Number of transferred electrons

The equilibration proceeds by electron transfer between the semiconductor and the electrolyte. The solution levels are almost intact ( REdox — redox)> since the number of transferred electrons is negligible relative to the number of the redox system molecules (cox and cred). On the other hand, the energy levels of the semiconductor phase may shift considerably. The region close to the interface is depleted of majority charge carriers and the energy bands are bent upwards or downwards as depicted in Fig. 5.60b. 

In addition, the current efficiency ( current yield ) is typical for an electrolysis process, the fraction of the electrical cell current - or (integrated over the time) the fraction of the transferred charge - which is used to form the product. The theoretical charge transfer for one mol product is given by the Faraday constant F, the charge of one mol electrons, F = 96 485 As/mol = 26, 8 Ah/mol, multiplied by the number of transferred electrons. 

This implies that the electrolyte is free of electric leaks and the electrodes are free of any parallel reactions. The fuel (2 for H2) determines the number of transferred electrons nel. The Faraday constant F is a constant value and the fuel inlet flow fi is the only variable influencing the relation between fuel utilisation Uf and current I. Fuel utilisation Uf and current I deliver the same expression if the fuel flow is kept a constant. 

The ratios given in Eq. (4.66) are only dependent on the electrode shape and size but not on parameters related to the electrode reaction, like the number of transferred electrons, the initial concentration of oxidized species, or the diffusion coefficient D. For fixed time and size, the values of f or Qf2 are characteristic for a simple charge transfer (see Fig. 4.4 for the plot of Qf2 calculated at time (ti + T2) for planar, spherical, and disc electrodes) and, as a consequence, deviations from this value are indicative of the presence of lateral processes (chemical instabilities, adsorption, non-idealities, etc.) [4, 32]. Additionally, for nonplanar electrodes, these values allow to the estimation of the electrode radius when simple electrode processes are considered. 

The valence state of ions listed in Table4.2.2 are obtained from the oxidation states of the atoms in the compounds. They are only formal values and they do not indicate the number of transferred electrons. In other words, the bonding type between the atoms is not considered. These radii are effective ionic radii and they can be used for rough estimation of the packing of ions in crystals and other calculations. 

Coulometers, like the balance, are basic instruments for absolute analysis and they are still used as the most reliable and precise instruments for the analysis of absolute standards. Coulometers are frequently used in elucidating electrochemical reactions because they allow determining the number of transferred electrons when the molar amount of electrolyzed compound is known (-> Faraday s law). When the charge is measured as a function of time, the technique is called chrono-coulometry. See also coulometric titration. 

With AG" = -nFE" (n number of transferred electrons for both half-reactions, F is the - Faraday constant) follows for the relation of the standard - potentials ... 

The number of electrons transferred, and the number of electrons transferred per metal atom, ejM, were estimated as a function of the mean diameter of the metal crystallites, d, employing two models pertaining to infinite and finite interfaces between the metal and the support [88]. The parameters employed correspond to metal with work functions of 5.0 or 6.0 eV (the corresponding contact potential differences, Vq, being 0.9 and 1.9 V, respectively), in contact with Ti02 doped with a donor impurity (W, for example) with donor concentration of 2 X 10 cm. The results obtained are shown in Figure 3, in which the number of transferred electrons, n, and the number of electrons transferred per metal atom, ejM, are plotted as a function of d [88]. The number of transferred electrons ranges from about 8000 for a 40-nm metal particle to approximately 60 electrons for a... 

Fig. 9.29 Photocurrent yield vs. wavelength at porous Ti02 electrodes, with PbS particles of different sizes adsorbed on the electrode surface, in 0.1 M Na2S solutions. Photocurrent yield defined as number of transferred electrons per incident photon. (After ref. [7])...

EPR spectrum. Thus, detection of the number of transferable electrons was possible (Fig. 14). Aqueous dithionite effectively reduced erythrocuprein. Plotting the height of the g signal versus dithionite concentra-... 

The fullerene skeleton can not only undergo nucleophilic additions, but it also enters into radical reactions very easily. The fullerene acts as a radical sponge in these reactions, and either dia- or paramagnetic derivatives are obtained depending on the number of transferred electrons. 

A major factor in the uncertainties of the redox status of an aqueous system is the time dependency of redox reactions. The fact that the rates of electron transfer are relatively slow and that the electrochemical response of an electrode is also time dependent makes the determination of pE or Ej undependable and of little general value as a single master variable. We wish to define a conservative quantity that will incorporate a comprehensive chemical analysis of the redox couples of an aqueous system into a single descriptive parameter for that redox system. This capacity factor is called the oxidative capacity (OXC) of a redox system and represents the total number of transferable electrons. This concept allows us to classify aqueous redox systems by a conservative quantity as is done with alkalinity and acidity measurements. This parameter will also allow investigators to better characterize the redox status of an aqueous system than is possible with a knowledge of the redox potential alone. 

AG° denotes the change in standard Gibb s energy while z denotes the number of transferred electrons for the half cell reaction. The Faraday constant is denoted F. AG is often used to determine whether or not a rewaction runs spontaneously. The total value of AG for a electrochemical reaction is determined as the sum of AG for the two half cell reactions. If AG is less than zero the reaction runs spontaneously. If AG is larger than zero energy must be added to the system in order to let the reaction take place. This we will look into in the following example ... 

In electrodeposition, an ion is transferred from solution to the surface of an electrode and retained as a solid. Typically, a metallic ion is reduced and deposited as the metal at the cathode. Deposition of oxy-ions at the cathode and oxidation at the anode also are employed. The rate of deposition depends on the applied voltage and factors such as the rate of stirring, volume and nature of the solution, and the material and area of the electrode. Little deposition occurs until a critical voltage is reached, after which the rate of deposition increases rapidly with increasing voltage. Consider the half reaction in which n is the number of transferred electrons per atom of A ... 

Here, n is the number of transferred electrons ( > 0), S the surface area, the cathodic rate constant, a the cathodic charge-transfer coefficient, and Zj the charge valence of the reactant. This expression should be modified to take into account the adsorption energies of the reactant and the product if the ET takes place for a species inside the compact layer [11]. The value of the coordinate, z, which determines the lr potential is a priori unknown. In most studies it was postulated that the ET took place at the species located at the outer Helmholtz plane (the boundary between the compact and diffuse layers). Then, ijf coincides with the potential drop within the diffuse layer, (poc, Eq. (17). 

II.1.5 Determination of Redox State and Number of Transferred Electrons... 

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