Half wave irreversible process

As ksh in this instance is very small, then according to the Butler-Volmer formulation (eqn. 3.5) the reaction rate of the forward reaction, K — 8,he "F(E 0)/flr, even at E = E°, is also very low. Hence Etppl. must be appreciably more negative to reach the half-wave situation than for a reversible electrode process. Therefore, in the case of irreversibility, the polarographic curve is not only shifted to a more negative potential, but also the value of its slope is considerably less than in the case of reversibility (see Fig. 3.21). In... 

Half-wave potentials for each of the electron transfer steps shown in Scheme V are listed in Table II. The first oxidations of (0EP)Ge(C6H5)Cl and (0EP)Ge(C H5)0H are irreversible and occur at Ep = 1.00 V for X = 0H. The second oxidations of these complexes are reversible and both occur at Ei/2 = 1.40 V. These second oxidation processes occur at identical to the Ei/2 values for oxidation of (0EP)Ge(C6H5)C10i, and this was presented as strong evidence for an oxidation of Cl on (OEP)Ge(CsHs)Cl and OH on (0EP)Ge(C6Hs)0H(35). 

For an irreversible reduction the half-wave potential is determined not only by the standard electrode potential but also by the polarographic overvoltage. For a simple electrode process the metal ion-solvent interaction is mainly responsible for the polarographic overvoltage and hence E[ j of such irreversible reductions may also be considered as a function of the solvation 119f... 

In acid solution the half-wave potentials for these processes are pH dependent. The overall reaction involves two electrons and is irreversible. Bond cleavage is believed to lead to the enol as shown in Scheme 5.4. Where, as with acetophenone, the ketone product is electroactive at more negative potentials, the wave height for ketone reduction is less than expected and is limited by the rate of enol to ketone tautomerism. This is because the enol is not electroactive. 

Azoxybenzene is reducible under polarographic conditions. The final product is hydrazobenzene formed in an irreversible process for which the half-wave potential [105] varies with pH as illustrated in Fig. 11.3. The half-wave potential is close to that of the nitrobenzene. Azobenzene, which is an intermediate in the process, is... 

As is apparent from Eqs (5.12) and (5.14), the half-wave potentials for irreversible processes are independent of the concentrations of Ox and Red, but are influenced by the values of transfer coefficient (a) and reaction rate constants (kf0 and kpo) Figure 5.7 illustrates the influences of such parameters. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Figure 9.1 illustrates the electrochemical reduction of 02 at platinum electrodes in aqueous media (1.0 M NaC104). The top curve represents the cyclic voltammogram (0.1 V s-1) for 02 at 1 atm ( 1 mM), and the lower curve is the voltammogram with a rotated-disk electrode (900 rpm, 0.5 V min-1). Both processes are totally irreversible with two-electron stoichiometries and half-wave potentials (EU2) that are independent of pH. The mean of the Em values for the forward and reverse scans of the rotated-disk voltammograms for 02 is 0.0 V versus NHE. If the experiment is repeated in media at pH 12, the mean Em value also occurs at 0.0 V. 

Fig. 27 Voltammogram obtained for an irreversible one-electron transfer at a hydrodynamic electrode (note a reversible one-electron process is also illustrated with equal half-wave potential for comparison).

Both wave heights and half-wave potentials are dependent on pH in reduction of the arylarsonic acids, and it was found that a plot of 1,2 vs pH in the pH range 1.0-2.0 was linear for all of the derivatives except the nitro-substituted one with slopes equal to the slopes of the log [(i i — OA] vs E plots. This behaviour corresponds to the involvement of one proton prior to the irreversible electron transfer step . The initial step, equations 16 and 19, in the reduction process therefore includes the microscopic steps described by equations 23 and 24. 

With only few exceptions, all of the electrochemical oxidation studies have been carried out in MeCN containing varying amounts of water. The compounds of the structure R R R M, R, R, R = aryl, alkyl, M = As, Sb (Bi), arc in most cases (for exceptions see below) oxidized in a chemically irreversible process in MeCN. Half-wave potentials for the chemically irreversible oxidations of R R R M are given in Table 14. 

Current/Voltage Relationships for Irreversible Reactions Many voltammetric electrode processes, particularly those associated with organic systems, are partially or totally irreversible, which leads to drawn-out and less well defined waves. The quantitative description of such waves requires an additional term (involving the activation energy of the reaction) in Equation 23-11 to account for the kinetics of the electrode process. Although half-wave potentials for irreversible reactions ordinarily show some dependence on concentration, diffusion currents are usually still linearly related to concentration many irreversible processes can, therefore, be adapted to quantitative analysis. 

Finally, it must be noted that standard electrode potential and half-wave potential are nearly identical only for reversible reduction processes 32). This is true for the alkali metal ions, T1+ and in most cases for Zn2+ and G12+. Similar trends are observed for both reversible and irreversible reductions (Figs. 3—6) and this may justify the conclusion that partial irreversibihty resiilts in most cases in a shift of curves along the E1/2 axis without any significant change in the general pattern. 

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