Coulometric methods

Coulometry and amperometry can be distinguished by the extent to which the analyte undergoes a Faradaic reaction at the working electrode, namely complete and partial, respectively. Coulometry is essentially high-efficiency amperometry with working electrodes of large surface area. Successful coulometric or amperometric detection can result only if the applied potential is chosen correctly. 

The generation of iodine coulometrically at the anode has an extensive application in the Karl Fischer (KF) technique of water determination. The current 

Coulometric methods are as accurate and precise as conventional gravimetric and volumetric procedures and, in addition, are readily automated. In contrast to gravimetric methods, coulometric procedures are usually rapid, and do not require that the product of the electrochemical reaction be a weighable solid. The methods are moderately sensitive, and offer a reasonably selective means for separating and determining a number of ions. 

The techniques of voltammetry/polarography, atomic absorption, ICP, etc., have in most cases supplanted the coulometric approach for the determination of inorganic analytes. Coulometry and the use of coulometry in food analysis have recently been reviewed [473,476]. 

Applications The coulometric Karl Fischer titration is a widely used moisture determination method (from ppm to 100%). In the presence of water, iodine reacts with sulfur dioxide through a redox process, as follows  

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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. 

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... 

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. 

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. 

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%. 

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. 

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 Karl Fischer procedure has now been simplified and the accuracy improved by modification to a coulometric method (Chapter 14). In this procedure the sample under test is added to a pyridine-methanol solution containing sulphur dioxide and a soluble iodide. Upon electrolysis, iodine is liberated at the anode and reactions (a) and (b) then follow the end point is detected by a pair of electrodes which function as a biamperometric detection system and indicate the presence of free iodine. Since one mole of iodine reacts with one mole of water it follows that 1 mg of water is equivalent to 10.71 coulombs. 

To measure gas and water vapor permeability, a film sample is mounted between two chambers of a permeability cell. One chamber holds the gas or vapor to be used as the permeant. The permeant then diffuses through the film into a second chamber, where a detection method such as infrared spectroscopy, a manometric, gravimetric, or coulometric method isotopic counting or gas-liquid chromatography provides a quantitative measurement (2). Die measurement depends on the specific permeant and the sensitivity required. 

Dissolved inorganic carbon is present as three main species which are H2CO3, HCOs and CO. Analytically we have to approach the carbonate system through measurements of pH, total CO2 or DIC, alkalinity (Aik), and PcOj- In an open carbonate system there are six unknown species H", OH , PcOj/ H2CO3, HCOs, and CO . The four equilibrium constants connecting these species are K, Ki, Kh, and fCw. The values of these equilibrium constants vary with T, P, and S (Millero, 1995). To solve for the six rmknowns we need to measure two of the four analytical parameters (Stumm and Morgan, 1996). Direct measurement of Pco is the best approach, but if that is not possible then the most accurate and precise pair (Dickson, 1993) is Total CO2 by the coulometric method Johnson et al., 1993) and pH by the colorimetric method (Clayton et ah, 1995). 

Parameter Potentiometry Voltammetric methods Coulometric methods... 

Verhoef and co-workers suggested omitting the foul smelling pyridine completely and proposed a modified reagent, consisting of a methanolic solution of sulphur dioxide (0.5 M) and sodium acetate (1M) as the solvent for the analyte, and a solution of iodine (0.1 M) in methanol as the titrant the titration proceeds much faster and the end-point can be detected preferably bipoten-tiometrically (constant current of 2 pA), but also biamperometrically (AE about 100 mV) and even visually as only a little of the yellow sulphur dioxide-iodide complex S02r is formed (for the coulometric method see Section 3.5). 

Berka et al [59] described an accurate and reproducible coulometric method, with chlorine electrogenerated at the anode, for the determination of micro quantities of primaquine phosphate. Titration was carried out in an anode compartment with a supporting electrolyte of 0.5 M sulfuric acid-0.2 M sodium chloride and methyl orange as indicator. One coulomb was equivalent to 1.18 mg of primaquine phosphate. The coefficients of variation for 0.02-0.5 mg of primaquine phosphate were 1-5%. Excipients did not interfere. 

Tsaikov [ 114] has described a coulometric method for the determination of boron in coastal seawaters. This method is based on the potentiometric titra-... 

Fast solution reactions between analyte and a reagent titration to stoichiometric point by volumetric or coulometric methods end-point detection by visual indicators, precipitation indicators or electrochemical means. 

Coulometric methods of analysis involve measuring the quantity of electricity required to effect a quantitative chemical or electrochemical reaction and are based on Faraday s laws of electrolysis ... 

The volumetric method is used (rather than the coulometric method) when the water content is higher (greater than about 1%). 

As stated previously, the iodine titrant is generated electrochemically in the coulometric method. Electrochemical generation refers to the fact that a needed chemical is a product of either the oxidation halfreaction at an anode or the reduction half-reaction at a cathode. In the Karl Fischer coulometric method, iodine is generated at an anode via the oxidation of the iodide ion ... 

Distinguish between the volumetric and coulometric methods for the Karl Fischer titration. 

In the volumetric method, the titrant is added from an external reservoir. In the coulometric method, the titrant (iodine) is generated internally via an electrochemical reaction. 

Dennison S, Bonnick DM. 1995. Stopped-flow thin-layer coulometric method for the determination of disinfectants in water. Anal Proc 32(1) 13-15. 

The iodine then reacts with the water that is present. The amount of water titrated is proportional to the total current (according to Faraday s law) used in generating the iodine necessary to react with the water. One mole of iodine reacts quantitatively with 1 mol of water. As a result, 1 mg of water is equivalent to 10.71 C. Based on this principle, the water content of the sample can be determined by the quantity of current that flows during the electrolysis. For this reason, the coulometric method is considered an absolute technique, and no standardization of the reagents is required. 

In the coulometric method, standardization is not necessary, since the current consumed can be measured absolutely. However, a standard with known water content should be checked periodically to ensure that the system is functioning properly. In this case, a certified water standard is generally used, and the amount of water is determined and compared with the amount that is certified to be present. Some coulometric titrators are equipped with an oven for liberating the moisture from samples that are either insoluble in methanol or that react with I2, methanol, or one of the other reagents. Solid standards (e.g., potassium citrate monohydrate) are available for checking the oven, and this check is performed after the coulometer function has been verified. 

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