Chemical and Electrochemical Potentials

The thermodynamics of solutions and solid-liquid interfaces can be well described in terms of the chemical and electrochemical potentials of the system. The basic definition of the chemical potential [6] is 

The chemical potential or free energy of a species, the latter being a component in a solid or in a solution, depends on the chemical environment. In the case of a charged species, such as an ion or an electron, we have to consider in addition the electrical energy required for bringing a charge to the site of the species. Accordingly, an electrochemical potential Mi s defined instead of the chemical potential. Both are related by 

It is important to realize that at equilibrium in a system the electrochemical potential, Mi, is constant over all contacting phases as far as the zth substance is exchangeable between these phases. Accordingly we have 

the following relation results for such an exchange under equilibrium conditions  

Considering for instance a reaction in a single phase we have ViAi V2A2 O 3 3 -+ V4A4 

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Fig. 14.10. Transmembrane electron movement and redox reactions. Also shown schematically are electrodes and circuit diagram for cyclic voltammetry. WE, working electrode SCE, saturated calomel electrode AE, auxiliary electrode, p, and /7 are chemical and electrochemical potentials, respectively. Bulk concentrations of reduced (RED) and oxidized (OX) species on either side of the membrane as indicated by subscripts 1 and 2 interface concentrations are designated by a superscripts (Reprinted from H. T. Tien, Aspects of Membrane Chemistry,...

The different notions of electric potential are laid out in section 3.1.1 (Volta and Galvani potentials). Other notions making use of this term potential will also be defined in section 3.1.2 (chemical and electrochemical potentials). 

Fig. 9-6. Variation of the electrical, chemical, and electrochemical potentials in the solid state galvanic cell illustrated in Fig. 9-5. The variation of the concentration of electrons is also shown. The transport number of the ions, in the electrolyte is equal to one.

When considering the thermodynamics of nucleation and the mechanism of the elementary acts of single ions attachment and detachment to and from a growing cluster or a crystal surface, it proves convenient to work not with molar but with molecular quantities. For that reason the molecular unit to be used in Chapters 1 and 2 ofthis book will be not a mol but uparticle - atom, ion or molecule - and aU physical quantities like chemical and electrochemical potential, electric charge etc. will be referred to this unit. In what follows we consider the conditions that characterize the thermod5Uiamic equilibrium in chemical and electrochemical systems. 

In Chapter 1.1.1 we defined the chemical and electrochemical potentials as molecular quantities. However, sometimes it proves convenient to work with the corresponding molar quantities. In that case the building unit of a given phase is selected to be not a particle but a mol. Bearing in mind the simple relation between the number m of moles and the number n of particles, m = h/Na where Na is the Avogadro number, the molar... 

Here, y and y are chemical and electrochemical potentials respectively of the corresponding substances (per mole). 

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