Coulometric analysis

If the initial concentration of Cu + is 1.00 X 10 M, for example, then the cathode s potential must be more negative than -1-0.105 V versus the SHE (-0.139 V versus the SCE) to achieve a quantitative reduction of Cu + to Cu. Note that at this potential H3O+ is not reduced to H2, maintaining a 100% current efficiency. Many of the published procedures for the controlled-potential coulometric analysis of Cu + call for potentials that are more negative than that shown for the reduction of H3O+ in Figure 11.21. Such potentials can be used, however, because the slow kinetics for reducing H3O+ results in a significant overpotential that shifts the potential of the H3O+/H2 redox couple to more negative potentials. 

Maintaining Current Efficiency To illustrate why changing the working electrode s potential can lead to less than 100% current efficiency, let s consider the coulometric analysis for Fe + based on its oxidation to Fe + at a Pt working electrode in 1 M H2SO4. 

Ladder diagrams for the controlled-current coulometric analysis of Fe + (a) without the addition of Ce +, and (b) with the addition of Ce +. The matrix is 1 M H2SO4 in both cases. 

End Point Determination Adding a mediator solves the problem of maintaining 100% current efficiency, but does not solve the problem of determining when the analyte s electrolysis is complete. Using the same example, once all the Fe + has been oxidized current continues to flow as a result of the oxidation of Ce + and, eventually, the oxidation of 1T20. What is needed is a means of indicating when the oxidation of Fe + is complete. In this respect it is convenient to treat a controlled-current coulometric analysis as if electrolysis of the analyte occurs only as a result of its reaction with the mediator. A reaction between an analyte and a mediator, such as that shown in reaction 11.31, is identical to that encountered in a redox titration. Thus, the same end points that are used in redox titrimetry (see Chapter 9), such as visual indicators, and potentiometric and conductometric measurements, may be used to signal the end point of a controlled-current coulometric analysis. For example, ferroin may be used to provide a visual end point for the Ce -mediated coulometric analysis for Fe +. 

Representative Examples for the Controlled-Potential Coulometric Analysis of Inorganic Ions... 

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. 

Quantitative Calculations The absolute amount of analyte in a coulometric analysis is determined by applying Faraday s law (equation 11.23) with the total charge during the electrolysis given by equation 11.24 or equation 11.25. Example 11.8 shows the calculations for a typical coulometric analysis. 

Coulometric analysis is an application of Faraday s First Law of Electrolysis which may be expressed in the form that the extent of chemical reaction at an electrode is directly proportional to the quantity of electricity passing through the electrode. For each mole of chemical change at an electrode (96487 x n) coulombs are required i.e. the Faraday constant multiplied by the number of electrons involved in the electrode reaction. The weight of substance produced or consumed in an electrolysis involving Q coulombs is therefore given by the expression... 

The fundamental requirement of a coulometric analysis is that the electrode reaction used for the determination proceeds with 100 per cent efficiency so that the quantity of substance reacted can be expressed by means of Faraday s Law from the measured quantity of electricity (coulombs) passed. The substance being determined may directly undergo reaction at one of the electrodes (primary coulometric analysis), or it may react in solution with another substance generated by an electrode reaction (secondary coulometric analysis). 

Two distinctly different coulometric techniques are available (1) coulometric analysis with controlled potential of the working electrode, and (2) coulometric analysis with constant current. In the former method the substance being determined reacts with 100 per cent current efficiency at a working electrode, the potential of which is controlled. The completion of the reaction is indicated by the current decreasing to practically zero, and the quantity of the substance reacted is obtained from the reading of a coulometer in series with the cell or by means of a current-time integrating device. In method (2) a solution of the substance to be determined is electrolysed with constant current until the reaction is completed (as detected by a visual indicator in the solution or by amperometric, potentiometric, or spectrophotometric methods) and the circuit is then opened. The total quantity of electricity passed is derived from the product current (amperes) x time (seconds) the present practice is to include an electronic integrator in the circuit. 

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

SEPARATION OF NICKEL AND COBALT BY COULOMETRIC ANALYSIS AT CONTROLLED POTENTIAL... 

Extensive summaries of the applications of coulometric analysis will be found in Refs 21 and 22. 

For coulometric analysis, the substance being examined must react in 100% current yields [i.e., other (secondary) reactions must be entirely absent]. In efforts to avoid side reactions, coulometry most often is performed potentiostatically (amperometrically) (i.e., the electrode potential is kept constant during the experiment), and the current consumed at the electrode is measured. The current is highest at the start of the... 

Now returning to the coulometric analysis proper we can. say that any determination that can be carried out by voltammetry is also possible by coulometry whether it should be done by means of the controlled-potential or the titration (constant-current) method much depends on the electrochemical properties of the analyte itself and on additional circumstances both methods, because they are based on bulk electrolysis, require continuous stirring. 

Nuclear Magnetic Resonance and Electron Spin Resonance Methods X-ray Spectrometry Vol. 2D Coulometric Analysis... 

In summary, large-area electrodes are a good way of increasing the speed at which a coulometric analysis can be performed, and are especially useful if large charges need to be passed, e.g. if concentrations of analyte are high. 

A major branch of analytical chemistry uses electrical measurements of chemical processes at the surface of an electrode for analytical purposes. For example, hormones released from a single cell can be measured in this manner. Principles developed in this chapter provide a foundation for potentiometry, redox titrations, electrogravimetric and coulometric analysis, voltammetry, and amperometry in the following chapters.1-2... 

K. Abresch and I. Claassen, Coulometric Analysis, Franklin Publishing, Englewood, NJ, 1966. 

Electroanalysis and Coulometric Analysis. Anal. Chem. (Reviews) 32, 31R (1960). 

Willner and coworkers demonstrated three-dimensional networks of Au, Ag, and mixed composites of Au and Ag nanoparticles assembled on a conductive (indium-doped tin oxide) glass support by stepwise LbL assembly with A,A -bis(2-aminoethyl)-4,4 -bipyridinium as a redox-active cross-linker.8 37 The electrostatic attraction between the amino-bifunctional cross-linker and the citrate-protected metal particles led to the assembly of a multilayered composite nanoparticle network. The surface coverage of the metal nanoparticles and bipyridinium units associated with the Au nanoparticle assembly increased almost linearly upon the formation of the three-dimensional (3D) network. A coulometric analysis indicated an electroactive 3D nanoparticle array, implying that electron transport through the nanoparticles is feasible. A similar multilayered nanoparticle network was later used in a study on a sensor application by using bis-bipyridinium cyclophane as a cross-linker for Au nanoparticles and as a molecular receptor for rr-donor substrates.8... 

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