Electron-transfer equilibria

Importantly, the purple color is completely restored upon recooling the solution. Thus, the thermal electron-transfer equilibrium depicted in equation (35) is completely reversible over multiple cooling/warming cycles. On the other hand, the isolation of the pure cation-radical salt in quantitative yield is readily achieved by in vacuo removal of the gaseous nitric oxide and precipitation of the MA+ BF4 salt with diethyl ether. This methodology has been employed for the isolation of a variety of organic cation radicals from aromatic, olefinic and heteroatom-centered donors.174 However, competitive donor/acceptor complexation complicates the isolation process in some cases.175... 

From the measured electron-transfer equilibrium constant and the known standard potential for the reference D /D- couple it has been possible to determine E for the PhO /PhO- couple. The method, however, is non-trivial and does not lend itself to the rapid determination of standard potentials for a large series of related compounds. 

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... 

The surface Fermi level, Cp, which depends on the surface state, is not the same as the interior Fermi level, ep, which is determined by the bulk impurity and its concentration. As electron transfer equilibrium is established, the two Fermi levels are equilibrated each other (ep = ep) and the band level bends downward or upward near the surface forming a space charge layer as shown in Fig. 2-31. 

In the case of nonpolaiizable interfaces, the inner and the outer potential differences, 4>a/b and v a/b, are determined by the equilibrium of chai transfer that occurs across the interface. Figure 4—8 shows the electron energy levels in two sohd metals A and B before and after they are brought into contact with each other. As a result of contact, electrons in a metal B of the hi er electron level (the lower work function ) move into a metal A of the lower electron level (the higher work fiuiction), and the Fermi levels of the two metals finally become equal to each other in the state of electron transfer equilibrium. The electrochemical... 

Next, we consider the interface M/S of a nonpolarizable electrode where electron or ion transfer is in equilibrium between a solid metal M and an aqueous solution S. Here, the interfadal potential is determined by the charge transfer equilibrium. As shown in Fig. 4-9, the electron transfer equilibrium equates the Fermi level, Enn) (= P (M)), of electrons in the metal with the Fermi level, erredox) (= P s)), of redox electrons in hydrated redox particles in the solution this gives rise to the inner and the outer potential differences, and respectively, as shown in Eqn. 4-10 ... 

The electrode potential. , in the electron transfer equilibrium does not depend on the nature of the electrode. However, determined by the electron transfer equilibrium (P (m> = P.(rsdox, s>), the potential across the electrode interface, = (He(M) - l eatEDox,s))/-e,does depend upon the nature of electrodes involved, because the chemical potential lt) of electron in the electrode differs with different electrode materials. 

For the hydrogen electrode, the interfadal potential between the electrode metal and the hydrogen gas film is determined by the electron transfer equilibrium and the interfacial potential between the hydrogen gas film and the aqueous... 

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 ... 

Figure 8-11 shows as a function of electron energy e the electron state density Dgdit) in semiconductor electrodes, and the electron state density Z e) in metal electrodes. Both Dsd.t) and AKe) are in the state of electron transfer equilibrium with the state density Z>bei)ox(c) of hydrated redox particles the Fermi level is equilibrated between the redox particles and the electrode. For metal electrodes the electron state density Ai(e) is high at the Fermi level, and most of the electron transfer current occurs at the Fermi level enio. For semiconductor electrodes the Fermi level enao is located in the band gap where no electron level is available for the electron transfer (I>sc(ef(so) = 0) and, hence, no electron transfer current can occur at the Fermi level erso. Electron transfer is allowed to occur only within the conduction and valence bands where the state density of electrons is high (Dsc(e) > 0). 

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.

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 order of reactivity of different alkyl-substituted benzenes is toluene > ethylbenzene > isopropylbenzene, which is opposite to the general reactivity expected from the C—H bond energies. This was explained in terms of an initiating electron transfer equilibrium between Co(OAc)3 and the arene as the rate-determining... 

One curious case of the effect of light on electron-transfer equilibrium involves the reduction of ,p-di(t-butyl)stilbcnc with potassium in DME. The reaction leads directly to a diamagnetic dianion a solution of this dianion remains ESR silent unless subjected to ultraviolet irradiation by a Hg/Xe lamp. The anion radical of a,(3-di(t-butyl)stilbene then formed from the dianion by the loss of an electron. The electron reverted within 5-10 min after ultraviolet irradiation was turned off, transforming the anion radical into the dianion (Gerson et al. 1996). This case deserves to be clarified. Maybe the light effect consists simply in singlet-triplet transformation of the dianion, with the formation of some more or less stable biradical state of the dianion, which possesses two unpaired electrons and can even be a paramagnetic one. 

This last reaction is not significant when the electron-transfer equilibrium is shifted to the right. Because acetic acid is weakly dissociated, the binding of acetate by an alien proton from ArMe+ leaves its own proton free to suppress the acid dissociation further. 

Because of the high concentration of isomer molecules (>0.1 mol-dm 3), the equilibrium depicted is established instantaneously. The ionization potential of trans-decalin is 0.02 eV lower than the ionization potential of d.v-dccalin (9.24 eV vs. 9.26 eV). Therefore, the electron-transfer equilibrium is shifted slightly to the left side. Thus, in terms of charge-transfer kinetics, the two ions behave as a single species. 

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