16.8 Free Energy and the Equilibrium Constant

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16.8 Free Energy and the Equilibrium Constant

• DG lt 0 spontaneous
• DG gt 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.

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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.

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Equilibrium Reaction Quotient

• 2H2(g) O2(g) ? 2H2O(g)
• Q PH2O2/PH22PO2
• 2H2(g) O2(g) ? 2H2O(l)
• Q 1/PH22PO2

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Group Quiz

• Write expressions for Q for the following three
  reactions.
• 6H2(g) P4(g) ? 4PH3(g) Q ?
• 2Na(s) Cl2(g) ? 2NaCl(s) Q ?
• PCl3 (aq) 3H2O(l) ? H3PO3 (aq) 3H(aq)
  3Cl-(aq) Q ?
• Q PPH34/PH26 PP4
• Q 1/PCl2
• Q H3PO3H3Cl-3/PCl3

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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.

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DGo and Equilibrium

• DG DGo RT ln Q
• no products Q 0
• no reactants Q
• standard state all P1, all X1, so Q 1 and
  ln Q ln 1 0, \ DG DGo
• Between the extremes, Q gt 0, but lt and DG
  changes as the reaction progresses (decreases as
  the reaction goes forward)

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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).

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DGo and Equilibrium

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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 gt 0 when K ltlt 1 (lies toward reactants)
• DGo lt 0 when K gtgt1 (lies toward products)
• DGo 0 when K 1 (equal amounts of reactants
  and products)

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DGo and Equilibrium

• The position of equilibrium depends on the value
  of DGo.

lt 0
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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