-pV(Ag) M H+(3)--i/x H2(2) + /i (Pt) t RT In aH+ t

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RT, - -=- In ac,-(3) r

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i.e. a relationship identical with Eq. (3.1.53). The correct formulation of the relationships for the Galvani potential differences leads to the same results

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tThe data have been recalculated from the previous standard pressure of 1.01325 x 105 to 105 Pa and those determined for unit activity on the molal scale to unit activity on molar scale (cf. Appendix A).

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165 as the procedure following from Eq. (3.1.39) or from Eqs (3.1.45) to (3.1.49). It should be noted that all terms concerning the electrons in the metals as well as those connected with the metals not directly participating in the cell reaction (Pt) have disappeared from the final Eq. (3.1.49). This result is of general significance, i.e. the EMFs of cell reactions involving oxidationreduction processes do not depend on the nature of the metals where those reactions take place. The situation is, of course, different in the case of a metal directly participating in the cell reaction (for example, silver in the above case). For cell reactions in general, both approaches yield the equation for the EMF: RT ln (3.1.60) nr where E is the standard EMF (standard cell reaction potential), n is the charge number and Q is the quotient of the activities of the reactants in the cell reaction raised to the appropriate stoichiometric coefficients; this quotient has the same form as the equilibrium constant of the cell reaction. For practical reasons it is often useful to separate the EMF of a galvanic cell into two terms and assign each of them to one of the electrodes. The half-cell reactions provide a basis for unambiguous separation. The equation for the overall EMF is converted to the difference between two expressions, in which the expression corresponding to the electrode on the left is subtracted from the expression corresponding to the electrode on the right. Thus, for example, it follows for Eq. (3.1.59), with inclusion of a term containing the relative hydrogen pressure, that ^ - ( w ) - RT In qcl-(w)

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ln/7H2 + PH+(W) + RT In

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(3.1.61) The terms Agci/Ag,ci- and EH+/H2 are designated as the electrode potentials. These are related to the standard electrode potentials and to the activities of the components of the system by the Nernst equations. By a convention for the standard Gibbs energies of formation, those related to the elements at standard conditions are equal to zero. According to a further convention, cf. Eq. (3.1.56), JI2,+(W) - AG}>(H+, w) = 0 Then ) (3.1.63) (3.1.62)

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166 It follows from Eqs (3.1.53) and (3.1.55) that RT EAgcuAg,ci- = ^Agci/Ag,ci- - In cr(w) r RT RT ln H Euvu2 = ~y{naH+~JP ^ 2 (3.1.64) (3.1.65)

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which are the Nernst equations. They will be discussed in detail in Section 3.2. It should be recalled that, in contrast to standard electrode potentials, which are thermodynamic quantities, the electrode potentials must be calculated by using the extrathermodynamic expressions described in Sections 1.3.1 to 1.3.4. The electrode potentials do not have the character of Galvani potential differences, but are simply operational quantities permitting simple calculation or interpretation of the EMF of a galvanic cell and are well suited to the application of electrochemistry in analytical chemistry, technology and biology. In the subsequent text the half-cell reactions will be used to characterize the electrode potentials instead of the cell reactions of the type of Eq. (3.1.42) under the tacit assumption that such a half-cell reaction describes the cell reaction in a cell with the standard hydrogen electrode on the left-hand side. The EMF of a cell is calculated from the electrode potentials (expressed for both electrodes with respect to the same reference electrode) as the difference of the potentials of these electrodes written on the right and left in the scheme:

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^cell = ^rhs ^lhs (3.1.66)

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In practice, it is very often necessary to determine the potential of a test (indicator) electrode connected in a cell with a well defined second electrode. This reference electrode is usually a suitable electrode of the second kind, as described in Section 3.2.2. The potentials of these electrodes are tabulated, so that Eq. (3.1.66) can be used to determine the potential of the test electrode from the measured EMF. The standard hydrogen electrode is a hydrogen electrode saturated with gaseous hydrogen with a partial pressure equal to the standard pressure and immersed in a solution with unit hydrogen ion activity. Its potential is set equal to zero by convention. Because of the relative difficulty involved in preparing this electrode and various other complications (see Section 3.2.1), it is not used as a reference electrode in practice. The term 'electrode potential' is often used in a broader sense, e.g. for the potential of an ideally polarized electrode ( 4) or for potentials in non-equilibrium systems ( 5). Similar to electrode potentials, standard electrode potentials have so far been referred to the standard hydrogen electrode (SHE). These data are thus designated by 'vs. SHE' after the symbol V, that is Agci/Ag,ci- =

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167 0.2224 V vs. SHE. Sometimes electrode potentials are referred to other reference electrodes, such as the saturated calomel electrode (SCE), etc. So far, a cell containing a single electrolyte solution has been considered (a galvanic cell without transport). When the two electrodes of the cell are immersed into different electrolyte solutions in the same solvent, separated by a liquid junction (see Section 2.5.3), this system is termed a galvanic cell with transport. The relationship for the EMF of this type of a cell is based on a balance of the Galvani potential differences. This approach yields a result similar to that obtained in the calculation of the EMF of a cell without transport, plus the liquid junction potential value A0 L . Thus Eq. (3.1.66) assumes the form cell = rhs - .hs + A0 L (3.1.67)

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However, in contrast to the EMF of a galvanic cell, the resultant expressions contain the activities of the individual ions, which must be calculated by using the extrathermodynamic approach described in Section 1.3. Concentration cells are a useful example demonstrating the difference between galvanic cells with and without transfer. These cells consist of chemically identical electrodes, each in a solution with a different activity of potential-determining ions, and are discussed on page 171. It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal {conditional) potentials are introduced, defined in terms of concentrations. Definitions are not given unambiguously in the literature; the following would seem most suitable. The formal (conditional) potential is the potential assumed by an electrode immersed in a solution with unit concentrations of all the species appearing in the Nernst equation; its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as EOf, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example '(Zn 2+ 4- 2e = Zn, 10"3M H2SO4). Coming back to equations for Galvani potential differences, (3.1.11) to (3.1.26), we find that equation (3.1.67) can be written in the form cci = A^220 - Agj'0 + A0 L (3.1.68)

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where A 20 is the Galvani potential difference between the right-hand side electrode and the solution S2 in which it is immersed and A '0 is the analogous quantity for the left-hand side electrode. When the left-hand side electrode is the standard electrode and A0 L is kept constant (see page 114), then Ecell can be identified with a formal electrode potential given by the

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168 approximate relationship + constant (3.1.69)

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Electrode potentials are relative values because they are defined as the EMF of cells containing a reference electrode. A number of authors have attempted to define and measure absolute electrode potentials with respect to a universal reference system that does not contain a further metalelectrolyte interface. It has been demonstrated by J. E. B. Randies, A. N. Frumkin and B. B. Damaskin, and by S. Trasatti that a suitable reference system is an electron in a vacuum or in an inert gas at a suitable distance from the surface of the electrolyte (i.e. under similar conditions as those for measuring the contact potential of the metal-electrolyte system). In this way a reference system is obtained that is identical with that employed in solid-state physics for measuring the electronic energy of the bulk of a phase. The system M;|S|M|Mr (3.1.70)

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where M is the studied electrode metal, S is the electrolyte solution and Mr = M^ is the reference electrode metal, has the EMF E = [<KMr) - <KM)] + [<KM) - <HS)] + [<KS) - <HMr)] (3.1.71) Examination of Eq. (3.1.12) yields 0(Mr) - 0(M) = so that substitution into Eq. (3.1.69) yields (3.1.72)

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(3.1.73,

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Thus the EMF has been separated into two terms, each containing a quantity related to a single electrode. If the surface potential of the electrolyte #(S) is added to each of the two expressions in brackets in Eq. (3.1.73), then the expression for the EMF contains the difference in the absolute electrode potentials; for the absolute electrode potential of metal M we have M(abs) = A V - ^ ^ + Z(S) (3.1.74) t This quantity corresponds to the minimal work required to transfer an electron from the bulk of metal M through the electrolyte solution into a vacuum. Equation (3.1.74) can be readily modified to yield (cf. the

169 definition of the electron work function on page 153)