TFriOct10

TFriOct10 - 1 Thermodynamics Aconcaqua 2 Thermodynamic...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 03/17/2010 for the course CH 3530 taught by Professor Consors during the Fall '10 term at WPI.

Page1 / 65

TFriOct10 - 1 Thermodynamics Aconcaqua 2 Thermodynamic...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online