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Chapter 17 Spontaneity, Entropy, and Free Energy

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Chapter 17 Table of Contents Copyright © Cengage Learning. All rights reserved 2 17.1Spontaneous Processes and Entropy 17.2 Entropy and the Second Law of Thermodynamics 17.3 The Effect of Temperature on Spontaneity 17.4Free Energy 17.5Entropy Changes in Chemical Reactions 17.6Free Energy and Chemical Reactions 17.7The Dependence of Free Energy on Pressure 17.8Free Energy and Equilibrium 17.9Free Energy and Work

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 3 Thermodynamics vs. Kinetics Domain of Kinetics Rate of a reaction depends on the pathway from reactants to products. Thermodynamics tells us whether a reaction is spontaneous based only on the properties of reactants and products.

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 4 Spontaneous Processes and Entropy Thermodynamics lets us predict whether a process will occur but gives no information about the amount of time required for the process. A spontaneous process is one that occurs without outside intervention.

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 5 Concept Check Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant. a)What should happen to the gas when you open the valve?

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 6 Concept Check Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant. b)Calculate H, E, q, and w for the process you described above. All are equal to zero.

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 7 Concept Check Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant. c) Given your answer to part b, what is the driving force for the process? Entropy

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 8 The Expansion of An Ideal Gas Into an Evacuated Bulb

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 9 Entropy The driving force for a spontaneous process is an increase in the entropy of the universe. A measure of molecular randomness or disorder.

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 10 Entropy Thermodynamic function that describes the number of arrangements that are available to a system existing in a given state. Nature spontaneously proceeds toward the states that have the highest probabilities of existing.

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 11 The Microstates That Give a Particular Arrangement (State)

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 12 The Microstates That Give a Particular Arrangement (State)

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 13 Positional Entropy A gas expands into a vacuum because the expanded state has the highest positional probability of states available to the system. Therefore: S solid < S liquid << S gas

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Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 14 Concept Check Predict the sign of S for each of the following, and explain: a)The evaporation of alcohol b)The freezing of water c)Compressing an ideal gas at constant temperature d)Heating an ideal gas at constant pressure e)Dissolving NaCl in water + – – + +

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Section 17.2 Atomic MassesEntropy and the Second Law of Thermodynamics Return to TOC Copyright © Cengage Learning. All rights reserved 15 Second Law of Thermodynamics In any spontaneous process there is always an increase in the entropy of the universe. The entropy of the universe is increasing. The total energy of the universe is constant, but the entropy is increasing. S universe = ΔS system + ΔS surroundings

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 16 Concept Check For the process A(l) A(s), which direction involves an increase in energy randomness? Positional randomness? Explain your answer. As temperature increases/decreases (answer for both), which takes precedence? Why? At what temperature is there a balance between energy randomness and positional randomness?

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 17 Concept Check Describe the following as spontaneous/non-spontaneous/cannot tell, and explain. A reaction that is: a)Exothermic and becomes more positionally random Spontaneous b)Exothermic and becomes less positionally random Cannot tell a)Endothermic and becomes more positionally random Cannot tell a)Endothermic and becomes less positionally random Not spontaneous Explain how temperature affects your answers.

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 18 ΔS surr The sign of ΔS surr depends on the direction of the heat flow. The magnitude of ΔS surr depends on the temperature.

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 19 ΔS surr

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 20 ΔS surr

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 21 ΔS surr Heat flow (constant P) = change in enthalpy = ΔH

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Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 22 Interplay of S sys and S surr in Determining the Sign of S univ

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Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 23 Free Energy (G) A process (at constant T and P) is spontaneous in the direction in which the free energy decreases. Negative ΔG means positive ΔS univ.

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Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 24 Free Energy (G) ΔG = ΔH – TΔS (at constant T and P)

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Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 25 Concept Check A liquid is vaporized at its boiling point. Predict the signs of: w q H S S surr G Explain your answers. – + + + – 0

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Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 26 Exercise The value of H vaporization of substance X is 45.7 kJ/mol, and its normal boiling point is 72.5°C. Calculate S, S surr, and G for the vaporization of one mole of this substance at 72.5°C and 1 atm. S = 132 J/K·mol S surr = -132 J/K·mol G = 0 kJ/mol

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Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 27 Spontaneous Reactions

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Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 28 Effect of H and S on Spontaneity

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Section 17.5 Entropy Changes in Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 29 Concept Check Gas A 2 reacts with gas B 2 to form gas AB at constant temperature and pressure. The bond energy of AB is much greater than that of either reactant. Predict the signs of: H S surr S S univ Explain. – + 0 +

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Section 17.5 Entropy Changes in Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 30 Third Law of Thermodynamics The entropy of a perfect crystal at 0 K is zero. The entropy of a substance increases with temperature.

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Section 17.5 Entropy Changes in Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 31 Standard Entropy Values (S°) Represent the increase in entropy that occurs when a substance is heated from 0 K to 298 K at 1 atm pressure. ΔS° reaction = Σ n p S° products – Σ n r S° reactants

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Section 17.5 Entropy Changes in Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 32 Exercise Calculate S° for the following reaction: 2Na(s) + 2H 2 O(l) 2NaOH(aq) + H 2 (g) Given the following information: S° (J/K·mol) Na(s) 51 H 2 O(l) 70 NaOH(aq) 50 H 2 (g) 131 S°= –11 J/K

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Section 17.6 Free Energy and Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 33 Standard Free Energy Change (ΔG°) The change in free energy that will occur if the reactants in their standard states are converted to the products in their standard states. ΔG° = ΔH° – TΔS° ΔG° reaction = Σ n p G° products – Σ n r G° reactants

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Section 17.6 Free Energy and Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 34 Concept Check A stable diatomic molecule spontaneously forms from its atoms. Predict the signs of: H° S° G° Explain. – – –

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Section 17.6 Free Energy and Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 35 Concept Check Consider the following system at equilibrium at 25°C. PCl 3 (g) + Cl 2 (g) PCl 5 (g) G° = 92.50 kJ What will happen to the ratio of partial pressure of PCl 5 to partial pressure of PCl 3 if the temperature is raised? Explain. The ratio will decrease.

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Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 36 Free Energy and Pressure G = G° + RT ln(P) or ΔG = ΔG° + RT ln(Q)

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Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 37 Concept Check Sketch graphs of: 1.G vs. P 2.H vs. P 3.ln(K) vs. 1/T (for both endothermic and exothermic cases)

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Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 38 The Meaning of ΔG for a Chemical Reaction A system can achieve the lowest possible free energy by going to equilibrium, not by going to completion.

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Section 17.8 Free Energy and Equilibrium Return to TOC Copyright © Cengage Learning. All rights reserved 39 The equilibrium point occurs at the lowest value of free energy available to the reaction system. ΔG = 0 = ΔG° + RT ln(K) ΔG° = –RT ln(K)

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Section 17.8 Free Energy and Equilibrium Return to TOC Copyright © Cengage Learning. All rights reserved 40 Change in Free Energy to Reach Equilibrium

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Section 17.8 Free Energy and Equilibrium Return to TOC Copyright © Cengage Learning. All rights reserved 41 Qualitative Relationship Between the Change in Standard Free Energy and the Equilibrium Constant for a Given Reaction

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Section 17.9 Free Energy and Work Return to TOC Copyright © Cengage Learning. All rights reserved 42 Maximum possible useful work obtainable from a process at constant temperature and pressure is equal to the change in free energy. w max = ΔG

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Section 17.9 Free Energy and Work Return to TOC Copyright © Cengage Learning. All rights reserved 43 Achieving the maximum work available from a spontaneous process can occur only via a hypothetical pathway. Any real pathway wastes energy. All real processes are irreversible. First law: You cant win, you can only break even. Second law: You cant break even.

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