Metal half-wave potentials

Here p is the coordination number of the complex ion formed, Xb is the ligand and n is the number of electrons involved in the electrode reaction. The concentration of the complex ion does not enter into equation (15), so that the observed half-wave potential will be constant and independent of the concentration of the complex metal ion. Furthermore, the half-wave potential is more negative the smaller value of Kinstabi, i.e. the more stable the complex ion. The half-wave potential will also shift with a change in the concentration... 

The shift of the half-wave potentials of metal ions by complexation is of value in polarographic analysis to eliminate the interfering effect of one metal upon another, and to promote sufficient separation of the waves of metals in mixtures to make possible their simultaneous determination. Thus, in the analysis of copper-base alloys for nickel, lead, etc., the reduction wave of copper(II) ions in most supporting electrolytes precedes that of the other metals and swamps those of the other metals present by using a cyanide supporting electrolyte, the copper is converted into the difficultly reducible cyanocuprate(I) ion and, in such a medium, nickel, lead, etc., can be determined. 

For the reduction of metal complexes, the half-wave potential is shifted to more negative potentials (vs. the true metal ion), reflecting the additional energy required for the decomposition of the complex. Consider the reversible reduction of a hypothetical metal complex, MLp ... 

Voltametric studies (34, 37) have revealed the electron transfers Mo(R2c/fc)4 Mo(R2C fc)4° MoCRjdfc) Mo(R2half wave potentials for the processes 0 +1 and + - + 2 depend upon the nature of R. The dependency can be described by the Taft relation =p2a where a is the Taft constant for the N-bonded substituents R. The rather low values of p indicate that the redox orbitals have mainly a metal character, the mixing of these orbitals with those of the ligands is rather small. This conclusion is in accordance with the interpretation of the electronic spectra and the results of Extended Hiickel MO calculations (37). Only the compound with R = Ph does not fit into the Taft relation, the Ej 2 value is lower than... 

The influence of the N-bonded substituents R on the half-wave potentials can be described by a Taft relation, like is found for Mo, W and Au. The small value of p points to the dominance of metal orbitals in the redox orbital (5(5). The phenyl derivates do not fit this relation, probably because of a mesomeric influence. Here, however, the n-butyl and cyclohexyl also show small deviations, probably because of steric effects. 

Some divalent transition and post-transition metal ions, Co", Nr, Cu", Zm, and Cd, have been studied in the same way, but these systems need a pH-control in order to avoid any precipitation. Although measurements have not been completed yet, a pair of waves has been observed only in the Cu system that is somewhat irreversible (—100 to —50 mV of the half-wave potential). In the other systems, any waves except ambiguous broad ones could not be obtained. While analyzing some waves, Cu seems to be facili-... 

For reversible transfer reactions of a simple ion, may be expressed in terms of the half-wave potential, A (pi/2, by direct transposition from the case of reversible eleetron transfer at a metal electrode-electrolyte solution interface [234] ... 

In agreement with the theory of electrolysis, treated in Sections 3.1 and 3.2, the parts of the residual current and the limiting current are clearly shown by the nature of the polarographic waves because for the cathodic reduction of Cd2+ and Zn2+ at the dme we have to deal with rapid electron transfer and limited diffusion of the cations from the solution towards the electrode surface and of the metal amalgam formed thereon towards the inside of the Hg drop, we may conclude that the half-wave potential, Eh, is constant [cf., Fig. 3.13 (a ] and agrees with the redox potential of the amalgam, i.e., -0.3521V for Cd2+ + 2e - Cd(Hg) and -0.7628 V for Zn2+ + 2e -> Zn(Hg) (ref. 10). The Nernst equation is... 

Notwithstanding all previous precautions taken, some difficulties may still remain. For instance, in the reductive polarography of monovalent metal ions the half-wave potentials should differ preferably by at least 0.30 V (see p. 120) in view of the net wave separation. Simply in order to detect the presence of a second metal a difference of at least 0.1 V is required, but interferences soon arise at low concentration although derivative polarography yields some improvement, these can best be overcome by complexation of one of the metals, so that its half-wave potential shifts to the more negative side. If we take the complexation of a metal Mn+ as an example, e.g. with X6- as the complexing ion, then... 

For metals which are soluble in mercury, such as the alkali and alkaline earth metals, the polarographic half-wave potential is a function of the... 

Since (b) and (c) are independent of the nature of the solvent, the half-wave potential for a reversible reduction is ameasure of the amount of interaction of the metal ion with the solvent molecules according to the reaction... 

For an irreversible reduction the half-wave potential is determined not only by the standard electrode potential but also by the polarographic overvoltage. For a simple electrode process the metal ion-solvent interaction is mainly responsible for the polarographic overvoltage and hence E[ j of such irreversible reductions may also be considered as a function of the solvation 119f... 

Certain transition metal ions such as Co2, Ti3 are known to form chelates with trimethylphosphate, i.e., dimethoxyphosphato complexes84 8S>. The chelate effect is responsible for the high stabilities of such complexes, which is expressed in the more negative values for the half-wave potentials. All ions producing such complexes are expected to undergo reduction in TMP at more negative potentials than would be expected from interpolation of the curves. 

Although no data are available in HMPA, it has been shown that due to steric effects metal ions are weaker coordinated than would be expected from its donicity 83). This observation suggests that the half-wave potentials will be found at more positive potentials than expected from extrapolation of the curves. 

In most other cases the relationship will allow the approximate prediction of the half-wave potentials of a given ion in a solvent of given donicity by interpolation. It may be expected that E jy2 for a certain metal ion in tetramethylene sulfone (DN = 14.8) will be similar to that in PDC (DN = 15.1), benzylcyanide (DN = 15.1) or ethylene sulfite (DN = 15.3). Likewise, the half-wave potentials are expected to be similar in nitrobenzene (DN = 4.4) and nitromethane (DN = 2.7). In an analogous manner the half-wave potentials may be predicted in methyl acetate, diethylether, pyridine, and various other solvents. 

An early electrochemical study of corannulene revealed the presence of two well-defined polarographic waves with half-wave potentials of-1.88 and -2.36 V (r-butylammonium perchlorate in acetonitrile). The first wave represented a reversible, one-electron reduction leading to radical anion formation (emerald green solution) further characterized by UV-VIS and ESR. The second wave was reported to be associated with the formation of a bright red species which is not paramagnetic, but it is not believed to be the dianion, but rather some decay product of it. Treatment of THF solutions of 8 with sodium and potassium metals also led to the formation of the same species. ... 

Anodic stripping voltammetry (ASV). This is an electrochemical technique in which the element to be analyzed is first deposited on an electrode and then redissolved, that is, stripped, from the electrode to form a more concentrated solution. For example, a drop of mercury hanging from a platinum electrode in a solution containing the species to be measured has been used as the deposition electrode. A potential slightly more negative than the half-wave potential for the ion of interest is applied to deposit the element on the electrode. After deposition of the metal for a given... 

All C60 adducts have low-lying LUMOs that can easily be populated by electrochemical methods. For C60 itself, six reduction couples have been observed by cyclic voltammetry (CV) or square-wave voltammetry (SWV), and as many as four reduction couples have been found for many organometallics (9,84). Most of the studies have been performed in thf or acetonitrile at lower temperatures, which increases the size of the potential window. Table VII lists the half-wave potentials for some metal complexes, and Fig. 7 shows the cyclic voltammogram for [Co(NO)(PPh3)2(i72-C60)]. 

According to the hard and soft acids and bases (HSAB) concept, hard acids tend to interact strongly with hard bases, while soft acids tend to interact strongly with soft bases. The HSAB concept applies also to solute-solvent interactions. Figure 2.5 shows the polarographic half-wave potentials of metal ions in N-methyl-2-pyrrolidinone (NMP) and N-methyl-2-thiopyrrolidinone (NMTP) [13]. Here, we can compare the half-wave potentials in the two solvents, because they are referred to the half-wave potential of the bis(biphenyl)chromium(l)/(0) couple,... 

Fig. 2.5 Comparison of the half-wave potentials of metal ions in N-methyl-2-pyr-rolidinone (NMP) and those in N-methyl-2-thiopyrrolidinone (NMTP) [13].

Equation (4.5) is also valid in this case. Reactions of this type are realized in polarography at a dropping mercury electrode, and the standard potentials can be obtained from the polarographic half-wave potentials ( 1/2)- Polarographic studies of metal ion solvation are dealt with in Section 8.2.1. Here, only the results obtained by Gritzner [3] are outlined. He was interested in the role of the HSAB concept in metal ion solvation (Section 2.2.2) and measured, in 22 different solvents, half-wave potentials for the reductions of alkali and alkaline earth metal ions, Tl+, Cu+, Ag+, Zn2+, Cd2, Cu2+ and Pb2+. He used the half-wave potential of the BCr+/BCr couple as a solvent-independent potential reference. As typical examples of the hard and soft acids, he chose K+ and Ag+, respectively, and plotted the half-wave potentials of metal ions against the half-wave potentials of K+ or against the potentials of the 0.01 M Ag+/Ag electrode. The results were as follows ... 

---