Coulometric titration method

Chloride can be determined by photometry, by a coulometric titration method or PISE. 

To change the value of <5, the coulometric titration method was applied in situ (see Section 1.4.8). 

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. 

Both the automatic coulometric titration of petroleum streams and the continuous monitoring of pesticides and sulfur-halogen compounds indicate that the coulometric titrator method is amenable to the automatic maintenance of the concentration of a component in a solution system. A manual version of this approach has been used to study the kinetics of hydrogenation of olefins as well as to determine the rate of hydrolysis of esters.12 The latter system is a pH-stat that is based on the principles of coulometric titrations. Equations (4.9)-(4.11) indicate how this approach is applied to the evaluation of the rate constants for ester hydrolysis. A similar approach could be used to develop procedures for kinetic studies that involve most of the electrochemical intermediates summarized in Table 4.1. The coulometric titration method provides a convenient means to extend the range of systems that can be subjected to kinetic study in solution. 

A coulometric titration method was introduced for sequential determination of sulfite, thiosulfate and ascorbic acid (1) in solutions containing sulfite-thiosulfate or sulfite-ascorbic acid couples. Formaldehyde or acetaldehyde can be used to mask the sulfite component. Two sequential measurements of coulometric time, one for both components in the mixture and one for the sample solution in which sulfite is masked, can be used to determine the concentrations of sutfite-thiosulfate and sulfite-ascorbic acid couples. The method is linear for 0.5-60 p,M 1 in the presence of 0.44-13 (xM sulfite, with RSD 0.1-4% and current efficiency of ca 98.0%. The method can be used for determination of the presence of sulfite and 1 in real sample matrices such as mineral waters and vitamin C tablets . 

The above example was given to show the versatihty of the coulometric titration method. A more typical example would be one where the constant current generates electrolyticaUy, with 100 percent, a substance which reacts immediately with the analyte species in solution. A typical example is the generation of iodine between two platinum electrodes immersed in an oxygen-free solution of potassium iodide. The generating reaction at the anode is ... 

Another broad field of applications involves continuous coulometric titrators which are employed in process stream analyzers. In these the generating current is continuously adjusted to maintain a small excess of electrogenerated titrant to react with material in the incoming liquid or gaseous sample stream. The level of generating current is a measure of the instantaneous concentration of the titrated substance (29, 30), Coulometric titration methods have also been used in chromatographic detectors and for determination of homogeneous reaction rates (31). 

Weppner and Huggins ° extensively applied the coulometric titration method. One example of the formation of intermetallic phases or compounds is the LiAl system. Here the electrolyte was a eutectic mixture of LiCl and KCl. Li was deposited into A1 by coulometric titration. The Li content in the A1 film electrode was increased in small steps. The potential was measured after equilibration of the alloy electrode. In Figure 3.18 the potential of an LiAl electrode versus an Li electrode is shown as function of y, the stoichiometric coefficient in the formula Li Al. 

In Figure 3.21 the second intermetallic compound LijSb also looks like a stoichiometric compound. The high accuracy of the coulometric titration method reveals that this compound has a very small region of variable stoichiometry of Lij+ Sb with = 10". This is shown in Figure 3.22. 

For the study of diffusion phenomena in solids it is also possible to work with potential pulses (potentiostatic pulses) or with constant current pulses (galvanostatic pulses). Examples described in the following paragraphs are based on the coulometric titration method described in Chapter 3. Weppner and Huggins reviewed these methods.In a continuous series of pulses the concentration of lithium in a sheet of aluminum is increased. The diffusion in each pulse is followed by either potential or current measurements. 

The coulometric titration method can be defined as charge controlled mass transfer of mobile component between electrodes of electrochemical ceU. This method is a very sensitive control of the composition of the nonstoichiometric phase, combined with emf measurements that yield very accurate thermod)mamic information fTretyakov et al., 1997],... 

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... 

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%. 

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. 

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

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. 

Instrumental methods for the determination of water in polymeric materials often rely on heat release of water from the polymer matrix. However, in some cases (e.g. PET) the polymer is hydrolysed and a simple Karl Fischer method is then preferred. Small quantities of water (10 pg-15mg) of water in polymers (e.g. PBT, PA6, PA4.6, PC) can be determined rapidly and accurately by means of a coulometric titration after heating at 50 to 240 °C with a detection limit in the order of 20 ppm. 

The water (moisture) content can rapidly and accurately be determined in polymers such as PBT, PA6, PA4.6 and PC via coulometric titration, with detection limits of some 20 ppm. Water produced during heating of PET was determined by Karl Fischer titration [536]. The method can be used for determining very small quantities of water (10p,g-15mg). Certified water standards are available. Karl Fischer titrations are not universal. The method is not applicable in the presence of H2S, mercaptans, sulfides or appreciable amounts of hydroperoxides, and to any compound or mixture which partially reacts under the conditions of the test, to produce water [31]. Compounds that consume or release iodine under the analysis conditions interfere with the determination. 

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. 

The result of the entire procedure, being a 100% conversion of Fe(II) to Fe(III), thus represents a so-called coulometric titration with internal generation of course, it seems possible to titrate Fe(II) with Ce(IV) generated externally from Ce(III), but in this way one would unnecessarily remove the solution of the 100% conversion problem hence the above titration with internal generation in the presence of a redox buffer as an intermediary oxidant represents an extremely reliable method, unless occasional circumstances are prohibitive for the remainder internal generation offers the advantage of no dilution of the analyte solution. 

It is certainly clear that a coulometric titration, like any other type of titration, needs an end-point detection system in principle any detection method that chemically fits in can be used, be it electrometric, colorimetric, photoabsorptionmetric, etc. for instance, in a few cases the colour change of the reagent generated (e.g., I2) may be observed visually, or after the addition of a redox, metal or pH indicator the titration end-point can be detected photoabsorptiometrically by means of a light source and photocell combination. Concerning the aforementioned coulometric titration of Fe(II), it is... 

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. 

The critical datum is not a buret reading, as it was in the case of the volumetric method. Rather, the amount of iodine used is determined coulometrically by computing the coulombs (total current over time) needed to reach the end point. The coulombs are calculated by multiplying the current applied to the anode-cathode assembly (a constant value) by the total time (seconds) required to reach the end point. The modern coulometric titrator automatically computes the amount of moisture from these data and displays it. 

Coulometric titrations ale quantitative methods based on constant... 

Recently, Mazzocchin et al. have studied several titration methods for determining relatively large amounts of technetium. The most precise results have been obtained by coulometric titration of TcO ions With electrogenerated tin (II) according to the procedure suggested by Bard and Lingaiie . The supporting electrolyte consists of 2.5 M sodium bromide, 0.15 M stannic chloride and 0.2 M hydrochloric acid. The titration reaction is very fast and currents up to 40 mA can readily be employed in the detection of the equivalence point. 

The oxidation of sulfite and thiosulfate becomes facile in the presence of iodide and novel disposable microband sensor electrodes have been developed by Williams and coworkers [187] to allow fast amperometric determination. A similar approach was proposed for the determination of sulfite in wine [188]. In this method, a coulometric titration is carried out in which S(IV) is indirectly oxidized to S(VI). Speciation of SO2 and sulfite was achieved down to micromolar levels. Sulfide and hydrogen sulfide can be determined elec-trochemically in the presence of an iodide mediator [189]. This process may be further enhanced at elevated temperatures. 

Clement and Paris [17] have devised a pair of methods for the determination of cobalt in steels, especially materials encountered in the nuclear industry. In the first technique, suitable for the analysis of solutions containing 8 to 160 mM cobalt(II), iron(III) is used to oxidize cobalt(II) in a picolinic acid medium, after which the resulting iron(II) is titrated po-tentiometrically with a standard solution of cerium(IV). An alternative procedure, for concentrations of cobalt(II) below 8 mM, involves a constant-current coulometric titration with electrogenerated cerium (IV) to measure the iron(II) that arises from the original reaction between cobalt(II) and iron(III). 

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. 

In principle the deviation <5 can be determined by the use of usual analytical chemistry or a highly sensitive thermo-balance. These methods, however, are not suitable for very small deviations. In these cases the following methods are often applied to detect the deviation physico-chemical methods (ionic conductivity, diffusion constant, etc.), electro-chemical methods (coulometric titration, etc.), and physical methods (electric conductivity, nuclear magnetic resonance, electron spin resonance, Mossbauer effect, etc.), some of which will be described in detail. 

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