Heyrovsky-Ilkovic equation

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

If the gradient is too low, however, then we can imply that the CnF/RTl term has been modified, i.e. that the reaction at the DME is electrochemically irreversible, such that a variant of the Heyrovsky-Ilkovic equation now needs to be employed, as follows ... 

The current at a dropping-mercury electrode (DME) is a function of potential, as described by the Heyrovsky-Ilkovic equation (equation (6.6)). At less extreme overpotentials, the current rises from zero to a maximum. The potential at which... 

Although the redox processes see Redox Properties Processes) occurring on the surface of a dropping mercury electrode are generally more complex than those in potentiometry, the simplicity of polarographic apparatus has led it to be widely used in equilibrium solution chemistry. If a reversible electrode process is assured, the half-wave electrode potential is given by the Heyrovsky-Ilkovic equation ... 

This equation was derived at first by Heyrovsky and Ilkovic [10] and is usually called the Heyrovsky-Ilkovic equation. In most cases the diffusion coefficients of the Ox and Red species are not very different, so that t/1/2 is essentially the standard redox potential. A theoretical current-potential curve in terms of /diff//jim vs. A shown in... 

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. 

SAQ 1.5c State the general form of the llkovic equation for a reduction process and explain the terms used. From this equation derive the form of the Heyrovsky-Ilkovic equation that applies to the reaction ... 

The application of the diffusion theory to the DME/solution interface leads to the ilkovic equation relating the diffusion current (7d) to the bulk analyte concentration. The Heyrovsky-Ilkovic equation leads directly to the shape of a typical polarogram (// (WE) curve) for a reversible process, and hence to the half-wave potential (Ei). Reversible and irreversible electrode reactions are considered and tests for reversibility given. The possibility of obtaining anodic waves and mixed waves in addition to cathodic waves is discussed. 

In Section 1.5 we used a graphical test for reversibility based on the Heyrovsky-Ilkovic equation. For a reversible reaction this gives a value of from an intercept on the plot. 

Having obtained a value of E i from the polarogram, what is the significance of this value If we inspect the Heyrovsky-Ilkovic equation we see (Eq. 1.5k) that ... 

Those of you who wish can differentiate the Heyrovsky-Ilkovic equation (l-5j) to obtain df/d/and then invert this to give d//d . Then put / = /(j/2, when E = Ei and show that ... 

Much attention, particularly among the Russian workers, has been given to the applicability of the Heyrovsky-Ilkovic versus the Kolthoff-Lingane equation for electrode reactions involving metal deposition. In practice, one plots the electrode potential versus log[(/i — /)//] or log(/ — i) and examines the linearity of the plot and also the value of the slope (theoretically 2.3RTjnF). It is expected that the Heyrovsky-Ilkovic equation should be applicable when alloy formation with the electrode material takes place and the metal formed diffuses away from the surface so that its surface activity is a function of the current density. Alloying and diffusion in the electrode will be functions of the metal deposited, electrode material, temperature, and the rate of deposition (current density) therefore, comparison is difficult or meaningless if several of these variables are varied simultaneously. 

Scrosati determined the solubility of PdO in the melt by chrono-potentiometry. The results, which are in good agreement with those obtained by potentiometry, indicated that PdO is completely dissociated in the melt. The diffusion coefficient for Pd - was reported. Schmidt et studied the reduction of Bi +, Pd +, Pt +, and Sb - voltammetrically with an inter-mittenly polarized platinum electrode. The shape of the current-voltage curves for Pd + and Pt was described by the Kolthoff-Lingane equation, whereas for Bi + and Sb + the Heyrovsky-Ilkovic equation was valid. The diffusion coefficients for the species were reported. 

Grebenik and Grachev ) studied the electrochemical behavior of Fe + and Fe " in NaCl-CaCls (58-42 mole %) melt. The voltammograms were well defined and obeyed the Heyrovsky-Ilkovic equation. The reduction of Fe + and Fe + was found to proceed directly to metal. On the other hand, Pokrovskii et measured the equilibrium potentials of... 

Pb + in LiNOg-NaNOg-KNOg eutectic by conventional polarography. The reduction of Cd +, Ni +, and Pb +, respectively, was a two-electron reversible process described by the Heyrovsky-Ilkovic equation, whereas the results for Co + were complex. The half-wave potentials and diffusion coefficients for these ions were reported. The results were compared with those reported previously. The discrepancies were attributed to the effect of impurities (i.e., HgO, Cl") in the melt. 

---