Electron-transfer standard electrode potentials

As outlined in Section 1.5, consecutive electron transfers possessing electrode potentials separated by less than 0.1 V afford in cyclic voltammetry more or less overlapping peak-systems which cannot be adequately resolved to obtain the precise standard electrode potential for each step. In these cases it is convenient to make use of pulsed techniques. 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

The standard electrode potential [1] of an electrochemical reaction is commonly measured with respect to the standard hydrogen electrode (SHE) [2], and the corresponding values have been compiled in tables. The choice of this reference is completely arbitrary, and it is natural to look for an absolute standard such as the vacuum level, which is commonly used in other branches of physics and chemistry. To see how this can be done, let us first consider two metals, I and II, of different chemical composition and different work functions 4>i and 4>ii-When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 2.2). No work is required to transfer an electron from metal I to metal II, since the two systems are in equilibrium. This enables us calculate the outer potential difference between the two metals in the following way. We first take an electron from the Fermi level Ep of metal I to a point in the vacuum just outside metal I. The work required for this is the work function i of metal I. 

Figure 2.1 Simplified schematic plots showing the exponential relationship between the current density i and the potential of the electrode, E. (The latter is represented here as being relative to the standard electrode potential of the couple undergoing electromodification for now, the abscissa ( — ) can be thought of as deviation from equilibrium.) Three examples of electron-transfer rate (/feei) are shown (a) (coincident with the y-axis) representing a very fast rate of electron transfer of 10 A cm" (b) representing an average rate of electron transfer of 10 A cm (c) representing a slow rate of electron transfer of 10 A cm . For each trace, T = 298 K and the reaction was symmetrical , i.e. a = 0.5, as defined later in Section 7.5.

Next, we need to decide on what we think is occurring in terms of the system actually before us. Let s suppose that we have a CV which looks as though it describes a simple single reversible electron-transfer reaction. From the experimental trace of current against potential, it should be easy to obtain the standard electrode potential E . In addition, before we start, we measure the area of the electrode. A, and the thermodynamic temperature, T. Next, knowing A, T and E , we estimate a value for the exchange current lo, run a simulation, and note how similar (or not) are... 

Electrons are transferred singly to any species in solution and not in pairs. Organic electrochemical reactions therefore involve radical intermediates. Electron transfer between the electrode and a n-system, leads to the formation of a radical-ion. Arenes, for example are oxidised to a radical-cation and reduced to a radical-anion and in both of these intermediates the free electron is delocalised along the 7t system. Under some conditions, where the intermediate has sufficient lifetime, these electron transfer steps are reversible and a standard electrode potential for the process can be measured. The final products from an electrochemical reaction result from a cascade of chemical and electron transfer steps. 

Standard electrode potentials for half-reactions and overall reactions are quoted with units of volts (V). However many electrons are transferred in... 

The most important thing about Equations 17-6 and 17-7 is that the equilibrium constant for electron-transfer reactions can be calculated from standard electrode potentials without ever having to make experimental measurements. 

The simplest situation that exists for balancing electron-transfer equations is the one in which a table of standard electrode potentials is at hand, and the two needed half-reactions are included in it. The following problem illustrates this situation. 

Electrode potentials for half-reactions are most easily obtained from a table of standard electrode potentials (Table 17-1, p 275) they may be modified for concentrations appreciably different from unit activity (p 276). A list of features characteristic of electron-transfer reactions is given on p 300. 

More recently it has been found15 that a correlation exists between spectroscopic parameters of the divalent aqua ions of the metals Cr to Ni, and the polarographic y2. A linear relationship was found between A0 and crystal field splitting parameter, ot the transfer coefficient, n the number of electrons transferred in the reduction, EVl the polarographic half-wave potential and E° the standard electrode potential. The use of the crystal field splitting parameter would seem to be a more sensible parameter to use than the position of Amax for the main absorption band as the measured Amax may not be a true estimate of the relevant electronic transition. This arises because the symmetry of the complex is less than octahedral so that the main absorption band in octahedral symmetry is split into at least two components with the result that... 

Marcus has introduced a model for, S N 2 reactions of the ET type based on two interacting states which takes into account the relevant bond energies, standard electrode potentials, solvent contributions, and steric effects.87 The rate constant for intramolecular electron transfer between reduced and oxidized hydrazine units in the radical cation of the tetraazahexacyclotetradecane derivative (43) and its analogues has been determined by simulation of then variable temperature ESR spectra.88 The same researchers also reported then studies of the SET processes of other polycyclic dihydrazine systems.89,90... 

Table 9.1 shows the numerical values of the standard redox potentials for a few reactions of electronic transfer at electrodes. Electrochemical handbooks provide the standard redox potentials for various other transfer reactions of redox electrons. As mentioned in section 9.3, the redox potential is independent of the electrode materials. 

Studies in nonaqueous dipolar aprotic solvents allowed the elucidation of the complicated role of the solvent nature in determining the - double layer structure and kinetics of electrochemical reactions. Special attention was paid to the phenomenon of ion - solvation and its effect on -> standard electrode potentials. Experimental studies of the various electrochemical systems in nonaqueous media greatly contributed to the advancement of the theory of elemental electron-transfer reactions across charged interfaces via the so-called energy of solvent reorganization. 

This equation includes the standard electrode potential E° and the familiar constant R. The Q in the equation is the concentration of the products divided by the concentration of the reactants. The variable n stands for the number of moles of electrons transferred. The equation also introduces a new symbol, the faraday. A faraday, f, is the charge on one mole of electrons, or about 96,352 coulombs of charge. For convenience it is rounded off as 96,500 C of charge. Because R and f are constants and most reactions occur at 298 K, the equation can be simplified to look like this ... 

AG ° (i) = standard free energy change for the transfer of i from water into the mixed solvent N = Avogadro s number e = electronic charge Dw = dielectric constant of water Ds = dielectric constant of the mixed solvent Th2o = radius of the water molecule Ew° = standard electrode potential in water EB° = standard electrode potential in the mixed solvent M = cation X = anion... 

Recently, it was reported that loading small amount of platinum onto tungsten(VI) oxide enhances the visible-light photocatalytic activity significantly and this is caused by the catalytic action of platinum to induce multiple-electron transfer to oxygen 44). Reactions of two and four-electron transfer processes are as follows (potential in parentheses is standard electrode potential versus standard hydrogen electrode at pH 0). 

The standard electrode potentials are far more anodic than that of one-electron transfer process, -0.284 V (SHE) and the visible-light photocatalytic activity of platinum-loaded tungsten(VI) oxide could be interpreted by enhanced multiple-electron transfer process by deposited platimun (45), since it is well known that platinum and the other noble metals catalyze such multiple-electron transfer processes. Similar phenomena, cocatalyst promoted visible-light photocatalytic activity, have been reported with palladium 46) and copper oxide (47). Thus, change of reaction process seems beneficial to realize visible-light photocatalytic activity. 

Backward electron (hole) transfer can be avoided thermodynamically only when the CB bottom and VB top are more positive and negative than standard electrode potentials of a reductant and an oxidant, respectively. 

The Edwards equation sums component processes modelling the transfer of the pair of bonding electrons from substrate to product. The component model processes are proton transfer to the nucleophile (the proton affinity) (Equation 27) and the polarisability of the nucleophile as judged by its standard electrode potential (E ) (Equation 28). 

In this equation, and represent the surface concentrations of the oxidized and reduced forms of the electroactive species, respectively k° is the standard rate constant for the heterogeneous electron transfer process at the standard potential (cm/sec) and oc is the symmetry factor, a parameter characterizing the symmetry of the energy barrier that has to be surpassed during charge transfer. In Equation (1.2), E represents the applied potential and E° is the formal electrode potential, usually close to the standard electrode potential. The difference E-E° represents the overvoltage, a measure of the extra energy imparted to the electrode beyond the equilibrium potential for the reaction. Note that the Butler-Volmer equation reduces to the Nernst equation when the current is equal to zero (i.e., under equilibrium conditions) and when the reaction is very fast (i.e., when k° tends to approach oo). The latter is the condition of reversibility (Oldham and Myland, 1994 Rolison, 1995). 

Where E is the potential of a half-cell, E° is the standard electrode potential, R the ideal gas constant, T the absolute temperature, n the number of electrons transferred in the course of the half reaction, F the Faraday constant, and c the concentration of the dissolved species. 

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