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Unformatted text preview: 1 Thermodynamics Aconcaqua 2 Thermodynamic Equilibrium Constant The expression for the molar free energy was written: for any number of moles this becomes: At constant temperature and pressure this can be written in terms of chemical potential, i.e. 2 ln P RT G G m m + = 2 ln P nRT G G + = TP n G ∂ ∂ = μ 2 ln P RT + = μ μ 3 … in terms of chemical potential Therefore, for our universal reaction: aA + bB cC + dD the Gibbs energy of A is given by: where μ A is the standard chemical potential of A which is the same as the Gibbs energy of 1 mole of A at a pressure of 1 bar. A A A A P aRT a a G ln + = = μ μ 4 Chemical Potential for all the Reactants and Products A A A A P aRT a a G ln + = = μ μ B B B B P bRT b b G ln + = = μ μ C C C C P cRT c c G ln + = = μ μ D D D D P dRT d d G ln + = = μ μ 5 Free Energy Change The change in Gibbs energy when a moles of A at a pressure of P A , react with b moles of B at a pressure of P B to give c moles of C at a pressure of P C and d moles of D at a pressure of P D is given by: and since and ( 29 B A D C b a d c G μ μ μ μ + + = ∆ + + = ∆ b B a A d D c C B A D C P P P P RT b a d c G ln μ μ μ μ ( 29 y x B A B y A x ln ln ln = + ( 29 x A A x 1 ln ln = 6 Thermodynamic Equilibrium Constant The first four terms of this expression can be replaced with ∆ G° which is the standard Gibbs energy change. The standard state is 1 bar. If the pressures are the pressures at equilibrium the Gibbs energy change is 0, and therefore:  = ∆ b B a A d D c C P P P P RT G ln 7 Equilibrium The term inside the bracket is now given the symbol for the equilibrium constant: If the initial and final pressures are not at equilibrium then we can write: P K RT G ln = ∆ + = ∆ b B a A d D c C P P P P P RT K RT G ln ln 8 In terms of Concentration For an ideal gas: where c is the concentration, i.e. number of moles per unit volume. The pressure equilibrium can now be written: cRT V nRT P = = ( 29 b a c d b a d c P RT B A D C K + = ] [ ] [ ] [ ] [ ( 29 ( 29 ∑ = + ν RT RT b a c d 9 ( 29 ( 29 ∑ = + ν RT RT b a c d The term Σν is called the stoichiometric sum. If the equilibrium constant is written in terms of concentration: then K P and K C are related by the expression: = b a d c C B A D C K ] [ ] [ ] [ ] [ ( 29 ∑ = ν RT K K C P 10 Example Write the equilibrium constant for the reaction: 2SO 2 (gas) + O 2 (gas) 2SO 3 (gas) expressions similar to this can be written using mole fractions, pressures, fugacities and activities. The last two apply to ideal gases and non ideal behavior....
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This note was uploaded on 03/17/2010 for the course CH 3530 taught by Professor Consors during the Fall '10 term at WPI.
 Fall '10
 CONSORS
 Equilibrium, Mole, Dynamic Equilibrium

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