The measurement of cell potentials

In the foregoing treatment of electrodes and cells we assumed implicitly that the electrode or cell was in equilibrium with respect to certain chemical and electrical transformations. By definition such an electrode or cell is reversible. To correlate measured values of cell potentials with the ones calculated by the Nernst equation, the measured values must be equilibrium or reversible values the potentiometric measurement in which no current is drawn from the cell is ideally suited for the measurement of reversible potentials. 

Consider the cell, Pt H2 H jjCu Cu, which we discussed in Sect. 17.9. The cell reaction is 

The copper is the positive electrode and the platinum is negative. Suppose that the cell is in balance with a potentiometer, as shown in Fig. 17.5. Now ifwe move the sliding contact, S, to the right of the balance point, that will make the copper more positive Cu will then leave the electrode as Cu and the electrons will move from right to left in the external circuit. On the platinum the electrons will combine with H to form H2. The entire reaction goes in the reverse direction from right to left. Conversely, if the slider is moved to the left, the electrons will move from left to right in the external circuit Hj will ionize to H and Cu will be reduced to copper. In this situation the cell produces work, while in the earlier circumstances work was destroyed. 

Since the values of equilibrium constants are obtained from the standard half-cell potentials, the method of obtaining the S° of a half-cell has great importance. Suppose we wish to determine the of the silver-silver ion electrode. Then we set up a cell that includes this electrode and another electrode the potential of which is known for simplicity we choose the SHE as the other electrode. Then the cell is 

Ifthesolutionwereanidealdilutesolution,wecouldreplaceaAg+ bym+ = m,themolality of the silver salt. Equation (17.53) would become 

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Predicting the cell potential requires knowledge of thermodynamic properties and transport processes ia the cell. Conversely, the measurement of cell potentials can be used to determine both thermodynamic and transport properties (4). 

Figure 5.2 Circuits for the measurement of cell potentials (a) two-electrode system with current passing through both working and reference electrodes (b) threePSlectrode system with current passing through the working and counter electrodes but not the reference electrode.

A practical application of this circuit is the measurement of cell potentials. We simply connect the cell to the op amp input as shown in Figure 2 IF-7b, and we connect the output of the op amp to a digital voltmeter to measure the voltage. Modern op amps are nearly ideal voltage-measurement devices and are incorporated into most ion meters and pH meters to monitor high-resistance indicator electrodes with minimal error. 

Numerical values for solubility-product constants, dissociation constants, and formation constants are conveniently evaluated through the measurement of cell potentials. One important virtue of this technique is that the measurement can be made without appreciably affecting any equilibria that may be present in the solution. For example, the potential of a silver electrode in a solution containing silver ion, cyanide ion, and the complex formed between them depends on the activities of the thiee species. It is possible to measure this potential with negligible current. 

There are many other types of solution data that support the half-wave reduction potential and charge transfer complex data. These include the measurement of cell potentials or equilibrium constants for electron transfer reactions. Another important condensed phase measurement involving a negative ion is the determination of electron spin resonance spectra. In these studies the existence of a stable molecular anion is established and the spin densities can be measured [79]. The condensed phase measurements support the electron affinities in the gas phase and extend the measurements to lower valence-state electron affinities. 

One method of estimating aApcj) is based on the measurement of cell potential differences [19]. Consider the cell... 

The measurement of cell potentials is the most powerful method of obtaining values of activities of electrolytes. Experimentally it is, in many cases at least, much easier to handle than measurements of colligative properties. It has the additional advantage that it can be used over a wide range of temperatures. Although cell potentials can be measured in nonaqueous solvents, the electrode equilibria often are not as easily established so that the experimental difficulties are much greater. 

Fig. 2.2 Schematic of electrochemical cell showing the measurement of cell potential.

It can therefore be seen that the measurement of cell potentials provides information about free energy changes. Furthermore, since... 

When dealing with potentials of electrodes and cells we can define a cell potential as the amount of work needed to transfer a unit charge from one electrode to the other. Let us now deal with the ways by which these cell potentials can be measured. Consider first the measurement of cell potential using Fig. 3. Here there are two electrodes and M2 dipping into the solutions Si and S2, respectively. The electrodes are connected through copper wires Cu to a resistance R, By a suitable calorimetric device the amount of heat generated at i in a unit time can be measured. 

Rottenberg, H. (1979). The measurement of membrane potential and ApH in cells, organelles and vesicles, Methods Enzym., 55, 547-569. 

As seen in Equations (14.2) and (14.4), the potential of cells and half-cells is dependent on the concentrations of the dissolved species involved. Clearly, the measurement of a potential can lead to the determination of the concentration of an analyte. This, therefore, is the basis for all quantitative poten-tiometric techniques and measurements to be discussed in this chapter. 

Potentiometry is the measurement of electrode potential in chemical analysis procedures for the purpose of obtaining qualitative and quantitative information about an analyte. The reference electrode is a half-cell that is designed such that its potential is a constant, making it useful as a reference point for potential measurements. Ground is the ultimate reference point in electronic measurements. 

Dickson et al. [5], calculated the Gibbs function for the ionization of the bisulfate ion by measurement of cell potentials in the temperature range from 50° to 250°C. They found that the Gibbs function could be represented by the equation... 

The method of determination from measurements of cell potentials depends on the possibility of carrying out a transformation reversibly in an electrical cell. (See Fig. 7.2.) In this case, the spontaneous tendency of the transformation wUl be opposed by an opposing potential just sufficient to balance the potential in the electrical ceU produced by that spontaneous tendency. The potential observed under such circumstances is related to the change of the Gibbs function for the reaction by Equation (7.84)... 

Ozkaya (76) studied conceptual difficulties experienced by prospective teachers in a number of electrochemical concepts, namely half-cell potential, cell potential, and chemical and electrochemical equilibrium in galvanic cells. The study identified common misconceptions among student teachers from different countries and different levels of electrochemistry. Misconceptions were also identified in relation to chemical equilibrium, electrochemical equilibrium, and the instrumental requirements for die measurement of cell potentials. Learning difficulties were attributed mainly to failure of students to acquire adequate conceptual understanding, and the insufficient explanation of the relevant... 

Good descriptions of practical experimental techniques in conventional electrophoresis can be found in Refs. [81,253,259]. For the most part, these techniques are applied to suspensions and emulsions, rather than foams. Even for foams, an indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis. In bubble microelectrophoresis the dispersed bubbles are viewed under a microscope and their electrophoretic velocity is measured taking the horizontal component of motion, since bubbles rapidly float upwards in the electrophoresis cells [260,261]. A variation on this technique is the spinning cylinder method, in which a bubble is held in a cylindrical cell that is spinning about its long axis (see [262] and p.163 in Ref. [44]). Other electrokinetic techniques, such as the measurement of sedimentation potential [263] have also been used. 

Figure 5.1 Cell and circuit elements for the measurement of electrode potentials. The upper system (a) illustrates the dilemma of attempts to measure single-electrode potentials.

In another technique, the solution is circulated through a capillary cell by a peristaltic pump (37). If part of the circulating loop is immersed in a constant-temperature bath, it is possible to measure the spectrum over a wide temperature range. A more sophisticated technique (38) allows the measurements of redox potentials and electronic spectra as well as Raman spectra using a circulating cell. 

The measured potential is a sum of several potential differences. When a current is made to flow through the cell, these potential differences are affected to different degrees, and the change in cell potential reflects the sum of all these changes. If we consider one of the examples shown in Fig. 3B we can express the change of cell potential resulting from an applied current i as follows ... 

It is necessary to distinguish between the concept of a potential and the measurement of a potential. Redox or electrode potentials (quoted in tables in Stability Constants of Metal-Ion Complexes or by Bard et al., 1985) have been derived from equilibrium data, thermal data, and the chemical behavior of a redox couple with respect to known oxidizing and reducing agents, and from direct measurements of electrochemical cells. Hence there is no a priori reason to identify the thermodynamic redox potentials with measurable electrode potentials. 

Fig. 14. Cell for the measurement of contact potential difference by the static condenser method.

The quantity Aaj/ai is the relative error in U associated with an absolute uncertainty AK in K. If, for example, AK is 0.001 V, a relative eiTor in activity of about 4tj% can be expected. It is important to appreciate that this error is characteristic of all measurements involving cells that contain a salt bridge and that this error cannot be eliminated by even the most careful measurements of cell potentials or the most sensitive and precise measuring devices. 

Sometimes it is useful to break the inner potential into two components called the outer (or Volta) potential, if/, and the surface potential, x- Thus, (f) = if/ + x- There is a large, detailed literature on the establishment, the meaning, and the measurement of interfacial potential differences and their components. See references 23-26. Although silver chloride is a separate phase, it does not contribute to the cell potential, because it does not physically separate silver from the electrolyte. In fact, it need not even be present one merely requires a solution saturated in silver chloride to measure the same cell potential. 

The electroreduction of zirconium halides in alkali halide melts has led to the measurement of reversible potentials (Table XXV) in the temperature range 670°-750°C (550). Phase rule studies of the mixed systems preceded the cell studies and revealed that the phase diagrams of the KCl-ZrCl2 and NaCl-ZrCl2 systems were of the simple eutectic type. The liquidus curves of these binary systems were established by freezing point measurements. The melting point of pure zirconium dichloride was found to be 722° 1°C. In the potassium chloride-zirconium dichloride system, the eutectic is found at 698° 1°C at... 

Living cells acting as parts of bioelectronic hybrid systems offer intriguing avenues for the development of biosensors, bioinformatics and implantable devices for the restoration of function. A crucial issue is the functional coupling of the output signal from the cell system to a micro-electronic or opto-electronic transducer unit. Tlie coupling of excitable cells with an array of field-effect transistors (FETs) integrated into the bottom of a cell culture dish allows the measurement of action potentials. 

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