Potentiometry—

Potentiometry is suitabie for the analysis of substances for which electrochemical equilibrium is established at a suitable indicator electrode at zero current. According to the Nemst equation (3.31), the potential of such an electrode depends on the activities of the potential-determining substances (i.e., this method determines activities rather than concentrations). 

As an example, consider the potentiometric determination of concentration of ions in a solution which is to be accomplished with the aid of an electrode of metal N. Using a simple cell with the reference electrode M /E,  

The problem can be simplified when the peculiar concentration cell 

An important condition for potentiometry is high selectivity the electrode s potential shonld respond only to the snbstance being examined, not to other components in the solntion. This condition greatly restricts the possibilities of the version of potentiometry described here when metal electrodes are nsed as the indicator electrodes. The solntion shonld be free of ions of more electropositive metals and of the components of other redox systems (in particnlar, dissolved air). Only corrosion-resistant materials can be nsed as electrodes. It is not possible at all with this method to determine alkali or alkaline-earth metal ions in aqneons solntions. 

Consider the same example, of determining the concentration of ions bnt now while using a membrane having ideal permselectivity (i.e., a membrane that is 

Potentiometry. Potentiometric methods rely on the logarithmic relationship between measured potential and analyte concentration. The most common involves an instrument called a pH-Stat , in which a glass (pH) electrode follows reactions that either consume or produce protons. Since pH changes cause changes in enzyme activity, the pH is maintained at a constant value by the addition of acid or base. The rate of titrant addition is then proportional to the rate of the enzymatic reaction. Precise measurements using the pH-Stat require low buffer concentrations in the enzymatic assay mixture. 

Other potentiometric methods employ gas-sensing electrodes for NH3 (for deaminase reactions) and C02 (for decarboxylase reactions). Ion-selective electrodes have also been used to quantitate penicillin, since the penicillinase reaction may be mediated with I or CN.  

Potentiometry involves measurement of the potential, or voltage, of an electrochemical cell. Accurate determination of the potential developed by a cell requires a negligible current flow during measurement. A flow of current would mean that a faradaic reaction is taking place, which would change the potential from that existing when no current is flowing. 

Measurement of the potential of a cell can be useful in itself, but it is particularly valuable if it can be used to measure the potential of a half-cell or indicator electrode 

Compare this equation with Eqs. (15.7) and (15.15). By convention, the reference electrode is connected to the negative terminal of the potentiometer (the readout device). The common reference electrodes used in potentiometry are the SCE and the silver/silver chloride electrode, which have been described. Their potentials are fixed and known over a wide temperature range. Some values for these electrode potentials are given in Table 15.3. The total cell potential is measured experimentally, the reference potential is known, and therefore the variable indicator electrode potential can be calculated and related to the concentration of the analyte through the Nemst equation. In practice, the concentration of the unknown analyte is determined after calibration of the potentiometer with suitable standard solutions. The choice of reference electrode depends on the application. For example, the Ag/AgCl electrode cannot be used in solutions containing species such as halides or sulfides that will precipitate or otherwise react with silver. 

The indicator electrode is the electrode that responds to the change in analyte activity. An ideal indicator electrode should be specific for the analyte of interest, respond rapidly to 

Metallic Electrodes. A metal electrode of the first kind is just a metal wire, mesh, or solid strip that responds to its own cation in solution. Cu/Cu, Ag/Ag, Hg/Hg , and Pb/Pb are examples of this type of electrode. There are significant problems encountered with these electrodes. They have poor selectivity, responding not only to their own cation but also to any other more easily reduced cation. Some metal surfaces are easily oxidized, giving erratic or inaccurate response unless the solution has been purged of air. Some metals can only be used in limited pH ranges because they will dissolve in acids or bases. Silver and mercury are the most commonly used electrodes of the first kind. 

Compare this equation with Equations 15.7 and 15.15. By convention, the reference electrode is connected to the negative terminal of the potentiometer (the readout device). The common reference electrodes used in potentiometry are the SCE and the silver/silver chloride electrode, which have been described. Their potentials are fixed and known over a wide temperature range. Some values for these electrode potentials are given in Table 15.3. The total cell potential is measured 

In potentiometry, the potential of a suitable indicator electrode is measured versus a reference electrode, i.e. an electrode with a constant potential. Whereas the indicator electrode is in direct contact with the analyte solution, the reference electrode is usually separated from the analyte solution by a salt bridge of various forms. The electrode potential of the indicator electrode is normally directly proportional to the logarithm of the activity of the analyte in the solution. Potentiometric methods have been and are still frequently used to indicate the end point of titrations. This use has been known since the end of the nineteenth century. Direct potentiometric determinations using ion-selective electrodes have been mainly developed in the second half of the twentieth century. 

It is an attractive feature of potentiometry that the equipment is rather inexpensive and simple one needs a reference electrode, an indicator electrode and a voltagemeasuring instrument with high input impedance. The potential measurement has to be accomplished with as low a current as possible because otherwise the potential of both electrodes would change and falsify the result. In the past, a widespread method was the use of the so-called Poggendorf compensation circuit. In most cases today, amplifier circuits with an input impedance up to 10 2 are used. The key element for potentiometry is the indicator electrode. Currently, ion-selective electrodes are commercially available for more than 20 different ions and almost all kinds of titrations (acid-base, redox, precipitation and complex titrations) can be indicated. In the following, some indicator electrodes and the origin of the electrode potentials will be described. 

The Galvani potential difference of a single electrode is not directly measurable, because it is not possible to connect the two phases of an electrode with a measuring 

Institut fur Biochemie, Universitat Greifswald, 17487 Greifswald, Germany e-mail hkahlert uni-greifswald.de 

When one of these Galvani potential differences, e.g. A is kept constant, this electrode can be used as a reference electrode. Then, the relative electrode potential of an electrode (indicated here as X) is the cell voltage of a galvanic cell, which consists of the electrode and the reference electrode (R). 

The formation of a charge transfer complex may also be indicated from potentiometry the electrode potential of an active electrode, usually Au or Pt, is measured against a reference electrode potential, say a saturated calomel electrode. Donor is then titrated against an acceptor solution, or vice versa, and a maximum or a minimum in the potential vs. tit rant concentration curve indicates the complex stochiometry. The technique has been applied to study the interactions between E. coli and antibiotics such as streptomycin and kanamycin, using a three-compartment cell.  

Electrochemical analytical techniques are some of the oldest in chemistry and can be divided into potentiometry, voltammetry and conductimetry. They are most important as detectors after chromatographic separations and as chemical and biological sensors. They generally involve the use of electrodes that are housed in electrochemical cells. All electrochemical cells contain two electrodes but some have three. The first electrode is the actual working electrode (also called a sensing or indicator electrode) and the second is a combined reference electrode and auxiliary (counter) electrode. If there are three electrodes, the reference and counter electrodes are separate. 

There are two types of electrochemical cells voltaic (galvanic), which produce energy from a chemical reaction, and electrolytic (voltammetric), which require or use up energy. In voltaic cells, a spontaneous chemical reaction produces electricity. These cells are important in potentiometry. In electrolytic cells, electrical energy is used to force a chemical reaction to take place such as in voltammetry. In summary  

Owing to its simplicity and flexibility, potentiometry is probably the most widely used analytical technique. It is most commonly used for measuring pH and for the selective determination of analyte concentrations in a wide variety of sample solutions. Potentiometry is based on the measurement of the potential difference between the reference and working electrodes in a voltaic cell. In this type of cell, as mentioned above, a spontaneous redox chemical reaction occurs due to one reagent being oxidised (losing electrons) at the anode 

Analytical Instrumentation A Guide to Laboratory, Portable and Miniaturized Instruments G. McMahon 

Potentiometry requires a reference electrode, a working electrode and a potentialmeasuring instrument, e.g. voltmeter, otherwise known as a potentiometer. The test solution must be in direct contact with the working electrode, which is sometimes referred to as the chemical sensor as it is sensing the output of a chemical reaction. The reference electrode can also be placed in the test solution or can be brought into contact with the test solution via a salt bridge. The measured potential can be related to the concentration of the species being measured and this approach is called direct potentiometry. 

Different electrochemical techniques depend on whether they are bulk methods as in conductometry or interfacial methods. The latter may be static as in potentiometry or dynamic. Dynamic methods are classified on the basis of the current used. Conductometry uses a constant current but controlled current methods include voltametry, amperometry and coulometry. 

When a metal M dips in an aqueous solution of its ions, M , whose activity is a (in dilute solution, a can be replaced by [M ]), a potential E is set up related to a by the Nernst equation  

The potential of such electrodes depends on the activity of a specific ion. The most widely used is the glass electrode. This consists of a tube ending in a special glass bulb filled with a O.IM HCI in which a Ag/AgCI electrode is inserted. The special glass is sensitive to H ions and is specific for pH measurements. A combined glass electrode is often used in which a calomel electrode is coupled with the glass electrode. The 

In acid/base titrations, when the solutions are coloured or when the titration curve does not exhibit a clear inflexion point, colour indicators cannot be used and the glass electrode is used with a pH meter. From the plot of pH vs volume of titrant, the endpoint can be located. This method is necessary when no suitable indicator for the pH range near the end-point is available. 

When an inert metal electrode, usually Pt, is immersed in a solution containing the oxidised and reduced forms of a metal ion or of an element, the electrode potential is given by  

The most common techniques utilised for the determination of the stability or solubility constants of metal hydroxide species and phases include ion exchange (solid-liquid extraction), distribution (liquid-liquid extraction), potentiometry, solubility and spectrophotometry. A brief outline of each of these techniques will be discussed. 

The main principle behind potentiometric titrations is the measurement of the activity of one or several aqueous species using ion-selective electrodes versus a selected standard (reference) electrode. In the case of the determination of 

Hydrolysis of Metal Ions, First Edition. Paul L. Brown and Christian Hdjerg. 

Potentiometric titrations are used for the determination of stoichiometric and thermodynamic properties of elements in solution and are usually based on the Nernst equation (Nernst, 1889)  

There are two methods that are considered fundamental in the use of potentiometric titrations to determine the properties of a solution. The first was developed by Bodlander and Fittig (1902). The main feature of this method was to obtain a description of the stoichiometric constant in a reaction between a metal (M) and a ligand (L). However, it is usually desirable to also obtain a value for the stability constant itself since only how the expression looks for the reaction is not sufficient. A method for doing this using potentiometric titrations was introduced by Bjerrum (1941). In this method, Bjerrum usedthe average ligand number defined by 

In order to make measurements of electrode potentials, or to study the changes that take place in a solution reaction, an appropriate electrochemical cell must be set up. 

The indicator electrode makes electrical contact with the solution and acts as a sensor, which responds to the activity of particular ions in solution and acquires a potential dependent on the concentration of those ions. 

The ideal electrode should respond to a single ion, but this is not often the case. The effectiveness of any indicator electrode is determined by its selectivity. 

The direct measurement of concentrations is possible using electrodes of high selectivity and reproducibility. The measurement may also be used to follow titrations. 

If a check is needed on the correctness of the measured value for an experimental cell, a standard cell, such as the Weston cadmium cell, may be used as a calibration, since the value of its emf is accurately known over a range of temperatures. The electrode potential is defined using the standard hydrogen electrode as reference, as described in Topic C2. 

As shown in Section 2.28, when a metal M is immersed in a solution containing its own ions M +, then an electrode potential is established, the value of which is given by the Nernst equation  

This procedure of using a single measurement of electrode potential to determine the concentration of an ionic species in solution is referred to as direct potentiometry. The electrode whose potential is dependent upon the concentration of the ion to be determined is termed the indicator electrode, and when, as in the case above, the ion to be determined is directly involved in the electrode reaction, we are said to be dealing with an electrode of the first kind . 

It is also possible in appropriate cases to measure by direct potentiometry the concentration of an ion which is not directly concerned in the electrode reaction. This involves the use of an electrode of the second kind , an example of which is the silver-silver chloride electrode which is formed by coating a silver wire with silver chloride this electrode can be used to measure the concentration of chloride ions in solution. 

The silver wire can be regarded as a silver electrode with a potential given by the Nernst equation as 

The silver ions involved are derived from the silver chloride, and by the solubility product principle (Section 2.6), the activity of these ions will be governed by the chloride-ion activity 

The potential developed by a single electrode in a solution is caused by the tendency of the solution either to donate or accept electrons and can be 

There can be no chemical reaction in such a system without a complementary electron donor or acceptor to complete the process. Each of these electrode systems is known as a half-cell and the potential developed by a halfcell cannot be measured in absolute terms but only compared with that of another half-cell. The chemical reaction occurring at each half-cell is known as a half-reaction. 

An active electrode consists of an element (M) in its uncombined state which is capable of establishing an equilibrium with a solution that contains its ions  

The ionization of atoms or molecules results in a potential being developed by such an electrode, the intensity of the potential being related to the concentration of the ions. The effective concentration of the ions (known as the activity of the ions) is more significant than the molar concentration. The values for activity and concentration are only the same in very dilute solutions. 

Inert electrodes, such as silver, platinum, and carbon, are used solely to make electrical contact with the solution and only reflect the potential of the solution. They are used to measure the potential of solutions containing mixtures of ions which have a tendency to transfer electrons between them, e.g. ferric and ferrous ions  

It is possible nowadays to determine with very high accuracy the concentration of various ions and gases in solution using combined-glass or selective electrodes these provide an inexpensive straightforward procedure for monitoring chemical reactions [51-55]. 

The measured property is the electrical potential which is related to the concentration of the target species by the Nernst equation (see Chapter 6) 

An important advantage of these techniques is that the measurements of electrical potential can be very accurate, which allows monitoring until almost complete conversion, or until equilibrium in a reversible process. In fact, potentiometry is extremely powerful for obtaining equilibrium constants [25]. However, there are also restrictions and limitations (a) the solution must be conducting (b) the response time of the electrode can be relatively long, so there is a limit to the speed of a reaction which can be monitored and (c) there can be appreciable interference from impurities, or intermediates and products. 

Formation of Cl- was monitored potentiometrically in the reaction of methionine and HOC1 shown earlier in the example in Section 3.3.3.1 and plotted in Fig. 3.4 [12]. The technique has also been used to study the elimination of HC1 from DDT [56] and various bromination reactions [57]. 

Potentiometric methods have eliminated the problems that beset earlier studies, due to the high electrolyte concentrations required for ideal electrode behavior. Following the so-called constant ionic medium principle [91], a large excess of an indifferent (or inert or swamping) electrolyte is added, so that the activity coefficients of the species can be considered constant when their concentration (very low compared to that of the indifferent electrolyte) are changed over a wide range. 

Electrodes sensitive to one of the ion-pair partners in the so-called constant ionic strength cell [95] proved to be valuable to measure the free ion concentration and to determine the stoichiometric equilibrium constant. The latter has a clear thermodynamic meaning if the ionic strength of the medium is indicated, since in this approach, the reference standard state is not the usual infinite dilution of all species dissolved in the solvent (y- 1, as c - 0), but is the infinite dilution of the reacting species in the constant ionic medium (7— 1, as c 0 at 1 = constant) [7]. Even if the constant ionic strength attenuates the variation of liquid junction potentials, the lower the association constant, the lower the consistency of the obtained constant. 

Potentiometric methods of analysis are based on measuring the potential of electrochemical cells without drawing appreciable current. For nearly a century, potentiometric techn iques have been used to locate end points in titrations. In more recent methods, ion concentrations are measured directly from the potential of ion-selective membrane electrodes. These electrodes are relatively free from interferences and provide a rapid, convenient, and nondestructive means of quantitatively determining numerous important anions and cations.  

Analysts make more potentiometric measurements than perhaps any other type of chemical instrumental measurement. The number of potentiometric measurements made on a daily basis is. staggering. Manufacturers measure the pH of many consumer products clinical laboratories determine blood gases as important indicators of disease. states industrial and municipal effluents are monitored continuously to determine pH and concentrations of pollutants and oceanographers determine carbon dioxide and other related variables in sea water. Potentiometric measurements are also used in fundamental studies to determine thermodynamic equilibrium comstants such as K, Ki, and ATsp. These examples are but a few of the many thousands of applications of potentiometric measurements. 

The equipment for potentiometric methods is simple and inexpensive and includes a reference electrode, an indicator electrode, and a potential-measuring device. The principles of operation and design of each of these components are described in the initial. sections of this chapter. Following these discussions, we investigate analytical applications of potentiometric measurements. 

A reference electrode is a half-cell having a known electrode potential that remains constant at constant temperature and is independent of the composition of the analyte solution. 

Reference electrodes are always treated as the left-hand electrode in this text. 

The relationship between the concentration of an ion in solution and the e.m.f. of the cell in which this ion is located can be expressed under ideal conditions by the Nernst equation. 

The above-mentioned equation only applies to infinite dilution, whereas the following applies to real solutions  

If two electrodes are immersed in a solution whose ions can react with the electrode, and the circuit is closed, the potential existing at the 

If the given constants are entered in the Nernst equation, the natural logarithm then converted to the Briggs logarithm, and the activities 

In practical terms, it is impossible to measure the potential difference in 

Most of this discussion of electrochemistry has dealt with effects involving a how of electrical current. It has been seen that chemical reactions can be used to produce an electrical current. It has also been seen that the flow of an electrical current through an electrochemical cell can be used to make a chemical reaction occur. Another characteristic of electricity is its voltage, or electrical potential, which was discussed as E and ° values above as a kind of driving force behind oxidation-reduction reactions. 

The potential of the fluoride measuring electrode at 25°C responds according to the Nernst equation in the form 

To measure pH, the pH meter must first be calibrated. This is done by placing the electrodes in a standard buffer solution of known pH (a buffer solution is one that resists changes in pH with added acid, base, or water, and a standard buffer solution is one made up to an accurately known pH). After calibration, the pH meter is then adjusted to read that pH. Next, the electrodes are removed from the buffer solution, rinsed to remove any buffer, and placed in the solution of unknown pH. This pH is then read directly from the pH meter. 

Corrosion is defined as the destructive alteration of metal through interactions with its surroundings—in short, rust. It is a redox phenomenon resulting from the fact that most metals are unstable in relation to their surroundings. Thus, the steel in cars really prefers to revert back to the iron oxide ore that it came from by reacting with oxygen in the air. The corrosion process is accelerated by exposure to water, which may contain corrosive salt placed on road ice, or acid from acid rain. It is only by the application of anticorrosive coatings and careful maintenance that the process is slowed down. 

The overall corrosion process is normally very complicated and involves a number of different reactions. Very commonly, bacteria are involved in corrosion. The bacterial cells derive energy by acting as catalysts in tiie corrosion reactions. 

Potentiometric techniques employ measurement of electrode potentials and their variation with changing chemical environment. It is less usual for electrode potentials to be used for direct concentration measurements although the most noteworthy exception is the case of hydrogen ion determination in pH measurements. Titration techniques, in which the variation of potentials during the addition of titrant is recorded, are of considerable importance and versatility. 

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The pK s of some 2-substituted 4-hydroxythiazoles have been determined by ultraviolet spectroscopy (403) and by potentiometry (419). They range between 6.65 and 6-85 pK. units. 

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). 

Techniques, such as spectroscopy (Chapter 10), potentiometry (Chapter 11), and voltammetry (Chapter 11), in which the signal is proportional to the relative amount of analyte in a sample are called concentration techniques. Since most concentration techniques rely on measuring an optical or electrical signal, they also are known as instrumental techniques. For a concentration technique, the relationship between the signal and the analyte is a theoretical function that depends on experimental conditions and the instrumentation used to measure the signal. For this reason the value of k in equation 3.2 must be determined experimentally. 

Finding the End Point Potentiometrically Another method for locating the end point of a redox titration is to use an appropriate electrode to monitor the change in electrochemical potential as titrant is added to a solution of analyte. The end point can then be found from a visual inspection of the titration curve. The simplest experimental design (Figure 9.38) consists of a Pt indicator electrode whose potential is governed by the analyte s or titrant s redox half-reaction, and a reference electrode that has a fixed potential. A further discussion of potentiometry is found in Chapter 11. 

The diversity of interfacial electrochemical methods is evident from the partial family tree shown in Figure 11.1. At the first level, interfacial electrochemical methods are divided into static methods and dynamic methods. In static methods no current passes between the electrodes, and the concentrations of species in the electrochemical cell remain unchanged, or static. Potentiometry, in which the potential of an electrochemical cell is measured under static conditions, is one of the most important quantitative electrochemical methods, and is discussed in detail in Section IIB. 

In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution s potential, its composition remains unchanged. For this reason, potentiometry is a useful quantitative method. The first quantitative potentiometric applications appeared soon after the formulation, in 1889, of the Nernst equation relating an electrochemical cell s potential to the concentration of electroactive species in the cell. ... 

When first developed, potentiometry was restricted to redox equilibria at metallic electrodes, limiting its application to a few ions. In 1906, Cremer discovered that a potential difference exists between the two sides of a thin glass membrane when opposite sides of the membrane are in contact with solutions containing different concentrations of H3O+. This discovery led to the development of the glass pH electrode in 1909. Other types of membranes also yield useful potentials. Kolthoff and Sanders, for example, showed in 1937 that pellets made from AgCl could be used to determine the concentration of Ag+. Electrodes based on membrane potentials are called ion-selective electrodes, and their continued development has extended potentiometry to a diverse array of analytes. 

Potentiometric measurements are made using a potentiometer to determine the difference in potential between a working or, indicator, electrode and a counter electrode (see Figure 11.2). Since no significant current flows in potentiometry, the role of the counter electrode is reduced to that of supplying a reference potential thus, the counter electrode is usually called the reference electrode. In this section we introduce the conventions used in describing potentiometric electrochemical cells and the relationship between the measured potential and concentration. 

In potentiometry, the concentration of analyte in the cathodic half-cell is generally unknown, and the measured cell potential is used to determine its concentration. Thus, if the potential for the cell in Figure 11.5 is measured at -1-1.50 V, and the concentration of Zn + remains at 0.0167 M, then the concentration of Ag+ is determined by making appropriate substitutions to equation 11.3... 

The potential of the indicator electrode in a potentiometric electrochemical cell is proportional to the concentration of analyte. Two classes of indicator electrodes are used in potentiometry metallic electrodes, which are the subject of this section, and ion-selective electrodes, which are covered in the next section. 

The potential of a metallic electrode is determined by the position of a redox reaction at the electrode-solution interface. Three types of metallic electrodes are commonly used in potentiometry, each of which is considered in the following discussion. 

Redox Electrodes Electrodes of the first and second kind develop a potential as the result of a redox reaction in which the metallic electrode undergoes a change in its oxidation state. Metallic electrodes also can serve simply as a source of, or a sink for, electrons in other redox reactions. Such electrodes are called redox electrodes. The Pt cathode in Example 11.1 is an example of a redox electrode because its potential is determined by the concentrations of Ee + and Ee + in the indicator half-cell. Note that the potential of a redox electrode generally responds to the concentration of more than one ion, limiting their usefulness for direct potentiometry. 

If metallic electrodes were the only useful class of indicator electrodes, potentiometry would be of limited applicability. The discovery, in 1906, that a thin glass membrane develops a potential, called a membrane potential, when opposite sides of the membrane are in contact with solutions of different pH led to the eventual development of a whole new class of indicator electrodes called ion-selective electrodes (ISEs). following the discovery of the glass pH electrode, ion-selective electrodes have been developed for a wide range of ions. Membrane electrodes also have been developed that respond to the concentration of molecular analytes by using a chemical reaction to generate an ion that can be monitored with an ion-selective electrode. The development of new membrane electrodes continues to be an active area of research. 

Electrochemical cell for potentiometry with an ion-selective membrane electrode. 

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. 

Wang and Taha described an interesting application of potentiometry called batch injection. As shown in the following figure, an ion-selective electrode is placed in an inverted position in a large-volume tank, and a fixed volume of a sample or standard solution is injected toward the electrode s surface using a micropipet. 

Additional information on potentiometry and ion-selective electrodes can be found in the following sources. 

Buck, R. P. Potentiometry pH Measurements and Ion Selective Electrodes. In Weissberger, A., ed.. Physical Methods of Organic Chemistry, Vol. 1, Part IIA. Wiley New York, 1971, pp. 61-162. Cammann, K. Working with Ion-Selective Electrodes. Springer-Verlag Berlin, 1977. 

Evans, A. Potentiometry and Ion-Selective Electrodes. Wiley New York, 1987. Frant, M. S. Where Did Ion Selective Electrodes Come From /. Chem. Educ. 1997, 74, 159-166. 

Other methods of instmmental analysis include polarography, potentiometry, emission spectroscopy, x-ray diffraction, and x-ray fluorescence. 

Numerous methods have been pubUshed for the determination of trace amounts of tellurium (33—42). Instmmental analytical methods (qv) used to determine trace amounts of tellurium include atomic absorption spectrometry, flame, graphite furnace, and hydride generation inductively coupled argon plasma optical emission spectrometry inductively coupled plasma mass spectrometry neutron activation analysis and spectrophotometry (see Mass spectrometry Spectroscopy, optical). Other instmmental methods include polarography, potentiometry, emission spectroscopy, x-ray diffraction, and x-ray fluorescence. 

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. 

Potentiometry is another useful method for determining enzyme activity in cases where the reaction Hberates or consumes protons. This is the so-called pH-stat method. pH is kept constant by countertitration, and the amount of acid or base requited is measured. An example of the use of this method is the determination of Hpase activity. The enzyme hydroly2es triglycerides and the fatty acids formed are neutralized with NaOH. The rate of consumption of NaOH is a measure of the catalytic activity. 

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