Coulometry

Coulometry is a chemical analysis based on counting the electrons used in a reaction. For example, cyclohexene can be titrated with Br2 generated by electrolytic oxidation of Br  

The initial solution contains an unknown quantity of cyclohexene and a large amount of Br. When Reaction 17-7 has generated just enough Br2 to react with all the cyclohexene, the moles of electrons liberated in Reaction 17-7 are equal to twice the moles of Br2 and therefore twice the moles of cyclohexene. 

A cathodic depolarizer is reduced in preference to solvent. For oxidation reoctions. anodic depolarizers include N2H4 (hydrazine) and NH2OH (hydroxylamine) 

Coutometric methods are based on measuring the number of electrons that participate in a chemical reaction. 

Both Br2 and Br must be present for the detector half-reactions to occur. Prior to the equivalence point, there is Br. but virtually no Br2. 

Coulometry can be regarded as an analog of titration where the substance being examined is quantitatively converted to a reaction product not by the addition of titrant, but by a certain amount of electric charge Q. As in titration, the endpoint must be determined. To determine the endpoint during current flow, one combines coulometry with another of the electrochemical methods described, and accordingly is concerned with conductometric, potentiometric, or amperometric coulometry. 

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. 

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 

The methods of coulometry are based on the measurement of the quantity of electricity involved in an electrochemical electrolysis reaction. This quantity is expressed in coulombs and it represents the product of the current in amperes by the duration of the current flow in seconds. The quantity of electricity thus determined represents, through the laws of Faraday, the equivalents of reactant associated with the electrochemical reaction taking place at the electrode of significance. In the analytical chemistry sense, the process of coulometry, carried out to the quantitative reaction of the analyte in question, either directly or indirectly, will yield the number of analyte equivalents involved in the sample under test. This will lead to a quantitative determination of the analyte in the sample. Analytical coulometry can be carried out either directly or indirectly. In the former the analyte usually reacts directly at the surface of either the anode or cathode of the electrolysis cell. In the latter, the analyte reacts indirectly with a reactant produced by electrolytic action at one of the electrodes in the electrolysis cell. In either case, the determination will hinge on the number of coulombs consumed in the analytical process. 

In general the relationship between the coulombs for an analytical process and the weight of analyte involved is given by  

Wm = gram-molecular weight of analyte (reactant) n = electron transfer for analyte (reactant) in the electrode reaction involved 

If DC voltage is applied to two electrodes immersed in an electrolyte solution, the positive ions migrate to the cathode and the negative ions to the anode under the influence of the electric field. Processes of exchange 

According to Faraday, the amount of any substance primarily dissolved or 

1) The amount of any substance dissolved at or deposited on an electrode is proportional to the electric charge necessary for this reaction 

2) The amounts of different substances dissolved or deposited by the passage of the same electric charge are in the ratio of their equivalent weights. 

Equivalent weight = AtOTic weight Oxidation number 

If we consider the Zn/Cu galvanic cell, we might consider how to reverse the reaction. If a sufficient voltage is applied in the opposite direction, from a power source or battery, there will be a tendency for these reactions to reverse, provided that no new reactions occur. In this case, if we try to electrodeposit Zn from aqueous solution by forcing the reaction Zn + + 2e Zn(s), the evolution of hydrogen from the water will take precedence by the reaction 2H+ + 2e H2(g). 

There is much more water in the cell than Zn, so the applied voltage goes to form H2 and we get no deposition of Zn(s). We say that the Zn/Zn (aq) half-cell is chemically irreversible. On the other hand, the copper will dissolve if made an anode in an acidic solution, so the reaction Cu(s) Cu + 2e is said to be chemically reversible. 

Frequently, the reaction that proceeds at either the anode or cathode is the decomposition of the solvent if water is the solvent, it may electrolyze. Note that water electrolysis depends on the pH  

This is based on Faraday s first law i.e. the extent of an electrochemical process is proportional to the quantity of electricity (= current x time). In primary analysis, the species to be analysed undergoes the reaction whereas in secondary analysis, a species generated at the electrode reacts with the species to be analysed. The mass W of the species produced or ions consumed when Q coulombs are passed through the solution are given by  

In coulometric titrations, a titrant is generated, at a controlled current, in the titration vessel. A high concentration of the electroactive species which generates the titrant ensures a 100% generation efficiency. The end-point of the titration is detected potentiometrically or by a suitable alternative. 

Polarography (Anal.Chem.S4 9Z2)69%A J.Chem.Educ.60( 9Z3)296, 47(1970)A81). When the dropping mercury electrode, DME, is used as the working electrode, the technique is referred to as polarography. The instrument used is called the polarograph which displays or records a polarogram. The anode of the cell is a pool of mercury 

The DME acquires an increasingly negative potential but as the potential rises, initially very little current passes from a to b. This small current is termed the residual current. At b the emf of the cell is sufficient to induce the reaction  

The potential is referred to as the decomposition potential of the cation. The rapid linear increase in current from b to c results from the depolarisation of the DME as the metal ions are discharged as M/Hg. The system obeys Ohm s law from b to c. The general electrode reaction is  

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The sample is reduced in a hydrogen stream at 800°C in the presence of a nickel catalyst. The ammonia formed is detected by coulometry and the test sensitivity is on the order of one part per million. 

For these different methods, the detection is either by volume measurement, gravimetry, conductimetry or coulometry. 

Techniques responding to the absolute amount of analyte are called total analysis techniques. Historically, most early analytical methods used total analysis techniques, hence they are often referred to as classical techniques. Mass, volume, and charge are the most common signals for total analysis techniques, and the corresponding techniques are gravimetry (Chapter 8), titrimetry (Chapter 9), and coulometry (Chapter 11). With a few exceptions, the signal in a total analysis technique results from one or more chemical reactions involving the analyte. These reactions may involve any combination of precipitation, acid-base, complexation, or redox chemistry. The stoichiometry of each reaction, however, must be known to solve equation 3.1 for the moles of analyte. 

Two other techniques that depend only on base SI units are coulometry and isotope-dilution mass spectrometry. Coulometry is discussed in Chapter 11. Isotope-dilution mass spectroscopy is beyond the scope of an introductory text, however, the list of suggested readings includes a useful reference. 

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. 

In potentiometry, the potential of an electrochemical cell under static conditions is used to determine an analyte s concentration. As seen in the preceding section, potentiometry is an important and frequently used quantitative method of analysis. Dynamic electrochemical methods, such as coulometry, voltammetry, and amper-ometry, in which current passes through the electrochemical cell, also are important analytical techniques. In this section we consider coulometric methods of analysis. Voltammetry and amperometry are covered in Section 1 ID. 

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. 

In coulometry, current and time are measured, and equation 11.24 or equation 11.25 is used to calculate Q. Equation 11.23 is then used to determine the moles of analyte. To obtain an accurate value for N, therefore, all the current must result in the analyte s oxidation or reduction. In other words, coulometry requires 100% current efficiency (or an accurately measured current efficiency established using a standard), a factor that must be considered in designing a coulometric method of analysis. 

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. 

Current-time curve for controlled-potential coulometry. 

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. 

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... 

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. 

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. 

Control led-Potential Coulometry The majority of controlled-potential coulometric analyses involve the determination of inorganic cations and anions, including trace metals and halides. Table 11.8 provides a summary of several of these methods. 

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. 

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). 

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. 

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. 

In voltammetry the working electrode s surface area is significantly smaller than that used in coulometry. Consequently, very little analyte undergoes electrolysis, and the analyte s concentration in bulk solution remains essentially unchanged. 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

The following four experiments describe useful and accessible applications of coulometry. 

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... 

Milner, G. W. C. Phillips, G. Coulometry in Analytical Chemistry. Pergamon New York, 1967. 

Curran, D. J. Constant-Current Coulometry. Chapter 20 in Kissinger, P. T. Heineman, W. R., eds. Eaboratory Techniques in Electroanalytical Chemistry. Marcel Dekker, Inc. New York, 1984, pp.539—568. 

Electrochemical Detectors Another common group of HPLC detectors are those based on electrochemical measurements such as amperometry, voltammetry, coulometry, and conductivity. Figure 12.29b, for example, shows an amperometric flow cell. Effluent from the column passes over the working electrode, which is held at a potential favorable for oxidizing or reducing the analytes. The potential is held constant relative to a downstream reference electrode, and the current flowing between the working and auxiliary electrodes is measured. Detection limits for amperometric electrochemical detection are 10 pg-1 ng of injected analyte. 

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