and Erecinska (b-562 and b-566 [7]). The NAD, Q, cytochrome b-562 and oxygen/water couples are assumed to equilibrate protonically with the M phase at pH 8 [7,8]. E j (A ,/ApH) for NAD, Q, 6-562, and oxygen/water are taken as —320 mV ( — 30 mV/pH), 66 mV (- 60 mV/pH), 40 mV (- 60 mV/pH), and 800 mV (- 60 mV/pH) [7-10]. FMN and the FeS centres of Complex I (except N-2) are assumed to be in redox equilibrium with the NAD/NADH couple, FeS(N-2) with ubiquinone [11], and cytochrome c, and the Rieske FeS centre with cytochrome c [10]. The position of cytochrome a in the figure stems from its redox state [6] and its apparent effective E -, 285 mV in...

In dealing with redox equilibria, we are also confronted with the problem of evaluating activity corrections or maintaining the activities under consideration as constants. The Nernst equation rigorously applies only if the activities and actual species taking part in the reaction are inserted in the equation. The activity scales discussed before, the infinite dilution scale and the ionic medium scale, may be used. The standard potential or standard pe on the infinite dilution scale is related to the equilibrium constant for / = 0 of the reduction reaction... 

Potentiometric transducers measure the potential under conditions of constant current. This device can be used to determine the analytical quantity of interest, generally the concentration of a certain analyte. The potential that develops in the electrochemical cell is the result of the free-energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition is satisfied. For electrochemical cells containing an anode and a cathode, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell. If the reaction is conducted under standard-state conditions, then this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must use the Nernst equation to determine the cell potential. Physical phenomena that do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion-concentration gradients across a semi-permeable membrane this can also be a potentiometric phenomenon and is the basis of measurements that use ion-selective electrodes (ISEs). 

In a solution, the equilibrium concentrations of the reduced and oxidized forms of a redox couple are linked to the potential (E) via the Nernst equation... 

We will use standard electrode potentials throughout the rest of this text to calculate cell potentials and equilibrium constants for redox reactions as well as to calculate data for redox titration curves. You should be aware that such calculations sometimes lead to results that are significantly different from those you would obtain in the laboratory. There are two main sources of these differences (1) the necessity of using concentrations in place of activities in the Nernst equation and (2) failure to take into account other equilibria such as dissociation, association, complex formation, and solvolysis. Measurement of electrode potentials can allow us to investigate these equilibria and determine their equilibrium constants, however. 

The Nernst equation is applicable only if the redox reaction is reversible. Not all reactions are completely reversible in natural systems activities of reacting components may be too low or equilibrium may be reached very slowly. In a sediment, the biotic microenvironment may create a redox potential that is different from the surrounding macroenvironment. For this reason, measurements of Eh in natural systems must be cautiously evaluated and not used strictly for calculations of chemical equilibria. Calculations of redox equilibria are in some cases valuable, in the sense that they will give information about the direction of chemical reactions. 

Consider, for example, the redox equilibrium Fe3++ e = I e2. When we define the total analytical concentration of iron in solution (regardless of its oxidation state) as C, it follows from the Nernst equation that the fractional concentrations of Fe3+and Fe2+are... 

Potential on Concentration Concentration Cells The Nernst Equation Ion-Selective Electrodes Calculation of Equilibrium Constants for Redox Reactions... 

The Nernst equation allows determination of the cell potential for a galvanic cell at nonstandard conditions. Write out the Nernst equation. What are nonstandard conditions What do %, n, and Q stand for in the Nernst equation What does the Nernst equation reduce to when a redox reaction is at equilibrium What are the signs of AG° and when < 1 When > 1 When = 1 Explain the following statement % determines spontaneity, while determines the equilibrium position. Under what conditions can you use to predict spontaneity ... 

One of the main advantages of the optically transparent thin-layer spectroelectrochemical technique (OTTLSET) is that the oxidized and reduced forms of the analyte adsorbed on the electrode and in the bulk solution can be quickly adjusted to an equilibrium state when the appropriate potential is applied to the thin-layer cell, thereby providing a simple method for measuring the kinetics of a redox system. The formal potential E° and the electron transfer number n can be obtained from the Nernst equation by monitoring the absorbance changes in situ as a function of potential. Other thermodynamic parameters, such as AH, AS, and AG, can also be obtained. Most redox proteins do not undergo direct redox reactions on a bare metal electrode surface. However, they can undergo indirect electron transfer processes in the presence of a mediator or a promoter the determination of their thermodynamic parameters can then... 

The quantitative capability of the Nernst equation to predict the activity of chemical species is valid only under equilibrium conditions. Most of the redox couples are not in equilibrium, except in highly reduced soils steady-state condition may result in pseudoequilibrium conditions. In soils, redox equilibrium is probably never reached because of the continuous addition of electron donors and acceptors. Biological systems add and remove electrons continuously. Thus, redox potential measurements cannot be used to accurately predict the activity of specific reductant and oxidant of the system. 

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