Potential of the normal hydrogen electrode

EPR spectrometers use radiation in the giga-hertz range (GHz is 109 Hz), and the most common type of spectrometer operates with radiation in the X-band of micro-waves (i.e., a frequency of circa 9-10 GHz). For a resonance frequency of 9.500 GHz (9500 MHz), and a g-value of 2.00232, the resonance field is 0.338987 tesla. The value ge = 2.00232 is a theoretical one calculated for a free unpaired electron in vacuo. Although this esoteric entity may perhaps not strike us as being of high (bio) chemical relevance, it is in fact the reference system of EPR spectroscopy, and thus of comparable importance as the chemical-shift position of the II line of tetra-methylsilane in NMR spectroscopy, or the reduction potential of the normal hydrogen electrode in electrochemistry. 

As described in Sec. 2.11, the electron level in the normal hydrogen electrode (gaseous hydrogen molecules at unit fiigacity and hydrated protons at unit activity) is -4.5 eV (or - 4.44 eV in the lUPAC report [Trasatti, 1986]). We, then, obtain the equilibrium potential of the normal hydrogen electrode nhe (= in Eqn. 4-32) as shown in Eqn. 4-34 ... 

The relative electrode potential nhe referred to the normal (or standard) hydrogen electrode (NHE) is used in general as a conventional scale of the electrode potential in electrochemistry. Since the electrode potential of the normal hydrogen electrode is 4.5 or 4.44 V, we obtain the relationship between the relative electrode potentiEd, Ema, and the absolute electrode potential, E, as shown in Eqn. 4-36 ... 

Values differ from those originally reported by Patterson, Cramer, and Truhlar (2001) by 0.08 V per electron consumed. This difference reflects a more accurate measurement of the absolute potential of the normal hydrogen electrode as 4.36 V instead of 4.44 V since the time of that pubhcation. See Lewis et al. (2004) and Section 11.4.1. 

By changing the reference potential in a series of redox monitors, it is then possible to determine the dependence of the cluster potential on the nuclearity. The general trend of increasing redox potential with nuclearity is the same for all metals in solution as it is illustrated in Fig. 2 in the case of E°(AgVAg,) q. However, in gas phase, the variation of the ionization potential IV(Ag ) exhibits the opposite trend versus the nuclearity n. Indeed, since the Fermi potential of the normal hydrogen electrode (NHE) in water is 4.5 eV, and since the solvation free energy of Ag decreases with size as deduced from the Born model, one can explain the two opposite variations with size of F°(Ag /AgJ q and IP (AgJ as illustrated in Fig. 2. 

Thus, the level of the electrochemical potential of the normal hydrogen electrode, Fredox(NHE), lies 4.4 eV below the energy level F... 

The notion of energetic levels of electrons in soUds can be extended to the case of an electrolytic solution containing a redox system (Gerischer, 1970). The occupied electronic levels correspond to the energetic states of the reduced species whereas the unoccupied ones correspond to the energetic states of the oxidized species. The Fermi level of the redox couple, ii redox, corresponds to the electrochemical potential of electrons in the redox system and is equivalent to the reduction potential, Vq. In order to correlate the energetic levels of a semiconductor to those of a redox couple in an electrolyte, two different scales can be used. The first is expressed in eV, the other one in V (Fig. 6.7a). The difference between the two scales is due to the fact that in solid state physics zero is the level of the electron in vacuum, whereas in electrochemistry the reference is the potential of the normal hydrogen electrode (NHE). The correlation between the two scales can be calculated from the value of potential of NHE which is equal to -4.5 eV when it is referred to that of the electron in vacuum (Lohmann, 1967). 

In electrochemistry, the electron level of the normal hydrogen electrode is important, because it is used as the reference zero level of the electrode potential in aqueous solutions. The reaction of normal hydrogen electrode in the standard state (temperature 25°C, hydrogen pressure 1 atm, and unit activity of hydrated protons) is written in Eqn. 2-54 ... 

The electrode potential as defined earlier is called the absolute electrode potential, and it is compared to the electrode potential referred to normal hydrogen electrode. The Fermi level of the normal hydrogen electrode has been estimated near —4.5 eV, and the normal hydrogen electrode potential is 4.5 V on the scale of the absolute electrode potential. 

FIGURE 22.6 Electron energy diagrams for an n-type semiconductor electrode in the dark (a) and in the photoexcited state (b) 8s = band edge level at the interface, eF(H+ — Fermi level of the normal hydrogen electrode reaction, Sp /ifeo) = Fermi level of the normal oxygen electrode reaction, Asph = photo potential, p p = quasi-Fermi level of photoexcited holes, and nsF = quasi-Fermi level of photoexcited electrons (nsF eF for n-type semiconductors). 

Figure 4.3. Standard potentials (vs. the normal hydrogen electrode) for redox reactions involving oxygen at 25°C. From Sawyer and Nanni (1981). Reprinted by permission of Academic Press.

One of the few periodic trends of the metals not to show a strong diagonal effect is the standard reduction potential. In fact, this trend follows more of a horizontal rule. The standard reduction potential, E°, is defined in Equation (5.21). The standard reduction potential for the normal hydrogen electrode (N.H.E.), or the half-reaction shown in Equation (5.22), is given a value of zero. Metal atoms with E s more n ative than the N.H.E. are easier to oxidize and harder to reduce. Metal atoms with s more positive than the N.H.E. are easier to reduce and harder to oxidize ... 

The pH is determined electrometrically by measuring the difference in potential between the measuring electrode (glass electrode) and the reference electrode with known potential (saturated calomel electrode used instead of the normal hydrogen electrode). 

The equilibrium potential of an electrochemical reaction is defined as the potential of an electrode (with respect to the potential of a normal hydrogen electrode) when immersed in an electrolytic cell containing the reactive species, but without current flow. When a current is applied, the electrode potential is shifted. In the case of an anodic reaction ... 

Practical developers must possess good image discrimination that is, rapid reaction with exposed silver haUde, but slow reaction with unexposed grains. This is possible because the silver of the latent image provides a conducting site where the developer can easily give up its electrons, but requires that the electrochemical potential of the developer be properly poised. For most systems, this means a developer overpotential of between —40 to +50 mV vs the normal hydrogen electrode. 

The Vacuum Reference The first reference in the double-reference method enables the surface potential of the metal slab to be related to the vacuum scale. This relationship is determined by calculating the workfunction of the model metal/water/adsorbate interface, including a few layers of water molecules. The workfunction, — < ermi. is then used to calibrate the system Fermi level to an electrochemical reference electrode. It is convenient to choose the normal hydrogen electrode (NHE), as it has been experimentally and theoretically determined that the NHE potential is —4.8 V with respect to the free electron in a vacuum [Wagner, 1993]. We therefore apply the relationship... 

A typical electrocapillarity system is shown in Figure 2.1(a). The mercury reservoir provides a source of clean mercury to feed a capillary tube the height of mercury in this tube can be varied such that the mass of the Hg column exactly balances the surface tension between the mercury and the capillary walls, see Figure 2.1(b). A voltage V is applied across the mercury in the capillary and a second electrode which is non-polarisable (i.e. the interface will not sustain a change in the potential dropped across it), such as the normal hydrogen electrode, NHE. The potential distribution across the two interfaces is shown in Figure 2.1(c). As can be seen ... 

In order to illustrate the approach suggested above, it is of value to consider a specific case. Visible or near-UV excitation of the complex RuCbpy results in excitation and formation of the well-characterized metal to ligand charge transfer (MLCT) excited state Ru(bpy)32+. The consequences of optical excitation in the Ru-bpy system in terms of energetics are well established, and are summarized in eq. 1 in a Latimer type diagram where the potentials are versus the normal hydrogen electrode (NHE) and are... 

Fig. 11 Correlation between electrochemical potentials and OMTS bands for more than ten compounds including polyacenes, phthalo-cyanines, and porphyrins. OMTS data were acquired both from tunnel junctions and STM measurements. The standard potential relative to the normal hydrogen electrode associated with the half reaction M(solution) + e-(vac) —> M-(solution) is the y axis. The three outliers are assigned to the ring oxidation of porphyrins. (Reprinted with permission from [26])...

A water-alone monolayer potential above the pzc is in accordance with an absolute work function measurement for the water monolayer on Pt(lll) of 4.8 eV (29). Comparing this to the hydrogen electrode (4.7 eV below vacuum (30) for the normal hydrogen electrode NHE) corrected by 7x0.059 V for a nominaI pH 7 yields a water-alone mono-layer potential of +0.5 V vs. RHE at pH 7. This lies 0.3 V above our proposed pzc of 0.2 V RHE. This relatively high apparent potential of the water monolayer has been noted previously (Sass, J.K., private communication), and has raised concern about the relevance of the UHV monolayer to real electrochemical conditions, since most electrochemical measurements of the pzc of polycrystalline Pt have been closer to 0.2 V than to 0.5 V (31). By showing that the water monolayer lies above, not at, the pzc, the present H.+H-O data remove part of the apparent discrepancy between the electrochemical and UHV results. If future UHV work function data show a large ( 0.3 V) decrease in the water monolayer work function upon addition of small (<20X saturation) amounts of hydrogen, all of the apparent discrepancy could be quantitatively accounted for. 

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