De Donder equation

Nonlinear systems of transport and chemical kinetics analyzed by the generalized Marcelin-de Donder equations consider two competing forward and backward directions of an elementary process. These equations characterize the flow of matter and energy through the energy barrier and contain potentials F = ( /jl/T, 1 IT) in exponential forms... 

The first step is a two-way process with a very unfavorable equilibrium A = — AGi = —15.7 kcal mol , at 298 K, with the superscript -e- standing for standard state. The second one is a one-way process, with a rate constant At2 that is 10 times larger than k-1 over an extended temperature range. The kinetic coupling between both steps at the kinetic steady state has the effect of pumping away the hydrogen atom concentration from its equilibrium value [H]e in the absence of the second step below, down to its steady state value [H]. In fact, application of the De Donder equation to an equimolar H2-Br2 mixture at half conversion to HBr at the steady state yields with [H2] = [Br2] = [HBr],... 

Another theoretical basis of the superheated liquid-film concept lies on the irreversible thermodynamics developed by Prigogine [43]. According to this theory, irreversible chemical processes would be described (Equation 13.17) by extending the equation of De Donder, provided that simultaneous reactions were coupled in a certain thermodynamic model, as follows ... 

Even if one of the processes is not chemical but is categorized as a phase change, for example, evaporation, the extended De Donder s equation (Equation 13.17), is known to be valid. Any large magnitude of entropy production rate (diS/dt) due to evaporation might give a correlation such as... 

Rate constants and reaction mechanisms for non-ideal systems (the Mar-celin-de Donder kinetic law) are subject to the same limitations. For them eqns. (69)-(71) include at(c ) instead of c the remaining equations and all the reasoning are the same [28]. 

As is shown in Table 1, the first step in the analysis of experimental results consists of describing the reaction system by a set of stoichiometric equations. Concepts associated with the word stoichiometry can be found in the pioneering works of De Donder [39], Jouguet [40] and Brinkley [41]. A considerable amount of literature about stoichiometry has appeared in recent years and the corresponding references are listed in a paper by Smith and Missen [42]. A general discussion of stoichiometric problems is given by Aris [23]. 

These equations are called the Clausius equations although the second, which relates the heat capacity change to the temperature coefficient of the heat of reaction, is also called Kirchhoff s equation and the last equation, giving the effect of volume on the heat of reaction, was first derived by De Donder. 

Furthermore, we have called a change involving the increase of by unity one equivalent of reaction. This is not entirely satisfactory since it is neither necessary nor always customary to write the stoichiometric equation for a reaction so that one chemical equivalent of each reactant and product is involved, but once the stoichiometric equation has been written down in order to define what is meant by the unit of reaction is also defined. The French phrase la reaction a marche une fois does not admit of direct translation. An alternative suggestion j has been made that when increases by unity the reaction should be said to have advanced by one de donder. 

The rate equations in the form of Eq. (8) are typically referred to as the De Donder relation. 

But it will be seen that theory allows the number of equations for the reactions which are strictly necessary to describe the chemical system precisely to be defined in a rigorous way, when the nature and the number of the constituents to be taken into account are themselves well-defined. The theory therefore provides the necessary and sufficient number of chemical variables (or JOUGUET-de DONDER variables) and equations to calculate the composition of the reaction mixture during the transformation. In particular, these equations can be applied to chemical equilibria. 

These approximations also provide elegant physicochemical insights into the mechanism as summarized in two recent papers by Stoltze [2] and Dumesic [3]. Thus, as shown by Stoltze [2], under the RDS approximation many characteristics of the microkinetic mechanisms, e.g., rate equations (De Donder relations), apparent activation energies, apparent reaction orders, etc., may be naturally partitioned into a sum of contributions associated with a special class of reactions involving only one surface species. Dumesic [3] extended the idea to general systems. 

The negative of the quantity ZviPi has been called by de Donder the affinity of the reaction. As is evident from the discussion near the end of 4 3, the afSnity must be positive if the reaction is to proceed spontaneously from left to right of the chemical equation as usually written, and it must be negative for reaction in the reverse direction. 

L. A. Donders, F. A. A. M. de Leeuw, and C. Altona, Relationship between proton-proton NMR coupling constants and substituent electronegativities. IV. An extended Karplus equation accounting for interaction between substituents and its application to coupling constant data calculated by the extended Hiickel method, Magn. Reson. Chem., 27 (1989) 556-563. 

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