Polarography half-wave potential

As already indicated, quantitative conventional d.c. polarography is limited at best to solutions with electrolytes at concentrations greater than 10-5M, and two different ions can only be investigated when their half-wave potentials differ by at least 0.2 V. These limitations are largely due to the condenser current associated with the charging of each mercury drop as it forms, and various procedures have been devised to overcome this problem. These include ... 

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... 

TABLE 26. Polarography and coulometry of Pt SnCE half-wave potentials and coulometric reading213... 

Diffusion Currents. Half-wave Potentials. Characteristics of the DME. Quantitative Analysis. Modes of Operation Used in Polarography. The Dissolved Oxygen Electrode and Biochemical Enzyme Sensors. Amperometric Titrations. Applications of Polarography and Amperometric Titrations. 

The direct access to the electrical-energetic properties of an ion-in-solution which polarography and related electro-analytical techniques seem to offer, has invited many attempts to interpret the results in terms of fundamental energetic quantities, such as ionization potentials and solvation enthalpies. An early and seminal analysis by Case etal., [16] was followed up by an extension of the theory to various aromatic cations by Kothe et al. [17]. They attempted the absolute calculation of the solvation enthalpies of cations, molecules, and anions of the triphenylmethyl series, and our Equations (4) and (6) are derived by implicit arguments closely related to theirs, but we have preferred not to follow their attempts at absolute calculations. Such calculations are inevitably beset by a lack of data (in this instance especially the ionization energies of the radicals) and by the need for approximations of various kinds. For example, Kothe et al., attempted to calculate the electrical contribution to the solvation enthalpy by Born s equation, applicable to an isolated spherical ion, uninhibited by the fact that they then combined it with half-wave potentials obtained for planar ions at high ionic strength. 

The Polarography of Oxonium Ions, Part II. The Half-wave Potentials of Five Tertiary Ions. G.E. Holdcroft, Kabir-ud-Din, and P.H. Plesch, Journal of Chemical Research, 1980, 390-391. 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Thermodynamic reduction potentials of numerous aromatics were first measured by Hoijtink and van Schooten in 96% aqueous dioxane, using polarography [15, 16]. These fundamental works were decisive tests of the HMO theory, showing that the polarographic half-wave potentials vary linearly with the HMO energies of the lowest unoccupied molecular orbitals (LUMO) of the hydrocarbons [1]. Hoijtink etal. had already noticed that most aromatics can be further reduced to their respective dianions [17]. They proposed a... 

In polarography, we obtained the half-wave potential E// by analysing the shapes of the polarographic wave. E1/2 is a useful characteristic of the analyte in the same way as E . In cyclic voltammetry, the position o/both peaks (both forward and back in Figure 6.13 cathodic and anodic, respectively, in this example) gives us thermodynamic information. Provided that the couple is fully reversible, in the thermodynamic sense defined in Table 6.3, the two peaks are positioned on either side of the formal electrode potential E of the analyte redox couple, as follows ... 

Half-wave potential, 1/2 An electrode potential from polarography that is characteristic of the analyte (see Section 6.3.2). 

This explanation for the two polarographic waves seen in Figure 3.2 suggests that the region of transition between the two waves will be sensitive to buffer concentration and composition. Such effects are seen in the polarography-pH profiles of steroid enones, some of which [88] show behaviour like that of cyclohexenone while others show only a linear variation of half-wave potential over the whole pH range of 2 — 11 [89, 90]. 

Coumarin shows a one-electron wave on polarography in aqueous buffers and the half-wave potential is independent of pH [136]. Reduction at a mercury cathode affords the meso- and ( )-isomers of the 4-coupled hydrodimer. Reduction of... 

Footnote (a) Half-wave potential from pulse polarography at a mercury electrode... 

Polarography of oximes and phenylhydrazones in aqueous buffers at pH 1.0. All give four-electron waves with half-wave potential dependent on pH. 

Reduction of aliphatic oximes is specifically catalysed by protons, The process exhibits a single four-electron wave on polarography and Ey, is dependent on pH. Some half-wave potentials are given in Table 10.7, Around pH 6-8 this wave decreases in height and finally disappears because protons can no longer be supplied... 

Figure U.3. Variation of half-wave potential with pH for the polarography of (a) azoxybenzene, a 4-clectron wave and (b) azobenzene, a 2-electron wave. Data from refs. (104,105. ...

Nevertheless, the mid-peak potentials determined by cyclic voltammetry and other characteristic potentials obtained by different electroanalytical techniques (such as pulse, alternating current, or square wave voltammetries) supply valuable information on the behavior of the redox systems. In fact, for the majority of redox reactions, especially for the novel systems, we have only these values. (The cyclic voltammetry almost entirely replaced the polarography which has been used for six decades from 1920. However, the abundant data, especially the half-wave potentials, 1/2, are still very useful sources for providing information on the redox properties of different systems.)... 

Half-wave potential in polarography, 1244 Hamelin, 1209 Hamilton, dendrites, 1338 Hamnet, 1133... 

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 ... 

The limiting current is proportional to the concentration of the electroactive species, whereas the half-wave potential is specific to the electroactive species, being close to the standard potential of the electrode reaction. Thus, by measuring polarographic waves, we can run qualitative and quantitative analyses. In DC polarography, many inorganic and organic substances (ions, complexes and mole-... 

Here, A is the electrode area, C and D are the concentration and the diffusion coefficient of the electroactive species, AE and co(=2nfj are the amplitude and the angular frequency of the AC applied voltage, t is the time, and j=nF (Edc-Ei/2) / RT. For reversible processes, the AC polarographic wave has a symmetrical bell shape and corresponds to the derivative curve of the DC polarographic wave (Fig. 5.14(b)). The peak current ip, expressed by Eq. (5.24), is proportional to the concentration of electroactive species and the peak potential is almost equal to the half-wave potential in DC polarography ... 

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