Coulometry controlled-current coulometrys

The largest division of interfacial electrochemical methods is the group of dynamic methods, in which current flows and concentrations change as the result of a redox reaction. Dynamic methods are further subdivided by whether we choose to control the current or the potential. In controlled-current coulometry, which is covered in Section IIC, we completely oxidize or reduce the analyte by passing a fixed current through the analytical solution. Controlled-potential methods are subdivided further into controlled-potential coulometry and amperometry, in which a constant potential is applied during the analysis, and voltammetry, in which the potential is systematically varied. Controlled-potential coulometry is discussed in Section IIC, and amperometry and voltammetry are discussed in Section IID. 

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. 

A second approach to coulometry is to use a constant current in place of a constant potential (Figure 11.23). Controlled-current coulometry, also known as amperostatic coulometry or coulometric titrimetry, has two advantages over controlled-potential coulometry. First, using a constant current makes for a more rapid analysis since the current does not decrease over time. Thus, a typical analysis time for controlled-current coulometry is less than 10 min, as opposed to approximately 30-60 min for controlled-potential coulometry. Second, with a constant current the total charge is simply the product of current and time (equation 11.24). A method for integrating the current-time curve, therefore, is not necessary. 

Current-time curve for controlled-current coulometry. 

Instrumentation Controlled-current coulometry normally is carried out using a galvanostat and an electrochemical cell consisting of a working electrode and a counterelectrode. The working electrode, which often is constructed from Pt, is also... 

The other necessary instrumental component for controlled-current coulometry is an accurate clock for measuring the electrolysis time, fe, and a switch for starting and stopping the electrolysis. Analog clocks can read time to the nearest +0.01 s, but the need to frequently stop and start the electrolysis near the end point leads to a net uncertainty of +0.1 s. Digital clocks provide a more accurate measurement of time, with errors of+1 ms being possible. The switch must control the flow of current and the clock, so that an accurate determination of the electrolysis time is possible. 

Coulometry may be used for the quantitative analysis of both inorganic and organic compounds. Examples of controlled-potential and controlled-current coulometric methods are discussed in the following sections. 

Controllcd-Currcnt Coulomctry The use of a mediator makes controlled-current coulometry a more versatile analytical method than controlled-potential coulome-try. For example, the direct oxidation or reduction of a protein at the working electrode in controlled-potential coulometry is difficult if the protein s active redox site lies deep within its structure. The controlled-current coulometric analysis of the protein is made possible, however, by coupling its oxidation or reduction to a mediator that is reduced or oxidized at the working electrode. Controlled-current coulometric methods have been developed for many of the same analytes that may be determined by conventional redox titrimetry. These methods, several of which are summarized in Table 11.9, also are called coulometric redox titrations. 

Scale of Operation Coulometric methods of analysis can be used to analyze small absolute amounts of analyte. In controlled-current coulometry, for example, the moles of analyte consumed during an exhaustive electrolysis is given by equation 11.32. An electrolysis carried out with a constant current of 100 pA for 100 s, therefore, consumes only 1 X 10 mol of analyte if = 1. For an analyte with a molecular weight of 100 g/mol, 1 X 10 mol corresponds to only 10 pg. The concentration of analyte in the electrochemical cell, however, must be sufficient to allow an accurate determination of the end point. When using visual end points, coulometric titrations require solution concentrations greater than 10 M and, as with conventional titrations, are limited to major and minor analytes. A coulometric titration to a preset potentiometric end point is feasible even with solution concentrations of 10 M, making possible the analysis of trace analytes. 

Precision Precision is determined by the uncertainties of measuring current, time, and the end point in controlled-current coulometry and of measuring charge in controlled-potential coulometry. Precisions of +0.1-0.3% are routinely obtained for coulometric titrations, and precisions of +0.5% are typical for controlled-potential coulometry. 

Time, Cost, and Equipment Controlled-potential coulometry is a relatively time-consuming analysis, with a typical analysis requiring 30-60 min. Coulometric titrations, on the other hand, require only a few minutes and are easily adapted for automated analysis. Commercial instrumentation for both controlled-potential and controlled-current coulometry is available and is relatively inexpensive. Low-cost potentiostats and constant-current sources are available for less than 1000. 

The way in which these alternatives with their particular measuring characteristics are carried out can be best described by (1) controlled-potential coulometry and (2) coulometric titration (controlled-current coulometry). Both methods require an accurate measurement of the number of coulombs consumed, for which the following instrumental possibilities are available (a) chemical coulometers, (b) electrochemical coulometers and (c) electronic coulometers. 

Coulometric titration. For this technique, often designated controlled-current or amperostatic coulometry, it is useful to distinguish between redox, complex-formation and precipitation titrations on the one hand and acid-base titrations on the other and to discuss each group separately. 

A method that completely electrolyzes the substances under study is used in electrogravimetry and coulometry. The method is also useful in electrolytic separations and electrolytic syntheses. Electrolysis is carried out either at a controlled potential or at a controlled current. 

In coulometry, the analyte is quantitatively electrolyzed and, from the quantity of electricity (in coulombs) consumed in the electrolysis, the amount of analyte is calculated using Faraday s law, where the Faraday constant is 9.6485309 xlO4 C mol-1. Coulometry is classified into controlled-potential (or potentiostatic) coulometry and controlled-current (or galvanostatic) coulometry, based on the methods of electrolysis [19, 20]. 

Controlled-current coulometry is also called coulometric titration. An apparatus for controlled-current coulometry is shown in Fig. 5.35 for the case of determination of an acid. It consists of a constant current source, a timer, an end-point detector (pH meter), and a titration cell, which contains a generating electrode, a counter electrode in a diaphragm, and two electrodes for pH detection. The timer... 

Fig. 5.35 Apparatus for controlled-current coulometry. The case for neutralization titration of an acid by internal cathodic generation of OhT. GE generating electrode CE counter electrode.

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.

Instructional Examples of Electrode Mechanisms of Transition Metal Complexes - 683 24. Electrochemical Preconcentration - 719 25. Controlled-Current Coulometry - 739 26. Electrochemistry in Pharmaceutical Analysis - 769... 

Controlled-current electrolysis in flowing solution has been extremely useful for analytical purposes. The prevalent techniques are constant-current coulometry and coulometric titrations, which are discussed in Chapter 25. 

Figure 25.4 Block diagram of an apparatus for controlled-current coulometry. A double-throw, double-pole switch is used to turn the timer and electrolysis current on and off. [Adapted from G.W. Ewing, in Am. Lab. 13(6) 16-22 (1981). Copyright 1981 by International Scientific Communications, Inc.]...

Figure 25.6 Block diagram of an all-solid-state apparatus for controlled-current coulometry.

Programmable constant-current sources can be constructed from programmable operational amplifiers or programmable power supplies. These devices coupled with the IFC produce a powerful approach to controlled-current coulometry. 

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