11.18.2011- Exam 3 start

11.18.2011- Exam 3 start - Chem 260, Lecture 31 Nov 18,...

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Unformatted text preview: Chem 260, Lecture 31 Nov 18, 2011 Today in Chemistry 260 Chemistry 260 •  The equilibrium condition •  Thermodynamics of the equilibrium state Lecture 31 Nov. 18, 2011 Next Week in Chemistry 260 •  Reading: Mon: 7.5-7.7 (A&D), 14.5 (Oxtoby); Wed: 7.8-7.10 (A&D), 14.6-14.7 (Oxtoby) •  Chemical reactions at equilibrium, predicting changes in equilibrium 1 The Equilibrium Condition 2 Equilibrium No net change in components •  Four Fundamental Characteristics of Equilibrium States: Number of molecules in each phase remains the same, though molecules are free to move between phases 1.They display no macroscopic evidence of change 2. They are reached through spontaneous processes 3. They show a dynamic balance of forward and reverse processes 4. They are the same regardless of direction of approach •  Can be used to distinguish a true equilibrium from a reaction so slow that changes in concentration are immeasurably small •  Different from steady states where there is a competition between processes that supply species to and processes that remove species from the system. 5 Equilibrium A+BAB Net quantities of products and reactant species remain the same even as they constantly undergo reactions A: 4 B: 4 AB: 10 A: 4 B: 4 AB: 10 6 The Chemical Potential At constant T and P a reaction mixture tends to adjust its composition until its Gibbs energy is at a minimum direction of reaction The Fundamental equation of chemical thermodynamics dG = VdP ! SdT + µ A dnA + µ B dnB " 0 Constant T and P dG = µ A dnA + µ B dnB ! 0 A change in composition will be spontaneous if it decreases G Chemical thermodynamics drives a reaction towards equilibrium 7 10 1 Chem 260, Lecture 31 Nov 18, 2011 At equilibrium: Gibbs Energy Chemical Equilibrium Consider a flask with hexatriene vapor Some percentage will be cZt How much? Why? cZt The Chemical Potential ΔGr = 0 Dalton's law: P = PA + PB ; Pj = tZt nj nA + nB ideal Constant T dGA = VdPA − SdT ⎯⎯⎯⎯ VdPA ≈ → gas Pure cZt Pure tZt cZt ! tZt P Each component obeys the ideal gas equation P = xj × P nA RT dPA PA P ' A P dPdPA ⎡P ⎤ ⇒G =An=RTRT ∫ A ⇒ ⇒AGP( PA− GA APP ° ) + nA RTln ⎡⎢ AA⎤⎥ dG A nA ∫ ) − G ( o = nA RT ln o° ' G (A A ) ⎢⎣P ⎥⎦ PA P⎦ ° P ⎣ Po P A () ⎡ PA ⎤ °1 ⇒GAA(( PA ) = GA ( P °o) + nAA RTln ⎢⎡ PA⎥⎤ ; PP= =.0 bar (standard pressure) G A) 1.0bar (standard + n RT ln ⎢ ° o ⎥ pressure) AP ⎣⎣P ⎦⎦ P G ( P ) G ( P ° ) nA RT ⎡ PA ⎤ ! A ( ) = GA ( P ⇒ µµ( PPA )= GA ( PA )) = A A = ! + ! P $ ln A A A µA nA = µ A + A T ln #nAA & ⎢ P ° ⎥ nR ⎣⎦ ! Chemical "P % 13 potential ⎡ PA ⎤ ⎡ PA ⎤ ° ° ° = µ A ( P ) + RT ln ⎢ ° ⎥ = µ A + RT ln ⎢ ° ⎥ ; µ A = µ A ( P ° ) ⎣P ⎦ ⎣P ⎦ () !G = µcZt !ncZt + µtZt !ntZt !G = µcZt !n " µtZt !n ΔGr = Recall the Gibbs energy of a gas (relate to standard conditions) ΔG = µcZt − µtZt Δn 12 ⎡P ⎤ ° ⇒ µ A ( PA ) = µ A + RT ln ⎢ A ⎥ ° ⎣P ⎦ Equilibrium Thermodynamics 2 NO2(g) An alternative way to the same result: Lets consider a slightly more complicated example: Equilibrium Thermodynamics µ N2O4 = µ ° N2O4 + RT ln N2O4(g) 1 N2O4(g) µ NO2 = µ ° NO2 + RT ln rxn 2 NO2(g) From Hess s Law ΔGrxn = ΔG1 + ΔG2 + ΔG3 PNO2 P° PN2O4 Referenced to 1 atm. P° ΔGr = 1µ N2O4 − 2 µ NO2 PNO2 ⎞ ⎛ ΔGr = µ ° N2O4 + RT ln − 2 ⎜ µ ° NO2 + RT ln ⎟ P° P° ⎠ ⎝ PN2O4 PNO2 ΔGr = µ °N2O4 − 2µ °NO2 + RT ln − 2RT ln P° P° 14 ΔGr ° PN2O4 2 NO2(g) N2O4(g) PN2O4 PNO2 ΔGr = µ ° N2O4 − 2µ ° NO2 + RT ln − 2 RT ln P° P° PN O PNO2 ΔGr = ΔGr ° + RT ln 2 4 − 2 RT ln P° P° Equilibrium Thermodynamics PNO2 ⎞ ⎛ PN O ΔGr = ΔGr ° + RT ⎜ ln 2 4 − 2ln ⎟ P° P° ⎠ ⎝ −2 Q ⎛ PN O ⎛ PNO2 ⎞ ⎞ reaction quotient ΔGr = ΔGr ° + RT ⎜ ln 2 4 + ln ⎜ ⎟⎟ ⎜ P° ⎝ P° ⎠ ⎟ ⎝ ⎠ ⎡⎛ PN O ⎞⎛ PNO ⎞−2 ⎤ 2 ΔGr = ΔGr ° + RT ln ⎢⎜ 2 4 ⎟⎜ ⎥ ⎢⎝ P° ⎠⎝ P° ⎠ ⎥ ⎡ P ⎤ ⎣ ⎦ ⎛ N 2O4 ⎞ ⎢⎜ ⎥ ⎟ P° ⎠ ⎥ ΔGr = ΔGr ° + RT ln ⎢⎝ 2 ⎢ ⎛ PNO2 ⎞ ⎥ ⎢ ⎜ ⎟⎥ ⎢ ⎝ P° ⎠ ⎥ ⎣ ⎦ 16 3 2 NO2(g) @ Po N2O4(g) @ Po 2 ⎛ ⎛ P⎞ Po ΔG1 = 2 ⎜ RT ln 2 ⎟ = 2 ⎜ RT ln ⎜ P⎠ PNO2 1 ⎝ ⎝ ⎞ PNO ⎞ ⎛ ⎟ = −2 ⎜ RT ln o2 ⎟ ⎟ P⎠ ⎝ ⎠ o ΔG2 = ΔGrxn = µ °N2O4 − 2µ °NO2 PN O P ΔG3 = RT ln 2 = RT ln 2o 4 P P 1 ΔGrxn = ΔG1 + ΔG2 + ΔG3 = −2RT ln PNO2 P° + µ ° N2O4 − 2µ ° NO2 + RT ln PN2O4 P° 15 Equilibrium Thermodynamics 2 NO2(g) ⎡⎛ PN O ⎢⎜ 2 4 P° ΔGr = ΔGr ° + RT ln ⎢⎝ ⎢ ⎢ ⎢ ⎣ N2O4(g) ⎞ ⎟ ⎠ ⎤ ⎥ ⎥ 2 ⎛ PNO2 ⎞ ⎥ ⎜ ⎟⎥ ⎝ P° ⎠ ⎥ ⎦ ΔGr = ΔGr ° + RT ln Q ΔGr = 0 At equilibrium, 0 = ΔGr ° + RT ln Qeq Key equation ΔGr ° = − RT ln Qeq ΔGr ° = − RT ln K p Kp, Equilibrium constant with the concentration of gases expressed in 17 partial pressures 2 Chem 260, Lecture 31 Nov 18, 2011 The Law of Mass Action: Reminder of the bottom line! Chemical equilibrium is a dynamical condition of mass transformation Lets consider a generic example: a A(g) + b B(g) c C(g) + d D(g) (P ) (P ) (P ) (P ) ΔGr ° = − RT ln K p c At equilibrium: KP = C A Gas phase reactions: d •  •  •  •  D a b B Chemical equilibrium Law of mass action Equilibrium calculations Predicting changes in equilibria A ratio of equilibrium partial pressures will yield a KP Aqueous reactions: A ratio of equilibrium concentrations will yield a KC Mixed phase reactions: Solids and liquids are taken as the standard state (1) K, KP, and KC Equilibrium Thermodynamics, Summary (P ) (P ) (P ) (P ) c KP = C d KC = D a A b [C]c [ D]d [A]a [ B]b a A(g) + b B(g) B Lets consider AGAIN a generic example c C(g) + d D(g) At equilibrium: ref. state of 1M ref. state of 1 atm, 760 torr, etc. ΔGr ° = − RT ln K P K c ⎡ −ΔGr ° ⎤ ⇒ K P = exp ⎢ ⎥ ⎣ RT ⎦ d eq ⎛ PCeq ⎞ ⎛ PD ⎞ ⎜ Po ⎟ ⎜ Po ⎟ ⎠ = exp ⎡ −ΔGr ° ⎤ ⎝ ⎠⎝ KP = a b ⎢ RT ⎥ eq eq ⎣ ⎦ ⎛ PA ⎞ ⎛ PB ⎞ o⎟ ⎜ o⎟ ⎜ P⎠⎝ P⎠ ⎝ dimensionless 23 !S = -46.7 kJ/mol Equilibrium Thermodynamics ALL of these describe equilibrium. ΔGro is NOT the same thing as ΔG. a A(g) + b B(g) c d c C(g) + d D(g) eq ⎛ PCeq ⎞ ⎛ PD ⎞ ⎜ ⎟ Po ⎠ ⎜ Po ⎟ ⎝ ⎠ = exp ⎡ −ΔGr ° ⎤ KP = ⎝ a b ⎢ RT ⎥ eq ⎣ ⎦ ⎛ PA ⎞ ⎛ PBeq ⎞ ⎜ Po ⎟ ⎜ Po ⎟ ⎝ ⎠⎝ ⎠ if ΔGro << 0 if ΔGro >> 0 K << 1 The forward reaction IS NOT thermodynamically favorable What can be understood from the value of K? if ΔGro = 0 K =1 K >> 1 The forward reaction IS thermodynamically favorable 24 3 ...
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This note was uploaded on 01/19/2012 for the course CHEM 260 taught by Professor Staff during the Fall '08 term at University of Michigan.

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