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.
Using a constant current does present two important experimental problems that must be solved if accurate results are to be obtained. First, as electrolysis oc- curs the analyte’s concentration and, therefore, the current due to its oxidation or reduction steadily decreases. To maintain a constant current the cell potential must change until another oxidation or reduction reaction can occur at the working electrode. Unless the system is carefully designed, these secondary reac- tions will produce a current efficiency of less than 100%. The second problem is the need for a method of determining when the analyte has been exhaustively electrolyzed. In controlled-potential coulometry this is signaled by a decrease in the current to a constant background or residual current (see Figure 11.20). In controlled-current coulometry, however, a constant current continues to flow even when the analyte has been completely oxidized or reduced. A suitable means of determining the end-point of the reaction, te, is needed.
To illustrate why changing the working electrode’s potential can lead to less than 100% current efficiency, let’s consider the coulomet- ric analysis for Fe2+ based on its oxidation to Fe3+ at a Pt working electrode in 1 M H2SO4.
Fe2+(aq) < = = = = > Fe3+(aq)+ e–
The ladder diagram for this system is shown in Figure 11.24a. Initially the potential of the working electrode remains nearly constant at a level near the standard-state potential for the Fe3+/Fe2+ redox couple. As the concentration of Fe2+ decreases, however, the potential of the working electrode shifts toward more positive values until another oxidation reaction can provide the necessary current. Thus, in this case the potential eventually increases to a level at which the oxidation of H2O occurs.
6H2O(l) < = = = = > O2(g)+ 4H3O+(aq)+ 4e–
Since the current due to the oxidation of H3O+ does not contribute to the oxidation of Fe2+, the current efficiency of the analysis is less than 100%. To maintain a 100% current efficiency the products of any competing oxidation reactions must react both rapidly and quantitatively with the remaining Fe2+. This may be accomplished, for example, by adding an excess of Ce3+ to the analytical solution (Figure 11.24b). When the potential of the working electrode shifts to a more positive potential, the first species to be oxidized is Ce3+.
Ce3+(aq) < = = = = > Ce4+(aq)+ e–
The Ce4+ produced at the working electrode rapidly mixes with the solution, where it reacts with any available Fe2+.
Combining these reactions gives the desired overall reaction of
Fe2+(aq) < = = = = > Fe3+(aq)+ e–
In this manner, a current efficiency of 100% is maintained. Furthermore, since the concentration of Ce3+ remains at its initial level, the potential of the working elec- trode remains constant as long as any Fe2+ is present. This prevents other oxidation reactions, such as that for H2O, from interfering with the analysis. A species, such as Ce3+, which is used to maintain 100% current efficiency, is called a mediator.
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 Fe2+ has been oxidized current continues to flow as a result of the oxidation of Ce3+ and, eventually, the oxidation of H2O. What is needed is a means of indicating when the oxidation of Fe2+ 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, such as visual indicators, and potentiometric and conductometric measurements, may be used to signal the end point of a controlled-current coulometric analysis. For exam- ple, ferroin may be used to provide a visual end point for the Ce3+-mediated coulo- metric analysis for Fe2+.
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 called the generator electrode since it is where the mediator reacts to generate the species reacting with the analyte. The counterelectrode is isolated from the analyti- cal solution by a salt bridge or porous frit to prevent its electrolysis products from reacting with the analyte. Alternatively, oxidizing or reducing the mediator can be carried out externally, and the appropriate products flushed into the analytical solu- tion. Figure 11.25 shows one simple method by which oxidizing and reducing agents can be generated externally. A solution containing the mediator flows under the influence of gravity into a small-volume electrochemical cell. The products gen- erated at the anode and cathode pass through separate tubes, and the appropriate oxidizing or reducing reagent can be selectively delivered to the analytical solution.
For example, external generation of Ce4+ can be obtained using an aqueous solution of Ce3+ and the products generated at the anode.
The other necessary instrumental component for controlled-current coulometry is an accurate clock for measuring the electrolysis time, te, 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.
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 determi- nation of Fe2+, that the oxidation of Fe2+ by Ce4+ 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
Compare this equation with the relationship between the moles of strong acid, N, titrated with a strong base of known concentration.
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.