Half-Wave Potentials prediction

The diffusion problem can be solved to predict that one wave in NPV or one pair of anodic and cathodic peak currents in CV are to be observed the half-wave potential is expressed by... 

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. 

A mathematical analysis of all four isomeric thiadiazoles by the simple molecular orbital method has provided molecular diagrams of the free base and conjugate acid of each thiadiazole, with electron densities, bond orders, and free valencies. On this basis, predictions have been made concerning the reactivities of the six non-equivalent carbon atoms, the basicities of the nitrogen atoms, and the delocalization energies in these molecules. The 5-position in free 1,2,4-thiadiazole should possess maximum reactivity in nucleophilic substitution reactions. The treatment also accounts for the order of the polarographic half-wave potentials and the position of the absorption maxima in the ultraviolet region of the spectra of 1,2,4- and 1,3,4-thiadiazoles.4... 

Figure 14-11 Reduction potential of ascorbic acid, showing its dependence on pH. (a) Graph of the function labeled formal potential in Equation 14-34. (b) Experimental polarographic halfwave reduction potential of ascorbic acid in a medium of ionic strength = 0.2 M. The half-wave potential, discussed in Chapter 17. is nearly the same as the formal potential. At high pH (>12), the half-wave potential does not level off to a slope of 0, as Equation 14-34 predicts. Instead, a hydrolysis reaction of ascorbic acid occurs and the chemistry is more complex than Reaction 14-32. [J. J. Ruiz, A. Aldaz. and M. Dominguez. Can. J. Chem. 1977,55.2799 ibid. 1978, 56. 1533.]...

Accordingly, HMO theory predicts that the half-wave potential and the HFSC of the anthryl protons should approach those of the unsubstituted anthracene ions when substitution causes 0 to approach 90°. But for smaller val-... 

These conditions are fulfilled for the reduction of phenacylsulpho-nium salts at low pH values cleavage of the C—S bond occurs in the first step and proton transfer is involved only in the consecutive steps. The observed shift of half-wave potentials (74) with pH follows the plot predicted by equation (27). The intersection of the two linear parts indicates that phenacylsulphonium salts are moderately strong acids with pK values between 7 and 8 (Fig. 20). Potentiometrically measured pK values, used for verification, are in good agreement with the approximate pK values obtained from polarographic data. The system involved in the first step can be described by scheme (28) ... 

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. 

Shifts of half-wave potentials towards more positive values in the presence of bulky groups can be explained in some cases also by changes in the mechanism of the electrode process. The most thoroughly studied example is the reduction of alkyl and cycloalkyl bromides (141). Departures of the half-wave potentials from predicted values for a-branched alkyl bromides, increasing in the sequence Et < — Pr nucleophilic substitutions. Hence a similar explanation, i.e. varying participation of SnI and 5N2-like... 

The half-wave potentials (corrected for changes in liquid-junction potential) for the one-electron reduction of aromatic hydrocarbons generally become more positive (the reduction is easier) as the dielectric constant of the solvent increases.44 This is in accord with the direction of the variation in solvation energy of the radical anions that is predicted by the simple Bom theory... 

The predicted shift was verified (Kem, 1954), but the height of the reduction waves of dehydroascorbic acid found (Ono et ai., 1953) and their half-wave potentials do not agree with this theory, indicating that the reaction scheme is more complex. 

The Hammett-type correlation for the rate constants of 5-allyl-5-R-barbiturates has been reported by Carstensen et al. and suggested for use in stability predictions.569 Similar correlations were also found for the hydrolysis of 5-arylidenebarbituric acids.363,567 Linear free energy relationships have also been reported for dissociation constants,45,51 polarographic half-wave potentials,570 fluorescence70 and luminescence phenomena,71 and 13C-NMR chemical shifts129 for different classes of barbituric acid derivatives. Application of the dual substituent parameters method in LFER analysis of barbiturates, using Taft s polar and steric constants for various chemical and physicochemical properties, was also evaluated.571... 

Fig. 12. The variation of experimentally determined half-wave potentials with the parameter a. The straight line corresponds to the theoretically predicted behaviour [eqn. (63)]. The data are from ref. 67.

In the polarography area, half-wave potentials have been ranployed as a tool for predicting the scope and limitation of the reaction of a,P-unsaturated ketones... 

This section introduces you to the factors that determine the overall rate of an electrode reaction in a system which is not stirred. This allows predictions of the shape of the resulting current/WE potential curves for a system which is under diffusion control. The work of llkovic in 1934 in deriving the current/analyte concentration relationship for the DME is covered and the llkovic equation is stated and partially derived. The Heyrovsky-Ilkovic equation (1935) is then derived this provides an explanation of the shape of the current WE potential curve. This curve now becomes a polarogram and the half-wave potential is defined and related to the polarogram. Finally the question of the reversibility of the electrode reaction is discussed and tests for reversibility are given. 

Hauk, A., Richartz, H., Schramm, K. W. and Fiedler, H. (1990) Reduction of nitrated phenols a method to predict half-wave potentials of nitrated phenols with molecular modelling. Chemosphere, 20, 717-28. 

A number of examples of the pH effect on the position of the half-wave potentials in polarography can be found when pH directly influences the a coefficients of the metal ion as well as the protonation of the buffer components in particular complexing ligands, such as polyamine polycarboxylic acids. These two effects often shift the wave toward more negative potentials. However, strictly thermodynamic considerations do not always make prediction possible as kinetic factors (reversibility of the electrode process) may also contribute to the final result. 

---