Thermodynamics formal potential

These effects will give rise to different molecular environments that could lead to surface inhomogeneities, i.e., different formal potentials (thermodynamic dispersion) or different rate constants (kinetic dispersion). 

Cr-Al, Mn-Al, and Ti-Al alloys can be obtained from acidic melt solutions containing Cr(II), Mn(II), or Ti(II), respectively, only if the deposition potential is held very close to or slightly negative of the thermodynamic potential for the electrodeposition of aluminum, i.e., 0 V. From these observations it can be concluded that the formal potentials of the Cr(II)/Cr, Mn(II)/Mn, and Ti(II)/Ti couples may be equal to or less than E0 for the A1(III)/A1 couple. Unlike the Ag-Al, Co-Al, Cu-Al, Fe-Al, and Ni-Al alloys discussed above, bulk electrodeposits of Cr-Al, Mn-Al, and Ti-Al that contain substantial amounts of A1 can often be prepared because problems associated with the thermodynamic instability of these alloys in the plating solution are absent. The details of each of the alloy systems are discussed below. 

The formal potential is the quantity determined from the analysis of a volta-mmogram, but the true thermodynamic quantity (the standard potential) can be derived by obtaining 0/(R/R ) for different bulk concentrations (c) and extrapolating to c = 0 (unit activity coefficients). The procedure is, however, seldom adopted in practice, (R/R-) is identified with the standard potential. The lower the concentration of the electroactive species, the better the assumption. 

In this scheme, H, G and HG in normal or subscript positions represent the host, guest and complex species respectively subscripts ox and red indicate that the corresponding symbols or parameters refer to molecules in oxidized and reduced states E° is the formal potential of the electron transfer reaction and K is the stability constant. According to thermodynamics, there are four relationships linking the concentrations of the four molecules at the four corners of the square. These are two Nernst equations for the upper (2) and lower (3) electron transfer reactions,... 

With respect to the formal potential of the surface electrode reaction, Figs. 2.45c and 2.46 show that the split peaks are symmetrically located around the formal potential, which enables precise determination of this important thermodynamic parameter. 

It is also common to measure by voltammetry the thermodynamic properties of purely chemical reactions that are in some way coupled to the electron transfer step. Examples include the determination of solubility products, acid dissociation constants, and metal-ligand complex formation constants for cases in which precipitation, proton transfer, and complexation reactions affect the measured formal potential. Also in these instances, studies at variable temperature will afford the thermodynamic parameters of these coupled chemical reactions. 

An electron transfer reaction, Equation 6.6, is characterised thermodynamically by the standard potential, °, i.e. the value of the potential at which the activities of the oxidised form (O) and the reduced form (R) of the redox couple are equal. Thus, the second term in the Nernst equation, Equation 6.7, vanishes. Here and throughout this chapter n is the number of electrons (for organic compounds, typically, n = 1), II is the gas constant, T is the absolute temperature and F is the Faraday constant. Parentheses, ( ), are used for activities and brackets, [ ], for concentrations /Q and /R are the activity coefficients of O and R, respectively. However, what may be measured directly is the formal potential E° defined in Equation 6.8, and it follows that the relationship between E° and E° is given by Equation 6.9. Usually, it maybe assumed that the activity coefficients are unity in dilute solution and, therefore, that E° = E°. 

The characterization of a non-reversible electrode process is logically more complex than that of a reversible one since it implies knowledge of thermodynamic (formal potential) and kinetic (heterogeneous rate constant and charge transfer coefficient) parameters of the process under study. 

Even in the simplest situation for which a = a2 = 0.5, the global behavior of the response depends upon three parameters, the difference between the formal potentials AEf, and the rate constants of both steps k(j and k. Thus, the observed current-potential curves are the result of the interaction of thermodynamic and kinetic effects so the appearance of two or one waves would not be due solely to thermodynamic stability or instability of the intermediate species but also to a kinetic stabilization or destabilization of the same [4, 31]. This can be seen in Fig. 3.19 in which the current-potential curves of an EE process with AE = 0 mV taking place at a planar electrode with a reversible first step... 

The electrochemical characterization of multi-electron electrochemical reactions involves the determination of the formal potentials of the different steps, as these indicate the thermodynamic stability of the different oxidation states. For this purpose, subtractive multipulse techniques are very valuable since they combine the advantages of differential pulse techniques and scanning voltammetric ones [6, 19, 45-52]. All these techniques lead to peak-shaped voltammograms, even under steady-state conditions. 

From a practical standpoint it is often useful to have the observed potential in the medium of measurement for the condition of equal concentrations of the oxidized and reduced species of a half reaction. Such potentials are known as formal potentials, E°, rather than standard potentials, and are not purely thermodynamic quantities. The term formal potential comes from the tradition of having the supporting electrolyte at a one formal concentration. However, other stated solution conditions are also included in many listings. Thus the indicated potential is what one would expect at the half-equivalence point under actual titration conditions. In other words, activity corrections have not been made. Table 2.3 summarizes a number of formal potentials for commonly encountered half-reactions. 

The formal potential, E0/, contains useful information about the ease of oxidation of the redox centers within the supramolecular assembly. For example, a shift in E0/ towards more positive potentials upon surface confinement indicates that oxidation is thermodynamically more difficult, thus suggesting a lower electron density on the redox center. Typically, for redox centers located close to the film/solution interface, e.g. on the external surface of a monolayer, the E0 is within 100 mV of that found for the same molecule in solution. This observation is consistent with the local solvation and dielectric constant being similar to that found for the reactant freely diffusing in solution. The formal potential can shift markedly as the redox center is incorporated within a thicker layer. For example, E0/ shifts in a positive potential direction when buried within the hydrocarbon domain of a alkane thiol self-assembled monolayer (SAM). The direction of the shift is consistent with destabilization of the more highly charged oxidation state. 

Conditional (apparent) equilibrium constants - Equilibrium constants that are determined for experimental conditions that deviate from the standard conditions used by convention in - thermodynamics. Frequently, the conditional equilibrium conditions refer to - concentrations, and not to - activities, and in many cases they also refer to overall concentrations of certain species. Thus, the formal potential, i.e., the conditional equilibrium constant of an electrochemical equilibrium, of iron(II)/iron(III) may refer to the ratio of the overall concentrations of the two redox forms. In the case of complex equilibria, the conditional - stability constant of a metal ion Mm+ with a ligand L" refers to the overall concentration of all complex species of Mm+ other than Conditional equilibrium... 

Formal potentials can be defined on different levels of conditions Thus the formal potential of the -> quinhydrone electrode may be defined (I) as including (a) the standard potential of the hydroquinone di-anion/quinone system, (b) the two acidity constants of the hydroquinone, and (c) the activity coefficients of the hydroquinone dianion and quinone, or, (II), it may also include (c) the pH value. In the latter case, for each pH value there is one formal potential, whereas in the first case one has one formal potential for all pH values, and an equation describing the dependence of the electrode potential as a function of that formal potential and the individual pH values. Formal potentials are strictly thermodynamic quantities, and no kinetic effects (e.g., by electrochemical -> irreversibility) are considered. 

The water electrolysis rest potential is determined from extrapolation to ideal conditions. Variations of the concentration, c, and pressure, p, from ideality are respectively expressed by the activity (or fugacity for a gas), as a = yc (or yp for a gas), with the ideal state defined at 1 atmosphere for a pure liquid (or solid), and extrapolated from p = 0 or for a gas or infinite dilution for a dissolved species. The formal potential, measured under real conditions of c and p can deviate significantly from the (ideal thermodynamic) rest potential, as for example the activity of water, aw, at, or near, ambient conditions generally ranges from approximately 1 for dilute solutions to less than 0.1 for concentrated alkaline and acidic electrolytes.91"93 The potential for the dissociation of water decreases from 1.229 V at 25 °C in the liquid phase to 1.167 V at 100 °C in the gas phase. Above the boiling the point, pressure is used to express the variation of water activity. The variation of the electrochemical potential for water in the liquid and gas phases are given by ... 

Several reports have addressed how interfacial electron transfer rate constants vary with thermodynamic driving force. The driving force is tuned by manipulating the conduction band edge through adsorption of specific cations, utilizing different semiconductors, or by keeping the semiconductor constant with a series of sensitizers with known formal potentials. A difficulty in these studies is that the position... 

A frequent complication is that several simultaneous equilibria must be considered (Section 3-1). Our objective is to simplify mathematical operations by suitable approximations, without loss of chemical precision. An experienced chemist with sound chemical instinct usually can handle several solution equilibria correctly. Frequently, the greatest uncertainty in equilibrium calculations is imposed not so much by the necessity to approximate as by the existence of equilibria that are unsuspected or for which quantitative data for equilibrium constants are not available. Many calculations can be based on concentrations rather than activities, a procedure justifiable on the practical grounds that values of equilibrium constants are obtained by determining equilibrium concentrations at finite ionic strengths and that extrapolated values at zero ionic strength are unavailable. Often the thermodynamic values based on activities may be less useful than the practical values determined under conditions comparable to those under which the values are used. Similarly, thermodynamically significant standard electrode potentials may be of less immediate value than formal potentials measured under actual conditions. 

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. 

The mentioned thermodynamic prerequisite that the formal potential of the substrate redox system must be more positive than the formal potential of the catalyst redox system means that, in principle, reduction of S is easier compared to Cat , but that kinetic constraints essentially hinder this process at potentials where the catalyst is oxidized. Then, the direct reduction of S does not proceed electrochemically at potentials where Cat is reduced (or maybe even at no accessible potential at all) but only via homogeneons redox reaction (Equation (3.2)) with CaC". In this context, the regeneration of the catalyst leads to much steeper concentration profiles of the catalyst in the diffusion reaction layer that is, to a steeper concentration gradient that (see Chapter 1) means larger current. 

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