Finding potentiometrically

K. Ren and A. Ren-Kurc, A New Numerical Method of Finding Potentiometric Titration End-points by Use of Rational Spline Functions. Talanta. 33 (1986), 641-647. 

Thus, for example, an analysis using coloured solutions can be carried out, where an indicator cannot be used. Moreover, it is not easy to find a redox indicator which will change colour at the right point. Potentiometric methods can fairly readily be made automatic. 

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. 

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. 

Initial attempts at developing precipitation titration methods were limited by a poor end point signal. Finding the end point by looking for the first addition of titrant that does not yield additional precipitate is cumbersome at best. The feasibility of precipitation titrimetry improved with the development of visual indicators and potentiometric ion-selective electrodes. 

In cases where it proves impossible to find a suitable indicator (and this will occur when dealing with strongly coloured solutions) then titration may be possible by an electrometric method such as conductimetric, potentiometric or amperometric titration see Chapters 13-16. In some instances, spectrophotometric titration (Chapter 17) may be feasible. It should also be noted that ifit is possible to work in a non-aqueous solution rather than in water, then acidic and basic properties may be altered according to the solvent chosen, and titrations which are difficult in aqueous solution may then become easy to perform. This procedure is widely used for the analysis of organic materials but is of very limited application with inorganic substances and is discussed in Sections 10.19-10.21. 

Electrochemical sensors play a crucial role in environmental and industrial monitoring, as well as in medical and clinical analysis. The common feature of all electroanalytical sensors is that they rely on the detection of an electrical property (i.e., potential, resistance, current) so that they are normally classified according to the mode of measurement (i.e., potentiometric, conductometric, amperometric). A number of surveys have been published on this immense field. The reader may find the major part of the older and recent bibliography in the comprehensive reviews of Bakker et al. [109-111]. Pejcic and De Marco have presented an interesting survey... 

Applications Potentiometry finds widespread use for direct and selective measurement of analyte concentrations, mainly in routine analyses, and for endpoint determinations of titrations. Direct potentiometric measurements provide a rapid and convenient method for determining the activity of a variety of cations and anions. The most frequently determined ion in water is the hydrogen ion (pH measurement). Ion chromatography combined with potentiometric detection techniques using ISEs allows the selective quantification of selected analytes, even in complex matrices. The sensitivity of the electrodes allows sub-ppm concentrations to be measured. 

In potentiometric titration a voltage is obtained from an electrode that is sensitive to an ionic species such as H-jO+, i.e., the pH of the solution in this case. We will consider the titration of the mixture of a strong acid (HC1) and a weak acid (CJ+jCOOH) with NaOH (ref. 10). As 2 ml volumes of the base are given to the acidic solution, the pH increases and when one of the acids is neutralized the pH changes very rapidly by a small addition of NaOH. We want to find these maximum points of the first derivative of the titration curve. In the following main program the DATA lines contain 32 data pairs, each consisting of the volume of the added NaOH in ml and the measured pH. 

By finding E° for the net reaction, we can compute K, for iron(II) carbonate. Potentiometric measurements allow us to find equilibrium constants that are too small or too large to measure by determining concentrations of reactants and products directly. 

Lil+>,Co02 is an anode for high-energy-density lithium batteries. Cobalt is present as a mixture of Co(III) and Co(II). Most preparations also contain inert lithium salts and moisture. To find the stoichiometry, Co was measured by atomic absorption and its average oxidation state was measured by a potentiometric titra-... 

At low hydroxyl numbers Olin (32) subsequently agrees with the earlier findings of Faucherre (12) that [Pb2(OH)]3+ species are necessary to explain the potentiometric titration data. 

As to Eq. (7), it is to be remembered that AG, in a general case is a function of p. Therefore, the experimental dependencies of p on concentration, chain length of oligomer and temperature may be employed to find thermodynamic parameters only for a fixed value of p, e.g., for p = 0.5 using Eqs. (8 a- b). These equations have been taken by various authors to calculate the enthalpy and entropy of complex formation between simple synthetic oligomers and polymers 28). In a number of cases the correspondence between the values of complex formation enthalpy thus obtained and determined, either by calorimetry or by potentiometric titration 26), has been found satisfactory although it is obvious that in a general case these values do not necessarily coincide. 

With these assumptions in mind, we now complete the outline of the solution of the diffusion-reaction problem as it applies to the most difficult case, the pH-based enzymatic sensors (potentiometric or optical). We assume only that there is no depletion layer at the gel/solution boundary (7), and that there is no fixed buffer capacity (4). The objective of this exercise is to find out the optimum thickness of the gel layer that is critically important for all zero-flux-boundary sensors, as follows from (2.26). 

For most potentiometric measurements, either the saturated calomel reference electrode or the silver/silver chloride reference electrode are used. These electrodes can be made compact, are easily produced, and provide reference potentials that do not vary more than a few mV. The silver/silver chloride electrode also finds application in non-aqueous solutions, although some solvents cause the silver chloride film to become soluble. Some experiments have utilised reference electrodes in non-aqueous solvents that are based on zinc or silver couples. From our own experience, aqueous reference electrodes are as convenient for non-aqueous systems as are any of the prototypes that have been developed to date. When there is a need to exclude water rigorously, double-salt bridges (aqueous/non-aqueous) are a convenient solution. This is true even though they involve a liquid junction between the aqueous electrolyte system and the non-aqueous solvent system of the sample solution. The use of conventional reference electrodes does cause some difficulties if the electrolyte of the reference electrode is insoluble in the sample solution. Hence, the use of a calomel electrode saturated with potassium chloride in conjunction with a sample solution that contains perchlorate ion can cause dramatic measurements due to the precipitation of potassium perchlorate at the junction. Such difficulties normally can be eliminated by using a double junction that inserts another inert electrolyte solution between the reference electrode and the sample solution (e.g., a sodium chloride solution). 

This principle is applied for the potential development in the EPMEs and for obtaining the intensity of the current in amperometric immuno-sensors. For the enantioselective, potentiometric electrodes, it is necessary to find a molecule with a special architecture that can accommodate the enantiomer. In this regard, cyclodextrins and their derivatives, maltodextrins, antibiotics and fullerenes and their derivatives were proposed [17-52]. 

For multistep complexation reactions and for ligands that are themselves weak acids, extremely involved calculations are necessary for the evaluation of the equilibrium expression from the individual species involved in the competing equilibria. These normally have to be solved by a graphical method or by computer techniques.26,27 Discussion of these calculations at this point is beyond the scope of this book. However, those who are interested will find adequate discussions in the many books on coordination chemistry, chelate chemistry, and the study and evaluation of the stability constants of complex ions.20,21,28-30 The general approach is the same as outlined here namely, that a titration curve is performed in which the concentration or activity of the substituent species is monitored by potentiometric measurement. 

A related form of an automatic potentiometric titrator is instrumentation that permits the maintenance of the acidity or basicity of a solution over a period of time. Such devices are known as pH-stats, and find application in kinetic studies of hydrolysis reactions. The general approach is (by either manual or automatic means) to add either acid or base such that the pH in the solution is maintained constant over a period of time. Normally the amount of acid or base added as a function of time is sought in order that kinetic measurements may be made for the system. In its simplest form the acidity of the solution is monitored with a pH meter and controlled at a preselected value by the addition of acid or base from a burette the quantity delivered as a function of time is recorded in a notebook. Obviously for the fast reactions this becomes difficult and dependent on the dexterity of the individual. 

Among the methods listed here, the amperometric determination has evoked the most interest.151160 172-181 Potentiometric measurements149182 183 also confirm the findings of these methods, although the equilibrium concentrations of free iodine are lower by one order of magnitude than those determined by photometric titration. For the reaction... 

The kinetics of the xanthation of sucrose were studied in the same year by Cherkasskaya, Pakshver, and Kargin, who determined potentiometric-ally the concentrations of the dithiocarbonate derivative and also of inorganic sulfide and trithiocarbonate. The rate of formation of 0-(sodium thiol-thiocarbonyl)sucrose was found to pass through a maximum with increasing alkali concentration, presumably due to a shift of the equilibrium in favor of side reactions in strongly alkaline solution. This result appears to parallel the qualitative findings of Lieser and Hackl for polysaccharides. 

A plot of pH against the volume of alkali added (mL) is known as a neutralization or titration curve (Fig. 22.2). The curve is generated by a potentiometric titration in which pH is measured after each addition of alkali (or acid). The significant feature of the curve is the very sharp and sudden change in pH near to the equivalence point of the titration. For a strong acid and alkali this will occur at pH 7. If either the acid or base concentration is unknown, a prehminary titration is necessary to find the approTumate equivalence point followed by a more accurate titration as described on p. 146. The ideal pH range for an indicator is 4.S-9.5. 

Two major types of end points find widespread use in neutralization titrations. The first is a visual end point based on indicators such as those described in Section 14A. The second is a potentiometric end point, in which the potential of a glass/calomel electrode system is determined with a voltage-measuring device. The measured potential is directly proportional to pH. Potentiometric end points are described in Section 21G. 

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