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# 6 - Chemical equilibrium(closed system The number of moles...

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1 Chemical equilibrium (closed system): The number of moles of each component remains constant. Goal: To find the equilibrium composition of the system. Assumption: Mechanical and thermal equilibrium, with uniform pressure and temperature throughout the system. , surr sur ss r sy sy TP P P T T == = = rate of establishing mechanical and therm Re al action r equilib ates rium ± The composition changes on a relatively slow time scale, such that mechanical and thermal equilibria are maintained as the chemical reaction proceeds.

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2 Questions regarding chemical reactions that thermodynamics CAN answer: • What is the composition of a system at chemical equilibrium? • How does the equilibrium composition depend on other parameters, such as temperature and pressure? •How fast will the chemical reaction be, and how will the reaction rate depend on external parameters such as pressure and temperature? (this is the domain of kinetics, molecular dynamics and non-equilibrium statistical mechanics). What BASIC PRINCIPLE dictates the composition at chemical equilibrium? The second law of thermodynamics! At constant temperature and pressure, the equilibrium composition of the reaction mixture is the one that minimizes the Gibbs free energy. Questions regarding chemical reactions that thermodynamics CANNOT answer: Reactive mixtures of ideal gases
3 Gas phase reaction with the reactants & products described by the ideal gas law Consider the chemical reaction: The Gibbs energy change due to converting moles of into moles of (at constant and ): Conse r ( vation of matter dictate ) ) s: ( AB BA A B A B dn A Ag d dn B PT d G Bg dn dd n nn d µ ξ =+ =− = U () , , At equilibrium: 0 0 0 For a mixture of ideal gases: ;. H e n c ln ln n : n 0 l l e r AA eq A A eq eq A BB eq B B eq eq B TP G dG d G dG G R RT P P P PP P T RT µµ ° °° ∂= =⇔∂ ∂ =⇔ − = −= + = ⎡⎤ = ⎣⎦ + ±²³²´ [] ( is the equilibrium constant in terms of partial pressur ln ln =0 , . exp es) eq e r q B eq B rP P Pr A eq A G GK K K P P RT T R P R P T G ° ° ° + ⇒== A direct relationship between the chemical equilibrium constant and the standard reaction Gibbs energy! ln ln (1 )ln(1 ) ln , where ; 1 11 ln(1 ) (1 ) ln ) ln ) ln ln 1 ln ln mix A A B B mix B A GR T x x x xR T xx d T d x RT RT RT x xP P RT RT P ξξ ∆= + = + == −− + + ⎢⎥ ⎛⎞ = = ⎜⎟ ⎝⎠ ln 0 e B r eq A q P T P R G ° + = 1/2 eq eq mix A B d Gx x d ∆⇒ = = 0 1 0 1; 0 0; eq eq eq e r q r G G ° ° ∆> = <⇒ = The equilibrium constant results from a compromise between two opposing tendencies: (1) Maximizing the mixing of reactant and product. (2) Maximizing the amount of the component with the lower chemical potential.

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4 () ( ) , , Consider the chemical reaction: ;; ; 0 0 AA B TP T B AB CC DD CD eq eq A eq B P dG d aA g bB g dn dd d dG d G d cC g dD g dn dn dn c dn d cd dn dn a dn b ab a G b G ξξ ξ µµ µ =+ === = ⇒= = + + ×× + + + −× −− + + = U [] 0 ln ln 0 e ln l ln n l xp n r eq eq eq eq eq eq eq eq eq eq eq C G D rr P Pr P a
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6 - Chemical equilibrium(closed system The number of moles...

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