Coulometry at constant current

Quiescent Solutions. Coulometry at constant current provides a simple method for measuring the quantity of electrogenerated species as long as the reaction proceeds with 100% current efficiency. However, this condition breaks down with depletion of the electroactive material in the diffusion layer (cf. chronopotentiometric transitions see Fig. 4.3). For low values of the applied current, the thermal and density gradients supplement diffusion sufficiently to sustain electrolysis without the potential shifting to a different reaction. This mode of radical generation has been employed successfully in the study of stable species. 

Coulometry at constant current is often considered as being less attractive than coulometry at constant potential. However, when the current density is low, the potential of the working electrode stays almost constant until approximately 90% of the substrate is consumed. Control of the current rather than the potential has, however, a number of advantages. First, the charge consumed during the reaction is directly proportional to the electrolysis time,... 

In coulometry, one must define exactly the amount of charge that was consumed at the electrode up to the moment when the endpoint signal appeared. In galvanosta-tic experiments (at constant current), the charge is defined as the product of current and the exactly measured time. However, in experiments with currents changing continuously in time, it is more convenient to use special coulometers, which are counters for the quantity of charge passed. Electrochemical coulometers are based on the laws of Faraday with them the volume of gas or mercury liberated, which is proportional to charge, is measured. Electromechanical coulometers are also available. 

Fig. 9.1 Determination of the number of electrons by controlled-current coulometry [2]. The case when 0.1 mmol of 2,3,5,6-tetraphenyl-l, 4-ditin in AN is electrolyzed at constant current (50 mA). The CV curves were measured, from left to right, after 0, 1, 2, 3, 4, 5 and 6 min, 0 1 2 3 4 5 6 7 respectively.

A different way of determining n values is based on the measurement of the amount of charge necessary for the exhaustive electrolysis of a known amount of substrate. This type of experiment, traditionally called coulometry, may be carried out either at constant potential or at constant current. 

During coulometry at constant potential, the amount of charge is obtained by integration of the current-time curve (Fig. 41). 

During coulometry at constant potential, the total amount of charge (g) is obtained by integration of the current (7) - time (0 curve or g can be determined directly by using a coulometer (electronic integrator). In principle, the end point 1 = 0, i.e., when the concentration of the species under study becomes zero, can be reached only at infinite time, however, in practice the electrolysis is stopped when the current has decayed to a few percent of the initial values. The change of I and g as a function of time at a constant potential >> e. for a stirred solutions and for an uncomplicated electrolysis, is as follows ... 

Coulometric methods of analysis are based on an exhaustive electrolysis of the analyte. By exhaustive we mean that the analyte is quantitatively oxidized or reduced at the working electrode or reacts quantitatively with a reagent generated at the working electrode. There are two forms of coulometry controlled-potential coulometry, in which a constant potential is applied to the electrochemical cell, and controlled-current coulometry, in which a constant current is passed through the electrochemical cell. 

Figure 4.19 A constant current coulometry titration cell. The reagent is produced at the working electrode and reacts with the sample. The indicator electrodes detect the changing potential or conductivity of the solution and the amount of change that takes place is measured and related to the concentration of the reactant in the sample.

The Karl Fischer titration of water uses a buret to deliver reagent or coulometry to generate reagent. In bipotentiometric endpoint detection, the voltage needed to maintain a constant current between two Pt electrodes is measured. The voltage changes abruptly at the equivalence point, when one member of a redox couple is either created or destroyed. 

The number of electrons exchanged on a time scale similar to that of a preparative electrolysis is determined by coulometry. A coulometry experiment involves the complete conversion of the substrate to product(s) and, accordingly, C 0 decreases with time, in principle to zero. This is in contrast to the electro analytical methods where C 0 stays essentially constant during the experiments. Coulometry is carried out at either constant potential or constant current and, usually, the solution is stirred magnetically. 

Fig. 6.26 Values of /°x recorded by voltammetry at 1-minute intervals during constant current coulometry...

Under conditions where the primary electrode product undergoes a slow chemical reaction, that is, ti/2 is of the order of seconds, the value of n determined by a relatively fast technique like LSV may differ from that obtained by a slow experiment like coulo-metry. This type of behavior was observed in the anodic oxidation of 2,3,5,6-tetraphenyl-1,4-dithiin in MeCN [278]. During CV the reversible oxidation to the radical cation is observed. However, when constant-current coulometry was carried out as described earlier, this time at i = 50 mA, 6.44 min was required to oxidize completely 0.1 mmol of the substrate to a product electroinactive in the potential region of interest, indicating an overall two-electron process (Fig. 43). Thus, apparently contradictory results may be obtained due to the difference in time scale between the two types of experiment. 

In controlled-potential coulometry, the working electrode potential is maintained at a constant value with respect to a reference electrode. In constant-current coulometry, the cell is operated so that the current is maintained at a constant value. 

There are two options. Coulometry can be conducted in the constant current and the constant potential modes. The former is inherently simpler as in this case the total charge is obtained directly from the measured time to the completion of the reaction. However, it can only be used successfully if there is only one redox-active species present in the sample or if at least the redox potentials of species present are succinctly different. In constant current coulometry, the cell voltage needs to follow the depletion of the concentration of the analyte according to Nemst s law (for an oxidation) ... 

The methods where the electrode reaction is not at equilibrium are numerous. In Figure 1, only the two most common methods are considered voltammetry and coulometry. In voltammetry, the electrical current is measured at different potentials and is linearly dependent on the concentration of the analyte. In coulometric methods, the current is integrated over a period of time giving the charge as the parameter measured. The amount of substance of the analyte is, according to Faraday s law, directly related to the charge consumed in the electrode reaction. Coulometric measurements may be performed either in the constant current or constant potential mode. Voltammetric and coulometric methods are not as specific as the potentiometric methods because... 

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