Electron reactions, equilibrium

Quinhydrone electrode. If the equimolar compound formed by (benzo)quin-one (Q) and (benzo)hydroquinone (QH2), the so-called quinhydrone (Q2H2), is dissolved in water, it dissociates to the extent of about 90% into the two components. In conjunction with H+ ions and electrons an equilibrium is established on the basis of a completely reversible redox reaction ... 

We shall be dealing throughout this chapter with many situations in which various atomic solutes in a solid solution can react to form a variety of complexes, which in turn can redissociate into their atomic constituents. Some of these may exist in different charge states, which can interconvert by emission or absorption of electrons or holes. When the various atomic or electronic reactions have come to equilibrium, the concentrations of the various species involved will have to obey certain equilibrium relations. In this section, we shall review these in a language suitable for analysis of the various experiments to be discussed in Section III. 

The oxidative conversions of the aromatic donors hexamethylbenzene, anthracene, dianthracene, bicumene and methoxytoluene by the nitrosonium cation, as described above, are rather unequivocal examples in which the establishment of an electron-transfer equilibrium is a clear prerequisite for the further (follow-up) reactions. There are other donors, including... 

Fig. 4-20. Reaction cycle and energy levels of metal ion and electron in equilibrium of metal ion transfer. = equilibrium electrode poten-...

Fig. 4-22. Electron energy levels of the hydrogen electrode in electron-and-ion transfer equilibrium Hjiju) = gaseous hydrogen molecule on electrode eaj>/H2, u) = gaseous redox electron in equilibrium with the hydrogen reaction, + 2e(H-/H p,) Hp, =...

Since the electron transfer of the interfacial redox reaction, + cm = H.a> on electrodes takes place between the iimer Helmholtz plane (adsorption plane at distance d ) and the electrode metal, the ratio of adsorption coverages 0h,j/ in electron transfer equilibrium (hence, the charge transfer coefficient, 6z) is given in Eqn. 5-58 as a function of the potential vid /diOMn across the inner Helmholtz layer ... 

Fig. 8-16. Electron state density for a redox electron transfer reaction of h3rdrated redox particles at semiconductor electrodes (a) in the state of band edge level pinning and (b) in the state of Fermi level pinning dashed curve = band edge levels in reaction equilibrium solid curve = band edge levels in anodic polarization e p,sq = Fermi level of electrode in anodic polarization e v and c c = band edge levels in anodic polarization.

Figures 8-16 and 8-17 show the state density ZXe) and the exchange reaction current io( ) as functions of electron energy level in two different cases of the transfer reaction of redox electrons in equilibrium. In one case in which the Fermi level of redox electrons cnxEDax) is close to the conduction band edge (Fig. 8-16), the conduction band mechanism predominates over the valence band mechanism in reaction equilibrium because the Fermi level of electrode ensa (= nREDOK)) at the interface, which is also dose to the conduction band edge, generates a higher concentration of interfadal electrons in the conduction band than interfadal holes in the valence band. In the other case in which the Fermi level of redox electrons is dose to the valence band edge (Fig. 8-17), the valence band mechanism predominates over the conduction band mechanism because the valence band holes cue much more concentrated than the conduction band electrons at the electrode interface.

Fig. S-19. Surface states participating in reaction equilibrium of redox electron transfer at a semiconductor electrode with a wide band gap t = smiace state level i c = exchange current via surface states.

Fig. 8-39. Electron state density in an electrode metal, Du, a semiconductor film, Dt, hydrated redox particles, Dredox, and exchange reaction current of redox electrons, t., in electron transfer equilibrium M = exchange current at a bare metal electrode, M/F= exchange current at a thin-film-covered metal electrode.

At equilibrium, log K = pe° for this one-electron transfer. Since pe° for this one-electron reaction is -1-20.75, Eq. 7.44 becomes... 

Solubility equihbrium is the final state to be reached by a chemical and the subsurface aqueous phase under specific environmental conditions. Equihbrium provides a valuable reference point for characterizing chemical reactions. Equilibrium constants can be expressed on a concentration basis (/ ), on an activity basis (K ), or as mixed constants (K" ) in which all parameters are given in terms of concentration, except for H, OH", and e" (electron) which are given as activities. 

For each reduction half-reaction, the Nernst equation is written with the proper E°, and the relationship is solved for E as a function of pH and the concentrations of the soluble species. For each reaction which does not involve electrons, the equilibrium expression is written with the pertinent K and is solved for pH as a function of the concentrations of the soluble species. 

Electrons in nonpolar liquids are either in the conduction band, trapped in a cavity in the liquid, or in special cases form solvent anions. The energy of the bottom of the conduction band is termed Vq. Vq has been measured for many liquids and its dependence on temperature and pressure has also been measured. New techniques have provided quite accurate values of Vq for the liquid rare gases. The energies of the trapped state have also been derived for several liquids from studies of equilibrium electron reactions. A characteristic of the trapped electron is its broad absorption spectrum in the infrared. 

Electron attachment rates have been measured for numerous solutes. Many of these studies were limited to three solvents cyclohexane, 2,2,4-trimethylpentane, and tetrame-thylsilane (TMS), and those rates are discussed here. What to expect in other liquids can be inferred from these results. Considerable insight has been gained into certain reactions. Equilibrium reactions of electrons are particularly interesting since they provide information not only on energy levels, as mentioned above, but also on the partial molar volume of trapped electrons. This has led to a better understanding of the mechanism of electron transport. 

Consider an overall electrodic reaction that takes place in n steps (Fig. 7.69). I et it be assumed, for convenience of exposition, that each step is a charge-transfer reaction with an electron acceptor receiving an electron. To simplify the treatment, let it also be assumed that the n individual electronation reactions are only slightly off equilibrium and that therefore, for each reaction, one can use the linear current-den-sity-overpotential law Hq. 7.25]. The rate of any one step in such a case is proportional to its overpotential t y62 ... 

This expression, known as Sand s equation, gives the variation of the interfacial concentration of M"+ with time after application of a constant current density. But one seeks also to know the time variation of the potential difference across the interface at which the electronation reaction M"+ + ne — M is occurring. To obtain this information, one recalls that the charge-transfer reaction across the interface is assumed in the present treatment to be virtually in equilibrium and therefore the Nenist equation (7.177) can be used to relate the potential difference to the concentration at the interface. That is, by substituting (7.181) in (7.177),... 

Experiment shows that when the transport of reactants cannot keep pace with the charge-transfer reaction, the potential d observed at the current density i is not equal to the zero-current, or equilibrium potential difference J< > =0 = J< >e. If an electronation reaction is considered,... 

Since in cathodic reactions is always smaller than c°, the concentration polarization has a negative sign, which adds to the activation overpotential in causing the electrode to depart from the equilibrium potential in the negative direction for an electronation reaction. 

At the outset, consider a self-driving, or energy-producing, cell with two interfaces 1 and 2, and let the equilibrium electrode potentials on the hydrogen scale be Ee j and Ee 2. Suppose Ee t is more positive than Ee Then, if an external load is provided, electrode 2 will taxi to be an electron sink for a net deelectronation reaction and electrode 1 will tend to be an electron source for a net electronation reaction. 

Similarly, if one assumes that the electronation reaction at interface 1 is far from equilibrium, then since by convention a net electronation current is negative, one has105... 

In addition, electrode reactions are frequently characterized by an irreversible, i.e., slow, electron transfer. Therefore, overpotentials have to be applied in preparative-scale electrolyses to a smaller or larger extent. This means not only a higher energy consumption but also a loss in selectivity as other functions within the molecule can already be attacked. In the case of indirect electrolyses, no overpotentials are encountered as long as reversible redox systems are used as mediators. It is very exciting that not only overpotentials can be eliminated but frequently redox catalysts can be applied with potentials which are 600 mV or in some cases even up to 1 Volt lower than the electrode potentials of the substrates. These so-called redox reactions opposite to the standard potential gradient can take place in two different ways. In the first place, a thermodynamically unfavorable electron-transfer equilibrium (Eq. (3)) may be followed by a fast and irreversible step (Eq. (4)) which will shift the electron-transfer equilibrium to the product side. In this case the reaction rate (Eq. (5)) is not only controlled by the equilibrium constant K, i.e., by the standard potential difference be-... 

The change in transition states with electrode potential is observed, for instance, in the complex 4-electron reaction of oxygen electroreduction on several electrode materials, the mechanism of which may also change with pH. At low negative overpotentials, the rds is reaction (124) with reaction (123) in pre-equilibrium. 

The breakdown at a pH higher than 10 of the parallelism between the Us(redox) and the redox potential of the redox couple in solution can be explained by assuming that the rate of the dissolution reaction, caused by the attack of H2O or OH- on the surface trapped hole, is so high in this pH range that the electron exchange equilibrium at the interface is no longer achieved. 

Platinum in the hydrogen electrode acts as a source or sink of electrons but does not take part in the reaction. It provides an electrical contact between H2 and the solution containing H+ ions and serves as a catalyst for the electrode reaction. Equilibrium between the hydrogen gas and H+ ions in this reaction is established slowly when a bright Pt (or Pd) is used. Equilibrium in the hydrogen electrode reaction is... 

---