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Entropy and Free Energy Chapter 19

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Laws of Thermodynamics First Law – Energy is conserved in chemical processes neither created nor destroyed converted from one form into another Second Law – For any spontaneous process, the entropy of the universe increases the real criterion for spontaneity changes in randomness of the universe is +

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Some definitions… Free energy- the energy that is available to do work. Entropy- a measure of the disorder of a system. Enthalpy-at constant pressure, it is the heat evolved or absorbed in the reaction. Spontaneous Reaction Non-spontaneous Reaction Law of Disorder-processes move in the direction of maximum disorder or randomness

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Entropy “Rules” (see p 729 for examples) 1. Entropy of a gas is greater than that of a liquid or a solid. 2. Entropy increases when a substance is divided into parts. 3. Entropy tends to increase in chemical reactions in which the total number of product molecules is greater than the total number of reactant molecules. 4. Entropy tends to increase when temperature increases.

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Reaction Spontaneity The size and direction of heat (enthalpy) changes and entropy changes together determine whether a reaction is spontaneous.

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How Δ H and Δ S Affect Reaction Spontaneity Δ H Δ S Spontaneous? Decreases (exothermic) Increases (more disorder in products than in reactants) Yes Increases (endothermic) Increases ΔS > ΔH Decreases (exothermic) Decreases (less disorder in products than in reactants) ΔH > ΔS Increases (endothermic) DecreasesNo

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Some background on the standard conditions for entropy… Units for S: J/K Usually given as J/K x mol because we are interested in a specific substance. S° signifies entropy at standard conditions (101.3 kPa and 25°C). Theoretical entropy of a perfect crystal at 0 K is zero.

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Entropy Calculations Standard Entropy change ( Δ S°) can be calculated using: Δ S° (reaction) = Δ S° (products) - Δ S° (reactants)

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Practice Problem: Calculate the standard entropy change ( Δ S°) that occurs when 1 mol H 2 O (g) at 25°C and 101.3 kPa condenses to 1 mol H 2 O (l) at the same temperature. H 2 O (g) S° = 188.7 J/K x mol H 2 O (l) S° = 69.94 J/K x mol Δ S°=69.94 – 188.7 = -118.8 J/K x mol The negative sign indicates that entropy decreases.

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Free Energy Calculations Josiah Gibbs formulated the Gibbs free Energy change ( Δ G) equation. It is the maximum amount of energy that can be coupled to another process to do useful work. The change in Gibbs free energy is related to the change in entropy ( Δ S) and the change in enthalpy ( Δ H) of the system by the following equation: Δ G = Δ H – T Δ S (T=temperature in Kelvin)

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ΔGΔGΔGΔG If –ΔG, reaction is spontaneous in forward direction If +ΔG, reaction is non-spontaneous in forward direction but spontaneous in reverse direction. Work must be supplied from surroundings to make it occur. If ΔG=0, reaction is at equilibrium All spontaneous processes release free energy. In a spontaneous reaction Δ G is negative because the system loses free energy.

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C 2 H 5 OH (l) + 3O 2(g) 2CO 2(g) + 3H 2 O (g) + 1235 kJ What is the sign of H? What is the sign of S? Plug signs into: ΔG = ΔH – TΔS Prediction??? spontaneous Qualitative Prediction of Spontaneity

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ΔG = ΔG° + RT ln Q( where R=8.314 J/mol K) At equilibrium ΔG=0 and Q=K, therefore: ΔG°=-RT ln K and K= e -ΔG°/RT (find these formulas on your AP cheat sheet) Turn to page 740 and try practice exercise 19.12 Free Energy and Keq

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G is the energy change by a system going from initial conditions to equilibrium G negative reaction proceeds right to equilibrium G positive reaction proceeds left to equilibrium G = 0 at equilibrium

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But… Infinite number of combinations of variables ◦conc, T, P, etc. Reference values based on standard conditions ◦gases at 1 atm ◦solids and liquids – most stable form at 1 atm and 298 K ◦solutions at 1 M

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Standard Enthalpy Tabulated H o f standard formation H o rxn H o rxn = n p H o f (products) - n r H o f (reactants)

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Standard Entropy Tabulated S o standard S o rxn S o rxn = n p S o (products) - n r S o (reactants) S of a pure crystal at 0 K = 0 Third Law of Thermodynamics

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Standard Free Energy one method Tabulated G o f G o rxn G o rxn = n p G o f (products) - n r G o f (reactants) formation

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Standard Free Energy another method G o rxn A reaction A G o rxn B G o rxn C G o rxn reaction B reaction C reaction of interest SUMSUM SUMSUM

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Standard Free Energy yet another method G o rxn H o rxn - T S o rxn =

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Standard Free Energy ALL THREE METHODS Standard states of all reactants and products 1 M ; 1 atm Equilibrium G o rxn

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Free Energy related to Standard Free Energy G rxn = G o rxn + RT lnQ

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