We consider a one-phase system (so that the assumptions of invertibility discussed in the preceding chapter are justified) in which a single chemical reaction is taking place, say, e.g.,
Equation (3.1.1) does not, of course, imply addition in the ordinary algebraic sense of the quantities CO and O2. The meaning of equation (3.1.1) is to recall the experimentally observed fact that, when a given number of moles of CO is consumed by the reaction, the same number of moles of CO2 is produced, and half as many moles of O2 are consumed. Let the components appearing in the reaction be numbered consecutively, say CO is B 1, O2 is B 2, and CO2 is B 3, and let σ j be the corresponding stoichiometric coefficients, say σ1 = −1, σ2 = −1/2, and σ3 = 1. We note that the stoichiometric coefficients of the species appearing on the left-hand side (the “reactants”) are assigned negative stoichiometric coefficients. Equation (3.1.1) can now be written as follows:
KeywordsFree Enthalpy Extensive Property Homogeneous Reaction Stoichiometric Coefficient Functional Derivative
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- The whole question of independence of chemical reactions, the influence of stoichiometry on the equilibrium behavior of reacting systems, and the stability of chemical equilibrium was discussed in detail long ago by E. Jouguet, J. Ecole Poly., II Ser. 21, 61, 181 (1921); a more recent formal discussion was given by.Google Scholar
- The general theory of homogeneous reacting mixtures, expressed in terms of internal state variables, has an ample literature. Some important references are M. E. Gurtin and A. S. Vargas, Arch. Rath Mech. Anal. 43, 179 (1971)Google Scholar
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- The question of writing the stoichiometric equation for a reaction in the form of equation (3.1.2), with stoichiometric coefficients which can be both positive and negative, also has an old tradition; see, e.g., K. G. Denbigh, The Thermodynamics of the Steady State, Methuen, London (1951).Google Scholar
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- The continuous description of mixtures was first developed by Th. De Donder, L’affinité—Seconde Partie, Gauthier-Villars, Paris (1931). The presentation in Section 3.6, as well as most modern analyses of continuous mixtures, is based on the methodology discussed in the fundamental work of.Google Scholar
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- A good source for studying functional analysis is F. Riesz and B. Nagy, Functional Analysis, Ungar, New York (1955).Google Scholar
- Liapounov functions are discussed in all textbooks on stability analysis; a good source is M. M. Denn. Stability of Reactions and Transport Processes, Prentice-Hall, Englewood Cliffs, NJ (1975).Google Scholar
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