12 - 12 Chemical Equilibrium and Dissociation Up to now...

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12 Chemical Equilibrium and Dissociation Up to now this book has concentrated on combustion problems which can be solved by methods based on equilibrium but which do not require an explicit statement of the fact, e.g. complete combustion of a hydrocarbon fuel in air can be analysed by assuming that the products consist only of H,O and CO,. These methods are not completely correct and a more rigorous analysis is necessary to obtain greater accuracy. Consider the combustion of carbon monoxide (CO) with oxygen (02); up until now the reaction has been described by the equation co + 1/20,-+CO, (12.1) It is implied in this equation that carbon monoxide combines with oxygen to form carbon dioxide, and as soon as that has happened the reaction ceases. This is not a true description of what happens in practice. The real process is one of dynamic equilibrium with some of the carbon dioxide breaking down into carbon monoxide and oxygen (or even more esoteric components) again, which might then recombine to form carbon dioxide. The breakdown of the CO, molecule is known as dissociation. To evaluate the amount of dissociation that occurs (the degree of dissociation) it is necessary to evolve new techniques. 12.1 Gibbs energy The concept of Gibbs energy, G, was introduced im Chapter 1. The change in the specific Gibbs energy, g, for a system of fixed composition was defined in terms of other properties as (12.2) It was also shown that for a closed system at constant temperature and pressure, dg= v dp - s dT performing only mechanical work, to be in equilibrium, dG),,, = 0 (12.3) Equations (12.2) and (12.3) are based on the assumption that G = mg = mg( p, T), and this is quite acceptable for a single component system, or one of fixed composition. If the system has more than one component, and these components can react to form other
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Gibbs energy 219 compounds, e.g. if the system contained carbon monoxide, oxygen and carbon dioxide as defined in eqn (12.1), then it is necessary to define the Gibbs energy as G=mg=mg(p, T,mi) where m, is the mass of component i, and m=C mi. The significance of changes of composition on the value of the Gibbs energy of a mixture will now be investigated. If G = mg = mg( p, T, m,) (12.4) and if it is assumed that G is a continuous function with respect to p, and T and the masses of constituents comprising the mixture, then the change of G with changes in the independent variables is dG = ( $)T,dp + ( $)p,ciT + (”) dm, + ... (*) drn, (12.5a) aml p,T,m,,l amn p.T.m,,, where dm, . . . dm, are changes in mass of the various constituents. A similar equation can be written in terms of amount of substance n, and is For the initial part of the development of these equations the mass-based relationship (eqn (12.5a)) will be used because the arguments are slightly easier to understand. The term represents the ‘quantity’ of Gibbs energy introduced by the transfer of mass dm, of constituent 1 to the system. (This can be more readily understood by considering the change in internal energy, dU, when the term (aU/am,)p,T,m,*, dm, has a more readily appreciated significance.) The significance of the terms on the right of eqn (12.5a) is as follows:
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This note was uploaded on 03/09/2010 for the course MECHANICAL ME9802701 taught by Professor Prof.william during the Spring '10 term at Institut Teknologi Bandung.

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12 - 12 Chemical Equilibrium and Dissociation Up to now...

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