Chemical equilibria thermodynamics electrochemical equilibrium

By analogy with the case of chemical reactions in volumes, the state of thermodynamic electrochemical equilibrium corresponds to a zero value for the electrochemical Gibbs energy of reaction ... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

The analysis of thermodynamic data obeying chemical and electrochemical equilibrium is essential in understanding the reactivity of a system to be used for deposition/synthesis of a desired phase prior to moving to experiment and/or implementing complementary kinetic analysis tools. Theoretical and (quasi-)equilibrium data can be summarized in Pourbaix (potential-pH) diagrams, which may provide a comprehensive picture of the electrochemical solution growth system in terms of variables and reaction possibilities under different conditions of pH, redox potential, and/or concentrations of dissolved and electroactive substances. 

Electrochemical methods are well established and use relatively inexpensive equipment to produce unique characterization information for molecules and chemical systems qualitative (speciation) and quantitative analytical data, thermodynamic data (equilibrium constants), and kinetic data (heterogeneous and homogeneous reaction rates). 

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. 

Here, the stoichiometric coefficients vs = — 1 and vP = 1 are used. The exchange current JI0 satisfies the microscopic reversibility at the state of thermodynamic equilibrium. These relations can be applied to chemical reactions with ionic substances by replacing the chemical potentials with electrochemical potentials. 

The influence of chemistry on physics is less direct. There have been important investigations in chemistry that led to developments in physics. The discovery of the third law of thermodynamics was a result of low temperature chemical equilibrium studies by Nernst. Chemical studies undoubtedly played a significant role in the early stages of the development of electromagnetism. In fact, it is electrochemical investigations by Faraday that led GJ. Stoney to coin the word electron and to estimate its charge (1874) before it was detected by J.J. Thomson in the gas phase (1897). To this list, we should add the modern atomic theory, which took root in chemistry before it found its way into physics. 

Figure V-9 Comparison between the temperature dependence of the Gibbs energy of formation for NiO obtained from electrochemical as well as chemical reduc-tion/oxidation equilibrium measurements and the prediction based on the present selection of thermodynamic properties for NiO.

From physics we know that the work needed to move a positive unit test charge between two points is proportional to the difference in electrostatic potential between these points. The expression for chemical equilibrium, eqn [1], is related to the energy for an ion in the external and resin phases, respectively. Therefore, a term for the electrostatic energy can be introduced in the expression for the chemical potential and the electrochemical potential is obtained. For a small ion B, the thermodynamic... 

Parallel events in the field of in situ IR spectroscopy (for a review of sulfate IR studies, see Ref. 26) resulted in a coupled shift to molecular level bi-sulfate anion was recognized in sulfate adlayer even in solutions with predominating sulfate. It was com-pletey new situation, when chemical equilibrium is affected by adsoibate-surface interactioa In usual terms of solution equilibria, the effect corresponds to increase of pKa from its bulk value (ca. 2) to 3.3-4.7 (pKa is potential-dependent). To agree this situation with bulk thermodynamics, one should simply use electrochemical potential instead of chemical. The phenomena of adsorption-induced protonation is relative to UPD, when adsoibate-surface interaction shifts redox equihbria. In more molecular terms, the species determined as bi-sidfate ions are probably interfacial ion pairs, i.e., the phenomenon can be considered as coadsorptioa This situation is screened in purely thermodynamic analysis, as excess surface protonation is hidden in Gibbs adsorptions of sulfate and H. However it becomes important for any further model consideration, as it can affect lateral interactions and the order in the adlayer. The excess adsorption-induced protonation of various anions is a very attractive field. In particular it is the only chance to explain why multicharged oxoanions can form complete mono-layers on platinum. 

In this book we offer a coherent presentation of thermodynamics far from, and near to, equilibrium. We establish a thermodynamics of irreversible processes far from and near to equilibrium, including chemical reactions, transport properties, energy transfer processes and electrochemical systems. The focus is on processes proceeding to, and in non-equilibrium stationary states in systems with multiple stationary states and in issues of relative stability of multiple stationary states. We seek and find state functions, dependent on the irreversible processes, with simple physical interpretations and present methods for their measurements that yield the work available from these processes. The emphasis is on the development of a theory based on variables that can be measured in experiments to test the theory. The state functions of the theory become identical to the well-known state functions of equilibrium thermodynamics when the processes approach the equilibrium state. The range of interest is put in the form of a series of questions at the end of this chapter. 

The heat source is related to the enthalpy change of the reactions, and the free-energy change of reactions (15a) and (15b) combined with (15e) determines the fuel cell Nernst potential. If chemical equilibrium is achieved in the system, the fuel composition, heat generation, and Nernst potential can be determined from thermodynamic theory. However, chemical equilibrium is usually not attained. In such cases, fuel composition and other information cannot be rigorously determined and must be approximated. The details of the reaction mechanism are complicated and usually not well understood, both for electrochemical and chemical reactions. 

This behaviour, since it corresponds to the second law, can be put more clearly in thermodynamic language (Chapter 4) [512]. At electrochemical equihbrium (open circuit, no internal fluxes) the equihbrimn voltage E just compensates the reaction affinity (see Section 4.2). The actual driving force for current flow is the electrochemical affinity A = —AG, which represents the deviation from electrochemical equilibrium. It is obtained, accordingly, from the difference between the chemical affinity and the voltage multiphed ly the charge transferred, and is thus proportional to E — U = —7. The entropy production (cf. Section 6.1) then is II = AR. oc /I > 0. This no longer applies in the same manner when permeation cells are concerned (cf. Section 7.2.2) since short ircuit currents occur (II 0), which do not manifest themselves in an external current (1=0). 

Similarly to chemical reactions, it is possible to treat electrochemical reactions in equilibrium with the help of the thermodynamics. 

---