Nernst equation redox reactions

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,... 

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... 

Although this treatment of buffers was based on acid-base chemistry, the idea of a buffer is general and can be extended to equilibria involving complexation or redox reactions. For example, the Nernst equation for a solution containing Fe + and Fe + is similar in form to the Henderson-Hasselbalch equation. 

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. 

You will recall from Chapter 6 that the Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. Consider, for example, a titration in which the analyte in a reduced state, Ared) is titrated with a titrant in an oxidized state, Tox- The titration reaction is... 

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 free energy changes of the outer shell upon reduction, AG° , are important, because the Nernst equation relates the redox potential to AG. Eree energy simulation methods are discussed in Chapter 9. Here, the free energy change of interest is for the reaction... 

However, under most conditions the activity coefficients cannot be neglected, certainly for a single redox couple where the ox/red concentration ratio cannot be simply calculated from the true standard potential and the potential directly observed. In order to overcome this difficulty the concept of the formal potential was introduced, which represents a formal standard potential E ° measured in an actual potentiometric calibration and obeying the Nernst equation, E = E ° + (0.05916/n) log ([ox]/[red]) at 25° C, E"0 must meet the conditions under which the analytical measurements have to be made. Sometimes the formal potential values are decisive for the direction of the reaction between two redox couples even when the E° values do not differ markedly10. 

In the practice of potentiometric titration there are two aspects to be dealt with first the shape of the titration curve, i.e., its qualitative aspect, and second the titration end-point, i.e., its quantitative aspect. In relation to these aspects, an answer should also be given to the questions of analogy and/or mutual differences between the potentiometric curves of the acid-base, precipitation, complex-formation and redox reactions during titration. Excellent guidance is given by the Nernst equation, while the acid-base titration may serve as a basic model. Further, for convenience we start from the following fairly approximate assumptions (1) as titrations usually take place in dilute (0.1 M) solutions we use ion concentrations in the Nernst equation, etc., instead of ion activities and (2) during titration the volume of the reaction solution is considered to remain constant. 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

We consider again the redox reaction Ox + ze = Red with a solution initially containing only the oxidized form Ox. The electrode is initially subjected to an electrode potential Ei where no reaction takes place. For the sake of simplicity, it is assumed that the diffusion coefficients of species Ox and Red are equal, i.e., D = D0x = DKeA. Now, the potential E is linearly increased or decreased with E(t) = Ei vt (v is a potential scan rate, and signs + and represent anodic scan and cathodic scan, respectively.) Under the assumption that the redox couple is reversible, the surface concentrations of Ox and Red, i.e., cs0x and 4ed, respectively, are always determined by the electrode potential through the Nernst equation... 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values and then apply the Nernst equation. If the Ecell turns out to be negative, it indicates that the reaction is not a spontaneous one (an electrolytic cell) or that the reaction is written backwards if it is supposed to be a galvanic cell. If it is supposed to be a galvanic cell, then all you need to... 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values,... 

The reducing equivalents transferred can be considered either as hydrogen atoms or electrons. The driving force for the reaction, E, is the reduction/oxidation (redox) potential, and can be measured by electrochemistry it is often expressed in millivolts. The number of reducing equivalents transferred is n. The redox potential of a compound A depends on the concentrations of the oxidized and reduced species [Aqx] and [Area] according to the Nernst equation ... 

Nernst equation The mathematical equation that relates the cell potential of a redox reaction to the temperature and concentrations of the reacting chemicals, e. g., E,ii=fi ,n-((RT/nE)lnQ). 

The course of electron transfer reactions (redox reactions, see p. 14) also follows the law of mass action. For a single redox system (see p.32), the Nernst equation applies (top). The electron transfer potential of a redox system (i. e., its tendency to give off or take up electrons) is given by its redox potential E (in standard conditions, E° or E° ). The lower the... 

For any reaction occurring under conditions other than standard ones, the Nernst equation for the redox potential E (often written as Eh) is used ... 

Some typical redox couples and metal ion-metal couples are shown below, with the corresponding Nernst equations. The effects of solvents on these reactions will be discussed in the next section. 

Redox Electrodes If a platinum electrode is immersed in a solution containing the oxidized and reduced forms (Ox, Red) of a redox reaction Ox+ne <=> Red, its potential is given by the Nernst equation (Section 5.2.1) ... 

The Nernst equation applies to the potentials of both half-reactions and total redox reactions. 

Values of E° by definition refer to conditions under which all species are in their standard states at 298 K. For non-standard conditions the electrode potential, E, of a redox reaction is given by the familiar Nernst expression (equation 24), where... 

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. 

It is important to note that the electrode potential is related to activity and not to concentration. This is because the partitioning equilibria are governed by the chemical (or electrochemical) potentials, which must be expressed in activities. The multiplier in front of the logarithmic term is known as the Nernst slope . At 25°C it has a value of 59.16mV/z/. Why did we switch from n to z when deriving the Nernst equation in thermodynamic terms Symbol n is typically used for the number of electrons, that is, for redox reactions, whereas symbol z describes the number of charges per ion. Symbol z is more appropriate when we talk about transfer of any charged species, especially ions across the interface, such as in ion-selective potentiometric sensors. For example, consider the redox reaction Fe3+ + e = Fe2+ at the Pt electrode. Here, the n = 1. However, if the ferric ion is transferred to the ion-selective membrane, z = 3 for the ferrous ion, z = 2. 

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 ... 

An electron transfer reaction, Equation 6.6, is characterised thermodynamically by the standard potential, °, i.e. the value of the potential at which the activities of the oxidised form (O) and the reduced form (R) of the redox couple are equal. Thus, the second term in the Nernst equation, Equation 6.7, vanishes. Here and throughout this chapter n is the number of electrons (for organic compounds, typically, n = 1), II is the gas constant, T is the absolute temperature and F is the Faraday constant. Parentheses, ( ), are used for activities and brackets, [ ], for concentrations /Q and /R are the activity coefficients of O and R, respectively. However, what may be measured directly is the formal potential E° defined in Equation 6.8, and it follows that the relationship between E° and E° is given by Equation 6.9. Usually, it maybe assumed that the activity coefficients are unity in dilute solution and, therefore, that E° = E°. 

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. 

As most of us recall from our struggles with balancing redox equations in our beginning chemistry courses, many electron-transfer reactions involve hydrogen ions and hydroxide ions. The standard potentials for these reactions therefore refer to the pH, either 0 or 14, at which the appropriate ion has unit activity. Because multiple numbers of H+ or OH- ions are often involved, the potentials given by the Nernst equation can vary greatly with the pH. 

The foregoing discussion was applicable to redox potentials, and the concentrations of reactants and products were assumed to be 1 M each. If it is not so, a correction must be made as was the case with AGq. Such a correction may be made via the Nernst equation, which for the reaction A + B —> C + D can be written as... 

Electrochemistry electrolytic and galvanic cells Faraday s laws standard halfcell potentials Nernst equation prediction of the direction of redox reactions... 

This equation, the Nernst redox equation, provides a way of relating E and E0 for any redox reaction or half-cell reaction. 

Half-cell reaction — The redox reaction (- electrode reaction) proceeding in a half-cell. The half-cell reaction changes the ratio of the activities of the reduced and oxidized forms. When the half-cell reaction is electrochemically reversible (see reversibility), the -> Nernst equation will describe the dependence of the -> electrode potential on the ratio of the activities of the reduced and oxidized forms. 

Applying the Nernst equation for such a process, which is a combined redox and acid-base reaction, we can write... 

For each of the redox couples, the potential can be calculated using the Nernst equation. This equation correlates Gibb s free energy, known as AG, and the electromotive force provided by an oxido-reduction reaction (such a reaction acts as a galvanic cell). Given the following equation due to a chemical reaction ... 

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... 

For the LSV and CV techniques, the concept of reversibility/irreversibility is therefore very important. Electrochemists are responsible for some confusion about the term irreversible, since a reaction may be electrochemically irreversible, yet chemically reversible. In electrochemistry, the term irreversible is used in a double sense, to describe effects from both homogeneous and heterogeneous reactions. In both cases, the irreversible situation arises when deviations from the Nernst equation can be seen as fast changes in the electrode potential, E, are attempted and the apparent heterogeneous rate constants, /capp, for the O/R redox couple is relatively small. The heterogeneous rate constant can be split into two parts a constant factor in terms of the standard rate constant, k°, and an exponential function of the overpotential E - Eq), as expressed in Eq. 59, where only the reductive process is considered (see also Eq. 5). 

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