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Thermodynamics Chapter 19 Liquid benzene Production of quicklime Solid benzene ⇅ CaCO 3 (s) ⇌ CaO + CO 2
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Gibbs Energy For a constant-pressure & constant temperature process: G = H sys - T S sys Gibbs energy (G) G < 0 The reaction is spontaneous in the forward direction G > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction G = 0 The reaction is at equilibrium
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Fig 19.17 Analogy between Potential Energy and Free Energy
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Fig 19.18 Free Energy and Equilibrium
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aA + bB cC + dD G° rxn n G° (products) f = m G° (reactants) f - Standard free-energy of reaction ( G o rxn ) ≡ free-energy change for a reaction when it occurs under standard-state conditions. Standard free energy of formation ( G°) Free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f
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Fig 19.19 Energy Conversion What’s “Free” About Gibbs Energy? ΔG ≡ the theoretical maximum amount of work that can be done by the system on the surroundings at constant P and T ΔG = − w max
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What’s “free” about the Gibbs energy? “Free” does not imply that the energy has no cost “Free” does not imply that the energy has no cost For a constant-temperature process, “free energy” For a constant-temperature process, “free energy” is the amount available to do work e.g., Human metabolism converts glucose to CO 2 and H 2 O with a ΔG° = -2880 kJ/mol This energy represents approx. 688 Cal or about two Snickers bars worth...
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Sample Exercise 19.9 Determining the Effect of Temperature on Spontaneity The Haber process for the production of ammonia involves the equilibrium Assume that ΔH° and ΔS° for this reaction do not change with temperature. (a)Predict the direction in which ΔG° for this reaction changes with increasing temperature. (b) Calculate the values ΔG° of for the reaction at 25 °C and 500 °C.
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(a)The temperature dependence of ΔG° comes from the entropy term. We expect ΔS° for this reaction to be negative because the number of molecules of gas is smaller in the products. Because ΔS° is negative, the term –T ΔS° is positive and grows larger with increasing temperature. As a result, ΔG° becomes less negative (or more positive) with increasing temperature. Thus, the driving force for the production of NH 3 becomes smaller with increasing temperature. G = H sys - T S sys
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Sample Exercise 19.9 Determining the Effect of Temperature on Spontaneity The Haber process for the production of ammonia involves the equilibrium Assume that ΔH° and ΔS° for this reaction do not change with temperature. (a)Predict the direction in which ΔG° for this reaction changes with increasing temperature. (b) Calculate the values ΔG° of for the reaction at 25 °C and 500 °C.
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G o = H sys - T S sys The reaction is nonspontaneous at 500 o C The reaction is spontaneous at 25 o C
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Gibbs Free Energy and Chemical Equilibrium We need to distinguish between ΔG and ΔG° During the course of a chemical reaction, not all products and reactants will be in their standard states In this case, we use ΔG When the system reaches equilibrium, the sign of ΔG° tells us whether products or reactants are favored What is the relationship between ΔG and ΔG°?
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Gibbs Free Energy and Chemical Equilibrium ΔG = ΔG° + RT lnQ R ≡ gas constant (8.314 J/Kmol) T ≡ absolute temperature (K) Q ≡ reaction quotient = [products] o / [reactants] o At Equilibrium: ΔG = 0 Q = K 0 = ΔG° + RT lnK ΔG° = − RT lnK When not all products and reactants are in their standard states:
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G° = - RT lnK Table 19.5 or
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Calculate ΔG° for the following process at 25 °C: BaF 2 (s) ⇌ Ba 2+ (aq) + 2 F − (aq); K sp = 1.7 x 10 -6 Example ΔG = 0 for any equilibrium, so: ΔG° = − RT ln K sp Equilibrium lies to the left ΔG° = − (8.314 J/mol∙K) (298 K) ln (1.7 x 10 -6 ) ΔG° = + 32.9 kJ/mol ΔG° ≈ + 33 kJ/mol
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Thermodynamics in living systems Many biochemical reactions have a positive ΔG o In living systems, these reactions are coupled to a process with a negative ΔG o (coupled reactions) The favorable rxn drives the unfavorable rxn
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C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) Metabolism of glucose in humans ΔG° = -2880 kJ/mol Does not occur in a single step as it would in simple combustion Enzymes break glucose down step-wise Free energy released used to synthesize ATP from ADP:
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Fig 19.20 Free Energy and Cell Metabolism ADP + H 3 PO 4 → ATP + H 2 O ΔG° = +31 kJ/mol (Free energy stored)
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