Coulometric methods, controlled-current

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 way in which these alternatives with their particular measuring characteristics are carried out can be best described by (1) controlled-potential coulometry and (2) coulometric titration (controlled-current coulometry). Both methods require an accurate measurement of the number of coulombs consumed, for which the following instrumental possibilities are available (a) chemical coulometers, (b) electrochemical coulometers and (c) electronic coulometers. 

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. 

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. 

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. 

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. 

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%. 

It must be realized that the constant current (-1) chosen virtually determines a constant titration velocity during the entire operation hence a high current shortens the titration time, which is acceptable at the start, but may endanger the establishment of equilibrium of the electrode potentials near the titration end-point in an automated potentiometric titration the latter is usually avoided by making the titration velocity inversely proportional to the first derivative, dE/dt. Now, as automation of coulometric titrations is an obvious step, preferably with computerization (see Part C), such a procedure can be achieved either by such an inversely proportional adjustment of the current value or by a corresponding proportional adjustment of an interruption frequency of the constant current once chosen. In this mode the method can be characterized as a potentiometric controlled-current coulometric titration. 

From these equations, it is seen that the experimental variables in a controlled-current coulometric experiment are current and time, and it is possible to identify the following components of an appropriate apparatus an electrolysis cell, a current source, a method of measuring elapsed time (or a method of measuring coulombs), and a switching arrangement to control experimental variables. Electrochemical experiments using controlled-current methods are widespread and include titrimetry, kinetic studies, process stream analysis, and others (see Chap. 4). 

In controlled-potential coulometry the total number of coulombs consumed in an electrolysis is used to determine the amount of substance electrolyzed. To enable a coulometric method, the electrode reaction must satisfy the following requirements (a) it must be of known stoichiometry (b) it must be a single reaction or at least have no side reactions of different stoichiometry (c) it must occur with close to 100% current efficiency. 

A single constant current source can be used to generate precipitation, complex formation, oxidation-reduction, or neutralization reageni.s. Furthermore, the coulometric method adapts easily to automatic titrations, because current can be controlled quite easily. 

Coulometry. Two methods of coulometry are used coulometry at controlled potential and coulometric titrations. The main advantage of the coulometric method is the elimination of the necessity of standardization as the Faraday constant is a standard. In analysis of complicated samples encountered in environmental analysis the coulometric titrations are more advantageous where 100% current efficiency can be more readily attained by suitable choice of the reagent-solvent system. Coulometric titrations are suitable for determining the amount of substance in the range 0.01 to 100 mg (and sometimes below 1 iJg). Under optimum conditions these titrations can be carried out with a precision and accuracy of 0.01%. Automatic coulometric analyzers for the determination of gaseous pollutants (SO2, O3, NO, etc.) have proven to be useful in environmental chemistry. 

Coulometry, milli- and microcouIometry< ) are also used for the determination of the number of electrons transferred. In these methods the quantity of electricity necessary to reduce a distinct amount of the substance is measured at the potential of the limiting current, controlled by a potentiostat. Coulometric methods are usually not very accurate, and sometimes side reactions occur when electrodes of constant surface are used instead of a dropping electrode. An insufficient separation of cathodic and anodic spacing can also cause complications. Coulometric methods are thus best suited for systems, where n = 1 or 2, but for higher numbers of electrons transferred, the decision is often difficult. 

Controlled-current coulometry uses a constant current. which passes through a cell until an indicator signals completion of the analytical reaction. The quantity of charge required to reach the end point is then calcuiated from the magnitude of the current and the time that the current passes. This method has enjoyed wider application than potentiostatic coulometry. It is frequently called a coulometric titration for reasons that we discuss in Section 24D. 

No direct controlled-potential coulometric methods for cyanide have been reported although Anson, Pool, and Wright (100) have generated cyanide ion by controlled-current reduction of Ag (CN)J at platinum cathodes in slightly alkaline media. Baker and Morrison (101) were able to determine 0-14 /ig of cyanide in 0.1 N sodium hydroxide by measurement of the current produced by spontaneous electrolysis between a platinum cathode and silver anode. Hypochlorite and sulphide interfered, but moderate quantities of nitrate, nitrite, chloride, sulphite, sulphate, phosphate, and ammonia did not. 

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. 

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. 

Coulometry employs either a constant current or a controlled potential. Constant-current methods, like the preceding Br2/cyclohexene example, are called coulometric titrations. If we know the current and the time of reaction, we know how many coulombs have been delivered from Equation 17-2 q = / t. 

Under proper conditions, coulometric titrations can be performed with typical accuracies of 0.1% or better, even with small quantities of compounds. (Work in the microgram range may, however, have errors on the order of 1%.) If special precautions are taken, accuracies can be obtained that are difficult to achieve by any other method. Taylor and coworkers, for example, have titrated milligram quantities of substances with precisions of 0.005% or better [5, 6]. For these titrations, series resistors in a constant-temperature oil bath are used to control and measure the current from a 48 V storage battery the oil bath dissipates heat and thus stabilizes the resistance. The current is determined by measuring the iR drop across a precision resistor with a very sensitive potentiometer and comparing it with a standard Weston cell maintained at 1.017875 V 0.8 /iV by careful thermostatic control. The titration time is measured with a quartz-crystal-controlled time-interval meter capable... 

The SEL approach has some advantages over co-deposition, because it allows simpler coulometric control of the precursor stoichiometry. The SEL method may also be more suitable for large-scale fabrication since there is no requirement to balance the deposition rates of several different metals, so higher current densities can be used. If an alloyed precursor is preferred for the sulfur annealing step, a short (<5min) heat treatment at 200-350 °C is sufficient to completely alloy the stacked precursor. In this section, we highlight some of our recent work on the fabrication of CZTS solar cells by the SEL route [11]. 

There are essentially two different coulometric processes, namely potentio-static and galvanostatic coulometry. The former functions with constant, controlled electrode potential, whereas the galvanostatic method - also called coulometric titration - functions with constant current strength and uncontrolled potential. Fig. 13 shows the basic circuit diagram for potentiostatic coulometry. 

As mentioned above, the high accuracy of the method is due to the calibration with electrolysis of water. This is done by changing the reaction vessel 2 with the oxygen electrode of the electrolysis of water (Conder et al. 1989). The current is coulometrically controlled with very high accuracy and, therefore, the amount of oxygen introduced into the apparatus also. For further information the author can be contacted. 

Other techniques for studying protein molecnles in solntion are less infln-enced by these microscopic effects. Square-wave voltammetry is widely used due to its great sensitivity, and even a low density of productive sites on the electrode may give rise to a sharp and analyzable response [28]. The electrode may also be rotated to achieve forced convection and hydrodynamic control of solution redox species, while amperometric (and coulometric) measurements—where the current (or charge) is recorded following a potential step—enable the time and potential domains to be deconvoluted [28,29]. These options complement each other to provide a detailed picture of the thermodynamics and kinetics of redox processes. Finally, bulk electrolytic methods enable samples of a particular redox state to be prepared quantitatively for spectroscopic examination, at precise electrode potentials that may lie outside the range of conventional chemical titrants. 

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