Relative potentiometric measurement

By contrast, in relative potentiometric measurements, changes in the potential observed during a titration, such as that in Figure 6-5, are relatively precise and... 

Potentiometric measurements give log(3/ values which are correct to within 10% but the relative accuracy is difficult to assess due to the successive, repetitive nature of the experiments. Probably the most significant source of error, as we have stated, is the variation of pH with time. At tracer concentrations the enthalpy AH0 can be determined only by the temperature differential method. However, the temperature differential method is not as precise as the calorimetric one. The enthalpy of formation for each complex is computed with the assumption that ACp is constant over the temperature range and that the range of error corresponds to 10%. 

Figure 15.1. Potentiometric measurement for pH. V), glass membrane V2, inner buffer solution V3, internal reference electrode relative to internal buffer V4, external reference electrode V5, diaphragm.

Potentiometric measurements are based on the determination of a voltage difference between two electrodes plunged into a sample solution under null current conditions. Each of these electrodes constitutes a half-cell. The external reference electrode (ERE) is the electrochemical reference half-cell, which has a constant potential relative to that of the solution. The other electrode is the ion selective electrode (ISE) which is used for measurement (Fig. 18.1). The ISE is composed of an internal reference electrode (IRE) bathed in a reference solution that is physically separated from the sample by a membrane. The ion selective electrode can be represented in the following way ... 

Selective electrodes have a variable specificity. Precision can be increased when they are used as indicating electrodes in potentiometric measurements. The concentration of ions present in solution and the ionic strength will undergo small variations during measurement relative to the concentration of the ion being measured. When two ionic species undergo stoichiometric reaction, this property can be used for their determination. The end point in the measurement is characterised either by the total disappearance of one of the species or by the appearance of an excess of one of the species. The appearance or disappearance of a secondary species can also be used to determine the end point. 

The result obtained by a titration is usually more precise than that obtained in a direct potentiometric measurement. It is usually not too difficult to create an end point with a precision of better than 5 %. In the direct potentiometric determination the relative error Frei is given by... 

The usefulness of pH as a measure of the acidity and alkalinity of aqueous media, the wide availability of commercial glass electrodes, and the relatively recent proliferation of inexpensive solid-state pH meters have made the potentiometric measurement of pH perhaps the most common analytical technique in all of science. It is thus extremely impoitant that pH be defined in a manner that is easily duplicated at various times and in various laboratories throughout the world. To meet this requirement, it is necessary to define pH in operational terms—that is, by the way the measurement is made. Only then will the pH measured by one worker be the same as that measured by another. 

One interesting result of this property is that the relative concentration error for direct potentiometric measurements is theoretically independent of the actual concentration. Unfortunately, the error is rather large—approximately 4n% per mV uncertainty in measurement, perhaps the most serious limitation of ISEs. Since potential measurements are seldom better than 0.1 mV total uncertainty, the best measurements for monovalent ions under near-ideal conditions are limited to about 0.5% relative concentration error. For divalent ions, this error would be doubled and in particularly bad cases where, for example, liquid-junction potentials may vary by 5 to 10 mV (as in high or variable ionic-strength solutions), the relative concentration error may be as high as 507o- This limitation may be overcome, however, by using ISEs as endpoint indicators in potentiometric titrations (Sec. 2.6). At the cost of some extra time, accuracies and precisions on the order of 0.1% or better are possible. 

Table 57. Relative Q -Acceptor Strength of Chloride Ion-Acceptor Chlorides towards Covalent (C6H5)3C1 and Polar (C2H5)4NC1 Chlorides as Found by Spectrophotometric and Potentiometric Measurements in Phenylphosphonic Bichloride...

The essential component of a potentiometric measurement is an indicator electrode, the potential of which is a function of the activity of the target analyte. Many types of electrodes exist (see Table 9.1), but those based on membranes are by far the most useful analytical devices. The broader field of potentiometry has been reviewed recently (1). The potential of the indicator electrode cannot be determined in isolation, and another electrode (a reference electrode) is required to complete the electrochemical cell. Undoubtedly the best known of the potentiometric indicator electrodes is the glass pH electrode, the operation and use of which has been adequately discussed (2). Ion-selective electrodes (ISEs) are also commonplace, and have been the subject of several books (3-5) there is even a review journal for ISEs (6). Unfortunately, the simplicity of fabrication and use of ISEs has given rise to the idea that ISEs are chemical sensors. At the best this is a half-truth certainly, they can behave like chemical sensors under well-controlled laboratory conditions, but in the real world their performance leaves much to be desired. Moreover, from a manufacturing point of view important features of a sensor are that it can be fabricated in relatively large numbers, and that each device is identical to all the others. Although some ISEs can be mass-produced , many cannot, and even those that do lend themselves to this form of production invariably require calibration before use. Nonetheless, in spite of the limitations of ISEs, transducers based on potentiometric membrane electrodes have much to contribute to the field of chemical sensing. 

Diphenylmethane is the conjugate acid of the diphenylmethyl carbanion, and the equilibrium acidity constants (Ka) have been measured both directly and indirectly in the gas phase and in solution [3]. The most extensive investigations of the effect of structure on acidity for carbon acids have been carried out in DMSO using a carbon indicator method to determine relative acidities and this scale was anchored with potentiometric measurements to provide an absolute scale of acidities [3, 43]. A summary of relevant pKg values for various carbon acids is shown in Table 2. The data in Table 2 are especially relevant for considering the reactivity of 1,1-diphenylmethyl carbanionic species as initiators in anionic polymerization. In general, an appropriate initiator for a given monomer is an anionic species that has a reactivity (stability) similar... 

The discussion in this section has introduced the idea of a reference electrode as a device which maintains a fixed value of its potential relative to the solution phase, ((preference - potentiometric measurements of another electrode system relative to the reference electrode. This requirement of a fixed value of ((prefercsnce - reference electrode has certain special properties to ensure that this potential value does indeed stay fixed. In particular any successful reference electrode will display the following properties. 

All stated pK values in this book are for data in dilute aqueous solutions unless otherwise stated, although the dielectric constants, ionic strengths of the solutions and the method of measurement, e.g. potentiometric, spectrophotometric etc, are not given. Estimated values are also for dilute aqueous solutions whether or not the material is soluble enough in water. Generally the more dilute the solution the closer is the pK to the real thermodynamic value. The pK in mixed aqueous solvents can vary considerably with the relative concentrations and with the nature of the solvents. For example the pK values for V-benzylpenicillin are 2.76 and 4.84 in H2O and H20/EtOH (20 80) respectively the pK values for (-)-ephedrine are 9.58 and 8.84 in H2O and H20/Me0CH2CH20H (20 80) respectively and for cyclopentylamine the pK values are 10.65 and 4.05 in H2O and H20/EtOH (50 50) respectively. pK values in acetic acid or aqueous acetic acid are generally lower than in H2O. 

---