E.M.F. cells

Randall and Halford (loc. cit.) record K = 2.62 x 10 mole 1 obtained by combining data for the acidity constant of hydrogen cyanide, the solubility of silver chloride, and the equilibrium constant for the reaction AgCl (c) + 2HCN Ag(CN)7 + 2H+ + Cl". A value could also be obtained by a study of e.m.f. cells of the type discussed in Problem 127, but this method has not been used. 

Each vertical line in the above representation denotes an interface and a potential is developed at each interface. The potential of the whole galvanic cell is the algebraic sum of the potentials developed by the glass (indicator) and the reference (Ag/AgCl or Hg/Hg2Cl2) electrodes, e.m.f. (cell) = e.m.f. (ref) + e.m.f. (glass)... 

Since e.m.f. (ref) is constant, e.m.f. (cell) varies only with a variation in the pH of test solution (if the temperature is constant). The modem glass electrodes develop potentials which give a linear relationship with pH changes. 

Figure 5 Part of an e.m.f. cell employing a solid electrolyte (Reproduced by permission from High Temp.-High Press, 1969, 1, 357)...

Daniell cell A ZnjZn lCu /Cu cell. The e.m.f. of the Daniell cell is MOV and is virtually independent of temperature. 

Nernst equation This equation relates the e.m.f. of a cell to the concentrations or, more accurately, the activities of the reactants and products of the cell reaction. For a reaction... 

For tire coupled redox cell, tire e.m.f. (E) results as ... 

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

Experimentally, the aqueous iron(II) is titrated with cerium(IV) in aqueous solution in a burette. The arrangement is shown in Figure 4.6, the platinum indicator electrode changes its potential (with reference to a calomel half-cell as standard) as the solution is titrated. Figure 4.7 shows the graph of the cell e.m.f. against added cerium(IV). At the equivalence point the amount of the added Ce (aq) is equal to the original amount of Fe (aq) hence the amounts of Ce (aq) and Fe (aq) are also equal. Under these conditions the potential of the electrode in the mixture is ( - - f)/2 this, the equivalence point, occurs at the point indicated. 

Fig. 1.20 Cell consisting of two reversible Ag /Ag electrodes (Ag in AgN03 solution). The rate and direction of charge transfer is indicated by the length and arrow-head as follows gain of electrons by Ag -he- Ag—> loss of electrons by Ag - Ag + e- —. (o) Both electrodes at equilibrium and (f>) electrodes polarised by an external source of e.m.f. the position of the electrodes in the vertical direction indicates the potential change. (K, high-impedance voltmeter A, ammeter R, variable resistance)...

By means of a resistance in the circuit the spontaneous corrosion reaction can be made to proceed at a predetermined rate, and the rate can be measured by means of an ammeter A. At the same time the potentials of the individual electrodes can be measured by means of a suitable reference electrode, a Luggin capillary and high-impedance voltmeters and Kj. At equilibrium there is no net transfer of charge (/ = A = 0). the e.m.f. of the cell is a maximum and equals the difference between the reversible potentials of the two electrodes... 

The driving force of the reaction is the free energy change AC which is related to the reversible or equilibrium e.m.f. of the cell by the relationship... 

As the rate of charge transfer is increased by decreasing the resistance in the circuit, the magnitudes of and increase thus decreasing the magnitude of the polarised e.m.f. of the cell p i. It follows from Fig. 1.23 that for any given rate of charge transfer I... 

The e.m.f. of a thermogalvanic cell is the result of four main effects (a) electrode temperature, (b) thermal liquid junction potential, (c) metallic thermocouple and (d) thermal diffusion gradient or Soret. 

The driving force of a thermogalvanic corrosion cell is therefore the e.m.f. attributable to these four effects, but modified by anodic and cathodic polarisation of the metal electrodes as a result of local action corrosion processes. 

Although Table 2.16 shows which metal of a couple will be the anode and will thus corrode more rapidly, little information regarding the corrosion current, and hence the corrosion rate, can be obtained from the e.m.f. of the cell. The kinetics of the corrosion reaction will be determined by the rates of the electrode processes and the corrosion rates of the anode of the couple will depend on the rate of reduction of hydrogen ions or dissolved oxygen at the cathode metal (Section 1.4). 

It is clear that to ensure adequate protection of a structure under cathodic protection it is necessary to measure its electrode potential. This can only be achieved by using a reference electrode placed in the same environment as the structure and measuring the e.m.f. of the cell so formed. Since the electrode potentials of different types of reference electrode vary, it is clear that the measured e.m.f. will also vary according to the particular reference electrode used. It follows that the potential measured must always be recorded with respect to the reference electrode deployed, which must always be stated. 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Thus the e.m.f. of the cell will be the resultant of the various interfacial potentials given above, i.e. 

For a reversible cell at equilibrium the Gibbs free energy and the reversible e.m.f. E, are related by... 

The above considerations show that the equilibrium e.m.f. of a reversible cell is determined solely by the interfacial potentials at the two electrodes constituting the cell, providing the liquid junction can be eliminated or made negligible, and under these circumstances the interfacial potentials will be related to the chemical potentials of the species involved in the equilibrium. In the case of an irreversible cell, e.g. 

An ideal reversible cell is characterised by an e.m.f. that remains constant irrespective of the rate of reaction in either direction, i.e. each interface constituting the cell must be so completely non-polarisable that it resists any attempt to change its potential. Although this is impossible to achieve in practice, a number of interfaces approximate to ideality providing the rate of reaction is maintained at a very low value. These reversible electrodes (or half-cells) are used as reference electrodes for determining the potential of a single electrified interface. 

It is evident that it is only possible to measure the e.,m.f. of a cell, and that in order to determine the potential at a single electrified interface it is necessary to assign an arbitrary potential to a specified electrified interface, which is then used as a reference for all others. The equilibrium at... 

It is apparent that since the electrode potential of a metal/solution interface can only be evaluated from the e.m.f. of a cell, the reference electrode used for that purpose must be specified precisely, e.g. the criterion for the cathodic protection of steel is —0-85 V (vs. Cu/CuSOg, sat.), but this can be expressed as a potential with respect to the standard hydrogen electrode (S.H.E.), i.e. -0-55 V (vs. S.H.E.) or with respect to any other reference electrode. Potentials of reference electrodes are given in Table 21.7. 

Concentration Cell a galvanic cell in which the e.m.f. is due to differences in the concentration of one or more electrochemically reactive constituents of the electrolyte solution. 

Electrode Potential (E) the difference in electrical potential between an electrode and the electrolyte with which it is in contact. It is best given with reference to the standard hydrogen electrode (S.H.E.), when it is equal in magnitude to the e.m.f. of a cell consisting of the electrode and the S.H.E. (with any liquid-junction potential eliminated). When in such a cell the electrode is the cathode, its electrode potential is positive when the electrode is the anode, its electrode potential is negative. When the species undergoing the reaction are in their standard states, E =, the stan-... 

Voltaic Cell a term sometimes used for an electrochemical cell it is sometimes used to refer to a cell in which chemical changes are caused by the application of an external e.m.f. 

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