Electron transfer number estimates

From the slope of the E vs ln fk,o)> the electron-transfer number (n) and coefficient (a) can be obtained, and from the intercept the exchange current density (f) can be estimated if is known. 

The oxidation potential observed here is consistent with the thermodynamic potential of 2.20 0.03 V, theoretically estimated for this redox pair in the literature [12]. however, the number of electrons transferred (napp) estimated from the ratio of the respective cyclic voltammetric peak currents is much larger than 3.0, which is expected from the stoichiometry. The stoichiometry shown by reaction 20.16 indicates that it is a three electron process requiring water as a reactant. In other words, the reaction would not proceed in a rigorously dry nonaqueous medium, which has heen shown to be true in dry acetonitrile. Only after a certain amount of water is added, the reaction proceeds in a similar way as observed in water. Also, the calculation of napp from chronoamperometric data as a function of time shows that it is 3.0... 

The voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

The current estimate for the number of ATPs made per 2 electrons is actually about 2.5. This is because of the uncertainties in the number of protons pumped out at each electron transfer step. This affects ATP yields from glucose (30 instead of 36), so be sure you ask your professor which to use. 

The coordinate pertaining to solvent reorganization, z, is the same fictitious charge number as already considered in the Hush-Marcus model of outer-sphere electron transfer (Section 1.4.2), and so is the definition of 2q [equation (1.27)] and the difference between the Hush and Marcus estimation of this parameter. The coordinated describing the cleavage of the bond is the bond length, y, referred to its equilibrium value in the reactant, yRX. Db is the bond dissociation energy and the shape factor ft is defined as... 

The charge transfer to s and p conduction band states cannot be obtained with the same accuracy in first-order perturbation theory. From the band calculation we know that the number of cation projected p-electrons is about 0.56. The repulsive pressure from these electrons may be estimated... 

For dissociative electron transfer, an analogous thermochemical cycle can be derived (Scheme 2). In this case the standard potential includes a contribution from the bond fragmentation. Using equations (40) and (41) one can derive another useful expression for BDFEab-, equation (42). While direct electrochemical measurements on solutions may provide b. b, for example, of phenoxides and thiophenoxides (Section 4), the corresponding values for alkoxyl radicals are not as easily determined. Consequently, these values must be determined from a more circuitous thermochemical cycle (Scheme 3), using equation (43). The values of E°h+/h io a number of common solvents are tabulated elsewhere. Values of pKa in organic solvents are available from different sources. " A comparison of some estimated E° values with those determined by convolution voltammetry can be found in Section 3. 

A photoinduced electron relay system at solid-liquid interface is constructed also by utilizing polymer pendant Ru(bpy)2 +. The irradiation of a mixture of EDTA and water-insoluble polymer complex (Ru(PSt-bpy)(bpy) +, prepared by Eq. (15)) deposited as solid phase in methanol containing MV2+ induced MV 7 formation in the liquid phase 9). The rate of MV formation was 4 pM min-1. As shown in Fig. 14, photoinduced electron transfer occurs from EDTA in the solid to MV2+ in the liquid via Ru(bpy)2 +. The protons and Pt catalyst in the liquid phase brought about H2 evolution. One hour s irradiation of the system gave 9.32 pi H2 after standing 12 h and the turnover number of the Ru complex was 7.6 under this condition. The apparent rate constant of the electron transfer from Ru(bpy)2+ in the solid phase to MV2 + in the liquid was estimated to be higher than that of the entire solution system. The photochemical reduction and oxidation products, i.e., H2 and EDTAox were thus formed separately in different phases. Photoinduced electron relay did not occur in the system where a film of polymer pendant Ru complex separates two aqueous phases of EDTA and MV2 9) (see Fig. 15c). 

It is interesting to estimate the maximum number of atoms which may be chemisorbed by an electron transfer process, in terms of the fraction of surface sites covered, 0max, and of the relative concentration of free electrons to the total number of atomic sites, n, on a semiconductor. Following the treatment of Weisz (24) we obtain, with 4.6 A as a typical size of a surface site ... 

Cyclic voltammetry can (i) determine the electrochemical reversibility of the primary oxidation (or reduction) step (ii) allow the formal potential, E°, of the reversible process to be estimated (iii) provide information on the number of electrons, n, involved in the primary process and (iv) allow the rate constant for the decomposition of the M"+ species to be measured. Additional information can often be obtained if intermediates or products derived from M"+ are themselves electroactive, since peaks associated with their formation may be apparent in the cyclic voltam-mogram. The idealized behaviour illustrated by Scheme 1 is a relatively simple process more complicated processes such as those which involve further electron transfer following the chemical step, pre-equilibria, adsorption of reactants or products on the electrode surface, or the attack of an electrogenerated product on the starting material, are also amenable to analysis. 

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... 

This immediately leads to a question How small must these excursions be in order for the predictions to be valid Theoretically, the answer is zero millivolts, a clever but uninteresting answer. Practically the answer usually found in the literature is between 8/n and 12/n mV where n is the number of electrons transferred in the electrochemical reaction. These numbers are arrived at by estimating what kind of deviation from theoretical behavior can be detected experimentally. For purposes of this discussion we will use 10 mV. At this point it is useful to remember that the exponential terms are of the form anF(E - E°)RT, where T is the absolute temperature and a is either a or 1 - a. The 10/n mV figure is based on an a of 0.5 at 25 °C. Any change in these parameters from their nominal value would influence this limit (particularly in the case of low-temperature electrochemistry in nonaqueous solvents). This leads to the obvious next question What happens if you exceed this limit The answer is that the response begins to deviate noticeably from the ideal, theoretical model. How great the deviation is depends upon how far one exceeds... 

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