Potentiometric Method

Introduction

we mentioned measurement of the potential of a solution and described a platinum electrode whose potential was determined by the half-reaction of interest. This was a special case, and there are a number of electrodes available for measuring solution potentials. In this chapter, we list the various types of electrodes that can be used for measuring solution potentials and how to select the proper one for measuring a given analyte. The apparatus for making potentiometric measurements is described along with limitations and accuracies of potentiometric measurements. The important glass pH electrode is described, as well as standard buffers required for its calibration. The various kinds of ion-selective electrodes are discussed. The use of electrodes in potentiometric titrations is described in Chapter 14. Potentiometric electrodes measure activity rather than concentration, a unique Review activities in Chapter 6, for an understanding of potentiometric measurements. feature, and we will use activities in this chapter in describing electrode potentials. An understanding of activity and the factors that affect it are important for direct potentiometric measurements, as in pH or ion-selective electrode measurements. You should, therefore, review the material on activity and activity coefficients in Chapter 6. Potentiometry is one of the oldest analytical methods, with foundations of electrode potentials and electrochemical equilibria laid down by J. Willard Gibbs (1839–1903) and Walther Nernst (1864–1941).

 Metal Electrodes for Measuring the Metal Cation 

An electrode of this type is a metal in contact with a solution containing the cation of the same metal. An example is a silver metal electrode dipping in a solution of silver nitrate. For all electrode systems, an electrode half-reaction can be written from which the potential of the electrode is described. The electrode system can be represented by M/Mn+, in which the line represents an electrode–solution interface. For the silver electrode, we have                                    Ag|Ag+ (13.1) 
and the half-reaction is 
                                          Ag+ + e− Ag (13.2)
 The potential of the electrode is described by the Nernst equation: 
E = E0 Ag+,Ag − 2.303RT nF log 1 aAg+ (13.3)
 where aAg+ represents the activity of the silver ion (see Chapter 6). The value of n here is 1. Because, in the interpretation of direct potentiometric measurements, significant errors would result if concentrations were used in calculations. Increasing cation activity always 
The potential calculated from Equation 13.3 is the potentialrelative to the normal causes the electrode potential to become more positive (if you write the Nernst equation properly). hydrogen electrode (NHE—see Section 13.3). The potential becomes increasingly positive with increasing Ag+ (the case for any electrode measuring a cation). That is, in a cell measurement using the NHE as the second half-cell, the voltage is Emeasd. = Ecell = Eind vs. NHE = Eind − ENHE (13.4) where Eind The indicator electrode is the one is the potential of the indicator electrode (the one that responds to the test that responds to the analyte. solution, Ag+ ions in this case). Since ENHE is zero, Ecell = Eind (13.5) corresponds to writing the cells as Eref |solution|Eind (13.6) and Ecell = Eright − Eleft = Eind − Eref = Eind − constant (13.7) where Eref The reference electrode completes is the potential of the reference electrode, whose potential is constant. Note the cell but does not respond to the analyte. It is usually separated from the test solution by a salt bridge. that Ecell (or Eind) may be positive or negative, depending on the activity of the silver ion or the relative potentials of the two electrodes. This is in contrast to the convention used in Chapter 12 for a voltaic cell, in which a cell was always set up to give a positive voltage and thereby indicate what the spontaneous cell reaction would be. In potentiometric measurements, we, in principle, measure the potential at zero current so as not to disturb the equilibrium, i.e., don’t change the relative concentrations of the species being measured at the indicating electrode surface—which establishes the potential (see measurement of potential, below). We are interested in how the potential of the test electrode (indicating electrode) changes with analyte concentration, as measured against some constant reference electrode. Equation 13.7 is arranged so that changes in Ecell reflect the same changes in Eind, including sign. This point is discussed further when we talk about cells and measurement of electrode potentials. Any pure substance does not The activity of silver metal above, as with other pure substances, is taken as numerically appear in the Nernst equation (e.g., Cu, H2O); their activities are taken as unity. unity. So an electrode of this kind can be used to monitor the activity of a metal ion in solution. There are few reliable electrodes of this type because many metals tend to form an oxide coating that changes the potential.

 METAL–METAL SALT ELECTRODES FOR MEASURING THE SALT ANION 

 The general form of this type of electrode is M|MX|Xn−, where MX is a slightly soluble salt. An example is the silver–silver chloride electrode: 
                                       Ag|AgCl(s)|Cl− (13.8)
 The (s) indicates a solid, (g) is used to indicate a gas, and (l) is used to indicate a pure liquid. A vertical line denotes a phase boundary between two different solids or a solid and a solution. 

The half-reaction is AgCl + e− Ag + Cl− (13.9) where the underline indicates a solid phase and the potential is defined by E = E0 AgCl,Ag − 2.303RT F log aCl− (13.10) The number of electrons, n, does not appear in the equation because here n = 1. This electrode, then, can be used to measure the activity of chloride ion in Increasing anion activity always causes the electrode potential to decrease. solution. Note that, as the activity of chloride increases, the potential decreases. This is true of any electrode measuring an anion—the opposite for a cation electrode. A silver wire is coated with silver chloride precipitate (e.g., by electrically oxidizing it in a solution containing chloride ion, the reverse reaction of Equation 13.9). Actually, as soon as a silver wire is dipped in a chloride solution, a thin layer of silver chloride and is usually not required. Note that this electrode can be used to monitor either aCl− or aAg+ . It really The Ag metal really responds to Ag+, whose activity is determined by K◦ sp and aCl− . senses only silver ion, and the activity of this is determined by the solubility of the slightly soluble AgCl. Since aCl− = Ksp/aAg+ , Equation 13.10 can be rewritten:
 E = E0 AgCl,Ag − 2.303RT F log Ksp aAg+ (13.11) E = E0 AgCl,Ag − 2.303RT F log Ksp − 2.303RT F log 1 aAg+ (13.12) Comparing this with Equation 13.3, we see that
 E0 Ag+,Ag = E0 AgCl,Ag − 2.303RT F log Ksp (13.13) 
Ksp here is the thermodynamic solubility product K◦ sp  since activities, rather than concentrations, were used in arriving at it in these equations. We could have arrived at an alternative form of 

Equation 13.10 by substituting Ksp/aCl− for aAg+ in Equation 13.3 
 In a solution containing a mixture of Ag+ and Cl− (e.g., a titration of Cl− with Ag+), the concentrations of each at equilibrium will be such that the potential of a silver wire dipping in the solution can be calculated by either Equation 13.3 or Equation 13.10.
 This is completely analogous to the statement in that the potential of one half-reaction must be equal to the potential of the other in a chemical reaction at equilibrium.
 Equations 13.2 and 13.9 are the two half-reactions in this case, and when one is subtracted from the other, the result is the overall chemical reaction.
                            Ag+ + Cl− AgCl (13.14)
 Note that as Cl− is titrated with Ag+, the former decreases and the latter increases. 
Equation 13.10 predicts an increase in potential as Cl− decreases; and similarly, Equation 13.12 predicts the same increase as Ag+ increases. The silver electrode can also be used to monitor other anions that form slightly soluble salts with silver, such as I−, Br−, and S2−. The E0 in each case would be that for the particular half-reaction
                             AgX + e− Ag + X−. 
Another widely used electrode of this type is the calomel electrode, Hg, Hg2Cl2(s)|Cl−. This will be described in more detail when we talk about reference electrodes.

 

 pH MeasurementofBlood—Temperature Is Important The pH measurement of blood 

 Because the equilibrium constants of the blood buffer samples must be made at body temperature to be meaningful. systems change with temperature, the pH of blood at the body temperature of 37◦ C is different than at room temperature. Hence, to obtain meaningful blood pH Christian7e c13.tex V2 - 08/13/2013 1:49 P.M. Page 423 13.16 PH MEASUREMENTS IN NONAQUEOUS SOLVENTS 423 measurements that can be related to actual physiological conditions, the measurements should be made at 37◦ C and the samples should not be exposed to the atmosphere. (Also recall that the pH of a neutral aqueous solution at 37◦ C is 6.80, and so the acidity scale is changed by 0.20 pH unit.) 

Some useful rules in making blood pH measurements are as follows: 

1. Calibrate the electrodes using a standard buffer at 37◦ C, making sure to select the proper pH of the buffer at 37◦ C and to set the temperature on the pH meter at 37◦ C (slope = 61.5 mV/pH). It is a good idea to use two standards for calibration, narrowly bracketing the sample pH; this assures that the electrode is functioning properly. Also, the electrodes must be equilibrated at 37◦ C before calibration and measurement. The potential of the internal reference electrode inside the glass electrode is temperature dependent, as may be the potential-determining mechanism at the glass membrane interface; and the potentials of the SCE reference electrode and the liquid junction are temperature dependent. (We should note here that if pH or other potential measurements are made at less than room temperature, the salt bridge or the reference electrode should not contain saturated KCl, but somewhat less concentrated KCl, because solid KCl crystals will precipitate in the bridge and increase its resistance.)
 2. Blood samples must be kept anaerobically to prevent loss or absorption of CO2. Make pH measurements within 15 min after sample collection, if possible, or else keep the sample on ice and make the measurements within 2 h. The sample is equilibrated to 37◦ C before measuring. (If a pCO2 measurement is to be performed also, do this within 30 min.) 
3. To prevent coating of the electrode, flush the sample from the electrode with saline solution after each measurement. A residual blood film can be removed by dipping for only a few minutes in 0.1 M NaOH, followed by 0.1 M HCl and water or saline.

 Ion-Selective Electrodes

 Various types of membrane electrodes have been developed in which the membrane an excellent tutorial (130-page beginners guide) on principles of pH and ion-selective electrodes, calibration, and measuring procedures. potential is selective toward a given ion or ions, just as the potential of the glass membrane of a conventional glass electrode is selective toward hydrogen ions. These electrodes are important in the measurement of ions, especially in small concentrations. Generally, they are not “poisoned” by the presence of proteins, as some other electrodes are, and so they are ideally suited to measurements in biological media. This is especially true for the glass membrane ion-selective electrodes. It is important to know what other None of these electrodes is specific for a given ion, but each will possess a certain analytes an ISE responds to and the relative response compared to the analyte of interest. See Professor’s Favorite Example at the end of this chapter - it is fortunate that that particular ISE produced a physically impossible result - had it produced a reasonable result, the presence of perchlorate in Martian soil would not have been so apparent. selectivity toward a given ion or ions. So they are properly referred to as ion-selective electrodes (ISEs).

 GLASS MEMBRANE ELECTRODES 

These are similar in construction to the pH glass electrode. Varying the composition of the glass membrane can cause the hydrated glass to acquire an increased affinity for various monovalent cations, with a much lower affinity for protons than the pH glass electrode has. The membrane potential becomes dependent on these cations, probably through an ion exchange mechanism similar to that presented for the glass pH electrode; that is, a boundary potential is produced, determined by the relative activities of the cations on the surface of the gel and in the external solution. Increased cation activity results in increased positive charge on the membrane and a positive increase in electrode potential. The construction is similar to Figure 13.6. The internal filling solution will The glass membrane pH electrode is the ultimate ion-selective electrode. usually be the chloride salt of the cation to which the electrode is most responsive. The sodium-sensitive type of electrode can be used to determine the activity of H+ is a common interferent with ISEs, and so the pH must be above a limiting value, depending on the concentration of the primary ion (the one being measured). sodium ion in the presence of appreciable amounts of potassium ion. Its selectivity for sodium over potassium is on the order of 3000 or more.

SOLID-STATE ELECTRODES 

The construction of these electrodes is shown in Figure 13.12. The most successful The fluoride ion-selective electrode is one of the most successful and useful since the determination of fluoride is rather difficult by most other methods. example is the fluoride electrode. The membrane consists of a single crystal of lanthanum fluoride doped with some europium(II) fluoride to increase the conductivity of the crystal. Lanthanum fluoride is very insoluble, and this electrode exhibits Nerstian response to fluoride down to 10−5 M and non-Nerstian response down to 10−6 M (19 ppb!). This electrode has at least a 1000-fold selectivity for fluoride ion over chloride, bromide, iodide, nitrate, sulfate, monohydrogen phosphate, and bicarbonate anions and a 10-fold selectivity over hydroxide ion. Hydroxide ion appears to be the only serious interference. The pH range is limited by the formation of hydrofluoric acid at the acid end and by hydroxide ion response at the alkaline end; the useful pH range is 4 to 9.