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Antelman, M. S., and F. J. Harris, Jr., The Encyclopedia of Chemical Electrode
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Potentials, Plenum Press, New York, 1982. Bard, A. J. (Ed.), Electrochemistry of Elements, Plenum Press, New York, individual volumes appear since 1974. Bard, A. J., J. Jordan, and R. Parsons (Eds), Oxidation-Reduction Potentials in Aqueous Solutions, Blackwell, Oxford, 1986. Butler, J. N., Reference electrodes in aprotic solvents, AE, 7, 77 (1970).
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Clark, W. M., Oxidation Reduction Potentials of Organic Systems, Williams and
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Wilkins, Baltimore, 1960.
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Ives, D. J., and G. J. Janz (Eds), Reference Electrodes, Theory and Practice,
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Academic Press, New York, 1961. Karpfen, F. M., and J. E. B. Randies, Ionic equilibria and phase-boundary potentials in oil-water systems, Trans. Faraday Soc, 49, 823 (1953). Koryta, J., Electrochemical polarisation of the interface of two immiscible electrolyte solutions I, Electrochim. Acta, 24, 293 (1979); II, Electrochim. Acta, 29, 445 (1984); III, Electrochim. Acta, 33, 189 (1988). Laity, R. W., /. Chem. Educ, 39, 67 (1962). Latimer, W. M., Oxidation Potentials, Prentice-Hall, New York, 1952. Michaelis, L., Oxidation Reduction Potentials, Lippincott, Philadelphia, 1930. Michaelis, L., Occurrence and significance of semiquinone radicals, Ann. New York Acad. ScL, 40,39(1940). Parker, A. J., Solvation of ions enthalpies, entropies and free energies of transfer, Electrochim. Acta, 21, 671 (1976). Vanysek, P., Electrochemistry at Liquid-Liquid Interfaces, Springer-Verlag, Berlin, 1985. Wawzonek, S., Potentiometry: oxidation reduction potentials, Techniques of Chemistry, (Eds. A. Weissberger and B. W. Rossiter), Vol. I, Part Ha, Wiley-Interscience, New York, 1971.
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191 3.3 Potentiometry
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Potentiometry is used in the determination of various physicochemical quantities and for quantitative analysis based on measurements of the EMF of galvanic cells. By means of the potentiometric method it is possible to determine activity coefficients, pH values, dissociation constants and solubility products, the standard affinities of chemical reactions, in simple cases transport numbers, etc. In analytical chemistry, potentiometry is used for titrations or for direct determination of ion activities. 3.3.1 The principle of measurement of the EMF The EMF of a galvanic cell is a thermodynamic equilibrium quatity. Thus, the potential of a cell must be measured under equilibrium conditions, i.e. without current flow. The measured EMF must be compensated by a known external potential difference. The measurement of the EMF of a cell is thus based on determination of a potential difference that exactly compensates the measured potential difference so that no current passes. This is easily achieved by the Poggendorf compensation method (see Fig. 3.13). At present, potentiometry is performed primarily using electronic instruments with solid-state elements. The EMF can be measured by compensation measurement using a transistor voltmeter, i.e. according to the scheme in Fig. 3.13, where the galvanometer is replaced by an amplifier and meter. A second possibility is to measure the tiny current passed on connecting the cell with a large external resistance. Typical instruments of this kind consist of three parts. The first part is the input circuit, acting as an impedance transducer. Mostly MOSFET elements or capacity diodes are used here. The second part contains a power amplifier, permitting the use of a meter with large energy consumption. Depending on whether the EMF measured by using an a.c. amplifier is modulated in the input circuit (by a d.c. amplifier), an electronic demodulation circuit must be connected in the second part to rectify the amplified alternating voltage. The third part is the indicator with a digital display. If a cell is to be used as a potential standard, then it must be prepared as simply as possible from chemicals readily available in the required purity and, in the absence of current passage, it must have a known, defined, constant EMF that is practically independent of temperature. In this case the efficiency, power, etc., required for cells used as electrochemical power sources is of no importance. The electrodes of the standard cell must not be polarizable by the currents passing through them when the measuring circuit is not exactly compensated. The mostly used Weston cell consists of mercurous sulphate and cadmium amalgam electrodes: Hg | Hg2SO4(s) | 3CdSO4.8H2O(sat.) | Cd,Hg(12.5 weight % Cd) (3.3.1)
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Fig. 3.13 Poggendorfs compensation circuit. A uniform resistance wire is connected at its ends (points a and b) to a stable voltage source (e.g. a storage battery). A part of this voltage between one end of the potentiometric wire and the sliding contact c is fed into the other circuit containing the measured source of voltage Ex, the null instrument G and the key. If no current flows through G the electrical potential difference compensates the EMF, Ex. The voltage fed to the potentiometric wire is calibrated by means of a standard cell, usually Weston cell, Es by means of the same compensation procedure
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3.3.2 Measurement of pH The potentiometric measurement of physicochemical quantities such as dissociation constants, activity coefficients and thus also pH is accompanied by a basic problem, leading to complications that can be solved only if certain assumptions are accepted. Potentiometric measurements in cells without liquid junctions lead to mean activity or mean activity coefficient values (of an electrolyte), rather than the individual ionic values. The EMF of the cell Ag | AgCl(s) | buffer,KCl(m) | H2,Pt (3.3.2) suitable for pH measurements is given by an expression containing the mean activity log aH3O+ = 0A343F/RT(E + - log (mcrycl-) (3.3.3) The pH value obtained in this way is accompanied by an error resulting from the approximation used for the calculation of y c r . Although this error may be small in dilute solutions, the pH values obtained in this manner are not exactly equal to the values corresponding to the absolute definition of
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193 the pH in Eq. (1.4.39). The pH values given by this absolute definition cannot, in principle, be exactly measured. For current practice, the described method of pH measurement is too tedious. Moreover, not hydrogen but glass electrodes are used for routine pH measurements (see Section 6.3). Then the expression for the EMF of the cell consisting of the glass and reference electrodes contains a constant term from Eq. (6.3.10), in addition to the terms present in Eq. (3.3.3); this term must be obtained by calibration. Further, a term describing the liquid junction potential between the reference electrode and the measured solution must also be included. In view of these difficulties an operational definition of pH has been introduced (cf. Section 1.4.6). This definition is based on the concept that the pH is measured with a hydrogen electrode, combined to the measuring galvanic cell with a suitable reference electrode. The reference electrode solution is connected with the solution of the hydrogen electrode through a salt bridge with KC1 of at least 3.5 mol kg"1 concentration. The hydrogen electrode is immersed first into the test solution X with pH(X) and the EMF E(X) is measured, and then into a standard solution S of pH(S), corresponding to potential E(S). It is assumed that the dependence of E on the pH is linear with the Nernst slope, 2.303RT/F. Under these conditions,
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(3.3.4)
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Now the origin of the scale must be defined, i.e. a pH value must be selected for a standard (as close as possible to the value expected on the basis of definition 1.4.46). A solution of potassium hydrogen phthalate with a molality of 0.05 mol-kg" 1 has been selected as the reference value pH standard (RVS). The pH of the saturated solution of potassium hydrogen phthalate containing chloride molarity m cl - is given by the equation p H = -0.4343F( + Ag/AgC1) + log [m c l -y c r ] (3.3.5) where E is the EMF of the cell (3.3.2). The first two terms on the right-hand side can be measured. If the pH of the cell (3.3.2) is determined for various values of m c r and if the sum of these two terms if plotted vs m cl -, a nearly linear dependence is obtained which may easily be extrapolated to zero concentration of chloride ions. For the pH(RVS), the pH of the standard phthalate solution alone, we have then pH(RVS) = - lim [0.4343F(E + E Ag/AgC1 )/ J Rr-logm C i-]+ lim log yc, .
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