Lecture Notes Alan D. Earhart Southeast Community College Lincoln, NE Chapter 16 Thermodynamics: Entropy, Free Energy, and Equilibrium John E. McMurry Robert C. Fay CHEMISTRY Fifth Edition Copyright © 2008 Pearson Prentice Hall, Inc.

Spontaneous Processes Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/2 Spontaneous Process: A process that, once started, proceeds on its own without a continuous external influence.

Spontaneous process Spontaneity reaction always moves a system toward equilibrium Both forward and reverse reaction depends on Temperature Pressure Composition of reaction mixture Q < K; reaction proceeds in the forward direction Q>K; reaction proceeds in the reverse direction Spontaneity of a reaction does not identify the speed of reaction

Spontaneous Processes Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/4

16.2 Enthalpy, Entropy, and Spontaneous Processes Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/5 State Function: A function or property whose value depends only on the present state, or condition, of the system, not on the path used to arrive at that state. Enthalpy Change (  H): The heat change in a reaction or process at constant pressure;  H =  E + P  V. Entropy (S): The amount of molecular randomness in a system.

Enthalpy, Entropy, and Spontaneous Processes Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/6 = kJ  H vap CO 2 (g) + 2H 2 O(l)CH 4 (g) + 2O 2 (g) H 2 O(l)H 2 O(s) H 2 O(g)H 2 O(l) = kJ H°H° = kJ  H fusion = kJ H°H° Endothermic: Exothermic: Na 1+ (aq) + Cl 1- (aq)NaCl(s) H2OH2O

Enthalpy, Entropy, and Spontaneous Processes Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/7  S = S final - S initial

Enthalpy, Entropy, and Spontaneous Processes Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/8

16.3 Entropy and Probability Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/9 S = k ln W k = Boltzmann’s constant = 1.38 x J/K W = The number of ways that the state can be achieved.

16.4 Entropy and Temperature Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/10 Third Law of Thermodynamics: The entropy of a perfectly ordered crystalline substance at 0 K is zero.

Entropy and Temperature

ΔS increases when increasing the average kinetic energy of molecules Total energy is distributed among the individual molecules in a number of ways Botzman- the more way (W) that the energy can be distributed the greater the randomness of the state and higher the entropy

16.4 Standard Molar Entropies and Standard Entropies of Reaction Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/13 Standard Molar Entropy (S°): The entropy of 1 mole of a pure substance at 1 atm pressure and a specified temperature.

Standard Molar Entropies and Standard Entropies of Reaction Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/14 cC + dDaA + bB  S° = S°(products) - S°(reactants)  S° = [cS°(C) + dS°(D)] - [aS°(A) + bS°(B)] Reactants Products

Example Calculate the standard entropy of reaction at 25 o C for the decomposition of calcium carbonate: CaCO 3 (s)  CaO(s) + CO 2 (g)

16.6 Entropy and the Second Law of Thermodynamics Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/16 First Law of Thermodynamics: In any process, spontaneous or nonspontaneous, the total energy of a system and its surroundings is constant. Helps keeping track of energy flow between system and the surrounding Does not indicate the spontaneity of the process Second Law of Thermodynamics: In any spontaneous process, the total entropy of a system and its surroundings always increases. Provide a clear cut criterion of spontaneity Direction of spontaneous change is always determined by the sign of the total entropy change

Entropy and the Second Law of Thermodynamics Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/17  S total > 0The reaction is spontaneous.  S total < 0The reaction is nonspontaneous.  S total = 0The reaction mixture is at equilibrium.  S total =  S sys +  S surr or  S total =  S system +  S surroundings

Entropy and the Second Law of Thermodynamics  s surr  -  H  s surr  T 1  s surr = T -  H

Example Consider the oxidation of iron metal 4 Fe(s) + 3 O 2 (g)  2 Fe 2 O 3 (s) Determine whether the reaction is spontaneous at 25 o C S o (J/K mol)H o f (kJ/mol) Fe(s)27.3 O2(g)205.0 Fe2O3(s)

Example Consider the combustion of propane gas: C 3 H 8 (g) + 5 O 2 (g)  3 CO 2 (g) + 4 H 2 O(g) a.Calculate the entropy change in the surrounding associated with this reaction occurring at 25.0 o C b.Determine the sign of the entropy change for the system c.Determine the sign of the entropy change for the universe. Will the reaction be spontaneous?

16.7 Free Energy Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/21  G =  H - T  S = -T  S total Free Energy: G = H - TS  G =  H - T  S  S =  S sys Using:  s surr = T -  H  S total =  S sys +  S surr

Free Energy Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/22  G < 0The reaction is spontaneous.  G > 0The reaction is nonspontaneous.  G = 0The reaction mixture is at equilibrium. Using the second law and  G =  H - T  S = -T  S total

The effect of H, S and T on Spontaneity ∆H∆SLow TemperatureHigh Temperature -+Spontaneous (G<0) +-Nonspontaneous (G > 0) --Spontaneous (G< 0)nonSpontaneous (G>0) ++Nonspontaneous (G>0)Spontaneous (G<0) Typo on the original note

Free Energy Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/24

Example Iron metal can be produced by reducing iron (III) oxide with hydrogen: Fe 2 O 3 (s) + 3H 2 (g)  2Fe(s) + 3 H 2 O(g) ΔH o = kJΔS o = J/K Is this reaction spontaneous under standard-state conditions at 25 o C? At what temperature will the reaction become spontaneous?

16.8 Standard Free-Energy Changes for Reactions Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/26 Thermodynamic Standard State: Most stable form of a substance at 1 atm pressure and at a specified temperature, usually 25 °C; 1 M concentration for all substances in solution.  G° =  H° - T  S°

Example One of the possible initial steps in the formation of acid rain is the oxidation of the pollutant of SO 2 to SO 3 by the following reaction SO 2 (g) + ½ O 2 (g)  SO 3 (g) ΔH o = kJΔS o = J/K Calculate the ΔG o for this reaction at 25 o C Is the reaction spontaneous at standard-state condition? Does the reaction become spontaneous at higher temperature?

Example Iron metal is produced commercially by reducing iron (III) oxide in iron ore with carbon monoxide: Fe 2 O 3 (s) + 3CO(g)  2Fe(s) + 3 CO 2 (g) H o = kJS o = J/K Calculate the ΔG o for this reaction at 25 o C Is the reaction spontaneous at standard-state condition? Does the reverse reaction become spontaneous at higher temperature?

16.9 Standard Free Energies of Formation Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/29  G° =  G° f (products) -  G° f (reactants)  G° = [c  G° f (C) + d  G° f (D)] - [a  G° f (A) + b  G° f (B)] ReactantsProducts cC + dDaA + bB

Standard Free Energies of Formation Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/30

Standard Free Energies of Formation Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/31 Using table values, calculate the standard free-energy change at 25 °C for the reduction of iron(III) oxide with carbon monoxide: 2Fe(s) + 3CO 2 (g)Fe 2 O 3 (s) + 3CO(g)

16.10 Free Energy Changes and the Reaction Mixture Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/32  G =  G° + RT ln Q  G = Free-energy change under nonstandard conditions. For the Haber synthesis of ammonia: 2NH 3 (g)N 2 (g) + 3H 2 (g) Q p = NH 3 P 2 H2H2 P N2N2 P 3

Free Energy Changes and the Reaction Mixture Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/33 C2H4(g)C2H4(g)2C(s) + 2H 2 (g) Calculate  G for the formation of ethylene (C 2 H 4 ) from carbon and hydrogen at 25 °C when the partial pressures are 100 atm H 2 and 0.10 atm C 2 H 4. Is the reaction spontaneous in the forward or the reverse direction?

16.11 Free Energy and Chemical Equilibrium Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/34  G =  G° + RT ln Q Q >> 1RT ln Q >> 0  G > 0 The total free energy decreases as the reaction proceeds spontaneously in the reverse direction. When the reaction mixture is mostly products: Q << 1RT ln Q << 0  G < 0 The total free energy decreases as the reaction proceeds spontaneously in the forward direction. When the reaction mixture is mostly reactants:

Free Energy and Chemical Equilibrium At equilibrium,  G = 0 and Q = K.  G° = -RT ln K  G =  G° + RT ln Q

Free Energy and Chemical Equilibrium Copyright © 2008 Pearson Prentice Hall, Inc. Chapter 16/37 Calculate K p at 25 °C for the following reaction: CaO(s) + CO 2 (g)CaCO 3 (s)

Example The value of ΔG o f at 25 o C for gaseous mercury is kJ/mol. What is the vapor pressure of mercury at 25 o C?