Coulometry at controlled potential

In a controlled-potential coulometric analysis, the current generally decreases exponentially with time according to the equation 

In electrolysis at controlled potential, the quantity of electricity Q (coulombs) passed from the beginning of the determination to time t is given by 

This equation is that of a first-order reaction process, and thus the fraction of material electrolysed at any instant is independent of the initial concentration. It follows that if the limit of accuracy of the determination is set at C, = 0.001 C0, the time t required to achieve this result will be independent of the initial concentration. The constant k in the above equation can be shown to be equal to Am/ V, where A is the area of the pertinent electrode, V the volume of the solution and m the mass transfer coefficient of the electrolyte.20 It follows that to make t small A and m must be large, and V small, and this leads to the 

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The oxidation state of Au in both Au-oxo complexes 3 and 4 was thoroughly investigated by several chemical and physicochemical methods 44). First, bulk electrolysis (coulometry at controlled potential) confirms the Au(III) oxidation state assignment in both 3... 

Meites, L. Submicrogram-Scale Analysis by Coulometry at Controlled Potential. Anal. Chim. Acta 20, 456 (1959). 

Direct coulometry is often referred to as coulometry at controlled potential. In the direct method, the electrode reaction nearly always involves the analyte... 

Controlled-potential coulometry has also found some use in the study of basic electrochemistry. It is not always obvious how many electrons are involved in a newly studied electrochemical reaction, e.g., in polarography. Thus, coulometry at controlled potential, in which a known quantity of the substance is electrolyzed and Q is measured, is often used to determine values for n and thereby help elucidate electrode mechanisms for a wide variety of compounds, both organic and inorganic. Very slow chemical reactions coupled with the electrochemical reaction may also be studied by controlled-potential coulometry [4] other electrochemical techniques usually are suitable only for much faster chemical reactions, with time scales of jusec to sec. 

Coulometry. Two methods of coulometry are used coulometry at controlled potential and coulometric titrations. The main advantage of the coulometric method is the elimination of the necessity of standardization as the Faraday constant is a standard. In analysis of complicated samples encountered in environmental analysis the coulometric titrations are more advantageous where 100% current efficiency can be more readily attained by suitable choice of the reagent-solvent system. Coulometric titrations are suitable for determining the amount of substance in the range 0.01 to 100 mg (and sometimes below 1 iJg). Under optimum conditions these titrations can be carried out with a precision and accuracy of 0.01%. Automatic coulometric analyzers for the determination of gaseous pollutants (SO2, O3, NO, etc.) have proven to be useful in environmental chemistry. 

In order to illustrate the application of LSV in mechanistic analysis we can look at the redox behavior of the formazan-tetrazolium salt system which we studied some years ago [17], 1,3,5-Triphenyl formazane was oxidized at controlled potential in CH3CN-Et4NC104 solution to 2,3,5-triphenyl tetrazolium perchlorate which was then isolated in quantitative yield. Coulometry showed that the overall electrode reaction was a two-electron oxidation. It has been shown that the rate of variation of Ep with log v was 30 mV per decade of sweep rate and that there was no variation of the peak potential with the concentration of 1,3,5-triphenylformazan. According to Saveant s diagnostic criteria (Table 1), four mechanistic schemes were possible e-C-e-p-p, e-C-d-p-p, e-c-P-e-p and e-c-P-d-p. If cyclization is the rate-determining step, then the resulting e-C-e-p-p and e-C-d-p-p mechanisms would not imply variation of Ep with the concentration of base. However, we have observed the 35 mV shift of Ep cathodically in the presence of 4-cyanopyridine as a b e. These observations ruled out the first two mechanisms. The remaining possibilities were then e-c-P-e and e-c-P-d, as shown in Scheme 3. 

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,... 

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. 

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 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... 

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. 

Studies aimed at characterizing the mechanisms of electrode reactions often make use of coulometry for determining the number of electrons involved in the reaction. To make such measurements a known amount of a pure compound is subject to a controlled-potential electrolysis. The coulombs of charge needed to complete the electrolysis are used to determine the value of n using Faraday s law (equation 11.23). 

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... 

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 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. 

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