Standard potential definition

For a substance in a given system the chemical potential gi has a definite value however, the standard potentials and activity coefficients have different values in these three equations. Therefore, the selection of a concentration scale in effect determines the standard state. 

It follows directly from the definition of the standard potential that, for the hydrogen electrode,... 

The previous derivation was made under the implicit assumption that the activity coefficients of A and B are both equal to unity. This assumption matches the definition of E° as a standard potential. There are two cases of practical interest, where these conditions are not fulfilled. One is when the activity coefficients differ from unity but do not depend on the relative amounts of A and B in the film. This type of situation may arise when the interactions between the reactants are weak but the presence of the supporting electrolyte decreases the activity coefficients of A and/or B, yA and yB, to below 1 while they remain constant over the entire voltammo-gram. The only change required is thus to replace the standard potential by the formal potential ... 

The entire cyclic voltammogram is no longer reversible according to the definition we have attached to this term so far. In other words, the symmetry and translation operations as in Figures 1.4 and 6.1 do no longer allow the superposition of the reverse and forward trace. It also appears that the midpoint between the anodic and cathodic peak potentials does not exactly coincide with the standard potential. The gap between the two potentials increases with the extent of the ohmic drop as illustrated in Figure 6.2 for typical conditions, which thus provides an estimate of the error that would result if the two potentials were regarded as equal. 

ECb. Evb. Ef. ancl Eg are, respectively, the energies of the conduction band, of the valence band, of the Fermi level, and of the band gap. R and O stand for the reduced and oxidized species, respectively, of a redox couple in the electrolyte. Note, that the redox system is characterized by its standard potential referred to the normal hydrogen electrode (NHE) as a reference point, E°(nhe) (V) (right scale in Fig. 10.6a), while for solids the vacuum level is commonly used as a reference point, E(vac) (eV) (left scale in Fig. 10.6a). Note, that the energy and the potential-scale differ by the Faraday constant, F, E(vac) = F x E°(nhe). where F = 96 484.56 C/mol = 1.60219 10"19 C per electron, which is by definition 1e. The values of the two scales differ by about 4.5 eV, i.e., E(vac) = eE°(NHE) -4-5 eV, which corresponds to the energy required to bring an electron from the hydrogen electrode to the vacuum level. 

Let us now suppose that the waveform of figure 16.3 is applied to study the reversible oxidation of a species R to R in a given solvent. The reaction occurs at the working electrode (anode), and /i°(R/R ) is the standard potential of the R/R- couple. Because the standard potential of the reference electrode in our cell is known accurately relative to the standard potential of the SHE (E° = 0 by definition), we can write the cell reaction and the Nernst equation as... 

Analysis of the transition state in terms of energy is certainly a key aspect of the S 2-ET problem. Entropy considerations may, however, bring about additional information, possibly helping us to conceive better the transition between the two mechanisms. It was observed in this connection that, whereas the entropy of activation of both the anthracene anion radical and of the ETIOPFe(O) porphyrin (pp. 99, 100) (which have about the same standard potential) is close to zero in their reaction with s- and t-butyl bromides a definitely negative value, ca. — 20 eu is obtained for the reaction of the porphyrin with n-butyl bromide (Lexa et al., 1988). The same was found for the reaction of two other iron porphyrins, TPPFe(o) and OEP-Fe(i). These activation entropies were estimated from (153), where Z is... 

In this equation, the standard chemical potential MAgjS 6e used because the deviation of 6 from stoichiometry is much less than 1. According to the definition of the standard potential, = 0, is the standard Gibbs energy of the element in the standard state AG . Then... 

The standard potential of equation 8.176 is = 1.228 V. At standard state, the activity of gaseous oxygen is 1 by definition, and standard potential thus refers to H2O in equilibrium with an atmosphere of pure O2 at T = 25 °C and P = bar. Applying the Nernst and Faraday relations to equation 8.176 and transforming natural logarithms into base 10 logarithms, we obtain... 

In aqueous solution, thorium exists as Th(IV), and no definitive data have been presented for the presence of lower-valent thorium ions in this medium. The standard potential for the Th(IV)/Th(0) couple has not been determined from experimental electrochemical data. The values presented thus far for the standard reduction potential have been calculated from thermodynamic data or estimated from spectroscopic measurements. The standard potential for the four-electron reduction of Th(IV) ions has been estimated as —1.9 V in two separate references 12. The reduction of Th(OH)4 to Th metal was estimated at —2.48 V in the same two publications. Nugent et al. calculated the standard potential for the oxidation ofTh(III) to Th(IV) as +3.7 V versus SHE, while Miles provides a value of +2.4 V [13]. The standard potential measurements from studies in molten-salt media have been the subject of some controversy. The interested reader is encouraged to look at the summary from Martinot [10] and the original references for additional information [14]. 

Stanski, electrodeposition, 1301,1303 Standard hydrogen electrode, 1108 see also hydrogen electrode potential, definition, 840, 1060, 1061 Steady state, 1147, 1212 current, 1248... 

Figure 30(a) concerns the EE mechanism for the reaction O + 2 e = R. The solid curve represents the standard free energy profile pertaining to the standard potential E° of the redox couple O/R. In this case, the energy levels of the initial and the final state are equal by definition. Well... 

Redox indicators are organic molecules whose oxidized and reduced forms show different colors. The two levels of oxidation form a redox system which can be described by the standard potential or rH value. A short definition of the two terms is given in [1], Here, some more practical properties are mentioned ... 

Thus the potential of the hydrogen electrode depends on the hydrogen-ion concentration in the solution and on the pressure of hydrogen gas above the solution. The standard potential, E9, can be measured in a system where the activity of hydrogen ions is unity in the solution and the pressure of hydrogen gas over the solution is 1 atm. We have seen that the standard potential, B, of such an electrode is by definition 0. 

According to this definition the standard potential of the hydrogen electrode is the arbitrary zero of potential [cf. equation (7a)] electrode potentials based on this zero are thus said to refer to the hydrogen scale. Such a potential is actually the e.m.f. of a cell obtained by combining the given electrode with a standard hydrogen electrode it has, consequently, a definite thermodynamic value. For example, the potential (E) on the hydrogen scale of the electrode M, M (aM+), which is reversible with respect to the 2-valent cations M, in a solution of activity aM is the E.M.F. of the cell... 

Since kxjk is a constant at definite temperature, this equation is obviously of the same form as the electrode potential equations derived by thermodynamic methods, e.g., equation (85) for an electrode reversible with respect to positive ions. The first term on the right-hand side of equation (30) is clearly the absolute single standard potential of the electrode it is equal to the standard free energy of the conversion of solid metal to solvated ions in solution divided by and its physical significance has been already discussed. 

Oxidation-Reduction Indicators.—A reversible oxidation-reduction indicator is a substance or, more correctly, an oxidation-reduction system, exhibiting different colors in the oxidized and reduced states, generally colored and colorless, respectively. Mixtures of the two states in different proportions, and hence corresponding to different oxidation-reduction potentials, will have different colors, or depths of color every color thus corresponds to a definite potential which depends on the standard potential of the system, and frequently on the hydrogen ion concentration of the solution. If a small amount of an indicator is placed in another oxidation-reduction system, the former, acting as a potential mediator, will come to an equilibrium in which its oxidation-reduction potential is the same as that of the system under examination. The potential of the given indicator can be estimated from its color in the solution, and hence the potential of the system under examination will have the same value. 

In contrast with the three halide ions, the specific adsorption is certainly involved in the photoanodic oxidation of ferrocyanide, Fe(CN)g , which has been observed to be strongly attached to the Ti02 surface ° . However, this case does not permit any definitive conclusion with regard to the mechanism of the Fe(CN)6 photo-oxidation, as the actual high current efficiency for this reaction is, in fact, expected from the position of the standard potential of the Fe(CN) /Fe(CN)6 couple (0.36 V). 

Because of thermodynamic and electrochemical conventions, standard potentials are defined in the direction of reduction, independently of the respective chemical stabilities of the molecules involved. Thus for the oxidation of toluene to its cation radical, E° refers to the reduction of the highly unstable cation radical into the highly stable toluene. To overcome such a priori chemical nonsence, E is frequently designated as the standard oxidation potential of toluene for example. However, such a term should not be accepted according to canonical rules because it formally implies that the cell now operates in a driven mode, that is, is connected to an external power supply [19]. Thus in this chapter we prefer to use the denomination standard reduction potentials, rather than the usual temi standard potential, as a reminder of the E° definition, although such as expression is basically a pleonasm. 

By definition, the standard potential for the second half-reaction is the potential where [Cl ] = 1.00. That is, when [Cl ] = 1.00, E = EAgci/Ag- Substituting these... 

In the above equation, if a = 1, then E = eP. The standard potential of an electrode eP is the potential of an electrode in contact with a solution of its ions of unit activity. The standard potentials are always expressed against the standard hydrogen electrode (SHE), the potential of which is zero by definition. The standard potentials are a function of temperature they are usually tabulated for 25° C. Standard electrode potential is also called normal electrode potential. 

The standard state is the hypothetical ideal solution of molality 1 molkg (or the relative activity of H 3 O+,aH3O+ = 1) at standard pressure. The standard pressure is 1 bar (earlier 1 atm = 1.01325 bar however, the shift is only 0.00026 V at the potential scale). By definition, the potential of this electrode is zero. Although the standard potential should not depend on the material of the metal, the SHE exclusively contains a platinum wire or a platinum sheet covered with platinum black (platinized platinum). Owing to the spontaneous dissociation (dissociative chemisorption) of H2 at Pt... 

It is emphasized that experiments only provide values of the EMF of the whole cell, and the polarity of one electrode with respect to the other. The arbitrary reference system, that is, the SHE, is introduced in order to establish a table of standard potentials for common electrodes. Since the standard potential for this system is zero by definition,... 

The symbol E ° is used to denote the so-called formal potential [74PAR]. The formal (or conditional ) potential can be regarded as a standard potential for a particular medium in which the activity coefficients are independent (or approximately so) of the reactant concentrations [85BAR/PAR] (the definition of E° parallels that of concentration quotients for equilibria). Therefore, from... 

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