Equilibrium potentiometric

A cell to make measurements at equilibrium (potentiometric measurement) needs only two electrodes an indicator and a reference electrode (Fig. 7.3). In general, the indicator electrode is an ion-selective electrode (Section 13.3) and the reference electrode (Table 2.1) is Ag j AgCl or calomel in aqueous solution. The difference in potential between the two electrodes is measured since the reference electrode potential is constant, changes in cell potential are due only to the indicator electrode which responds logarithmically to the activity of the species in solution to which it is sensitive. 

One of the advantages of mixed potential sensors is that it is possible for both electrodes to be exposed to the same gas. The elimination of a need to separate the two electrodes simplifies the sensor design, which in turn reduces fabrication costs. Although this simpler planar design is often used, the electrodes are sometimes separated to provide a more stable reference potential. As with equilibrium potentiometric sensors, the minimum operating temperature is often limited by electrolyte conductivity. However, the maximum operation temperatures for nonequilibrium sensors are typically lower than those of equilibrium sensors, because the electrode reactions tend towards equilibrium as the temperature increases. This operating temperature window depends on the electrode materials, as will be discussed later in the chapter. 

For a two-electrode cell, the net reaction comprises two half-reactions, involving the processes at the two electrodes. As already mentioned, usually only one of these processes is of interest, and this occurs at the working electrode in dynamic electrochemistry experiments or indicator electrode in equilibrium (potentiometric) experiments. The other electrode is made up such that it maintains a constant composition throughout the measurement, thus providing a reference potential. The most common reference for aqueous solution is the saturated calomel electrode (SCE), depicted in Fig. 1, and this provides... 

NON-EQUILIBRIUM POTENTIOMETRIC RESPONSES 7.4.1 Mixed ion-transfer potentials... 

Electrochemical methods may be classified into two broad classes, namely potentiometric metiiods and voltannnetric methods. The fonner involves the measurement of the potential of a working electrode iimnersed in a solution containing a redox species of interest with respect to a reference electrode. These are equilibrium experiments involving no current flow and provide themiodynamic infomiation only. The potential of the working electrode responds in a Nemstian maimer to the activity of the redox species, whilst that of the reference electrode remains constant. In contrast, m voltannnetric methods the system is perturbed... 

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... 

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. 

Potentiometric electrodes are divided into two classes metallic electrodes and membrane electrodes. The smaller of these classes are the metallic electrodes. Electrodes of the first kind respond to the concentration of their cation in solution thus the potential of an Ag wire is determined by the concentration of Ag+ in solution. When another species is present in solution and in equilibrium with the metal ion, then the electrode s potential will respond to the concentration of that ion. Eor example, an Ag wire in contact with a solution of Ck will respond to the concentration of Ck since the relative concentrations of Ag+ and Ck are fixed by the solubility product for AgCl. Such electrodes are called electrodes of the second kind. 

Sta.bilizers. Cyanuric acid is used to stabilize available chlorine derived from chlorine gas, hypochlorites or chloroisocyanurates against decomposition by sunlight. Cyanuric acid and its chlorinated derivatives form a complex ionic and hydrolytic equilibrium system consisting of ten isocyanurate species. The 12 isocyanurate equilibrium constants have been determined by potentiometric and spectrophotometric techniques (30). Other measurements of two of the equilibrium constants important in swimming-pool water report significantly different and/or less precise results than the above study (41—43). A critical review of these measurements is given in Reference 44. 

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. 

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

In systems such as the 2- and 6-hydroxypteridine series, rapid potentiometric or spectrophotometric pA determinations on neutral solutions usually give values near to the acidic pA of the hydrated series. (Exceptions include 2-hydroxy-4,6,7-trimethyl-, 6-hydroxy-7-methyl-, and 4,6-dihydroxy-pteridine, where the neutral solution contains comparable amounts of hydrated and anhydrous species. In such cases, rapid potentiometric titrations show two well-defined and separated curves, one for the hydrated, the other for the anhydrous, species.) Similarly, from solutions of the anion, an approximate pA value for the anhydrous species is obtained. For convenience, the anhydrous molecule is referred to as HX, its anion as X , the hydrated neutral molecule as HY, and its anion as Y, and the two equilibrium constants are defined as follows ... 

This figure demonstrates that also under potentiometric conditions (- no external current flow) electrochemical net reactions occur. The EMF of the zinc-amalgam in a given Zn2 -ion solution depends on the current-voltage characteristic of other ions (in this example, Cu2 and Pb2 are interfering ions with respect to the Zn2 equilibrium potential) at the amalgam electrode. EMF drifts are thus explainable. 

In such reactions, even though the indicator electrode functions reversibly, the maximum value of AE/AV will not occur exactly at the stoichiometric equivalence point. The resulting titration error (difference between end point and equivalence point) can be calculated or can be determined by experiment and a correction applied. The titration error is small when the potential change at the equivalence point is large. With most of the reactions used in potentiometric analysis, the titration error is usually small enough to be neglected. It is assumed that sufficient time is allowed for the electrodes to reach equilibrium before a reading is recorded. 

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