Potentiometric titrations

A titration is a technique for determining the concentration of a material in solution by measuring the volume of a standard solution that is required to react with the sample. One of the most common titrations is the acid-base titration in which the concentration of a base can be determined by adding a standard solution of an acid to the sample until the base is exactly neutralized. The exact neutralization point is found by the use of an indicator that changes color when the end-point is reached. 

There are, however, various cases where the visual method of detecting the end-point cannot be used. For example, the solution may be dark or no appropriate indicator is available. In such cases, physicochemical techniques can be employed. A potentiometric titration is one of this type wherein the end-point is detected by an abrupt change in voltage (between an electrode and the body of the solution) that may be observed as titrant is added to the solution. 

In some cases a plot of mL of titrant vs. voltage can be provided. Such plots are usefiil to determine whether there is more than one titratable material in the sample and to learn something about the character of the material titrated. 

Titratable functional groups such as chloride, sulfide, mercaptide, weak or strong acids, weak or strong bases, and certain amines may be determined by this technique. 

Titrations are relatively simple and rapid. They provide information concerning chemically reactive functional groups that would be difficult to obtain by other techniques. 

Acid-base, redox, precipitation and chelometric titrations are usually dealt with in textbooks on analytical chemistry. The titration curves in these titrations can be obtained potentiometrically by use of appropriate indicator electrodes, i.e. a pH-glass electrode or pH-ISFET for acid-base titrations, a platinum electrode for redox titrations, a silver electrode or ISEs for precipitation titrations, and ISEs for 

The experimental apparatus for a potentiometric titration can be quite simple only a pH or millivolt meter, a beaker and magnetic stirrer, reference and indicator electrodes, and a burette for titrant delivery are really needed for manual titrations and point-by-point plotting. Automatic titrators are available that can deliver the titrant at a constant rate or in small incremental steps and stop delivery at a preset endpoint. The instrument delivers titrant until the potential difierence between the reference and indicator electrodes reaches a value predetermined by the analyst to be at, or very near, the equivalence point of the reaction. Alternatively, titrant can be delivered beyond the endpoint and the entire titration curve traced. Another approach to automatic potentiometric titration is to measure the amount of titrant required to maintain the indicator electrode at a constant potential. The titration curve is then a plot of volume of standard titrant added versus time, and is very useful, for example, for kinetic studies. The most extensive use of this approach has been in the biochemical area with so-called pH-stats—a combination of pH meter, electrodes, and automatic titrating equipment designed to maintain a constant pH. Many enzymes consume or release protons during an enzymatic reaction therefore, a plot of the volume of standard base (or acid) required to maintain a constant pH is a measure of the enzyme activity, the amount of enzyme present. 

Since potentiometric titrations are an old and well-known technique, particularly in regard to acid-base and oxidation-reduction titrations, only a few selected examples will be presented here. For more detailed treatments, the student is urged to consult the bibliography at the end of the chapter. It will be assumed that the student is already familiar with titration curves and their calculation from ionic equilibria and other pertinent data. 

The acetic-acid content of household vinegar can be determined by potentiometric titration with sodium hydroxide. Mixtures of carbonate and bicarbonate can be analyzed by titration with HCl. 

Acid-Base Titrations in Nonaqueous Solvents. It is a fact that the apparent acidity or basicity of a compound is strongly dependent on the acid-base properties of the solvent. For example, very strong acids such as HCl and HNO3 cannot be individually titrated in water because water is sufficiently basic that these acids appear to be totally ionized. Very weak bases, such as amines, cannot be successfully titrated with strong acid in water. Many acids or bases that are too weak for titration in an aqueous medium, however, become amenable to titration in appropriate nonaqueous solvents. As a consequence, there are now many neutralization methods that call for solvents other than water [23-25]. 

The earliest advantages recognized arose from the use of amphiprotic solvents, those that have both acidic and basic properties. The prototype is water. Significant differences in acid-base properties are seen in the case of either protogenic solvents (more acidic than water), for example acetic acid, or protophilic solvents (more basic than water), for example ethylenediamine. In the protogenic cases it was found that bases too weak to be titrated in water could be successfully titrated with a strong acid dissolved in the same solvent. For example, primary, secondary, and tertiary amines can be titrated in acetic acid with perchloric acid in acetic add as titrant. Medicinal sulfonamides, which have a primary amino group, can be titrated 

Any titration involves the progressive change of the activities (or concentrations) of the titrated and titrating species and, in principle, can be done potentiometrically. However, for an accurate determination it is necessary that there is a fairly rapid variation in equilibrium potential in the region of the equivalence point. Useful applications are redox, complexation, precipitation, acid-base titrations, etc. From the titration curve it is possible to calculate values of the formal potentials of the titrated and titrating species, as explained below. 

An important question is whether we can use any indicator electrode. A redox electrode, i.e. inert in the range of potential where measurements are being done, is a possibility, especially for redox titrations. In other cases, the use of electrodes selective to the ion being titrated is better, such as pH electrodes in acid-base titrations. The method of analysis of the data obtained is, naturally, the same in all cases and independent of electrode material. 

We illustrate with the general case of a simple redox titration  

Before the equivalence point the couple OjRi is in excess and determines the potential, and after the equivalence point the couple in excess is 02/R2 and this determines the potential. Therefore, by use of expressions (13.1) and (13.2) it is possible to construct the theoretical titration curve if the values of and Ef are known (Fig. 13.1). 

Ef is the potential when half of the volume necessary to reach the equivalence point has been added—see (13.1) EY is the potential when twice the titrant volume needed to reach equiv has been added—it can also be calculated from (13.4), given a knowledge of equiv and 

In Nebraska, state regulations require that the chemical makeup of animal feed sold in the state be accurately reflected on the labels found on the feed bags. The Nebraska State Agriculture Laboratory is charged with the task of performing the analytical laboratory work required. An example is salt (sodium chloride) content. The method used to analyze the feed for sodium chloride involves a potentio-metric titration. A chloride ion-selective electrode in combination with a saturated calomel reference electrode is used. After dissolving the feed sample, the chloride is titrated with a silver nitrate standard solution. The reaction involves the formation of the insoluble precipitate silver chloride. The electrode monitors the decrease in the chloride concentration as the titration proceeds, ultimately detecting the end point (when the chloride ion concentration is zero). 

Charlie Focht of the Nebraska State Agriculture Laboratory refills a saturated calomel electrode with saturated potassium chloride while preparing to analyze animal feed samples for sodium chloride via a poten-tiometric titration. 

In addition, potentiometric titration methods exist in which an electrode other than an ion-selective electrode is used. A simple platinum wire surface can be used as the indicator electrode when an oxidation-reduction reaction occurs in the titration vessel. An example is the reaction of Ce(IV) with Fe(II)  

If this reaction were to set be up as a titration, with Ce4+ as the titrant and the Fe2+ in the titration vessel and the potential of a platinum electrode dipped into the solution monitored (vs. a reference electrode) as the titrant is added, the potential would change with the volume of titrant added. This is because as the titrant is added, the measured E would change as the [Fe2+] is decreased, the [Fe3+] is increased, and the [Ce3+] is increased. At the end point and beyond, all the Fe2+ is consumed and [Fe3+] and [Ce3+] change only by dilution thus E is dependent mostly on the change in [Ce4+]. At the end point, there would be a sharp change in the measured E. 

Automatic titrators have been invented that are based on these principles. A sharp change in a measured potential can be used as an electrical signal to activate a solenoid and stop a titration. 

Internal filling solution phosphate buffer pH 7.0 containing KCI and saturated with AgCI 

The potential which developes on the inner and outer glass surfaces of the electrode is due to the following equilibria  

The number of Gb sites on the outer membrane increases with decreasing [H ] and thus its potential becomes increasingly negative with respect to inner surface with increasing pH. The Nernst equation can be simplified and written in the following form for the glass electrode when the temperature is 20°C  

When potentiometric titration is carried out, the volume of titrant added is plotted against the measured potential. Since the electrode takes time to equilibrate, the volume of titrant required to reach the end-point is first calculated and a volume of titrant is added to within ca 1 ml of the end-point. Then the titrant is added in 0.1 ml amounts until the steep inflection in the titration curve is passed. The end-point of the titration is the point where the slope of the titration curve is at its maximum. 

Potentiometric titration provides the principal method for determining pKa values and it is best applied to substances with pATa values 11. For example the pATa of benzoic acid can be determined as follows A 0.01 M solution of benzoic acid (50 ml) is titrated with 0.1 M KOH. The KOH is added in 0.5 ml increments it would be expected that 5 ml of 0.1 M KOH would be required to neutralise the 

The potential of a suitable indicator electrode is convenient for determining the equivalence point for a titration (apoicniiometric lilralion). A polenliomet-ric titration provides different information than does a direct potenliometric nteasuroment, l or example, the 

The potenliometric end point is widely applicable and provides inhcrenily more accurate data than the corresponding method with indicators. It is particularly useful for tilralioti ofcolorod or turbid solutions and for delecting the presence of unsuspected species in a solution. Unfortunatelv. it is more limc-consuininu than 

Simulaiion L.carn more about polentionietric titralions. 

FIGURE 23-19 High-performance automated titrator. Accommodates up to six buret drives, has user-programmable software, permits high sample throughput with an automatic sample turntable (not shown). The unit can be adapted for several different types of titrations. (Copyrighl 2006 Mettler-Toledo, Inc.) 

23-1 What is meant by nernstian beha ior of an indicator electrode  

The alkalinity is defined as the amount of hydrogen ions in moles required to neutralise the proton acceptors in 1 kg of seawater. Dickson (1981) suggested that bases formed from weak acids with p 4.5 (at 25° and zero ionic strength) be considered as proton acceptors, i.e., defined as part of the alkalinity. This leads to the following definition of alkalinity in seawater  

In the potentiometric titration methods, the pH change diuing titration of a seawater sample with hydrochloric acid is followed with an electrochemical cell (described in Chapter 7). The titration serves to transfer the bases defined as part of the alkalinity to their acidic forms. 

Recommendations as to the electrochemical cell are given in Chapter 7. Because At is not affected by the exchange of carbon dioxide between sample and air, it is acceptable to use an open titration vessel if At only is to be estimated, while Ct or pH is measured separately. For the evaluation of Cxas well as At from the titration, it is necessary to use a closed 

For good throughput of samples and optimum reproducibility it is reconunended that the alkalinity titration be computer controlled. The computer is used for data collection from the voltmeter as well as for addition of acid from the burette. Software for PCs for this purpose is commercially available. A suitable resolution for the burette, which is generally of a motor driven piston type, is 1 uL. 

Hydrochloric acid (pro analyst) Concentration 0.01-0.1 mol/L, depending on the sample volume. 

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The measurement of pK for bases as weak as thiazoles can be undertaken in two ways by potentiometric titration and by absorption spectrophotometry. In the cases of thiazoles, the second method has been used (140, 148-150). A certain number of anomalies in the results obtained by potentiometry in aqueous medium using Henderson s classical equation directly have led to the development of an indirect method of treatment of the experimental results, while keeping the Henderson equation (144). 

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

Values for fQi and K 2 for acids of the form H2A are determined from a least-squares analysis of data from a potentiometric titration. 

Dilute solutions of nominally 0.001 M NaOH and HGl are used to demonstrate the effect of an indicator s color transition range on titration error. Potentiometric titration curves are measured, and the indicator s color transition range is noted. Titration errors are calculated using the volume of titrant needed to effect the first color change and for a complete color change. 

Directions are provided in this experiment for determining the dissociation constant for a weak acid. Potentiometric titration data are analyzed by a modified Gran plot. The experiment is carried out at a variety of ionic strengths and the thermodynamic dissociation constant determined by extrapolating to zero ionic strength. 

Potentiometric titration curves are used to determine the molecular weight and fQ or for weak acid or weak base analytes. The analysis is accomplished using a nonlinear least squares fit to the potentiometric curve. The appropriate master equation can be provided, or its derivation can be left as a challenge. 

A potentiometric titration is used to determine if an unknown sample is pure Na2G03, a mixture of Na2G03 and NaHG03, pure Na3P04, or a mixture of Na3P04 and Na2HP04. 

This experiment outlines a potentiometric titration for determining the valency of copper in superconductors in place of the visual end point used in the preceding experiment of Harris, Hill, and Hewston. The analysis of several different superconducting materials is described. 

Powell, J. R. Tucker, S. A. Acree, Jr., et al. A Student-Designed Potentiometric Titration Quantitative Determination oflron(ll) by Caro s Acid Titration, ... 

The titration of a mixture ofp-nitrophenol (pfQ = 7.0) and m-nitrophenol pK = 8.3) can be followed spectrophotometrically. Neither acid absorbs at a wavelength of 545 nm, but their respective conjugate bases do absorb at this wavelength. The m-nitrophenolate ion has a greater absorbance than an equimolar solution of the p-nitrophenolate ion. Sketch the spectrophotometric titration curve for a 50.00-mL mixture consisting of 0.0500 M p-nitrophenol and 0.0500 M m-nitrophenol with 0.100 M NaOH, and compare the curve with the expected potentiometric titration curves. 

The potentiometric titration curve shown here was recorded on a 0.4300-g sample of a purified amino acid that was dissolved in 50.00 ml of water and titrated with 0.1036 M NaOH. Identify the amino acid from the possibilities listed in the following table. 

The text listed below provides more details on how the potentiometric titration data may be used to calculate equilibrium constants. This text provides a number of examples and includes a discussion of several computer programs that have been developed to model equilibrium reactions. 

The potentiometric determination of an analyte s concentration is one of the most common quantitative analytical techniques. Perhaps the most frequently employed, routine quantitative measurement is the potentiometric determination of a solution s pH, a technique considered in more detail in the following discussion. Other areas in which potentiometric applications are important include clinical chemistry, environmental chemistry, and potentiometric titrations. Before considering these applications, however, we must first examine more closely the relationship between cell potential and the analyte s concentration, as well as methods for standardizing potentiometric measurements. 

Potcntiomctric Titrations In Chapter 9 we noted that one method for determining the equivalence point of an acid-base titration is to follow the change in pH with a pH electrode. The potentiometric determination of equivalence points is feasible for acid-base, complexation, redox, and precipitation titrations, as well as for titrations in aqueous and nonaqueous solvents. Acid-base, complexation, and precipitation potentiometric titrations are usually monitored with an ion-selective electrode that is selective for the analyte, although an electrode that is selective for the titrant or a reaction product also can be used. A redox electrode, such as a Pt wire, and a reference electrode are used for potentiometric redox titrations. More details about potentiometric titrations are found in Chapter 9. 

Selig, W. S. Potentiometric Titrations Using Pencil and Graphite Sensors, /. Chem. Educ. 1984, 61, 80-81. 

The routine compositional and functional testing done on the adhesives includes gas chromatographic testing for purity, potentiometric titrations for acid stabilizer concentrations, accelerated thermal stabiUty tests for shelf life, fixture time cure speed tests, and assorted ASTM tests for tensile shear strengths, peel and impact strengths, and hot strengths. 

The method of choice for determining carboxyl groups in lignin is based on potentiometric titration in the presence of an internal standard, /)-hydroxybenzoic acid, using tetra- -butylammonium hydroxide as a titrant (42). The carboxyl contents of different lignins are shown in Table 6. In general, the carboxyl content of lignin increases upon oxidation. 

Referee Methods. The American Society for Testing Materials (ASTM) has collected a series of standard referee methods for the analysis of magnesium and its alloys (78). These methods are accurate over a larger range of concentration than the production methods, but are time consuming ia thek apphcation. The methods are based on potentiometric titration, photometric methods, or gravimetric methods. The photometric methods are most common and are relatively straightforward. 

The free maleic acid content in maleic anhydride is determined by direct potentiometric titration (166). The procedure involves the use of a tertiary amine, A/-ethylpipetidine [766-09-6J, as a titrant. A tertiary amine is chosen as a titrant since it is nonreactive with anhydrides (166,167). The titration is conducted in an anhydrous solvent system. Only one of the carboxyhc acid groups is titrated by this procedure. The second hydrogen s dissociation constant is too weak to titrate (166). This test method is not only used to determine the latent acid content in refined maleic acid, but also as a measure of the sample exposure to moisture during shipping. 

Analytical and Test Methods. Potentiometric titration with sodium hydroxide [1310-73-2] is employed. Both equivalent points are... 

The enthalpies of these hydrolysis reactions have also been determined (112). Polynuclear complexes such as[(Pu02)2(OH2], [(Pu02)3 (OH) ), and [(Pu02)4(0H)y] have been inferred from potentiometric titrations (105). 

Amides can be titrated direcdy by perchloric acid ia a nonaqueous solvent (60,61) and by potentiometric titration (62), which gives the sum of amide and amine salts. Infrared spectroscopy has been used to characterize fatty acid amides (63). Mass spectroscopy has been able to iadicate the position of the unsaturation ia unsaturated fatty amides (64). Typical specifications of some primary fatty acid amides and properties of bisamides are shown ia Tables 5 and 6. 

The potentiometric micro detection of all aminophenol isomers can be done by titration in two-phase chloroform-water medium (100), or by reaction with iodates or periodates, and the back-titration of excess unreacted compound using a silver amalgam and SCE electrode combination (101). Microamounts of 2-aminophenol can be detected by potentiometric titration with cupric ions using a copper-ion-selective electrode the 3- and... 

Titration of thioglycolate esters is also realized by iodine in alcohoHc solution. Titration of thioglycolic acid (acid number) in thioglycolate esters is effected by potentiometric titration with potassium hydroxide. 

Hydroxides. Thorium (TV) is generally less resistant to hydrolysis than similarly sized lanthanides, and more resistant to hydrolysis than tetravalent ions of other early actinides, eg, U, Np, and Pu. Many of the thorium(IV) hydrolysis studies indicate stepwise hydrolysis to yield monomeric products of formula Th(OH) , where n is integral between 1 and 4, in addition to a number of polymeric species (40—43). More recent potentiometric titration studies indicate that only two of the monomeric species, Th(OH) " and thorium hydroxide [13825-36-0], Th(OH)4, are important in dilute (<10 M Th) solutions (43). However, in a Th02 [1314-20-1] solubiUty study, the best fit to the experimental data required inclusion of the species. Th(OH) 2 (44). In more concentrated (>10 Af) solutions, polynuclear species have been shown to exist. Eor example, a more recent model includes the dimers Th2(OH) " 2 the tetramers Th4(OH) " g and Th4(OH) 2 two hexamers, Th2(OH) " 4 and Th2(OH) " 2 (43). 

The trimetaUic uranyl cluster (U02)3(C03) 3 has been the subject of a good deal of study, including nmr spectroscopy (179—182) solution x-ray diffraction (182), potentiometric titration (177,183,184), single crystal x-ray diffraction (180), and exafs spectroscopy in both the soHd and solution states (180). The data in this area have consistendy led to the proposal and verification of a trimeric (U02)3(C03) 3 cluster (181,182,185). 

The analysis of solutions of technical xanthates by Ag+ potentiometric titration, with the addition of ammonium hydroxide, has been successfully used at Dow (95). 

There are four basic sulfates that can be identified by potentiometric titration using sodium carbonate (39,40) langite [1318-78-17, CuSO -3Cu(OH)2 H2 i brochantite [12068-81 -4] CuSO -3Cu(OH)2 antedite [12019-54-4] CuSO -2Cu(OH)2 and CuS0 -Cu0-2Cu(0H)2-xH20. The basic copper(II) sulfate that is available commercially is known as the tribasic copper sulfate [12068-81 ] CuS04-3Cu(0H)2, which occurs as the green monoclinic mineral brochantite. This material is essentially insoluble in water, but dissolves readily in cold dilute mineral acids, warm acetic acid, and ammonia solutions. 

Perhaps the most precise, reHable, accurate, convenient, selective, inexpensive, and commercially successful electroanalytical techniques are the passive techniques, which include only potentiometry and use of ion-selective electrodes, either direcdy or in potentiometric titrations. Whereas these techniques receive only cursory or no treatment in electrochemistry textbooks, the subject is regularly reviewed and treated (19—22). Reference 22 is especially recommended for novices in the field. Additionally, there is a journal, Ion-Selective Electrode Reviews, devoted solely to the use of ion-selective electrodes. 

Potentiometric Titrations. If one wishes to analyze electroactive analytes that are not ions or for which ion-selective electrodes are not available, two problems arise. First, the working electrodes, such as silver, platinum, mercury, etc, are not selective. Second, metallic electrodes may exhibit mixed potentials, which may arise from a variety of causes. For example, silver may exchange electrons with redox couples in solution, sense Ag" via electron exchange with the external circuit, or tarnish to produce pH-sensitive oxide sites or Ag2S sites that are sensitive to sulfide and haUde. On the other... 

Fig. 9. Voltammograms demonstrating a potentiometric titration using dual-polarized electrodes, where the dashed lines indicate the anodic and equal-but-opposite cathodic currents that must be carded by the two opposing electrodes during the titration. Terms are defined in text.

There is also evidence for stable 3,4-adducts from the X-ray analysis of 2-amino-4-ethoxy-3,4-dihydropteridinium bromide, the nucleophilic addition product of 2-aminopteridine hydrobromide and ethanol (69JCS(B)489). The pH values obtained by potentiometric titration of (16) with acid and back-titration with alkali produces a hysteresis loop, indicating an equilibrium between various molecular species such as the anhydrous neutral form and the predominantly hydrated cation. Table 1 illustrates more aspects of this anomaly. 2-Aminop-teridine, paradoxically, is a stronger base than any of its methyl derivatives each dimethyl derivative is a weaker base than either of its parent monomethyl derivatives. Thus the base strengths decrease in the order in which they are expected to increase, with only the 2-amino-4,6,7-trimethylpteridine out of order, being more basic than the 4,7-dimethyl derivative. 

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