Coulometric

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. 

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. 

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. 

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 +. 

Method for the external generation of oxidizing and reducing agents in coulometric titrations. 

Coulometric Titrations Controlled-current coulometric methods commonly are called coulometric titrations because of their similarity to conventional titrations. We already have noted, in discussing the controlled-current coulometric determination of Fe +, that the oxidation of Fe + by Ce + is identical to the reaction used in a redox titration. Other similarities between the two techniques also exist. Combining equations 11.23 and 11.24 and solving for the moles of analyte gives... 

The titrant in a conventional titration is replaced in a coulometric titration by a constant-current source whose current is analogous to the titrant s molarity. The time needed for an exhaustive electrolysis takes the place of the volume of titrant, and the switch for starting and stopping the electrolysis serves the same function as a buret s stopcock. 

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. 

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. 

Coupling the mediator s oxidation or reduction to an acid-base, precipitation, or complexation reaction involving the analyte allows for the coulometric titration of analytes that are not easily oxidized or reduced. For example, when using H2O as a mediator, oxidation at the anode produces H3O+... 

If the oxidation or reduction of H2O is carried out externally using the generator cell shown in Figure 11.25, then H3O+ or OH can be dispensed selectively into a solution containing a basic or acidic analyte. The resulting reaction is identical to that in an acid-base titration. Coulometric acid-base titrations have been used for... 

Representative Examples of Coulometric Titrations Using Acid-Base, Complexation, and Precipitation Reactions... 

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. 

The purity of a sample of Na2S203 was determined by a coulometric redox titration using as a mediator, and as the titrant. A sample weighing 0.1342 g is transferred to a 100-mL volumetric flask and diluted to volume with distilled water. A 10.00-mL portion is transferred to an electrochemical cell along with 25 mL of 1 M KI, 75 mL of a pH 7.0 phosphate buffer, and several drops of a starch indicator solution. Electrolysis at a constant current of 36.45 mA required 221.8 s to reach the starch indicator end point. Determine the purity of the sample. 

From Table 11.9 we see that the coulometric titration of 8203 with 13 is... 

Representative Method Every controlled-potential or controlled-current coulo-metric method has its own unique considerations. Nevertheless, the following procedure for the determination of dichromate by a coulometric redox titration provides an instructive example. 

Description of the Method. The concentration of Cr207 in a sample is determined by a coulometric redox titration using Fe + as a mediator and electrogenerated Fe + as the "titrant." The end point of the coulometric redox titration is determined potentiometrically. 

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. 

Accuracy The accuracy of a controlled-current coulometric method of analysis is determined by the current efficiency, the accuracy with which current and time can be measured, and the accuracy of the end point. With modern instrumentation the maximum measurement error for current is about +0.01%, and that for time is approximately +0.1%. The maximum end point error for a coulometric titration is at least as good as that for conventional titrations and is often better when using small quantities of reagents. Taken together, these measurement errors suggest that accuracies of 0.1-0.3% are feasible. The limiting factor in many analyses, therefore, is current efficiency. Fortunately current efficiencies of greater than 99.5% are obtained routinely and often exceed 99.9%. 

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. 

Sensitivity For a coulometric method of analysis, the calibration sensitivity is equivalent to tiF in equation 11.25. In general, coulometric methods in which the analyte s oxidation or reduction involves a larger value of n show a greater sensitivity. 

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. 

Coulometric methods are based on Earaday s law that the total charge or current passed during an electrolysis is proportional to the amount of reactants and products in the redox reaction, ff the electrolysis is f00% efficient, in that only the analyte is oxidized or reduced, then the total charge or current can be used to determine... 

The titration of ascorbic acid using coulometrically generated I2 and Br2 is described in this experiment. Details are also given for the polarographic analysis of ascorbic acid. 

The iodine number of fats and oils provides a quantitative measurement of the degree of unsaturation. A solution containing a 100% excess of IGl is added to the sample, reacting across the double-bonded sites of unsaturation. The excess IGl is converted to I2 by adding KI. The resulting I2 is reacted with a known excess of Na2S203. To complete the analysis the excess 8203 is back titrated with coulometrically generated I2. 

Directions are provided for constructing an inexpensive constant-current source and demonstrate its use in determining the concentration of HGl coulometrically. 

The concentration of H2S in the drainage from an abandoned mine can be determined by a coulometric titration using KI as a mediator and as the titrant. ... 

A 50.00-mL sample of water is placed in a coulometric cell, along with an excess of KI and a small amount of starch as an indicator. Electrolysis is carried out at a constant current of 84.6 mA, requiring 386 s to reach the starch end point. Report the concentration of H2S in the sample in parts per million. 

One method for the determination of H3ASO3 is by a coulometric titration using as a titrant. The relevant reactions and standard-state potentials are summarized as follows. 

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