Nils Walter: Chem 260Principles of chemical equilibriumAtkins, Chapter 7At constant T and p a reaction mixture tends to adjust its composition until its Gibbs energy is at a minimumdirection of reactionNils Walter: Chem 260Describing equilibrium quantitatively: The reaction Gibbs energyExample 1Glucose-6-phosphateFructose-6-phosphateG6P(aq) →→→→F6P(aq); change by ∆∆∆∆n⇒⇒⇒⇒∆∆∆∆G = µµµµF6Px ∆∆∆∆n -µµµµG6Px ∆∆∆∆n GnGrPGPF∆=−=∆∆66µµ⇒⇒⇒⇒Example 2N2(g) + 3 H2(g) →→→→2 NH3(g)change by ∆∆∆∆n⇒⇒⇒⇒∆∆∆∆G = µµµµNH3x 2∆∆∆∆n -µµµµN2x ∆∆∆∆n -µµµµH2x 3∆∆∆∆n GnGrHNNH∆=+−=∆∆)3(2223µµµgeneral: aA + bB→→→→cC + dD ⇒⇒⇒⇒)()(BADCrbadcGµµµµ+−+=∆Nils Walter: Chem 260What is the reaction Gibbs energy?)()(BADCrbadcGµµµµ+−+=∆slopeMore products formedMore reagents formedequilibriumNils Walter: Chem 260Variation of ∆∆∆∆rG with compositionJJJaRTln+=µµOComposition dependence of chemical potential:O}lnlnlnln{)}(){()}ln()ln({)}ln()ln({BADCBADCBBAADDCCrabaaadacRTbadcaRTbaRTaaRTdaRTcG−−+++−+=+++−+++=∆µµµµµµµµOO O O OO O⇒⇒⇒⇒⇒⇒⇒⇒ObBaAdDcCrraaaaRTGG××+∆=∆lnOGr∆Standard reaction Gibbs energy (standard state of pure materials)reaction quotient Q: products/reactants⇒⇒⇒⇒QRTGGrrln+∆=∆ONils Walter: Chem 260∆∆∆∆rG at and far from equilibrium⇒⇒⇒⇒OKRTGGrrln0+∆==∆@ equilibrium: Q →→→→K ⇒⇒⇒⇒mequilibriubBaAdDcCaaaaK××=⇒⇒⇒⇒OKRTGrln−=∆∆∆∆∆rG = ∆∆∆∆rH - T∆∆∆∆rS O OONils Walter: Chem 260∆∆∆∆rG can be calculated∆∆∆∆rG = ΣνΣνΣνΣνGm (products) -ΣνΣνΣνΣνGm (reactants)= ΣνΣνΣνΣν ∆∆∆∆fG (products) -ΣνΣνΣνΣν ∆∆∆∆fG (reactants)= ∆∆∆∆rH - T ∆∆∆∆rS1 M; 1 bar}endergonic}exergonictabulatedElements: ∆∆∆∆fG = 0 kJ
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