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16.8 Free Energy and the Equilibrium Constant

16.8 Free Energy and the Equilibrium Constant. D G < 0 spontaneous D G > 0 not spontaneous, but reverse reaction is spontaneous D G = 0 not spontaneous in either direction This is a state of equilibrium between reactants and products; they coexist in a stable condition.

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16.8 Free Energy and the Equilibrium Constant

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  1. 16.8 Free Energy and the Equilibrium Constant • DG < 0 spontaneous • DG > 0 not spontaneous, but reverse reaction is spontaneous • DG = 0 not spontaneous in either direction • This is a state of equilibrium between reactants and products; they coexist in a stable condition. • Many situations are not in the standard state, so we need some way to relate DG to DGo and the existing conditions.

  2. Equilibrium • We define the reaction quotient to describe the extent of reaction. • aA + bB ⇌ cC + dD • Q = PCc PDd PAa PBb • Reminder: Only the pressure of gases (PA) or the concentration ([A]) of dissolved substances appear in the reaction quotient; pure solids and pure liquids are omitted.

  3. Equilibrium: Reaction Quotient • 2H2(g) + O2(g) ⇌ 2H2O(g) • Q = PH2O2/PH22PO2 • 2H2(g) + O2(g) ⇌ 2H2O(l) • Q = 1/PH22PO2

  4. DGo and Equilibrium • Q can be used to relate DG to DGo DG = DGo + RT ln Q R = 8.314 J/mol K T = absolute temperature (K) ln is natural logarithm; find this button on your calculator because it will be useful throughout the semester.

  5. DGo and Equilibrium DG = DGo + RT ln Q • no products: Q = 0 • no reactants: Q = ¥ • standard state: all P=1, all [X]=1, so Q = 1 and ln Q = ln 1 = 0, \ DG = DGo • Between the extremes, Q > 0, but < ¥ and DG changes as the reaction progresses (decreases as the reaction goes forward)

  6. DGo and Equilibrium • CO(g) + H2O(g) ⇌ CO2 (g) + H2(g) • Q = PCO2PH2/PCOPH2O • Initially, Q = 0, but then it increases • As the reaction progresses, DG decreases until a minimum value of G is reached; at this point, DG = 0 and net reaction ceases (though the forward and reverse reactions still occur, but they offset one another).

  7. DGo and Equilibrium

  8. DGo and Equilibrium • When DG = 0 = DGo + RT ln Q, we call this a state of equilibrium and Q = Qequil = K, the equilibrium constant. • Thus, DGo = - RT ln K or K = e-DGo/RT DGo > 0 when K << 1 (lies toward reactants) DGo < 0 when K >>1 (lies toward products) DGo = 0 when K = 1 (equal amounts of reactants and products)

  9. DGo and Equilibrium • The position of equilibrium depends on the value of DGo. < 0

  10. Group Work DGo = - RT ln K • Calculate K for the following reaction at 25oC. H2(g) + Br2(g) ⇌ 2HBr(g) DGo = - 53.2 kJ/mol • -53,200 J/mol = - 8.314 J/mol K x 298 K x ln K • ln K = 21.47 • K = 2.12 x 109 (K has no units) • When K is this large, the reaction proceeds far toward products to reach equilibrium. • PH2 = PBr2 = 4.72 x 10-10 atm when PHBr = 1 atm

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