110c-lecture19 - Chapter 26: Chemical Equilibrium (pp...

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Chapter 26: Chemical Equilibrium (pp 1049-1063) Problems: 2, 3, 6, 7, 8, 12, 14, 19, 24, 61, 63 Reactants Products n A = n A0 - ν A ξ n B = n B0 + ν B dn A = - ν A d dn B = + ν B d Reactants consumed (-) Products formed (+) General gas phase reaction: () () g B g A B A ν Extent of reaction ( ) varies from 0 to 1. = 0 at beginning (all reactants) = 1 all reactants converted to products Monitor reaction as j j j n n ± = 0 (+ for products and – for reactants) What is the Gibbs free energy of gas phase reaction at constant T and P? () ... , , , 2 1 n n P T G G = + + = j j j i n P T j i n T i n P dn n G dP P G dT T G dG , , , , B P T B A P T A dn n G dn n G VdP SdT dG , , + + + = At const T,P : A A B B dn dn dG µ + = dG = B B d A A d A A B B P T G δξ δ = ,
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The Extent of Reaction ( ξ ) A B ξ A B P T G G µ δξ δ = = , 01 A A A x RT ln 0 + = B B B x RT ln 0 + = x B = 1- x A = + ξ Initial: 1 0 Final: 1- ξ + ξ ξ 9 ] [ ] [ = EQ EQ A B 1 ] [ ] [ = EQ EQ A B 1 . 0 ] [ ] [ = EQ EQ A B ν A A ν B B 5 . 0 5 . 0 ) )( 1 ( 1 ) )( 1 ( 0 = + 1 . 0 9 . 0 ) )( 1 ( 1 ) )( 1 ( 0 = + 9 . 0 1 . 0 ) )( 1 ( 1 ) )( 1 ( 0 = + Initial: 1 0 Final: 1- ν A ξ + ν B ξ ν A =1 ν B =1 ξ =fraction of A to B = + = 1 1 1 A x
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Free Energy Change ( r G) vs. Extent of Reaction ( ξ ) () () ( ) ( ) g Z g Y g B g A Z Y B A ν + = + B B A A Z Z Y Y dn dn dn dn dG µ + + + = Initial: n A0 n B0 0 0 Final: n A0 - ν A ξ n B0 - ν B ξ + ν Y ξ + ν Z ξ ( ) ξ d dG B B A A Z Z Y Y + = dn j = - ν A d ξ - ν B d ξ + ν Y d ξ + ν Z d ξ For a chemical reaction, d dn j j ± = (+ sign for products and – sign for reactants). () d dn dG B B A A Z Z Y Y j j j + = = at const T,P. d dG B B A A Z Z Y Y final initial + = 1 0 B B A A Z Z Y Y P T r G G ∂ξ + = = , () () bar P RT P T P T j j j 1 ln , , 0 + = For gas phase reaction, monitor extent of reaction ( ) by measuring partial pressures. What is r G in terms of partial pressure of products and reactants (P A , P B , …)?
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r G vs. Partial Pressure of Reactants and Products () () () ( ) g Z g Y g B g A Z Y B A ν + = + B B A A Z Z Y Y G µ + = For gas phase reaction, expand each chemical potential in terms of partial pressure: () () 0 0 ln , , P P RT P T P T j j j + = the 0 refers to a standard pressure of 1 bar (P 0 =1bar) + + + + = 0 0 0 0 0 0 0 0 ln ln ln ln P P RT P P RT P P RT P P RT G B B B B A A A A Z Z Z Z Y Y Y Y r () + + + = 0 0 0 0 0 0 0 0 ln ln ln ln P P P P P P P P RT G B B A A Z Z Y Y B B A A Z Z Y Y r ( ) + = B A Z Y P P P P P P P P RT G G B A Z Y r r 0 0 0 0 0 ln rxn r r Q RT G G ln 0 + = Q is reaction quotient (not a partition function). B B A A Z Z Y Y rxn P P P P Q = where each 1 0 = P bar. ( ) 0 0 0 0 0 B B A A Z Z Y Y r G + = rxn r Q RT G ln 0 0 + = 0 = G r (At equil) where P 0 = 1 bar ( ) ( ) B B A A Z Z y Y P P P P P P P P Q 0 0 0 0 = P EQ B A Z Y r K RT P P P P G B A Z Y ln 0 = =
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r Gº: Final Equilibrium vs Initial Standard State () () () ( ) g Z g Y g B g A Z Y B A ν + = + B B A A Z Z Y
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This note was uploaded on 06/22/2010 for the course CHEM 21360 taught by Professor Ame during the Spring '09 term at East Los Angeles College.

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110c-lecture19 - Chapter 26: Chemical Equilibrium (pp...

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