Controlled potential coulometry

Selecting a Constant Potential In controlled-potential coulometry, the potential is selected so that the desired oxidation or reduction reaction goes to completion without interference from redox reactions involving other components of the sample matrix. To see how an appropriate potential for the working electrode is selected, let s develop a constant-potential coulometric method for Cu + based on its reduction to copper metal at a Pt cathode working electrode. 

The potential needed for a quantitative reduction of Cu + can be calculated using the Nernst equation 

Current-time curve for controlled-potential coulometry. 

The difference between the potential actually required to initiate an oxidation or reduction reaction, and the potential predicted by the Nernst equation. 

The change in current as a function of time in controlled-potential coulometry is approximated by an exponential decay thus, the current at time t is 

Faraday s law of electrolysis states that a given amount of chemical change caused by electrolysis is directly proportional to the amount of electricity passed through the cell  

This law may be applied to the quantitative analysis of a variety of substances, provided conditions are such that the reaction proceeds with 100% current efficiency (no side reactions). One approach to 100% current efficiency is to hold the potential of the working electrode at such a value that only one reaction will occur, as can be 

Some of the first methods of measuring quantities of electricity involved the use of chemical coulometers. To do this, an electrolytic cell is placed in seri with the sample electrolysis cell so that the same current passes through both. A typical coulometer cell consists of a platinum crucible containing a silver-nitrate solution and a silver anode. Silver metal is deposited on the preweighed platinum crucible and the latter reweighed to determine the amount of electricity passed Q is calculated from Equation 4.10. 

A similar gas coulometer that uses hydrazine sulfate as an electrolyte is more accurate at low currents. In this case the hydrazine is oxidized to nitrogen at the anode (see Eqn. 4.6) so the gas mixture consists of nitrogen and hydrogen. 

Controlled-potential coulometry may be applied to the analysis of a wide variety of substances. Clearly, metals like copper could be deposited and determined without the necessity of weighing the electrode. More importantly, mercury electrodes can be used and thus most of the metals more difficult to reduce can be determined. Also, it is possible to apply coulometry to systems in which both oxidized and reduced forms are soluble, such as determining iron by reducing iron(III) to iron(II). Anions such as chloride or bromide may be converted to AgCl or AgBr by deposition on a silver anode. 

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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. 

Minimizing Electrolysis Time The current-time curve for controlled-potential coulometry in Figure 11.20 shows that the current decreases continuously throughout electrolysis. An exhaustive electrolysis, therefore, may require a long time. Since time is an important consideration in choosing and designing analytical methods, the factors that determine the analysis time need to be considered. 

From this equation we see that increasing k leads to a shorter analysis time. For this reason controlled-potential coulometry is carried out in small-volume electrochemical cells, using electrodes with large surface areas and with high stirring rates. A quantitative electrolysis typically requires approximately 30-60 min, although shorter or longer times are possible. 

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. 

The ability to control selectivity by carefully selecting the working electrode s potential, makes controlled-potential coulometry particularly useful for the analysis of alloys. For example, the composition of an alloy containing Ag, Bi, Cd, and Sb... 

Another area where controlled-potential coulometry has found application is in nuclear chemistry, in which elements such as uranium and polonium can be determined at trace levels. Eor example, microgram quantities of uranium in a medium of H2SO4 can be determined by reducing U(VI) to U(IV) at a mercury working electrode. 

Controlled-potential coulometry also can be applied to the quantitative analysis of organic compounds, although the number of applications is significantly less than that for inorganic analytes. One example is the six-electron reduction of a nitro group, -NO2, to a primary amine, -NH2, at a mercury electrode. Solutions of picric acid, for instance, can be analyzed by reducing to triaminophenol. 

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. 

In controlled-potential coulometry, accuracy is determined by current efficiency and the determination of charge. Provided that no interferents are present that are easier to oxidize or reduce than the analyte, current efficiencies of greater than 99.9% are easily obtained. When interferents are present, however, they can often be eliminated by applying a potential such that the exhaustive electrolysis of the interferents is possible without the simultaneous electrolysis of the analyte. Once the interferents have been removed the potential can be switched to a level at... 

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 purity of a sample of picric acid, C6H3N3O7, is determined by controlled-potential coulometry, converting the picric acid to triaminophenol, C6H9N3O. A 0.2917-g sample of picric acid is placed in a 1000-mL volumetric flask... 

It is also possible to reduce the time required for conventional controlled-potential coulometry by adopting the procedure of predictive coulometry.27 A given determination will need a certain number ofcoulombs(Qx)for completion, and if at time t, Q, coulombs have been passed, then QR further coulombs will be required to complete the determination, and <2 = Qx - Qv By choosing a number of times tl,t2,t 3 separated by a common interval (say 10 seconds) and measuring the corresponding numbers of coulombs passed Ql,Q2,Q3, it can be shown that... 

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. 

For controlled-potential coulometry the voltage drop over a standard resistor is measured as a function of time by means of a voltage-to-frequency converter the output signal consists of a time-variant and integrally increasing number of counts (e.g., 10 counts mV-1), which by means of an operational amplifier-capacitor yields the current-time curve and integral158. 

The reduction of cyanocobalamin gives three possible oxidation states for the cobalt atom (Fig. 2). Electron spin resonance studies with Bi2-r reveals that this molecule is the only paramagnetic species giving a spectrum expected for a tetragonal low spin Co(II) complex. Controlled potential reduction of cyanocobalamin to Bi2-r proves that this reduction involves one electron, and further reduction of Bi2-r to B12-S requires a second single electron (16—19). At one time B12-S was considered to be a hydride of Co(III), but controlled potential coulometry experiments provided evidence against a stable hydride species (16). However, these experimental data do not exclude the possibility of a stable Co(III) hydride as the functional species in enzyme catalyzed oxidation reduction reactions. 

An early study on C02 reduction in non-aqueous solvents was carried out by Haynes and Sawyer (1967) who employed chronopotentiometry, controlled potential coulometry and galvanostatic methods to study the reduction of C02 at Au and Hg in dimethylsulphoxide (DMSO). 

Controlled-potential coulometry involves nearly complete reduction or oxidation of an analyte ion at a working electrode maintained at a constant potential and integration of the current during the elapsed time of the electrolysis. The integrated current in coulombs is related to the quantity of analyte ion by Faraday s law, where the amps per unit time (coulomb) is directly related to the number of electrons transferred, and thus to the amount of analyte electrolyzed. 

Elmer Lujan, a technician with the Los Alamos National Laboratory in New Mexico, prepares metal samples to be analyzed for plutonium using controlled-potential coulometry. (Photo by Laurie Walker.)... 

The best method to determine the number n of electrons involved in a redox process is through controlled potential coulometry. 

The principle of controlled potential coulometry is very simple. If, for instance, we wish to study the usual process ... 

Table 3 Diagnostic criteria in controlled potential coulometry...

Ferrocene gives rise to an anodic process, which in controlled potential coulometry involves one electron per molecule. As a consequence of the exhaustive oxidation the original yellow solution turns blue-green, a colour typical of the iron-centred ferrocenium ion (/Uax = 620 nm). The voltammogram of the final solution is complementary to that shown in Figure 2. 

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