Titration, coulometric

The basic approach in coulometric titrations is to generate electrochemically (at constant current) a titrant in solution that subsequently reacts by a secondary chemical reaction with the species to be determined. For example, a large excess of cerium(III) is placed in the solution together with an iron(II) sample. When a constant current is applied, the cerium(III) is oxidized at the anode to produce cerium(IV), which subsequently reacts with the iion(II)  

Should any iron(II) reach the anode, it also would be oxidized and thus not require the chemical reaction of Eq. (4.13) to bring about oxidation, but this would not in any way cause an error in the titration. This method is equivalent to the constant-rate addition of titrants from a burette. However, in place of a burette the titrant is electrochemically generated in the solution at a constant rate that is directly proportional to the constant current. For accurate results to be obtained the electrode reaction must occur with 100% current efficiency (i.e., without any side reactions that involve solvent or other materials that would not be effective in the secondary reaction). In the method of coulometric titrations the material that chemically reacts with the sample system is referred to as an electrochemical intermediate [the cerium(III)/cerium(IV) couple is the electrochemical intermediate for the titration of iron(II)]. Because one faraday of electrolysis current is equivalent to one gram-equivalent (g-equiv) of titrant, the coulometric titration method is extremely sensitive relative to conventional titration procedures. This becomes obvious when it is recognized that there are 96,485 coulombs (C) per faraday. Thus, 1 mA of current flowing for 1 second represents approximately 10-8 g-equiv of titrant. 

Coulometric titration procedures have been developed for a great number of oxidation-reduction, acid-base, precipitation, and complexation reactions. The sample systems as well as the electrochemical intemediates used for them are summarized in Table 4.1, and indicate the diversity and range of application for the method. An additional specialized form of coulometric titration involves the use of a spent Karl Fischer solution as the electrochemical intermediate for the determination of water at extremely low levels. For such a system the anode reaction regenerates iodine, which is the crucial component of the Karl Fischer titrant. This then reacts with the water in the sample system according to the 

For this titration the dual-polarized amperometric endpoint detection system provides good sensitivity and rapid response. 

The instrumentation for coulometric titrations consists of a galvanostat (a constant-current source), a cell equipped with an endpoint detector, and a timer. 

In coulometry, the analyte is quantitatively electrolyzed and, from the quantity of electricity (in coulombs) consumed in the electrolysis, the amount of analyte is calculated using Faraday s law, where the Faraday constant is 9.6485309 xlO4 C mol-1. Coulometry is classified into controlled-potential (or potentiostatic) coulometry and controlled-current (or galvanostatic) coulometry, based on the methods of electrolysis [19, 20]. 

In controlled-potential coulometry, the analyte is electrolyzed quantitatively with 100% current efficiency and the quantity of electricity Q is measured with a coul-ometer  

m and M are the amount and the molar mass of the analyte. The coul-ometer is usually an electronic one that integrates the current during the electrolysis, although chemical coulometers, e.g. a silver coulometer and a gas coulometer, can also be used. In this method, the deposition of the analyte is not a necessary process. All substances that are electrolyzed with 100% current efficiency can be 

Recently flow coulometry, which uses a column electrode for rapid electrolysis, has become popular [21]. In this method, as shown in Fig. 5.34, the cell has a columnar working electrode that is filled with a carbon fiber or carbon powder and the solution of the supporting electrolyte flows through it. If an analyte is injected from the sample inlet, it enters the column and is quantitatively electrolyzed during its stay in the column. From the peak that appears in the current-time curve, the quantity of electricity is measured to determine the analyte. Because the electrolysis in the column electrode is complete in less than 1 s, this method is convenient for repeated measurements and is often used in coulometric detection in liquid chromatography and flow injection analyses. Besides its use in flow coulometry, the column electrode is very versatile. This versatility can be expanded even more by connecting two (or more) of the column electrodes in series or in parallel. The column electrodes are used in a variety of ways in non-aqueous solutions, as described in Chapter 9. 

Controlled-current coulometry is also called coulometric titration. An apparatus for controlled-current coulometry is shown in Fig. 5.35 for the case of determination of an acid. It consists of a constant current source, a timer, an end-point detector (pH meter), and a titration cell, which contains a generating electrode, a counter electrode in a diaphragm, and two electrodes for pH detection. The timer 

Suppose it is desired to titrate ceric ion with ferrous ion according to the reaction 

The next most easily reduced material is Fe , which is reduced to Fe . The Fe is stirred out into the bulk of the solution where it reacts with the remaining Ce. If a higher current (12) were originally selected, then the current divides from the beginning between the reduction of Ce and Fe +. The net result is the same, however, since all of the Ce eventually is reduced, either directly at the electrode or indirectly by Fe . If the ferric ammonium sulfate were not added, the current-versus-potential curve would have the original plateau (A) but then would follow the dashed curve D. In this case, either at the start of the titration (level 12), or sometime during the titration (level ii), hydrogen would be produced and be lost from solution. Under these conditions the titration efficiency would be less than 

Commercially available instruments usually read directly in microequivalents. This is accomplished by setting the current in some multiple of the Faraday constant so that the microequivalents are simply equal to some decimal fraction or multiple of the seconds of generation (see Prob. 4). 

Suppose the solution of unknown Ce was coulometrically titrated with a constant current of 75.00 mA and required 650.0 sec to complete. Then, 

Naturally, some means of detecting the endpoint of the titration must be available. Indicators can be used (although their sensitivity is not good at the low levels usually investigated), as well as essentially any other method available for regular titrations. Potentiometry (Chap. 2) or amperometry with two similar electrodes is often used because of increased sensitivity over visual indicators. 

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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. 

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+... 

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

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

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. 

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 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. ... 

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. 

Explain why the coulometric titration must be done in neutral solutions (pH = 7), instead of in strongly acidic solutions (pH<0). 

Several methods are available for the detection of end points in coulometric titrations. These are the following. 

The principle of coulometric titration. This involves the generation of a titrant by electrolysis and may be illustrated by reference to the titration of iron(II) with electro-generated cerium(IV), A large excess of Ce(III) is added to the solution containing the Fe(II) ion in the presence of, say IM sulphuric acid. Consider what happens at a platinum anode when a solution containing Fe(II) ions alone is electrolysed at constant current. Initially the reaction... 

A number of coulometric titrators are available commercially and are simple to operate. Suitable apparatus can also be assembled from readily available equipment. The essential requirements are ... 

Figure 14.2(a) is a schematic diagram of a suitable circuit for coulometric titration with internal generation of titrant and using the dead-stop or... 

The limitations of coulometric titration with internal generation of the titrant include the following. 

In the following pages experimental details are given for some typical coulometric titrations at constant current. 

By virtue of its inherent accuracy, coulometric titration is very suitable for the determination of substances present in small amount, and quantities of the order of 10 7-1(U5 mole are typical. Larger amounts of material require very long electrolysis times unless an amperostat capable of delivering relatively large currents (up to 2 A) is available. In such cases, a common procedure is to start the electrolysis with a large current, and then to switch to a much lower output as the end point is approached. 

Discussion. Iodine (or tri-iodide ion Ij" = I2 +1-) is readily generated with 100 per cent efficiency by the oxidation of iodide ion at a platinum anode, and can be used for the coulometric titration of antimony (III). The optimum pH is between 7.5 and 8.5, and a complexing agent (e.g. tartrate ion) must be present to prevent hydrolysis and precipitation of the antimony. In solutions more alkaline than pH of about 8.5, disproportionation of iodine to iodide and iodate(I) (hypoiodite) occurs. The reversible character of the iodine-iodide complex renders equivalence point detection easy by both potentiometric and amperometric techniques for macro titrations, the usual visual detection of the end point with starch is possible. 

A selection of coulometric titrations of different types is collected in Table 14.2. It may be noted that the Karl Fischer method for determining water was first developed as an amperometric titration procedure (Section 16.35), but modern instrumentation treats it as a coulometric procedure with electrolytic generation of I2. The reagents referred to in the table are generated at a platinum cathode unless otherwise indicated in the Notes. 

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