Standard and Formal Electrode Potentials

When will the standard and formal electrode potentials be the same ... 

The electrostatic aspects of electrochemical systems will be introduced first and the electrochemical potential as a key concept is presented (Sects. 1.2-1.4). The electrochemical equilibrium is discussed and Nemst s equation and standard and formal electrode potentials are introduced (Sect. 1.5). The study of electrochemical interfaces under equilibrium ends with the phenomenological and theoretical treatment of the electrical double layer (Sect. 1.6). 

Appendix 4 Formation Constants at 25°C A-10 Appendix 5 Standard and Formal Electrode Potentials A-12 Appendix 6 Use of Exponential Numbers and Logarithms A-15 Appendix 7 Volumetric Calculations Using Normality and Equivalent Weight A-19... 

APPENDIX THREE SOME STANDARD AND FORMAL ELECTRODE POTENTIALS... 

It is important to obtain experimental information on the thermodynamics of electrode processes to ascertain the tendency of a particular reaction to occur under a given set of experimental conditions namely temperature, pressure, system com H)sition and electrode potential. Such information is provided by the standard- or formal-electrode potentials for the redox couple under consideration. Appropriate combinations of these potentials enable the thermodynamics of homogeneous redox processes to be determined accurately. However, such quantities often are subject to confusion and misinterpretation. It is, therefore, worthwhile to outline their significance for simple electrochemical reactions. This discussion provides background to the sections on electrochemical kinetics which follow. The evaluation of formal potentials for various types of electrode-reaction mechanisms is dealt with in 12.3.2.2. 

Parameter E° in Eqs. (3.30) and (3.32) is called the standard electrode potential it corresponds to the value of electrode potential that is found when the activities of the components are unity. Values E° differ somewhat from values E°. For a more distinct differentiation between these parameters, E° is called the formal electrode potential. 

C = concentration of the active species in the bulk of the solution E° = formal electrode potential of the couple Ox/Red. It differs from the thermodynamic standard potential E° by a factor related to the activity coefficients of the two partners Ox and Red ... 

In general, the study of the variation of the formal electrode potential of a redox process with temperature has thermodynamic implications. Hence, one is interested in the measurement of AG°, AS° and AH° for the electron transfer process. It is recalled from thermodynamics that, under standard conditions, AE° is directly proportional to the free energy of the redox reaction according to the equation ... 

Related to is the formal electrode potential, (as discussed in Chapter 6), which can be called the standard electrode potential at 298 K, and unit concentrations throughout . The differences between and E are discussed in Chapter 6. 

Comparisons of electrochemical results obtained from different laboratories are complicated by differing preferences for solvents, electrolytes, working electrode surfaces and, most significantly, reference electrodes. Rather than relating the data to a common electrochemical reference, we cite the data as given in the original literature together with an indication of the conditions employed. Furthermore, we have included the formal electrode potential of any internal standard (typically ferrocene or decamethylferrocene) used in the study where available. 

Formal potential — Symbol Efr (SI Unit V), has been introduced in order to replace the standard potential of -> cell reaction when the values of - activity coefficients of the species involved in the cell reaction are unknown, and therefore concentrations used in the equation expressing the composition dependence of ceii instead of activities. It also involves the activity effect regarding the -+ standard hydrogen electrode, consequently in this way the formal electrode potential is also defined. Formal potentials are similar to conditional (apparent) equilibrium constants (-> equilibrium constant), in that, beside the effect of the activity coefficients, side reaction equilibria are also considered if those are not known or too complex to be taken into account. It follows that when the logarithmic term which contains the ratio of concentrations in the -> Nernst... 

For solution redox couples uncomplicated by irreversible coupled chemical steps (e.g. protonation, ligand dissociation), a standard (or formal) potential, E°, can be evaluated at which the electrochemical tree-energy driving force for the overall electron-transfer reaction, AG c, is zero. At this potential, the electrochemical rate constants for the forward (cathodic) and backward (anodic) reactions kc and ka (cms-1), respectively, are equal to the so-called "standard rate constant, ks. The relationship between the cathodic rate constant and the electrode potential can be expressed as... 

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). 

Some Standard and Formal Reduction Electrode Potentials... 

The for a half-reaction is the potential of that reaction versus the standard hydrogen electrode, with all species at unit activity. Most reduction potentials are not determined under such conditions, so it is expedient to define a formal reduction potential. This is a reduction potential measured under conditions where the reaction quotient in the Nernst equation is one and other nonstandard conditions are described solvent, electrolyte, pN, and so on. Formal reduction potentials are represented by °. Reduction potentials determined by cyclic voltammetry are usually formal potentials. The difference between standard and formal potentials is not expected to be great. Other definitions of the formal potential are offered. ... 

Fig. 14.6 Standard (or formal) reduction potentials of actinium and the actinide ions in acidic (pH 0) and basic (pH 14) aqueous solutions (values are in volts vs standard hydrogen electrode).

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

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). 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

M p = (z - l)F(pJRT. E is the electrode potential, is the standard potential, or more exactly the formal potential when activity effects cannot be neglected, and z is the charge number of the reactant. Thus, the current-electrode potential relationship characterizing the kinetics of an outer sphere electron-transfer reaction is given by (22) (/ is the current flowing through... 

Due to the presence of interactions, the apparent redox potential of a redox couple inside a polyelectrolyte film can differ from that of the isolated redox couple in solution (i.e. the standard formal redox potential) [121]. In other words, the free energy required to oxidize a mole of redox sites in the film differs from that needed in solution. One particular case is when these interations have an origin in the presence of immobile electrostatically charged groups in the polymer phase. Under such conditions, there is a potential difference between this phase and the solution (reference electrode in the electrolyte), knovm as the Donnan or membrane potential that contributes to the apparent potential of the redox couple. The presence of the Donnan potential in redox polyelectrolyte systems was demonstrated for the first time by Anson [24, 122]. Considering only this contribution to peak position, we can vwite ... 

Standard, Formal, and Other Characteristic Potentials of Selected Electrode Reactions... 

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