Ilkovic equation, polarography

Ilkovic equation The relation between diffusion current, ij, and the concentration c in polarography which in its simplest form is... 

As a consequence of the particular geometry of the dme and its periodically altering surface area, the theory of polarography necessarily requires an amplification of what has already been stated about the theory of electrolysis in Sections 3.1 and 3.2. Such an amplification was given in 1934 by Ilkovic in close collaboration with Heyrovsky, and resulted in the well known Ilkovic equation ... 

Polarography is the classical name for LSV with a DME. With DME as the working electrode, the surface area increases until the drop falls off. This process produces an oscillating current synchronized with the growth of the Hg-drop. A typical polarogram is shown in Fig. 18b. 10a. The plateau current (limiting diffusion current as discussed earlier) is given by the Ilkovic equation... 

Ideal gas, standard state, 936 Ilkovic equation, 1246 Ilkovic, D., polarography, 1424 Image dipole, 896... 

Current-Sampled Polarography. As follows from the Ilkovic equation [Eq. (3.10)], the current at the electrode that results from the electrolysis of an electroactive species (Faradaic current) increases proportionally to tU6 during the life of the mercury drop. However, the electrical double layer is a capacitor that must be charged as potential is applied via a charging current (icc)... 

Figure 20.3 Polarographic cell and diffusion current. The solution must be free from dissolved oxygen which otherwise causes an interfering double wave (see Figure 20.6). On the right, graph of the diffusion current, growing over time for each drop of mercury in a static solution (unstirred solution). Direct polarography is a slow method of analysis. The recording of a voltamogram requires at least one hundred droplets. A calculation of % max is possible with the Ilkovic equation if the coefficient 607 is replaced by 706 in equation 20.2.

For reversible systems (with fast eleetron-transfer kinetics), the shape of the polarographie wave can be deseribed by the Heyrovsky—Ilkovic equation ... 

This equation may take a variety of forms depending upon the behaviour of the oxidised and reduced species at the electrode. The version presented here is applicable to a situation where the oxidised species is the only species in the solution and this species is being reduced at a cathode where the reduced species either goes into solution or forms an amalgam with mercury. This equation is then directly relevant to most of the applications of dc polarography. Consider the Ilkovic equation applied to the reaction ... 

In AC polarography, peaks instead of steps are recorded, facilitating the evaluation of the polarogram. The strength of the diffusion current i j is given by the Ilkovic equation ... 

The possibility of applpng the simple IlkoviC equation for calculations of the number of electrons ( ) cannot be recommended, for the exact values of the diffusion coefficients are usually unknown under the conditions used in polarography (i.e. at low concentrations). Moreover, it would be necessary to use the extended form of the Ilkovi6 equation ) to obtain precise values. Thus the usual operation is to compare the height of the wave under examination, with the height for a substance in the same molar concentration in the same supporting electrolyte. The number of electrons transferred for the latter substance must be known precisely under the conditions used. The standard substance must be a well-defined chemical entity, and the molecular... 

This is the Ilkovic equation, which was developed by solving the diffusion equations directly very early in the history of polarography. It shows that the diffusion current varies with (Obviously the maximum current will depend on r/, where is the duration of drop life.) It also shows that the current depends on the rate of flow of mercury. However, the quantity m is not very easily determined, although it can be measured if needed. The parameter that can be measured easily is the height of the surface of the mercury in the reservoir (Fig. 12) above the tip of the capillary, h, Poiseuille s equation states that m is proportional to h and that is inversely proportional to h. Thus // is proportional to h. Thus, in order to determine whether a current measured with the d.m.e. is diffusion controlled, all that is necessary is to check whether I is proportional to both and The current actually measured and reported in polarography is not the instantaneous one but an average current... 

Characteristics of diffusion-controlled polarographic waves The magnitude of diffusion-controlled currents are direct functions of depolarizer concentration and in this fact lies the quantitative analytical significance of polarography. All quantitative analysis by the technique is based on the direct proportionality between the limiting diffusion controlled current and depolarizer concentration as expressed in the Ilkovic equation viz.,... 

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. 

The use of an equation as complex as Eq. (67) requires a lot of numerical calculations so that approximate solutions are very favorable. The first model to describe the adsorption at the surface of a growing drop was derived by Ilkovic in 1938 (107). The boundary conditions were chosen such that the model corresponded to a mercury drop in a polarography experiment. These conditions, however, are not suitable for describing the adsorption of surfactants at a liquid-drop surface. Delahay and coworkers (108, 109) used the theory of Ilkovic and derived an approximation suitable for the description of adsorption kinetics at a growing drop. The relationship was derived only for the initial period of the adsorption process ... 

The mercury dropping electrode was first introduced to electrolysis by J. Heyrovsky.< > The most important milestones in the theoretical development of polarography were the exact deduction of the equation for the limiting diffusion current by D. Ilkovi(5,< > of the equation for the shape of polarographic wave by J. Heyrov-sky and D. Ilkovic, the introduction of the conception of halfwave potentials by the same authors, the recognition of catalytic< > and adsorption currents by R. Brdicka and the development of the theory of kinetic currents by K. Wiesner, R. Brdicka, J. 

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