AP Chemistry

Unit 9.2

ABSOLUTE ENTROPY AND ENTROPY CHANGE

Unit 9.2

Enduring Understanding:

• Some chemical or physical processes cannot occur without intervention

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Learning Objective:

• Calculate the entropy change for a chemical or physical process based on the absolute entropies of the species involved in the process

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Calculating Entropy

• Entropy can be described both quantitatively and qualitatively
• In 9.1 we described it qualitatively
• Now, we’ll ruin it with math
• Second Law of Thermodynamics: the entropy of the universe increases for a spontaneous process and remains unchanged for a system at equilibrium

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Calculating Entropy

• For a spontaneous process:
• ΔS°_universe = ΔS°_system + ΔS°_surroundings > 0

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• For a process at equilibrium
• ΔS°_universe = ΔS°_system + ΔS°_surroundings = 0

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Entropy of the System

• Entropy of the system: the entropy of of the reaction we’re studying
• ΔS°_system is the same as ΔS°_rxn
• This can be calculated with the following equation:

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ΔS°_rxn = ΣΔS°_products - ΣΔS°_reactants

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Entropy of the System

• Let’s apply this to a sample reaction

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ΔS°_rxn = ΣΔS°_products - ΣΔS°_reactants

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aA + bB → cC + dD

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Entropy of the System

• Let’s apply this to a sample reaction

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ΔS°_rxn = ΣΔS°_products - ΣΔS°_reactants

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aA + bB → cC + dD

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ΔS°_rxn = [(cΔS°_C)+(dΔS°_D)] - [(aΔS°_A)+(bΔS°_B)]

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Entropy of the System

• Let’s apply this to a sample reaction

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ΔS°_rxn = ΣΔS°_products - ΣΔS°_reactants

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aA + bB → cC + dD

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ΔS°_rxn = [(cΔS°_C)+(dΔS°_D)] - [(aΔS°_A)+(bΔS°_B)]

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• ΔS°_rxn = the sum of the standard entropies of the reactants multiplied by their coefficients subtracted from the standard entropies of the products multiplied by their coefficients

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Entropy of the System

• Let’s apply this to a sample reaction

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ΔS°_rxn = ΣΔS°_products - ΣΔS°_reactants

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aA + bB → cC + dD

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ΔS°_rxn = [(cΔS°_C)+(dΔS°_D)] - [(aΔS°_A)+(bΔS°_B)]

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• ΔS°_rxn = the sum of the standard entropies of the reactants multiplied by their coefficients subtracted from the standard entropies of the products multiplied by their coefficients
• (Standard enthalpy values can be found HERE)

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Practice: I Do

1. Use the thermodynamic data to calculate ΔS°_rxn:

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4NH₃ (g) + 7O₂ (g) → 4NO₂ (g) + 6H₂O (g)

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Practice: I Do

• Use the thermodynamic data to calculate ΔS°_rxn:

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4NH₃ (g) + 7O₂ (g) → 4NO₂ (g) + 6H₂O (g)

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ΔS°_rxn = ΣΔS°_products - ΔS°_reactants

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NO₂ : 4 moles x (240.1 J / mol・K) = 960.4 J/K

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H₂O: 6 moles x (188.8 J / mol・K) = 1132.8 J/K

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NH₃ : 4 moles x (192.8 J / mol・K) = 771.2 J/K

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O₂: 7 moles x (205.3 J / mol・K) = 1437.1 J/K

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Practice: I Do

• Use the thermodynamic data to calculate ΔS°_rxn:

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4NH₃ (g) + 7O₂ (g) → 4NO₂ (g) + 6H₂O (g)

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ΔS°_rxn = ΣΔS°_products - ΔS°_reactants

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NO₂ : 960.4 J/K NH₃: 771.2 J/K

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H₂O: 1132.8 J/K O₂: 1437.1 J/K

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ΔS°_rxn = [(960.4 + 1132.8) - (771.2 + 1437.1)] = -115.1 J/K

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