Nemst equation reversible electrode potential

The reversible electrode potential of a chemical reaction can be obtained from the Nemst equation ... 

The Nemst equation solves the potential of an electrochanical cell containing a reversible system with fast kinetics and it is valid only at equilibrium and at the surface of the electrode ... 

Under conditions of reversibility, there is a relationship called the Nemst equation between the potential E, the standard electrode potential and the activity a of the ion M" ... 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

It is not a trivial point that 0fj vs. E curves are practically linear. In a reversible system the electrode potential can be linked to the activities (concentrations) of the potential-determining substances. In the system being discussed, this substance is atomic hydrogen. According to the Nemst equation we have E = const - (RTIF) X In Cjj. It follows that the degree of coverage, 0, is linearly related to the logarithm of concentration c in the solution ... 

In this review, wherever electrochemistry is concerned, the reversibility of a reaction refers firstly to the chemical reversibility. It also requires that the electron transfer reaction occurs at such a rate that the rate of the whole electrodic process, which is measured by the output current of the electrode, is controlled by the diffusion of the redox species towards the electrode surface. Furthermore, the surface concentrations of O and R at a given potential should be governed by the Nemst equation. 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

We can state this argument in reverse - alteration of the potential at the electrode solution interface will itself cause the ratio of a(O) to a(R) to alter to that dictated by the Nernst equation, and the conversion of material from its reduced to its oxidized forms (or back) requires the production (or consumption) of charge. In fact, we can write a variant of the Nemst equation (equation (3.8)), as follows ... 

When the electrode reaction (2.30) is electrochemically reversible, (2.37) and (2.38) are combined with the Nemst equation (1.8) yielding an integral eqnation that relates the current with time and the electrode potential. The nnmerical solntion derived by the step function method [52] is given by the following recursive formulae ... 

E vs. log(id-i)/f which should be linear with a slope of 59.1/n mV at 25 °C if the wave is reversible. This method relies however upon a prior knowledge of n, and if this is not known then the method is not completely reliable as theory predicts that when the electron transfer process itself is slow, so that equilibrium at the electrode between the oxidized and reduced forms of the couple is established slowly and the Nemst equation cannot be applied, then an irreversible wave is obtained and a similar plot will also yield a straight line but of slope 54.2/ana mV at 25 °C (a = transfer coefficient, i.e. the fraction of the applied potential that influences the rate of the electrochemical reaction, usually cu. 0.5 na = the number of electrons transferred in the rate-determining step). Thus a slope of 59.1 mV at 25 °C could be interpreted either as a reversible one-electron process or an irreversible two-electron process with a = 0.45. If the wave is irreversible in DC polarography then it is not possible to obtain the redox potential of the couple. 

A non-polarizable electrode-solution interface is a reversible electrode. Therefore, the potential is determined by the composition of the solution based on the Nemst equation (given by Eq. 1.36). So, for example, for the copper electrode in a solution of CuS04 the potential is given by... 

For an electrode reaction to be considered reversible, it is necessary to compare the rate of the charge transfer process and the rate of the mass transport of electroactive species. When the mass transport rate is slower than the charge transfer one, the electrode reaction is controlled by the transport rate and can be considered as electrochemically reversible in that the surface concentration fulfills the Nemst equation when a given potential is applied to the electrode. In Electrochemistry, knowledge of the behavior of reversible electrode processes is very important, since these can be used as a benchmark for more complex systems (see Chap. 5 in [1] and Sect. 1.8.4 for a detailed discussion). 

In this section, a non-reversible electrode reaction will be addressed. An exact definition of a slow charge transfer process is not possible because the charge transfer reaction can be reversible, quasi-reversible, or irreversible depending on the duration of the experiment and the mass transport rate. So, an electrode reaction can be slow or non-reversible when the mass transport rate has a value such that the measured current is lower than that corresponding to a reversible process because the rate of depletion of the surface species at the electrode surface is less than the diffusion rate at which it reaches the surface. Under these conditions, the potential values that reduce the O species and oxidize the R species become more negative and more positive, respectively, than those predicted by Nemst equation. 

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

The polarographic current-potential wave illustrated by Figure 3,3 conforms to the Nemst equation for reversible electrochemical processes. However, it is more convenient to express the concentrations at the electrode surface in terms of the current i and the diffusion current jd. Because id is directly proportional to the concentration of the electroactive species in the bulk and i at any point on the curve is proportional to the amount of material produced by the electrolysis reaction, these quantities can be directly related to the concentration of the species at the electrode surface. For a generic reduction process [Eq. (3.1)] the potential of the electrode is given by the Nemst equation ... 

Properties of the Ideal Reference Electrode. An ideal reference electrode should show the following properties (1) it should be reversible and obey the Nemst equation with respect to some species in the electrolyte (2) its potential should be stable with time (3) its potential should return to its initial value after small currents are passed through the electrode (no hysteresis) (4) if it is an electrode of the second kind (e.g., Ag/AgCl), the solid phase must not be appreciably soluble in the electrolyte and (5) it should show low hysteresis with temperature cycling. 

The theoretical decomposition voltage of chlorides can be calculated from the value of equilibrium oxidation potential of the chlorine electrode e t. cia1 ci-in the anolyte and the reversible reduction potential of the hydrogen electrode 7Toh- Ha. pt in alkaline catholyte. If we apply the Nemst equations for the corresponding electrochemical processes [see (XI-9) and (XI-10)] we obtain the... 

A nonpolarizable electrode is, in effect, a reversible electrode. The potential is determined by the electrochemical reaction taking place and the composition of the solution, through the Nemst equation. For a copper electrode in a solution containing CuSO this is... 

Similarly one could use a silver wire coated with AgCl in a chloride-containing test solution as a reversible Ag/AgCl/Cl electrode, which responds to the concentration of Cl ions in solution following the Nemst equation. The advantage of indicator electrodes is that they always measure the reversible potential with respect to the ion being studied, regardless of its concentration in solution. 

The electrode potential of a redox couple varies with the activities of the reduced and oxidized forms of the couple in the sense that increasing activity of oxidant increases the value of the potential. Quantitatively, for the reversible half-reaction (12-9) we have the Nemst equation... 

Expressions (3.61) and (3.62) are different forms of the Nemst equation, which gives the electrode potential in volts of a reduction halfreaction as a function of E° for that reaction and the activities of the oxidized (reactants) and reduced (products) species raised to the power of their respective coefficients in the balanced redox equation. Note that if reactants and products were reversed (as is the case in some texts) the sign on the right side would be different. If the resulting E is equal to zero, there is no potential to do work and the system is at equilibrium. It then follows from Eq. (3.62) that... 

First, we consider cyclic voltammetry and focus on the non-turnover experiment in which there is no substrate in solution. As the potential is scanned, electrons transfer back and forth between the electrode and the redox-active site(s), producing a current peak in each direction. These two peaks constitute the signal . Provided the scan rate is slow enough to equilibrate all the processes required in the redox reaction, the signal obtained will be as predicted by the Nemst equation that holds for a reversible electron-transfer process. The current peaks will be compact and... 

Indeed, there are no factors limiting the reversible operation of gas oxygen electrodes at high and low pO values. Theoretically, if the concentration of the potential-determining particle in the solution is equal to zero, then the absolute magnitude of the potential of the corresponding electrode approaches infinity ( oo). This conclusion has no physical sense it means that the Nemst equation is applicable to the description of the electrochemical processes in the solution, if their concentration exceeds the certain limit. In practice, the deviations from the Nernst equation arise because of the effect of the binary electric layer... 

The Au(02) electrode was demonstrated to be reversible to oxide ions, and the slope of the E-pO plot was twice as high as the value predicted by the Nemst equation (2.4.2), i.e. that there was a one-electron potential-determining process at the electrode. 

Since these first reports, Iwahara and other investigators have studied the conductivities (both ionic and electronic), conduction mechanism, deuterium isotope effect, and thermodynamic stability of these materials. The motivation for most of this work derives from the desire to utilize these materials for high temperature, hydrogen-fiieled solid oxide fuel cells. In a reverse operation mode, if metal or metal oxide electrodes are deposited onto a dense pellet of this material and heated to temperature T, the application of an electric potential to the electrodes will cause a hydrogen partial pressure difference across the pellet according to the Nemst equation ... 

The characteristics of an ideal reference electrode are that it should have a fixed potential over time and temperature, long term stability, the ability to return to the initial potential after exposure to small currents (i.e., it should be reversible), and it should follow the Nemst equation. Two common reference electrodes that come close to behaving ideally are the saturated calomel electrode and the silver/silver chloride electrode. 

To predict the current response versus applied potential, the simplified diffusion-layer model may be combined wi the Nemst equation (for a reversible system) to yield the familiar hydrodynamic voltammogram. The latter relationship states that the potential of the electrode is determined by the concentration activity ratio of the oxidized and reduced forms of the redox couple at the electrode surface (Fig. 9A). ... 

---