Electrochemical cell calculations

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

Most of the methods we have described so far give the activity of the solvent. Often the activity of the solute is of equal or greater importance. This is especially true of electrolyte solutions where the activity of the ionic solute is of primary interest, and in Chapter 9, we will describe methods that employ electrochemical cells to obtain ionic activities directly. We will conclude this chapter with a discussion of methods based on the Gibbs-Duhem equation that allow one to calculate activities of one component if the activities of the other are known as a function of composition. 

The vapor pressures (fugacities) shown in Figure 6.14 were reported by J. J. Fritz and C. R. Fuget, Vapor Pressure of Aqueous Hydrogen Chloride Solutions", Chem. Eng. Data Ser., 1, 10-12 (1956). The vapor pressures are too small to measure directly. The values reported were calculated from the results of emf measurements made on an electrochemical cell. In Chapter 9, we will describe this and other cells in detail. 

C19-0135. Consider an electrochemical cell consisting of two vessels connected by a porous separator. One vessel contains 0.500 M HCl solution and an Ag wire electrode coated with AgCl solid. The other vessel contains 1.00 M MgCl2 solution and an Mg wire electrode, (a) Determine the net reaction, (b) Calculate E for the cell (see Appendix F). (c) Draw a molecular picture showing the reactions at each electrode. 

Summarized as measured and calculated data for electrochemical cells and active electrodes with practical dimensions of the electrodes of 128x148mm are shown in Table 2 (please see cell assembly detail in section 2.2). 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

Empirically it has been demonstrated that Si (Oehrlein et al., 1981 Pearton et al., 1984b), Ge (Pearton et al., 1984a), and GaAs (Chevallier et al., 1985) can be hydrogenated in simple two electrode (externally biassed) electrochemical cells. In most of these cases, exposures of many minutes were involved cell currents were monitored during treatment but could not be directly used to calculate H influx because of the competing evolution of gaseous H2 ... 

A reaction in an electrochemical cell comprises two half-cell reactions. Even when we want to focus on a single half-cell, we must construct a whole cell and determine its cell emf, which is dehned as (positive electrode) - E(negative electrode) - Only when we know both the emf and the value of one of the two electrode potentials can we calculate the unknown electrode potential. 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

Constant current electrolysis is an easy way to operate an electrochemical cell. Usually, it is also applied in industrial scale electrolysis. For laboratory scale experiments, inexpensive power supplies for constant current operation are available (also a potentiostat normally can work in galvanostatic operation). The transferred charge can be calculated directly by multiplication of cell current and time (no integration is needed). 

We will now look at the effects of Ej on thermodynamic calculations, and then decide on the various methods that can be used to minimize them. One of the most common reasons for performing a calculation with an electrochemical cell is to determine the concentration or activity of an ion. In order to carry out such a calculation, we would first construct a cell, and then, knowing the potential of the reference electrode, we would determine the half-cell potential, i.e. the electrode potential E of interest, and then apply the Nemst equation. 

The magnitude of the voltage in an electrochemical cell is mainly determined by e in Eqn (7.10) the entropy term gives a variation on the scale of kT/e = 25 mV (Fig. 7.10), and U is typically a small fraction of an electron volt. Calculations of e are complicated by the strong interactions between ions and electrons. We are not yet able to predict site energies reliably from first principles, and so we have to be content to identify different contributions to e. 

Coated specimens were placed in an electrochemical cell. After 4 hours of temperature, open-circuit potentials were measurements were made on duplicate samples, in a salt spray test cabinet (ASTM B117-73) for 1, 17 and 96 hours respectively and their surfaces photographed in order to calculate the percentage of surface covered by corroded spots and blisters (ASTM D610-68). 

Batteries are everywhere in modern societies. They provide the electric current to start our automobiles and to power a host of products such as pocket calculators, digital watches, heart pacemakers, radios, and tape recorders. A battery is an electrochemical cell, a device for interconverting chemical and electrical energy. A battery takes the energy released by a spontaneous chemical reaction and uses it to produce electricity. 

---