Electrochemical-potential thermodynamic equilibrium

Potential-pH Equilibrium Diagram (Pourbaix Diagram) diagram of the equilibrium potentials of electrochemical reactions as a function of the pH of the solution. The diagram shows the phases that are thermodynamically stable when a metal reacts with water or an aqueous solution of specified ions. 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

Regarding the electrode/electrolyte interface, it is important to distinguish between two types of electrochemical systems thermodynamically closed (and in equilibrium) and open systems. While the former can be understood by knowing the equilibrium atomic structure of the interface and the electrochemical potentials of all components, open systems require more information, since the electrochemical potentials within the interface are not necessarily constant. Variations could be caused by electrocatalytic reactions locally changing the concentration of the various species. In this chapter, we will focus on the former situation, i.e., interfaces in equilibrium with a bulk electrode and a multicomponent bulk electrolyte, which are both influenced by temperature and pressures/activities, and constrained by a finite voltage between electrode and electrolyte. 

Before we will discuss the electrochemical system, it is important to define the properties and characteristics of each component, especially the electrolyte. In the following, we assume macroscopic amounts of an electrolyte containing various ionic and nonionic components, which might be solvated. In the case that this bulk electrolyte is in thermodynamic equilibrium, each of the species present is characterized by its electrochemical potential, which is defined as the free energy change with respect to the particle number of species i ... 

At constant pressure and temperature, after the building up of the interface, thermodynamic equilibrium is obtained when the electrochemical potentials for each component distributed between the two phases are equal ... 

Redox potential (thermodynamic derivation). Suppose we take an electrochemical cell represented by Fig. 2.7. We shall now address the question of both the potential values and the equilibrium state that can be finally attained... 

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

The mixed-potential model demonstrated the importance of electrode potential in flotation systems. The mixed potential or rest potential of an electrode provides information to determine the identity of the reactions that take place at the mineral surface and the rates of these processes. One approach is to compare the measured rest potential with equilibrium potential for various processes derived from thermodynamic data. Allison et al. (1971,1972) considered that a necessary condition for the electrochemical formation of dithiolate at the mineral surface is that the measmed mixed potential arising from the reduction of oxygen and the oxidation of this collector at the surface must be anodic to the equilibrium potential for the thio ion/dithiolate couple. They correlated the rest potential of a range of sulphide minerals in different thio-collector solutions with the products extracted from the surface as shown in Table 1.2 and 1.3. It can be seen from these Tables that only those minerals exhibiting rest potential in excess of the thio ion/disulphide couple formed dithiolate as a major reaction product. Those minerals which had a rest potential below this value formed the metal collector compoimds, except covellite on which dixanthogen was formed even though the measured rest potential was below the reversible potential. Allison et al. (1972) attributed the behavior to the decomposition of cupric xanthate. 

Electrochemical phase diagrams have been used to investigate the collector water mineral system in which the experimental potential for flotation is compared with thermodynamic equilibriums for reactions in mineral/oxygen/collector system to... 

The thermodynamic condition of equilibrium requires that the electrochemical potentials for the right- and left-hand sides of the scheme in Equation 15.13 satisfy the condition [3] ... 

A Criterion of Thermodynamic Equilibrium between Two Phases Equality of Electrochemical Potentials. It has been stated that ihe total driving force responsible for Ihe flow or transport of a species j is the gradient d lj/dx of its electrochemical potential. However, when there is net flow or flux of any species, this means that the system is not at equilibrium. Conversely, for the system to be at equilibrium, it is essential that there be no drift of any species—hence, that there should be zero gradients for the electrochemical potentials of all the species. It follows, therefore, that, for an interface to be at equilibrium, the gradients of electrochemical potential of the various species must be zero across the phase boundary, i.e.,... 

Hence, the equality of electrochemical potentials on either side of the phase boundary implies that the change in free energy of the system resulting from the transfer of particles from one phase to the other should be the same as that due to the transfer in the other direction. This is only another way of stating that when a thermodynamic system is at equilibrium, its free energy is a minimum, Le.,... 

Nonpolarizable Interfaces and Thermodynamic Equilibrium. It has just been shown that for an interface to be in thermodynamic equilibrium, the electrochemical potentials of all the species must he the same in both the phases constituting the interface. Since the difference in electrochemical potential of a species i between two phases is the work done to cany a mole of this species from one phase (e.g., the electrode) to the other (e.g., the solution), it must be the same as the work in the opposite direction. This implies a free flow of species across the interface. However, an interface that maintains an open border is none other than a nonpolarizable interface (see Section 63.3). 

If a redox couple is present in a solution and the equilibrium is attained in accordance with reaction (1), the concept of electrochemical potential of electrons in an electrolyte solution, Fredox, can be introduced. Let us stress the fact that from the point of view of thermodynamics a detailed mechanism of attaining the equilibriun is of no importance, so one may assume, in particular,... 

Since the quantities fiTCd and depend only on the properties of Ox and Red components in the solution bulk, the quantity Fredox defined by Eq. (6) is in no way related to the electrode nature and does not depend on the interface structure. Moreover, under thermodynamic equilibrium between the electrode and solution it is Fredox that determines the electrochemical potential of electrons in the electrode. This implies, in particular, that the value of F is the same for any electrode that is in equilibrium with a given redox system. Thus, the position of the Fredox level in a solution is determined by the redox system contained in it. The more positive the equilibrium potential of this system [Pg.262]

The symbols in parentheses denote the electrochemical potential levels for the corresponding reaction (the level Fdec is a particular case of the level Fred0J for a redox reaction, in which the electrode material is destructed). Once Fdec is calculated (from tabular values of thermodynamic characteristics of substances involved see, for example, Latimer, 1952), the equilibrium potentials of the reactions of anodic [Pg.286]

Solid state reactions occur mainly by diffusional transport. This transport and other kinetic processes in crystals are always regulated by crystal imperfections. Reaction partners in the crystal are its structure elements (SE) as defined in the list of symbols (see also [W. Schottky (1958)]). Structure elements do not exist outside the crystal lattice and are therefore not independent components of the crystal in a thermodynamic sense. In the framework of linear irreversible thermodynamics, the chemical (electrochemical) potential gradients of the independent components of a non-equilibrium (reacting) system are the driving forces for fluxes and reactions. However, the flux of one independent chemical component always consists of the fluxes of more than one SE in the crystal. In addition, local reactions between SE s may occur. 

This interface is also known as the perm-selective interface (Fig. 6.1a). It is found in ion-selective sensors, such as ion-selective electrodes and ion-selective field-effect transistors. It is the site of the Nernst potential, which we now derive from the thermodynamic point of view. Because the zero-current axis in Fig. 5.1 represents the electrochemical cell at equilibrium, the partitioning of charged species between the two phases is described by the Gibbs equation (A.20), from which it follows that the electrochemical potential of the species i in the sample phase (S) and in the electrode phase (m) must be equal. 

To find thermodynamic relationships for charged systems, we just replace chemical potentials in equations for uncharged systems by electrochemical potentials. For example, for equilibrium of a charged particle at a phase boundary, we have, in analogy to Eq. (24) of Chapter 6,... 

In thermodynamic equilibrium, the electrochemical potential of a particle k (juk = Hk + zkeq>, juk = chemical potential,

electrical potential, zk = charge number of the particle, e = elementary charge) is constant. Gradients in jlk lead to a particle flux Jk and from linear irreversible thermodynamics [95] the fundamental transport... 

Finally, the equality /Tsu(Na+) = jTS0(Na ), provided by thermodynamics (Eq. s2.1), is only a statement of electrochemical equilibrium, not a conclusion relating to the details of ionic interactions within soil suspensions. This equality says nothing, for example, about the electric potentials experienced by Na+(aq) in either the suspension or the solution, nor can it do so, because the division of each electrochemical potential into electrical and chemical parts would be, in this case, a completely arbitrary step without chemical significance. 

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