Extract from: Hibbert D.B., Introduction to Electrochemistry, Macmillan, London, 350pp. 1993. Available via the institutional repository of the University of New South Wales, UNSWorks: HUwww.unsworks.unsw.edu.auU U © D. Brynn Hibbert 1993 Reproduced and communicated by permission of the publisher: Palgrave Macmillan. RIGHTS OF USE Material deposited in UNSWorks is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs Licence, which permits that material accessed from UNSWorks can be used as follows: You are free to share - to copy, distribute and transmit the work - under the following conditions: • Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). • Noncommercial. You may not use this work for commercial purposes. • No Derivative Works. You may not alter, transform, or build upon this work. 9 Electroanalytical chemistry: potentiometric methods 9.1 Introduction Electroanalytical chemistry started life with one of the great analytical tools, the pH elect~ode. It has gone on to promise many wonderful things and in some ways the world still waits for the ultimate sensor. The appeal­ ing thing about electrochemical sensors, particularly potentiometric sen­ sors, is that they_have no moving parts, their output is readily assimilated by a computer and they can be made small and cheap. Although electro­ chemical detectors for chromatography are now available, electrochemis­ try is in fact in direct conflict with chromatography. In chromatography by clever separations the detection step is almost trivial, as each analyte comes through as a separate entity. ~J~ctroc_h~mistrYhQP~s-!oc!irectly J!leasure the concentration ofan analyte witl191,1tpJ:'igr Jleparati9J). This puts much greater constraints on the method: it must discriminate between analyte and the myriad of interfering compounds, it must operate over a range of concentrations and it must be quick. Research still continues attempting to find better electrodes and to develop numerical methods to allow for interferences. This chapter and the next are organised about the different electrochemi­ cal methods. In this chapter I describe techniques that are performed at equilibrium, the measurement of potentials and the conductance of solu­ tions. Then comes voltammetry, in which the potential is controlled and the current measured. Of these, polarography has a special mention, being the first and probably still most used of all voltammetric methods. Then follow amperometric and coulometric methods. 190 191 9.2 Potentiometric methods of analysis 9.2. 7 Ib~N~IQ~tJ?9L.l9tloI}IDanaly!!~(JL 9hemlstry All potentiometric measurements rely on some difference in electrochemi­ cal potential between a...referenc~tsJ'.~~m _amLthe_ test system. This may be exploited by establishing a redox potential or a membrane potential. In any case the measured voltage of the cell will be related to the activity of the species in question by the kl~rnst equation or something very like it. In general, therefore, all potentiometric cells follow _'_~meas = Econst ± R ~L~ Fin (a)!1 (9.1) where a is the activity_oLth_~ ~nalyte. In situations in which the ionic strength is low, the activitl__I1l~~~~ace~_by th~~c:>ncel}trat!on __~!th~uti loss of accuracy. However, this does mean that more concentrated solu­ tionsneed to. be buffered-tothesime ionic strength as the reference !~~tiort:~-usually by the addition ()fanon-interfering_elec!rolyte. There are two basic types of potentiometric sensor. The most widely used is the !9!l~.se1ecti.veelectrQ_<!~ (ISE), in which a membrane separates the _~J;talyte soh.~li~n from an internal reference solution. An ion-exchange ~guili~!iul!! j!~~!~!Jli!Qed _a~ _thC:Lm~mQI~D~ _~J;td_!-J!()te!lt!al_deYel()ps. Examples of ISEs are the pH glass electrode and the ftuorideelectro(je. The second class of potentiometric sensors are based oiiiradiiTonal redox reactions. These are useful for specific applications but are prone to in­ terferences, as any redox couple in the solution will compete for electrons v M e m X- b X- r •n ••·.ref e I •. Figure 9.1 Ion-selective membrane electrode 192 Introduction to electrochemistry v Reference electrode Indicator electrode Figure 9.2 Oxidation-reduction (redox) electrode from the electrode. We start with the measurement of pH, for which electrochemical methods encompass both ISEs and redox electrodes. Sensitivity of potentiometric methods The strength of an analytical method that follows good old Nernst is that a very wide range of concentrations are encompassed by a measurable range of voltages. For a one-electron process at 25 QC the change is 0.06 V for every tenfold change in activity. To put it another way, 1 V spans more than a 1016 change in activity. The drawback is that small errors in the measurement of the voltage lead to large errors in the calculated analyte concentration. If you work it out, 1 mV leads to about a 4% change in concentration. See Problem 9.1. Interferences In an ideal world there would be an electrode for each analyte that would respond only to that substance and nothing else. Alas, you do not need me to tell you that this is not the case despite the very best efforts of genera­ tions of electrochemists. If a voltage is generated at an electrode by more than one analyte, each of which follows the Nernst equation, the total potential measured is Electroanalytlcal chemIstry 193 -0.1 -0.15 -0.2 -0.25 > iU -0.3 -0.35 -0.4 -0.45 -8 -7 Figure 9.3 Plot of Ecell against log/o (aJ for a solution containing one interfering ion (X+) of activity ax. The numbers on the curves give the value of k1j ax /z E cell = Econs' + RT / n Fin (aj + I kjj ar ) (9.2) aj is the activity of the analyte of interest and aj the activity of interfering species j that has charge z. The sum is over all interfering ions. k jj is known as the selectivity coefficient and may be determined experimentally. Values of kij are specific to each electrode and analyte solution, and Equation (9.2) hQlds only over quite small ranges of concentration. Values of k less than 1. mean that the interfering species has a smaller effect on the .voltage than the_analyte, and greater than 1 show the species has a larger effect. See Problem 9.5. Figure 9.3 shows the effect on the plot of E cell against aj of interfering ions at different concentrations and with different kjjs (Le. different values of the product kij Qj)' See Problems 9.2 and 9.5. From the above it is clear that a reasonable amount of an interfering ion can render an ISE almost useless. Often halides and cyanide mutually interfere; silver, copper and mercury interfere with the determination of other metals, and, in general, similar ions (charge, size) interfere. Interferences can arise because of complex formation that removes the free ion (e.g. EDTA complexing most metals), Of by reactjon~t th~electrode (for example, cyanide leaches chloride from silver chloride). 194 Introduction to electrochemlstry 9.2.2 Potentiometric measurement of pH DefinitiQn QtpH The quantity pH is defined as the negative logarithm to the base 10 of the hydrogen ion activity (pAnything is the negative logarithm to the base 10 of Anything): pH = -loglO(aH +) (9.3) ~ 14 The equilibrium constant of H20 H+ + OH- is 10- at 25 QC (the pK of water is 14), so the pH of water should be 7. Interestingly enough, nice and simple as the definition is, because of the impossibility of measuring single ion activities it is useless as it stands. 'But', you will say, 'what about the pH meter?' This is an electrochemical device that gives a direct reading of pH, but it is only relative to a defined solution of known pH (the buffer you use to calibrate the instrument). The problem arises in making a cell for which the measured voltage reflects only the change in hydrogen ion activity. Cells may have liquid junction potentials, although these can be minimised, and the activities of the different species will vary with ionic strength. Luckily, analytical chemists are very practical people, and the International Union of Pure and Applied Chemistry (IUPAC) has agreed an operational definition of pH derived from the electrochemical method of measurement: pH = pHbuf + (E - Ebuf) F / R TIn (10) (9.4) E is the potential of an electrode that responds to H+, and the subscript buf refers to a standard reference buffer solution of known or defined pH. The National Bureau of Standards in the USA defines the pHs of buffers from measurements of the potential of a cell containing a hydrogen electrode and silver-silver chloride reference electrode: Pt, H 2 I buffer, Cl- I AgCI, Ag. This has the advantage of not having a liquid junction potential. Assumptions are made about activity coefficients and the defined pH is hopefully near enough the true -loglO (aH +). There are seven NBS primary standard buffer solutions. These are given in Table 9.1. A review of different electrodes that have been used for the measurement of pH is given in Table 9.2. Measurement by redox electrodes Although seldom used, the quinhydrone electrode is a good example of a redox electrode that can be used for the measurement of pH. Quinhydrone is the name of an equimolar mixture of quinone and hydroquinone. In solution at a platinum electrode the redox equilibrium in Figure 9.4 is established. Both quinone and hydroquinone are sparingly soluble in Electroanalytical chemistry 195 Table 9.1 NBS primary buffer standard solutions Buffer Composition (m = molality) pH (25 QC) Potassium hydogen tartrate (KHTar) Saturated KHTar 3.557 Potassium dihydrogen citrate (KH2Cit) 0.05 m KH2Cit 3.776 Potassium hydrogen phthalate (KHPhth) 0.05 m KHPhth 4.004 Phosphate 0.025 m KHzP04 6.863 (equimolal) 0.025 m NaH2P04 Phosphate 0.008 695 m KHzP04 7.415 (35: 1) 0.03043 m NaH2P04 Borax 0.01 m NazB40 7 .1O H 20 9.183 Carbonate 0.025 m NaHC03 10.014 0.025 m NaZC03 Table 9.2 Characteristics of electrodes used for the measurement of pH Electrode pH range (error) Interferences Remarks Hydrogen 0-14 Redox, air, heavy Nernstian.