Eqb = E*u + \nK[K2 in .NET

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Eqb = E*u + \nK[K2
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(3.2.36)
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Thus a plot of the dependence of Eqh on the pH (Fig. 3.11) will yield a curve with three linear regions (the second of which is poorly defined), with slopes of 0.0591, 0.0295 and 0 (at 25 C). The intersections of each two neighbouring extrapolated linear portions yield the pK[ and pA^ values, as follows from comparison of Eqs (3.2.34) to (3.2.36). Figure 3.12 gives examples of the dependence of the apparent formal potential on the pH for other organic systems (see also p. 465).
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Fig. 3.11 The dependence of the potential of the quinhydrone electrode qh(V) on pH. The straight line (1) corresponds to Eq. (3.2.34), (2) to (3.2.35) and (3) to (3.2.36)
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In cases where the potential of an inert electrode, in the presence of the redox system of interest, is established slowly, another redox system may then be added as a 'mediator'. The latter system should react rapidly with the former and quickly establish an equilibrium at the electrode. As a very small amount of the mediator is added, concentration changes in the measured system compared to the original state can be neglected. Suitable mediators are Ce 4+ -Ce 3+ , methylene blue-leucoform, etc. Standard redox potentials can be determined approximately from the titration curves for suitably selected pairs of redox systems. However, these curves always yield only the difference between the standard potentials and a term containing the activity coefficients, i.e. the formal potential. The large values of the terms containing the activity coefficients lead to a considerable difference between the formal potential and the standard potential (of the order of tens of millivolts). 3.2.6 Electrode potentials in non -aqueous media While the laws governing electrode potentials in non-aqueous media are basically the same as for potentials in aqueous solutions, the standardization in this case is not so simple. Two approaches can be adopted: either a suitable standard electrode can be selected for each medium (e.g. the hydrogen electrode for the protic medium, the bis-diphenyl chromium(II)/ bis-diphenyl chromium(I) redox electrode for a wide range of organic
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Fig. 3.12 The dependence on pH of the oxidation-reduction potential for cOx = cRcd: (1) 6-dibromphenol indophenol, (2) Lauth's violet, (3) methylene blue, (4) ferricytochrome c/ferrocytochrome c, (5) indigo-carmine solvents or, for example, the chlorine electrode for some melts cf. Section 3.2.1), or, on the other hand, all the potentials can be related to the aqueous standard hydrogen electrode on the basis of a suitable convention. The first approach is based on the discussion in Section 3.1.5 and requires no further explanation. To decide whether a unified electrode potential scale is of some advantage, consider cells (3.1.40) in both aqueous medium and in protic medium s: Pt|H2|HCla ,w|AgCl|Ag|Pt Pt|H2|HClfl ,s|AgCl|Ag|Pt
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186 The EMFs of these cells are given by the relationships (w) =
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RT - In a ,Hci(w) In (3.2.37)
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(3.2.38) It is assumed that the activities are based on the same concentration scale and that limC|_>0flf7c/= 1. For 0 >Hci(s) = 0 ,HCI(W), the difference between E(s) and E(w) is given by the relationship
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where A G ^ ^ is the overall standard Gibbs energy of transfer of HC1 from water to the solvent s and A G ; ^ and AG^cr 8 are the individual standard Gibbs energies of transfer of H + and Cl~ from water to the solvent s (Eq. 1.4.35). It should be noted that, so far, the derivation has been concerned with the transfer of a species between two pure solvents, so that in this case, the standard Gibbs transfer energy will be somewhat different from the values measured for distribution equilibria. This type of standard Gibbs transfer energy must be determined on the basis of the solubility of the given electrolyte, present as a solid or gaseous phase, in equilibrium with each of the pair of solvents. The derivation for equilibrium between a solution and a gaseous phase is based on the Henry law constant kif defined on page 5. The standard Gibbs energy of the transfer of HC1 from a solution into water is = RT I ( ^ Y ^ \ n (3.2.40)
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For the transfer equilibrium between a solution and a solid phase of the electrolyte BA it holds that A G - T = RT in (%&)
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\PBA(S)/
= 2RTln " ^ W m BA (s)r (s)
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(3.2.41)
where the P B A' S a r e the solubility products, the mBA's the solubilities and y 's the mean activity coefficients in each of the two phases. As separation of the standard Gibbs transfer energy of the electrolyte as a whole into the individual contributions for the anion and the cation can, of
course, not be carried out by a thermodynamic procedure, a suitable extrathermodynamic assumption must be selected. A suitable extrathermodynamic approach is based on structural considerations. The oldest assumption of this type was based on the properties of the rubidium(I) ion, which has a large radius but low deformability. V. A. Pleskov assumed that its solvation energy is the same in all solvents, so that the Galvani potential difference for the rubidium electrode (cf. Eq. 3.1.21) is a constant independent of the solvent. A further assumption was the independence of the standard Galvani potential of the ferricinium-ferrocene redox system (H. Strehlow) or the bis-diphenyl chromium(II)-bis-diphenyl chromium(I) redox system (A. Rusina and G. Gritzner) of the medium. While the validity of these assumptions has been criticized, that adopted by A. J. Parker has received the widest acceptance, i.e. that tetraphenylarsonium tetraphenylborate (Ph4AsPh4B),
yields ions with the same standard Gibbs energy of solvation in the same medium. In other words, the standard Gibbs energy for the transfer of the tetraphenylarsonium cation and of the tetraphenylborate anion between an arbitrary pair of solvents is always the same (called the TATB assumption), that is
The structure of the ions, where the bulky phenyl groups surround the central ion in a tetrahedron, lends validity to the assumption that the interaction of the shell of the ions with the environment is van der Waals in nature and identical for both ions, while the interaction of the ionic charge with the environment can be described by the Born approximation (see Section 1.2), leading to identical solvation energies for the anion and cation. The determination of the standard Gibbs transfer energy for an arbitrary ion and arbitrary pair of solvents is based on the determination of the solubility product of Ph4AsPh4B in both solvents or on the determination of the distribution coefficient of Ph4AsPh4B between the two solvents. These experimental data then yield the standard Gibbs energies for the individual ions, Ph4As+ and Ph4B~. If, for example, the standard Gibbs energy is to be determined for the transfer of the arbitrary cation C + between a pair of solvents, the experimental data are determined for the salt CPh4B and the
188 required quantity is found from the equation PTJ(3.2.43) These quantities can be used to rearrange the equation for the EMF of a cell in non-aqueous medium into the form of a difference between the electrode potentials on the hydrogen scale for aqueous solutions with additional terms. Equations (3.2.37), (3.2.38) and (3.2.39) yield the potential of the silver-silver chloride electrode in non-aqueous medium ^Agci/Ag,ci-(s) = -p r