Nernst redox equation

With rapid electron transfer we can substitute the above [ox] and [red] relationships into the Nernst redox equation, from which n, F, A and 5 then disappear, so that... 

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

NAD + H + 2e" NADH SOLUTION The Nernst redox equation in this case is... 

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... 

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. 

Given the problems inherent to the electrode measurement of in soil solution, it would seem desirable to consider other methods of estimating Eh. Theoretically, one could analyze the soil solution for the reduced and oxidized species of a redox couple, say dissolved Fe " and Fe, and use the Nernst relation (equation 7.2) to calculate Eh. Usually, however, there are difficulties with this approach. In the case of the Fe couple, Fe solubility in all but very acid soil solutions is extremely low (below detection), so that an assumption must be made about the activity of the free Fe " ion. It might reasonably be assumed that the solubility product of Fe oxide limits this activity, but Fe oxides have a rather wide range of solubilities depending on oxide crystallinity, structure, and purity. A better approach to measuring E would be to use an indicator chemical that undergoes reversible electron transfer with natural redox couples in soil solution, that is,... 

Nernst s Equation In closing, we will talk about the concentration dependency of the redox potential. We obtain the following relation for a simple redox pair Rd Ox + VgC by inserting the // (Rd/Ox) defining equation into Eq. (23.3) ... 

Therefore, the potential of a redox couple only depends on its own thermodynamic data. More generally, by applying the conventions previously outlined, we end up with the following Nernst law equation ... 

In these equations we assume that the mobile counterion is uninegative and the electron-hopping process involves the transfer of a single electron. We also assume that the covalently attached redox center is unipositive in its oxidized form and neutral in its reduced form, hence the redox center experiences ion pairing in the oxidized state. The usual form of the Nernst-Planck equation applies to the mobile counterion C, which has a valence of —1. Of course extension to the case of a fixed mononegative reduced form of the redox center paired with a monopositive mobile electroinactive counterion and a fixed neutral oxidized form is... 

This equation looks similar to the well-known Nernst equation for one-electron redox Equation (10.12) ... 

Finally, when a half-redox reaction is accompanied by a complexation reaction, it is also useful to define an apparent standard potential or normal potential in order to predict redox reactions quickly. For example, in the case of the couple AuCl4 /Au(s), Nernst s equation can be written as... 

In order to conveniently locate the potential interval change in the conditions of the titration, it is more judicious to use the formal potentials of the internal redox indicators than their standard potentials. Therefore, Nernst s equation is written ... 

Surprisingly, at first sight, redox indioators may also be used in some cases to detect the endpoint of a complexometric titration with EDTA. In fact, the endpoint of an EDTA titration may be accompanied by a ehange in the redox potential of the solution. When a mixture of Fe + and Fe + is titrated with EDTA, Fe + disappears before Fe + since Fe gives more stable eomplexes with EDTA than Fe + does. A simple inspection of Nernst s equation shows that in these conditions, the solution s redox potential decreases markedly, in particular at the equivalence point. The sharp change may be detected by potentiometry with a platinum electrode or with a redox indicator such as Variamine blue. 

Basic understanding of such systems can still be derived from the redox polymer model. Consider the fact that the density of states varies according to a Nernst-type equation. Thus, on a linear concentration scale, a coating of the polypyrrole type may be practically completely in the reduced state, independent of the actually applied electrode potential. The rate of reduction of a depolarizer according to Eq. (48) may be defined by the current (165,166),... 

J is the flux of the redox species given by the Nernst-Planck equation (8.26) The initial condition is given by an equation similar to Equation 8.28 ... 

The change in the redox potential is given quantitatively by the Nernst equation ... 

The redox (electrode) potential for ion-ion redox systems at any concentration and temperature is given by the Nernst equation in the form... 

Thus under standard conditions chloride ions are not oxidised to chlorine by dichromate(Vr) ions. However, it is necessary to emphasise that changes in the concentration of the dichromate(VI) and chloride ions alters their redox potentials as indicated by the Nernst equation. Hence, when concentrated hydrochloric acid is added to solid potassium dichromate and the mixture warmed, chlorine is liberated. 

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... 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

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... 

A classification of electrodes has already been given in Section 1.3.1. The function of the indicator electrode is to indicate by means of its potential the concentration of an ion or the ratio of the concentrations of two ions belonging to the same redox system. Under non-faradaic conditions, the relationship between the potential and these concentrations is given by the Nemst or the more extended Nernst-Van t Hoff equation, as explained below. As a single potential between an electrode and a solution cannot be measured in the absolute sense but only in a relative manner, a reference electrode is needed its function is merely to possess preferably a constant potential or at any rate a known potential under the prevailing experimental conditions. Often both electrodes cannot be placed in the same solution, so that a second solution... 

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. 

Let us first take the example of titrating Fe2+ with Ce4+ and vice versa. There are two redox couples, Fe3+ /Fe2+ (1) and Ce4+ /Ce3+ (2), for each of which the Nernst equation... 

In agreement with the theory of electrolysis, treated in Sections 3.1 and 3.2, the parts of the residual current and the limiting current are clearly shown by the nature of the polarographic waves because for the cathodic reduction of Cd2+ and Zn2+ at the dme we have to deal with rapid electron transfer and limited diffusion of the cations from the solution towards the electrode surface and of the metal amalgam formed thereon towards the inside of the Hg drop, we may conclude that the half-wave potential, Eh, is constant [cf., Fig. 3.13 (a ] and agrees with the redox potential of the amalgam, i.e., -0.3521V for Cd2+ + 2e - Cd(Hg) and -0.7628 V for Zn2+ + 2e -> Zn(Hg) (ref. 10). The Nernst equation is... 

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