Polarograph diffusion current

The magnitude of the polarographic diffusion current is given by the Ukovic... 

The entire subject of amperometric titrations has been reviewed in a number of monographs on electrochemistry 4-6 a definitive work on this subject also has been published.7 Because the amperometric titration method does not depend on one or more reversible couples associated with the titration reaction, it permits electrochemical detection of the endpoint for a number of systems that are not amenable to potentiometric detection. All that is required is that electrode conditions be adjusted such that either a titrant, a reactant, or a product from the reaction gives a polarographic diffusion current. 

Control of Temperature and Pressure. Diffusion coefficients in aqueous solution have a temperature coefficient of about +2% deg 1,42 which means that polarographic diffusion currents or voltammetric peak currents increase about 1-2% deg-1. The rates of follow-up chemical reactions of reactive species produced at the electrode surface depend even more strongly on temper-... 

Diffusion Current at the Dropping Mercury Electrode To derive an equation for polarographic diffusion currents, we must take into account the rate of growth of the spherical electrode, which is related to the drop time in seconds, t the rate of flow of mercury through the capillary m in mg/s and the diffusion coefficient of the analyte D in cm-/s. These variables are taken into account in the Ilkovic equation ... 

The current thus depends on the area of the electrode, on the concentration of the electroactive species, and on its diffusion coefficient. Apart from the difference in the value of the proportionality constant k, the peak current ip shows a dependence on the number of electrons transferred (n) different from that observed in polarog-raphy in DC polarography, the diffusion current is directly proportional to n, whereas in linear-sweep voltammetry the peak current is proportional to Finally, the essential difference between the currents obtained by the two techniques is in the dependence of the peak currents on the rate of scanning, v, which becomes an important variable, whereas polarographic diffusion currents are not dependent on v. 

The diffusion current constant Ja is used to correct polarographic diffusion currents for differences in capillary characteristics. For average currents... 

The rates of slow chemical reactions in solution can generally be studied by quite simple and conventional methods. The reactants are mixed in some vessel and the progress of the reaction is followed by titrating aliquots of the mixture or by measuring, at known times, a physical property of the solution such as optical absorption or polarographic diffusion current. 

Lingane JJ, Kolthoff IM (1939) Fundamental studies with the dropping mercury electrode. I. The Ilkovic equation of polarographic diffusion currents. J Am Chem Soc 61 825-834. doi 10.1021/ja01873a016... 

KouTECKf, J. and von Stackelberg, M., The Equation for Polarographic Diffusion Currents and the Limits of its Validity, in Progress in Polarography (P. Zuman, I. M. Kolthoff, editors), Vol. 1, p. 21, Interscience, New York (1962) where further references are given... 

The vanadium(ii) reduction of nitrate ion has been investigated using the time dependence of polarographic diffusion currents. At pH < 2... 

Meites (59) has determined cobalt in the presence of nickel by measurement of polarographic diffusion currents at —0.70 V vs. SCE before and after oxidation of cobalt (II) to cobalt (III) with perman ganate. The same author has also determined cobalt (H) by reduction to the metal at —1.45 V vs. SCE in an ammoniacal supporting electrolyte after pre-reduction at —1.10 V vs. SCE to convert all of the cobalt to the 2 state. 

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. 

Polarographic maxima. Current-voltage curves obtained with the dropping mercury cathode frequently exhibit pronounced maxima, which are reproducible and which can be usually eliminated by the addition of certain appropriate maximum suppressors . These maxima vary in shape from sharp peaks to rounded humps, which gradually decrease to the normal diffusion-current curve as the applied voltage is increased. A typical example is shown in Fig. 16.3. Curve A is that for copper ions in 0.1 M potassium hydrogencitrate solution, and curve B is the same polarogram in the presence of 0.005 per cent acid fuchsine solution. 

Here Ee is the standard potential of the reaction against the reference electrode used to measure the potential of the dropping electrode, and the potential E refers to the average value during the life of a mercury drop. Before the commencement of the polarographic wave only a small residual current flows, and the concentration of any electro-active substance must be the same at the electrode interface as in the bulk of the solution. As soon as the decomposition potential is exceeded, some of the reducible substance (oxidant) at the interface is reduced, and must be replenished from the body of the solution by means of diffusion. The reduction product (reductant) does not accumulate at the interface, but diffuses away from it into the solution or into the electrode material. If the applied potential is increased to a value at which all the oxidant reaching the interface is reduced, only the newly formed reductant will be present the current then flowing will be the diffusion current. The current / at any point... 

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 ... 

With a well-defined polarographic wave where the limiting current plateau is parallel to the residual current curve, the measurement of the diffusion current is relatively simple. In the exact procedure, illustrated in Fig. 16.6(a), the actual... 

Polarograms are sometimes distorted by polarographic maxima, where the current in individual segments of the I vs. E curves is much higher (several times) than the limiting diffusion current. A number of reasons exist for the development of these maxima. 

Hence, the reduction of arenesulfenates at the mercury electrode can proceed by the formation of intermediate arenethiomercuric derivatives. Such derivatives are reduced just after their formation and more easily than the initial arenesulfenates. In line with this argument, it logically follows that the limiting currents of the polarographic waves would depend solely on the diffusion of substances to the electrode. In fact, diffusion currents have been observed experimentally. Experiments of electrolysis on mercury (a preparative scale) confirmed the general conclusion (Todres 1988). 

Figure 3.2. Variation of halt-wave potential (Ek) and diffusion current constant (I) for the two polarographic waves of cyclohexenone in aqueous buffers. Data from ref. [84].

Figure 19.3—Polarographic cell and diffusion current. Dissolved oxygen, which leads to an interfering double wave, has to be removed from the sample solution by degassing. On the right features of the diffusion current are shown. These increase with time for every drop of mercury in a static (unstirred) solution. Direct polarography is a slow method of analysis. More than 100 droplets are needed to record the voltammogram.

To apply equation (3) for calculation of the equilibrium constant K waves Ia and ic must both be limited by diffusion. To prove this the current is measured under conditions when it is 15% or less of the total limiting current and its dependence on the mercury pressure is followed. A diffusion current must, under these conditions, show a linear dependence on the square root of the height of the mercury column. Whenever possible, polarographic dissociation curves should be compared with data on dissociation obtained by other methods, e.g. potentiometry, N.M.R. or spectrophotometry. In the latter case it is important to show that the species responsible for a given polarographic wave is identical with that responsible for the observed absorption peak. 

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