Standard gaseous electron

Fig. 2-35. Localized electron levels of gaseous redox particles, Fe /Fe I = ionization energy of Fe A = electron affinity of Fe (STO) = standard gaseous electrons tsro = standard gaseous electron level (reference zero level).

Figure 2-36 shows the occupied electron level (donor level) of reductant Fe ,, ) and the vacant electron level (acceptor level) of oxidant FeJ,) referred to the standard gaseous electron level at the outer potential of aqueous solution. 

The electron level in hydrated redox particles consists of the energy AGmt (< 0) required for the standard gaseous electron to combine with or to be released from the gaseous redox partides and the energy AG ,(>0) required for the redox particles to form their hydrate structures. Since the donor and acceptor levels of gaseous redox particles Pefi j/Fe, equal each other, the difference between the... 

Fig. 2-36. Electron energy levels in hydrated oxidant Fe and reduc-tantFe AG = energy to organize hydrate structures dGj t = energy required for dehydrated redox ions to donate or accept gaseous electrons ep.2> o = most probable electron donor level of Fe Spe +.A = most probable electron acceptor level of Fe Hj05,2.,p,j = hydrated structures cgn) = standard gaseous electron level (s 0).

The redox reaction of hydrated particles referred to the standard gaseous electron may be represented by the following four steps, as shown for a redox reaction of hydrated iron ions in Fig. 2-37 ... 

Taking the standard gaseous electron e(sn ) as the reference electron at the zero level, we write the reaction in Eqn. 2-56 ... 

In the foregoing reaction steps, , nhe) is the real potential of an equilibrium redox electron of the reaction of normal hydrogen electrode (NHE), which is the energy required for transferring a standard gaseous electron Ccstd) at the outer... 

Fig. 2-44. Energy balance and electron energy levels in the normal hydrogen electrode reaction Ch- = standard gaseous proton level Estd = standard gaseous electron level.

Fig. 4-11. Energy diagram for electron transfer from a standard gaseous electron across a solution/vacuum interface, through an electrolyte solution, and across a metal/solution interface into a metal electrode = real potential of electrons e,s) in electrolyte...

Fig. 4-12. Electron energy levels in electron transfer from a standard gaseous electron throu an electrol3rte solution into an electrode a,(M/sn)) = real potential of electron in electrode E = electrode potential (absolute electrode potential).

The electrode potential in the equilibrium of redox electron transfer may also be defined by the free enthalpy change in the reaction of the hydrated redox particles with the standard gaseous electron eisro) as shown in Eqn. 4—20 ... 

It, thus, follows that the electrode potential in equilibrium of metal ion transfer is given by the free enthalpy for the formation of a solid metal from both hydrated metal ions and standard gaseous electrons as shown in Eqn. 4—25 ... 

In electrochemistry, the electrode potential is defined by the electronic energy level in a solid electrode referred to the energy level of the standard gaseous electron just outside the surface of an electrolyte (aqueous solution) in which the electrode is immersed [6] ... 

Pm(M) is the energy required to form the solid metal from the standard gaseous metal ion and the standard gaseous electrons xM(m> consists of the sublimation energy of the metal and the ionization energy of the metal atom... 

In electrochemistry, we deal with the energy level of charged particles such as electrons and ions in condensed phases. The electrochemical potential, Pi,of a charged particle i in a condensed phase is defined by the differential work done for the charged particle to transfer from the standard reference level (e.g. the standard gaseous state) at infinity = 0) to the interior of the condensed phase. The electrochemical potential may be conventionally divided into two terms the chemical potential Pi and the electrostatic energy Zi e as shown in Eqn. 1-21 ... 

The redox reaction is illustrated with gaseous iron ions Fef , - Fe > + Cjsto) ", where eism) is the gaseous electron in the standard state. The occupied... 

The metal ion sublimation of Eqn. S—4 is also equivalent to the process that consists of the sublimation of a siuface metal atom M. followed by both the ionization of a gaseous metal atom Motd) and the injection of a gaseous electron e(STD) into the metal phase to produce a standard gaseous metal ion leaving an electron eu in the solid metal as shown in Eqn. 3-5 and in Fig. 3-3 (h) ... 

The unitary level of the surface ion referred to the standard gaseous ion S sTD) at the outer potential of the semiconductor is represented by the unitary real potential, Ug. (= - 7s). This unitary real potential is equivalent to the sum of the standard free enthalpy AG of sublimation of the semiconductor, the ionization energy Is of the gaseous atom S, and the electron energy sy at the upper edge level of the valence band as shown in Eqn. 3-14 ... 

Fig. 4-10. Electron energy levels in (a) an isolated solid metal and in (b) a metal electrode immersed in an electrolyte solution M = metal S = electrolyte solution e(STD) = gaseous electrons in the standard state e

Figures 4-11 and 4-12 show schematic energy diagrams for the electron transfer from the standard gaseous state through the electrolyte solution into the metal electrode. As mentioned in Chap. 2, the electron level (the real potential of electron) a s/v> in an electrolyte solution consists of an electrostatic energy...

The quantities AGf° and AHf° refer to free energies and enthalpies of formation from the elements with consumption or production of gaseous electrons if necessary. Standard states of elementary hydrogen and oxygen are one atmosphere fugacity. The standard state of the... 

A thermodynamic breakdown of the standard enthalpy change for the formation of a gaseous halide ion from the elemental halogen and a gaseous electron. 

The standard enthalpies of formation of the gaseous compounds and the enthalpy of disruption derived therefrom are given in Table 13. An interesting problem arises as to how these results are to be evaluated. If the value of AHf [M(CO)s, g] derived15,1 ) from electron impact measurements on M2(CO)io (M = Mn, Re) is used, then as outlined earlier this will be expected to give an upper limit to the value of D(M-M). It has been shown16) that for all values of Z)(M-M) below specified upper limits the following relation holds... 

Adiabatic detachment energy [7]. Abbreviations used rcoy (Em) = covalent radius of element E in a trivalent compound BE(E-E) = bond enthalpy of a single E-E bond D°298(E2) = dissociation enthalpy of the E2 molecule at standard conditions IE = ionization enthalpy EA = electron affinity AHf°(E2 g) = standard enthalpy of formation of the gaseous E2 molecule. 

The enthalpy of reaction 2.45 cannot be determined directly. As shown in figure 2.5, it is calculated by using several experimental quantities the standard enthalpy of formation of the solid alkoxide, the standard sublimation enthalpy and the ionization energy of lithium, and the standard enthalpy of formation and the adiabatic electron affinity of gaseous methoxy radical (equation 2.47). 

Fig. 2-43. Energy balance in the reaction of normal hydrogen electrode H2(sid.p>j = hydrogen molecule in the gaseous standard state (at 1 atm) H( gro. i) = hydrated proton of unit activity = real potential of the hydrated proton of unit activity a.ajHE) = real potential of the equilibrium electron of NHE (= Fermi level cpcnhe) of NHE).

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