Chapter 17 Spontaneity, Entropy, and Free Energy

Chapter 17 Table of Contents Copyright © Cengage Learning. All rights reserved Spontaneous 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

Section 17.1 Spontaneous Processes and Entropy Return to TOC Why does a reaction occur in a particular direction? Kinetics –Gives info about amount of time required for the process. –Rate of a reaction depends on the pathway from reactants to products. Copyright © Cengage Learning. All rights reserved 3 Thermodynamics –Predicts whether a reaction is spontaneous based only on the properties of reactants and products.

Section 17.1 Spontaneous Processes and Entropy Return to TOC Spontaneity & Entropy spontaneous process - occurs without outside intervention –Spontaneous does NOT mean fast. –Ex: heat flows from hot object to cooler one, but not the reverse Copyright © Cengage Learning. All rights reserved 4

Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 5 Entropy, S - a measure of molecular randomness or disorder. The driving force for a spontaneous process is an increase in the entropy of the universe Order (lower entropy) to disorder (higher entropy) Thermodynamic function that describes the number of arrangements (positions and/or energy levels) available to a system in a given state. Associated with probability. Nature spontaneously proceeds toward states that have the highest probabilities of existing.

Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 6 The Expansion of An Ideal Gas Into an Evacuated Bulb Why do the gas molecules evenly spread throughout the container when the valve is open?? Why is it spontaneous?

Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 7 The Microstates That Give a Particular Arrangement (State) Consider a system with 4 gas molecules in a two- bulbed container. Microstate – a particular arrangement. How many states (arrangements) are possible? Which state is most likely to occur?

Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 8 Positional Entropy A gas expands into a vacuum because the expanded state has the highest positional probability (probability based upon configurations in space) of states available to the system. Changes of state: S solid < S liquid << S gas Formation of solutions: increase in entropy because of increased volume available for a given particle.

Section 17.1 Spontaneous Processes and Entropy Return to TOC Copyright © Cengage Learning. All rights reserved 9 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 + – – + +

Section 17.2 Atomic MassesEntropy and the Second Law of Thermodynamics Return to TOC Copyright © Cengage Learning. All rights reserved 10 Second Law of Thermodynamics spontaneous process -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

Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 11 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?

Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 12 ΔS surr The sign of ΔS surr depends on the direction of the heat flow. The magnitude of ΔS surr depends on the temperature. –directly proportional to quantity of heat transferred –Inversely proportional to temperature * Exothermic reactions increase the entropy of the surroundings Heat flow (constant P) = change in enthalpy (system) = ΔH

Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 13 ΔS surr

Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Example: Sb 2 S 3 (s) + 3Fe (s)  2Sb (s) + 3FeS (s) ΔH = -125 kJ Calculate Δ surr for the reaction above. Copyright © Cengage Learning. All rights reserved 14

Section 17.3 The MoleThe Effect of Temperature on Spontaneity Return to TOC Copyright © Cengage Learning. All rights reserved 15 Interplay of  S sys and  S surr in Determining the Sign of  S univ

Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 16 Free Energy (G) Another thermodynamic function used to predict spontaneity. Is the maximum usable energy that can be utilized or trapped to do work. Useful when considering temperature dependence of spontaneity. ΔG = ΔH – TΔS (at constant T and P) ΔG° = ΔH ° – TΔS ° –ΔH at constant P = to energy flow as heat –T = temp in K –ΔS (ΔS sys ) = change in entropy in J/K –°=> standard state

Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 17 Free Energy (G) A process (at constant T and P) is spontaneous in the direction in which the free energy decreases. –Spontaneous : ΔG <0 - ΔG means + ΔS univ. –At equilibrium: ΔG = 0

Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 18 Concept Check A liquid is vaporized at its boiling point. Predict the signs of: HH SS  S surr GG Explain your answers. + + – 0

Section 17.4 Free Energy Return to TOC Will ∆G be negative (& process spontaneous)? Copyright © Cengage Learning. All rights reserved 19 Which dominates: ∆H or ∆S? Also can depend on T. *Always spontaneous: exothermic & increase in entropy; always NONspontaneous: endothermic & decrease in entropy

Section 17.4 Free Energy Return to TOC Example: Predict whether each of the following sets of data represent spontaneous or nonspontaneous processes. Copyright © Cengage Learning. All rights reserved 20 ΔH (kJ)ΔS (J/K)T (K)

Section 17.4 Free Energy Return to TOC Example For mercury, the enthalpy of vaporization is kJ/mol and the entropy of vaporization is J/K∙mol. What is the normal boiling point of mercury? Copyright © Cengage Learning. All rights reserved 21

Section 17.4 Free Energy Return to TOC Copyright © Cengage Learning. All rights reserved 22 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

Section 17.5 Entropy Changes in Chemical Reactions Return to TOC ΔS sys is related to positional probabilities of the reactants Reaction involving only gas phase: increase in total # of moles of gas means higher entropy. Reaction with different phases: production of gas generally increases entropy more than an increase in # moles of a liquid or solid. Copyright © Cengage Learning. All rights reserved 23 Example: Predict the sign of ΔS°for each of the reactions: 1.(NH 4 ) 2 Cr 2 O 7 (s)  Cr 2 O 3 (s) + 4H 2 O (l) + N 2 (g) 2.Mg(OH) 2 (s)  MgO (s) + H 2 O (g)

Section 17.5 Entropy Changes in Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 24 Third Law of Thermodynamics The entropy of a perfect crystal at 0 K is zero. Standard entropy values: 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

Section 17.5 Entropy Changes in Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 25 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

Section 17.6 Free Energy and Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 26 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. Three methods of calculating ΔG°: 1)ΔG° = ΔH° – TΔS° 2)By manipulating known equations, (similar to Hess’s law) 3)ΔG° reaction = Σ n p G f (products) – Σ n r G f (reactants)

Section 17.6 Free Energy and Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 27 Concept Check A stable diatomic molecule spontaneously forms from its atoms. Predict the signs of:  H°  S°  G° Explain. – – –

Section 17.6 Free Energy and Chemical Reactions Return to TOC Copyright © Cengage Learning. All rights reserved 28 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.

Section 17.7 The Dependence of Free Energy on Pressure Return to TOC System at constant T and P proceed spontaneously in the direction that lowers its free energy. Reactions proceed until equilibrium is reached. –Equilibrium position: lowest free energy value available to a particular reaction system. Free energy at nonstandard pressures: –For ideal gas: entropy is affected by pressure but enthalpy is not. S large volume > S small volume S low pressure > S high pressure Copyright © Cengage Learning. All rights reserved 29

Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 30 Free Energy at NON Standard pressures G = G° + RT ln(P) or ΔG = ΔG° + RT ln(Q) ΔG°= free energy change at 1 atm ΔG = free energy change at specified pressure P T = temp in K R = J/K∙mol Q = reaction quotient in terms of P

Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Example CO (g) + 2H 2 (g)  CH 3 OH (l) Calculate ∆G at 25°C for this reaction where CO at 5.0 atm and H 2 gas at 3.0 atm are converted to liquid methanol. Copyright © Cengage Learning. All rights reserved 31

Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 32 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. –∆G<0 does NOT mean system proceeds to pure products –∆G>0 does NOT mean system remains at pure reactants System spontaneously goes to equilibrium, the lowest possible free energy available. SO what is this value of ∆G at equilibrium???

Section 17.8 Free Energy and Equilibrium Return to TOC Copyright © Cengage Learning. All rights reserved 33 The equilibrium point occurs at the lowest value of free energy available to the reaction system. G products = G reactants or ΔG = 0 so… ΔG = 0 = ΔG° + RT ln(K) so… ΔG° = –RT ln(K)

Section 17.8 Free Energy and Equilibrium Return to TOC Copyright © Cengage Learning. All rights reserved 34 Qualitative Relationship Between the Change in Standard Free Energy and the Equilibrium Constant for a Given Reaction Given ∆G, which direction will the system shift to reach equilibrium? –Look at the value of K! ShiftRIGHT RIGHT LEFT

Section 17.8 Free Energy and Equilibrium Return to TOC Example The rusting of iron by oxygen is: 4Fe (s) + 3O 2 (g)  2Fe 2 O 3 (s) Using the following data, calculate the equilibrium constant for this reaction at 25ºC. Copyright © Cengage Learning. All rights reserved 35 SubstanceΔHf° (kJ/mol)S° (J/K*mol) Fe 2 O 3 (s) Fe (s)027 O 2 (g)0205

Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 36

Section 17.9 Free Energy and Work Return to TOC Copyright © Cengage Learning. All rights reserved 37 Maximum possible useful work obtainable from a process at constant temperature and pressure is equal to the change in free energy. w max = ΔG

Section 17.9 Free Energy and Work Return to TOC Copyright © Cengage Learning. All rights reserved 38 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 can’t win, you can only break even. Second law: You can’t break even.