Chemical_equilibrium

Chemical_equilibrium - © M S Shell 2009 1/11 last modified Chemical equilibrium ChE210A A review of basic reaction concepts Previously we studied

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Unformatted text preview: © M. S. Shell 2009 1/11 last modified 11/30/2009 Chemical equilibrium ChE210A A review of basic reaction concepts Previously we studied the equilibrium behavior of non-reacting systems. Here, we examine equilibrium when there are reactions present, at both the macroscopic and microscopic levels. Recall from basic ideas in chemistry that a reversible reaction can be described by an equili- brium constant g G¡ . Consider for example the reaction, ¢ £ 2¤ ¥ ¦§ ¨© ª In earlier courses on chemistry, you may have seen the equilibrium constant related to the equilibrium concentrations in moles/molecules per volume of the species involved: g G¡ « ¬ª­ ¬¢­¬¤­ ® where the powers of the concentrations are determined by the stoichiometric coefficients. Notice that we can consider the case of irreversible reactions as just a special subset of reversi- ble ones, in which the equilibrium constant is very large. In this lecture, we will understand the origins of the equilibrium constant in terms of thermo- dynamic potentials and microscopic ensembles. Chemical equilibrium at the macroscopic level First, let’s understand a reacting system from the point of view of macroscopic thermodynamic potentials. We will take the specific reaction above as an example, and consider the behavior of a system at constant temperature and pressure. At constant ¯ and ° , the relevant thermo- dynamic potential is the Gibbs free energy and at equilibrium, it is at a minimum. Consider that we have an initial system of components ¢,¤, and ª . If reactions are not permit- ted, and we can independently control the respective amounts of the species, the Gibbs free energy of the system is given by ±²¯,°,³ ´ ,³ µ ,³ ¶ · © M. S. Shell 2009 2/11 last modified 11/30/2009 What happens now if we allow the reaction to proceed? In this case, the numbers of molecules of each species can change, subject to a certain conservation rule. That rule says that the changes in mole numbers are related by the stoichiometric coefficients: gG ¡ ¢ £gG ¤ gG ¥ ¢ £2gG ¤ These equations say that for every ¦ molecule we get due to the reaction, we have to lose a § one. Similarly, for every § molecule we lose, we also get two ¨ molecules. Here, there is one macroscopic degree of freedom that can vary due to the reaction. You could think of that as the number of § molecules that react. If we know how much § has reacted, we instantly know how much ¦ and ¨ have reacted by the considerations above. More generally, there is one reaction and hence one extent of reaction . If the reaction is allowed to proceed from some initial specified composition of the three components, at equilibrium the Gibbs free energy will be minimized. The change in © with the amount of the species, at constant ª and « is: g© ¢ ¬ g© gG ¡ ­ ®,¯,° ± ,° ² gG ¡ ³ ¬ g© gG ¥ ­ ®,¯,° ´ ,° ² gG ¥ ³ ¬ g© gG ¤ ­ ®,¯,° ´ ,° ± gG ¤ ¢ µ ¡ gG ¡ ³ µ ¥ gG ¥ ³ µ...
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This note was uploaded on 12/29/2011 for the course CHE 210a taught by Professor Staff during the Fall '08 term at UCSB.

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Chemical_equilibrium - © M S Shell 2009 1/11 last modified Chemical equilibrium ChE210A A review of basic reaction concepts Previously we studied

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