Thermodynamics chemical irreversibility

The theory of the thermodynamics of irreversible systems (Prigogine, 1979 Prigogine and Stengers, 1986) shows that the differential quotient of entropy with time (the change of entropy with time) can be expressed as the sum of products, the terms of which contain a force factor and a flow factor. In chemical systems, the... 

This criterion is good for establishish whether a process is under thermodynamic control. Care should be taken however to understand the term reversibility in this case. The folding of a protein is generally per se a chemically irreversible process, in the sense that the chemical equilibrium is overwhelmingly shifted towards the folded form - there is not a low activation energy barrier between the native folded and the unfolded form and a corresponding chemical equilibrium in the native state between the two forms. Thus, in the case of the thermodynamic hypothesis of... 

Catalytic reactions in electrochemistry — When the product of an electrochemical reduction reaction is regenerated by a chemical reoxidation, or when the product of an electrochemical oxidation is regenerated by a re-reduction, the regeneration reaction is called a catalytic reaction. For thermodynamic reasons the chemical oxidant (or the reductant) has to be electro-chemically irreversible in the potential range where the catalyst is electroactive. The reduction of Ti(IV) in the presence of hydroxylamine is an example for an oxidative regeneration [i, ii] ... 

Irreversibility — This concept - as also the - reversibility - is used in several ways. We speak of chemical irreversibility when the reaction can proceed only in one direction. Irreversibility in a thermodynamic sense is when a process generates - entropy [i, ii]. 

As for eqn. (46), this relation can be applied to chemically irreversible, as well as to reversible, electrochemical reactions since the influence of the reaction thermodynamics is cancelled out. Of the relatively few tests of eqn. (47) that have been made [64, 97, 116, 120], reasonable accordance with the experimental data has been obtained. 

Earlier [26,27,43,46] a phenomenological approach, based on the premise that the thermodynamics of irreversible processes [29] joined with Nemst-Planck equations for ion fluxes, would be useful was applied to the solution of intraparticle diffusion controlled ion exchange (IE) of fast chemical reactions between B and A counterions and the fixed R groups of the ion exchanger. In the model, diffusion within the resin particle, was considered the slow and sole controlling step. 

Modern opinion views the Nernst-Plank theory as a special case of applying the thermodynamics of irreversible processes to ion exchange. It may also be argued theoretically and experimentally that the observed characteristics of ion exchange rate behaviour can only be fully explained by including chemical reaction as a flux-coupling mechanism as well as the diffusion potential. From a research standpoint it is most probable that future theoretical advances in ion exchange kinetics will result from the further application of non-equilibrium thermodynamics. 

The van t Hoff-Nemst approach thus lacks a function of state associated with the chemical reaction. A second objection is that although stress is placed on the chemical reaction, consideration is in effect limited to a study of equilibrium states and of reversible changes despite the fact that quantities like the heat of reaction only have a precise and simple meaning in practice if the system considered actually undergoes a chemical reaction in a finite time. In other words a thermodynamics of chemical reactions must necessarily be a thermodynamics of irreversible phenomena. 

A cell that is chemically irreversible cannot behave reversibly in a thermodynamic sense. A chemically reversible cell may or may not operate in a manner approaching thermodynamic reversibility. 

In contrast to equilibrium thermodynamics, the thermodynamics of irreversible processes portray the application of thermodynamic methods as dynamic and therefore time-dependent procedures. The name Prigo-gine must be mentioned in relationship to this—he received for his work in this area the Nobel Prize in the year 1977. A new, very complex thermodynamics originated from his examination method for chemical reactions, and was developed by us, to come to a successful description of heterogenous multiphase polymer systems. This theory interprets crazing fracture energy dissipation and fracture mechanism in a totally new way on the basis of dissipative structures in polymer blends and their dynamics, For a list of abbreviations used in this section sec page 610,... 

The thermodynamics of irreversible processes begins with three basic microscopic transport equations for overall mass (i.e., the equation of continuity), species mass, and linear momentum, and develops a microscopic equation of change for specific entropy. The most important aspects of this development are the terms that represent the rate of generation of entropy and the linear transport laws that result from the fact that entropy generation conforms to a positive-definite quadratic form. The multicomponent mixture contains N components that participate in R independent chemical reactions. Without invoking any approximations, the three basic transport equations are summarized below. 

Now, in a multicomponent system, the variation of the chemical potential with space can be expressed in terms of the molar fractions, or concentrations as function of space. Further the velocity of the particles can be expressed in terms of a material flux across an imaginary perpendicular surface to the respective axis. In this way, the equation of diffusion can be derived from thermodynamic arguments. We emphasize that we have now silently crossed over from equilibrium thermodynamics to irreversible thermodynamics. 

The thermochemical cycle in Scheme 6 has been used to estimate the effect of a one-electron oxidation on the thermodynamic acidities of metal hydrides. The method has been similarly used on organic systems. Measurement of the oxidation potentials for the metal hydride and its conjugate base gives access to relative values for the metal hydride and its one-electron oxidized counterpart through Equation (14), Scheme 6. In many reported cases, one (or even both) electrode potentials are obtained from chemically irreversible voltammograms, with consequential uncertainties in the derived thermodynamic data. Table 7 gives a comprehensive list of M-H data comparing MH and MH species as determined with this thermochemical cycle. 

Based on thermodynamics of irreversible processes, that is, on the restrictions imposed on the heat and mass fluxes by the second law of thermodynamics, one can state that the mass flux of a-constituent is proportional to the gradient of chemical potential p and gravity potential... 

Transport of a substance caused by a thermodynamic force which arises from the gradient of its chemical potential is termed diffusion. It can be formulated phenomenologically by application of the thermodynamics of irreversible processes [19]. In what follows we confine ourselves to binary systems consisting... 

The Use of Linear Thermodynamics of Irreversible Processes (LTIP) for Calculation of Parameters Related to Conservative Mechanisms in the Process of Light-to-Chemical Energy Conversion P/2e Calculation and Analysis Thermodynamic Efficiency and Energetic Coupling Analysis Experimental Validation of the Proposed Model for Different Simple Geometric Structures of a Photobioreactor... 

Callen illustrates the point by pointing out that failure of H2 to satisfy certain thermodynamic equations motivated the investigations of the ortho- and para-forms of H2 (loc. cit.). Whether concepts applicable under equilibrium conditions continue to apply under non-equilibrium conditions calls for careful consideration. Temperature, for example, is a thermodynamic concept not applicable to a body which is not at equilibrium. But an extension of thermodynamics to irreversible thermodynamics allows that, tmder not too radical non-equilibrium conditions, thermodynamic concepts such as temperature can be applied to points at instants of time, varying smoothly from one point and time to another. In that case, even though a body not at equilibrium doesn t have a temperature, it may well be possible to assign a temperature gradient over the body. A similar distribution of substances may be possible throughout a body subject to diffusion and chemical reactions. 

In the earlier chapters, transport phenomena involving a barrier have been discussed from the angle of (i) basic understanding of the physico-chemical phenomena and (ii) test of the linear thermodynamics of irreversible processes. Similar phenomena in continuous systems such as thermal diffusion (Soret effect)/Dufour effect are of equal... 

As the extent of reaction is a thermodynamic variable, the general definition of the rate of reaction as dX/dt is also a thermodynamic quantity and indeed it plays a central role in the thermodynamics of irreversible processes. Being a thermodynamic quantity, it is totally unrelated to any molecular interpretation as to how the chemical reaction actually otcurs. In particular, the definition applies to any single reaction, i.e., one the advancement of which... 

Equilibrium is characterized by the equality of the chemical potential. Nonequilibrium is therefore induced by the gradient of the chemical potential. In the thermodynamics of irreversible processes, chemical potential gradient is the fundamentally correct driving force for diffusion. According to the Gibbs-Duhem equation (2.3-5), we have ... 

This law (1931) was the first attempt to use the thermodynamics of irreversible processes as a useful instrument for the rationalisation of physical-chemical systems. An example of the application of the above is the Seebeck effect in the thermoelectric field. If the extremities of a bimetallic couple reach different temperatures, there will be a flow of electrical current I caused by the potential difference. Considering Table 4.1 and the discontinuous system gives ... 

In the form of eq. (5-30), Pick s second law applies only to one-dimensional problems in an isotropic medium. The index i on the diffusion coefficient has been removed in order to make it clear that this is no longer the component diffusion coefficient D,-, but rather, it is the chemical interdiffusion coefficient. Normally, the chemical interdiffusion coefficient will be a function of the individual component diffusion coefficients Di because of the coupling of the fluxes in the lattice system. When local thermodynamic equilibrium prevails, the coefficients Di are, in turn, unique functions of the composition. From the thermodynamics of irreversible processes it can be shown [6] that in binary systems there is only one independent transport coefficient, and in general, in n-component systems there can only be (n - 1) /2 independent transport coefficients. 

The reader who may be somewhat unfamiliar with the thermodynamics of irreversible processes, of which the chemical and electrochemical aspects are of most concern here, will find help, we hope, in our three monographs, in the two monographs of Prigogine, and in the treatise by Prigogine and Defay(in which electrochemistry is not touched, but where the essentials of chemical thermodynamics are clearly presented in terms of affinities and chemical potentials). 

Each thermodynamic system strives to equalise gradients in temperature, pressure and chemical potentials which induces heat flow, liquid or gas flow or diffusive mass flows. The entropy production associated with a diffusive mass flow is proportional to the product of mass flow density and gradient in chemical potential. Gradients in the chemical potentials are therefore considered within the scope of thermodynamics of irreversible processes as the generalised driving force for diffusive mass flow (Prigogine 1961). In a thermodynamic equilibrium state not only temperature and pressure are equal, but the chemical potentials are also. 

PrisORin Ilya (1917-2003) Russian-born Belgian chemist who researched the thermodynamics of irreversible chemical processes and learned how to handle processes far from equilibrium. For this work, he was awarded the 1977 Nobel Prize in chemistry. 

In his pioneering work on the thermodynamics of chemical processes, Theophile De Bonder (1872-1957) [14-16] incorporated the uncompensated transformation or uncompensated heat of Clausius into the formalism of the Second Law through the concept of affinity, which is presented in the next chapter. This modem approach incorporates irreversibility into the formalism of the Second Law by providing explicit expressions for the computation of entropy produced by irreversible processes [17-19]. We shall follow this more general approach in which, along with thermodynamic states, irreversible processes appear explicitly in the formalism. 

Though Gibbs did not consider irreversible chemical reactions, equation (4.1.1) that he introduced included all that was needed for the consideration of irreversibility and entropy production in chemical processes. By making the important distinction between the entropy change S due to exchange of matter and energy with the exterior, and the irreversible increase of entropy djS due to chemical reactions [2, 3], De Bonder formulated the thermodynamics of irreversible chemical transformations. And we can now show he took the uncompensated heat of Clausius and gave it a clear expression for chemical reactions. 

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