Reversible systems polarographic waves

The potential at the point on the polarographic wave where the current is equal to one-half the diffusion current is termed the half-wave potential and is designated by 1/2. It is quite clear from equation (9) that 1/2 is a characteristic constant for a reversible oxidation-reduction system and that its value is independent of the concentration of the oxidant [Ox] in the bulk of the solution. It follows from equations (8) and (9) that at 25 °C ... 

For reversible systems (with fast electron-transfer kinetics), the shape of the polarographic wave can be described by the Heyrovsky—Ilkovic equation ... 

The direct electrochemical reduction and oxidation of bacteriorhodopsin, a bacterial photoreceptor protein, have recently been described. The redox site of this molecule is organic, being a conjugated double bond system and a Schiff base. As previously noted for other proteins, strong adsorption onto mercury is evident with bacteriorhodopsin. The adsorbed molecules undergo reduction-oxidation reactions near -0.8 V which appear to be polarographically reversible. An oxidation wave is observed at platinum at +0.80 V and has been ascribed to the chromophore. ... 

Hence, for a reversible system, the well-known linear relation is obtained between the potential E and log (/iim -///). Other equations have been derived for those reversible systems that involve semiquinone formation, dimerization, or the formation of complex compounds with mercury. Logarithmic analysis of the polarographic wave is often the only proof of reversibility which is considered but recently several authors, in particular Zuman and Delahay, " have pointed out that it is inadequate to assume that an electrode process is reversible on this evidence alone. For a reversible reaction, plots of E vs. In (/lim - ///) give the electron number z from the slope of the plot, RT/zF, A clearer indication of irreversibility is the evaluation of slopes of log i-E curves for higher concentrations (for i < /lim). Irreversible processes will give Tafel behavior. 

When dissociation occurs for oxidized or reduced forms of a reversible system, the half-wave potentials are shifted with the pH of the solution. The shift depends on the number of electrons transferred, the number of protons dissociated, the pH-value and the standard potential of the substance studied. From polarographic measurements of reversible systems the approximate values for the dissociation constants can be estimated. 

Many handbooks like the CRC Handbook of Chemistry and Physics provide, on behalf of electrochemistry investigation, values of standard reduction potentials, listed either in alphabetical order and/or in potential order. These must be considered as potentials of completely reversible redox systems. In current analytical practice one is interested in half-wave potentials of voltammetric, mostly polarographic analysis in various specific media, also in the case of irreversible systems. Apart from data such as those recently provided by Rach and Seiler (Spurenanalyse mit Polarographischen und Voltammetrischen Methoden, Hiithig, Heidelberg, 1984), these half-wave potentials are given in the following table (Application Note N-l, EG G Princeton Applied Research, Princeton, NJ, 1980). 

An investigation of the dc and ac polarographic responses of 24 pharmaceuticals in an aprotic solvent system has been described [82]. Barbiturates, salicylates, corticosteroids, and alkaloids were examined in acetonitrile-tetra-butylammonium perchlorate. The majority of the compounds yielded one-electron reversible waves in this solvent they were suitable for analytical pur-... 

When dehydration occurs as a consecutive reaction, its effect on polarographic curves can be observed only, if the electrode process is reversible. In such cases, the consecutive reaction affects neither the wave-height nor the wave-shape, but causes a shift in the half-wave potentials. Such systems, apart from the oxidation of -aminophenol mentioned above, probably play a role in the oxidation of enediols, e.g. of ascorbic acid. It is assumed that the oxidation of ascorbic acid gives in a reversible step an unstable electroactive product, which is then transformed to electroinactive dehydroascorbic acid in a fast chemical reaction. Theoretical treatment predicted a dependence of the half-wave potential on drop-time, and this was confirmed, but the rate constant of the deactivation reaction cannot be determined from the shift of the half-wave potential, because the value of the true standard potential (at t — 0) is not accessible to measurement. 

The electrochemical reduction of a number of furoxan derivatives has been studied polarographically. The products depend on the pH of the medium. Benzofuroxan appears to be reduced first to the dioxime anion and then further to diaminophenazine and o-phenylenediamine.138,433,434 Naphthofuroxan behaves similarly, in that the number of waves which are observed depends on the acidity and that the dioxime is the first product.433 Other electroreduction experiments have been carried out, particularly with bibenzofuroxan sulfone, with a view to the development of a reversible depolarizer for nonaqueous battery systems.435-437 The results of ESR measurements on the electrochemical reduction products of several furoxans are mentioned in Section III,E. 

The shapes and positions of irreversible waves can furnish only kinetic information. One may be able to determine such parameters as kf, 1, or a, but thermodynamic results, such as and free energies, are not available (28, 33, 34). As a rule of thumb, a system with > 2 X 10 cm/s appears reversible on the classical polarographic time scale of a few seconds when D is on the order of 10 cm /s. A heterogeneous charge transfer with < 3 X 10 cm/s will behave in a totally irreversible manner under the same conditions, and one can evaluate the rate parameters as described above. Systems with between these limits are quasireversible, and some kinetic information can be obtained from them through the treatment prescribed by Randles (33, 34). Naturally, the precision of the kinetic information deteriorates as the reversible limit is approached. See Section 5.5.4 for much more information about the interpretation of irreversible waves. 

The Metrohm 646 VA Processor is another microprocessor based instrument. Used in tandem with the 647 VA Electrode Stand and 675 VA Sample Changer, this system is capable of performing automated data acquisition, including the use of the standard additions method. Data analysis features include smoothing and differentiation, and a peak shape analysis routine that performs independently of the base current. Pulse polarographic techniques that can be performed include dp, which can be optimized for reversible and irreversible systems staircase, with current measurement during the final 20 ms of each current step and Barker square wave, which employs a waveform composed of five square wave oscillations superimposed upon a staircase, with currents measured for 2 ms at the end of each half cycle of the second, third and fourth oscillations. The 1988 price of this instrument is 14,000. 

To summarize, equilibrium constants can be determined polarographically from the shifts of half-wave potentials for reversible electrode systems, or from the ratio of heights of two... 

---