Ilkovic equation

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

The constant 607 is a combination of natural constants, including the Faraday constant it is slightly temperature-dependent and the value 607 is for 25 °C. The IlkoviC equation is important because it accounts quantitatively for the many factors which influence the diffusion current in particular, the linear dependence of the diffusion current upon n and C. Thus, with all the other factors remaining constant, the diffusion current is directly proportional to the concentration of the electro-active material — this is of great importance in quantitative polarographic analysis. 

The original IlkoviC equation neglects the effect on the diffusion current of the curvature of the mercury surface. This may be allowed for by multiplying the right-hand side of the equation by (1 + ADl/2 t1/6 m 1/3), where A is a constant and has a value of 39. The correction is not large (the expression in parentheses usually has a value between 1.05 and 1.15) and account need only be taken of it in very accurate work. 

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

Hence, from the Ilkovic equation, (equation 3.3), we obtain... 

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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 ... 

As at the limiting (diffusion-controlled) current c0 - 0, the Ilkovic equation... 

Many extensions have been derived for the Ilkovic equation from the consideration that the dme does not behave as a flat electrode but in fact shows a spherical growth. For instance, Fick s second law of diffusion (cf., eqn. 3.2) becomes12... 

Derivations based on the introduction of this modified equation lead to a small correction factor within the Ilkovic equation, viz.,... 

Influence of mercury column height. In the above Ilkovic equations for the average limiting current m and [Pg.134]

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... 

The derivation of the Ilkovic equation assumes that the drops of mercury are spherical the rate of flow of mercury is constant, the way analyte diffuses toward the DME obeys the Cottrell equation, and the diflusion current is truly limiting, i.e. that Csurfacc = 0-... 

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... 

At extreme overpotentials, the current is independent of potential. This maximum current is said to be limiting, that is, current a Cbuik- It is termed the diffusion current, /j. The dependence of la on concentration, drop speed, etc., is described by the Ilkovic equation (equation (6.5)), although calibration graphs or standard addition methods (Gran plots) are preferred for more accurate analyses. 

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This equation—in which i is in amperes, v in grains per second, t, in seconds, DA in square centimeters per second, and c° in moles per cubic centimeter—is known as the Ilkovic equation. 

In practice, this pseudo-mathematical expression, known as the Ilkovic equation, which takes into account several factors, is replaced by the simplified formula below where K is a graphical constant that includes several parameters related to the method and the instrument used. 

Firstly, owing to the importance of the Ilkovic equation, we follow Ilkovic s argument [52] in the calculation of the limiting current, which although not completely rigorous, was later shown by MacGillavry and Rideal [53] to be correct under Ilkovic s assumptions. There are three steps to the argument. 

The diffusion current (over the lifetime of a drop) is expressed by the Ilkovic equation,... 

The other factor that can show the influence of kinetic, catalytic, and adsorption effects on a diffusion-controlled process is the temperature coefficient.10 The effect of temperature on a diffusion current can be described by differentiating the Ilkovic equation [Eq. (3.11)] with respect to temperature. The resulting coefficient is described as [In (id,2/id,iV(T2 — T,)], which has a value of. +0.013 deg-1. Thus, the diffusion current increases about 1.3% for a one-degree rise in temperature. Values that range from 1.1 to 1.6% °C 1, have been observed experimentally. If the current is controlled by a chemical reaction the values of the temperature coefficient can be much higher (the Arrhenius equation predicts a two- to threefold increase in the reaction rate for a 10-degree rise in temperature). If the temperature coefficient is much larger than 2% °C-1, the current is probably limited by kinetic or catalytic processes. 

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)... 

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