Electrochemical-potential

The analytical treatment of electric field effects on chemical distributions may be started by recalling Guggenheim s original concept of the electrochemical potential For a single (isolated) ion fik is written in the form 

In the presence of other ions it is necessary to account for the screening effect of the ionic atmosphere. It is then useful to introduce a more general form of the electrostatic potential term of Eq. (3.66) by a charging integral 

In a collection of species Bk the total electric work, of charging 

Recalling the (neutral) chemical work term from Eq. (3.27)  

The fundamental Gibbs Eq. (3.26) for ionic species may then be expressed as 

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Here, the only surface adsorption is taken to be that of the charge balancing the double-layer charge, and the electrochemical potential change is equated to a change in o- Integration then gives... 

The treatments that are concerned in more detail with the nature of the adsorbed layer make use of the general thermodynamic framework of the derivation of the Gibbs equation (Section III-5B) but differ in the handling of the electrochemical potential and the surface excess of the ionic species [114-117]. The derivation given here is after that of Grahame and Whitney [117]. Equation III-76 gives the combined first- and second-law statements for the surface excess quantities... 

The chemical potential pi, has been generalized to the electrochemical potential Hj since we will be dealing with phases whose charge may be varied. The problem that now arises is that one desires to deal with individual ionic species and that these are not independently variable. In the present treatment, the difficulty is handled by regarding the electrons of the metallic phase as the dependent component whose amount varies with the addition or removal of charged components in such a way that electroneutrality is preserved. One then writes, for the ith charged species. 

The electrochemical potentials pi, may now be expressed in terms of the chemical potentials pt, and the electrical potentials (see Section V-9) ... 

The electrochemical potential is defined as the total work of bringing a species i from vacuum into a phase a and is thus experimentally defined. It.may be divided into a chemical work p , the chemical potential, and the electrostatic work ZiC0 ... 

When two dissimilar metals are connected, as illustrated in Fig. V-16, ]here is a momentary flow of electrons from the metal with the smaller work function to the other so that the electrochemical potential of the electrons becomes the same. For the two metals a and /3... 

The chemical potential now includes any such effects, and one refers to the gmvochemicalpotential, the electrochemical potential, etc. For example, if the system consists of a gas extending over a substantial difference in height, it is the gravochemical potential (which includes a tenn m.gh) that is the same at all levels, not the pressure. The electrochemical potential will be considered later. 

In these equations the electrostatic potential i might be thought to be the potential at the actual electrodes, the platinum on the left and the silver on the right. However, electrons are not the hypothetical test particles of physics, and the electrostatic potential difference at a junction between two metals is nnmeasurable. Wliat is measurable is the difference in the electrochemical potential p of the electron, which at equilibrium must be the same in any two wires that are in electrical contact. One assumes that the electrochemical potential can be written as the combination of two tenns, a chemical potential minus the electrical potential (- / because of the negative charge on the electron). Wlien two copper wires are connected to the two electrodes, the... 

If two metals with different work functions are placed m contact there will be a flow of electrons from the metal with the lower work function to that with the higher work fimction. This will continue until the electrochemical potentials of the electrons in the two phases are equal. This change gives rise to a measurable potential difference between the two metals, temied the contact potential or Volta potential difference. Clearly... 

Figure Bl.28.9. Energetic sitiration for an n-type semiconductor (a) before and (b) after contact with an electrolyte solution. The electrochemical potentials of the two systems reach equilibrium by electron exchange at the interface. Transfer of electrons from the semiconductor to the electrolyte leads to a positive space charge layer, W. is the potential drop in the space-charge layer.

The driving force for migration is established by the different electrochemical potentials (AU) that exist at the two interfaces of the oxide. In other words, the electrochemical potential at the outer interface is controlled by the dominant redox species present in the electrolyte (e.g. O2). 

The relations between structure and electrochemical potential are an important aspect in the study of dyes, since effective sensitizers require both the correct absorption wavelength and suitable electrochemical potentials. 

An equation relating electrochemical potential to the concentrations of products and reactants. 

The relationship between electrochemical potential and the concentrations of reactants and products can be determined by substituting equation 6.23 into equation 6.3... 

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

To evaluate a redox titration we must know the shape of its titration curve. In an acid-base titration or a complexation titration, a titration curve shows the change in concentration of H3O+ (as pH) or M"+ (as pM) as a function of the volume of titrant. For a redox titration, it is convenient to monitor electrochemical potential. 

You will recall from Chapter 6 that the Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. Consider, for example, a titration in which the analyte in a reduced state, Ared) is titrated with a titrant in an oxidized state, Tox- The titration reaction is... 

The electrochemical potential for the reaction is the difference between the reduction potentials for the reduction and oxidation half-reactions thus,... 

After each addition of titrant, the reaction between the analyte and titrant reaches a state of equilibrium. The reaction s electrochemical potential, Frxm therefore, is zero, and... 

Before the equivalence point, the solution s electrochemical potential is determined by the concentration of excess Fe + and the concentration of Fe + produced by the titration reaction. Using values from Table 9.17, we plot E for 5.0 mb and 45.0 mb of titrant (Figure 9.35c). 

Derive a general equation for the electrochemical potential at the equivalence point for the titration of Fe + with Mn04 the reaction is... 

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