GENERAL CHEMISTRY PRINCIPLES AND MODERN APPLICATIONS ELEVENTH EDITION

Spontaneous Change: Entropy and Gibbs Energy Slide 13 - 2 CONTENTS 13 -1 Spontaneity:

The melting of an ice cube occurs spontaneously at temperatures above 0°C Slide 13

13 -1 Entropy: Boltzmann’s View Microstates Macroscopic systems are made up of many particles.

FIGURE 13 -1 Enumeration of microstates Slide 13 - 5 General Chemistry: Chapter 13

The Boltzmann Equation for Entropy S = k. B ln. W Entropy, S, is

• When the space available to the particles of a system is fixed,

Slide 13 - 8 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

FIGURE 13 -2 Expansion of an ideal gas into a vacuum Slide 13 -

Microscopic Interpretation of Entropy Change FIGURE 13 -3 The mixing of ideal gases Slide

A(g) + B(g) mixture of A(g) and B(g) ∆S = k. B ln Wf

Describing Entropy Change for Some Simple Processes FIGURE 13 -4 Three processes in which

Four situations generally produce an increase in entropy: • Pure liquids or liquid solutions

13 -2 Entropy Change: Clausius’s View (13. 2) Slide 13 - 14 General Chemistry:

Phase transitions Slide 13 - 15 General Chemistry: Chapter 13 Copyright © 2017 Pearson

ΔStr = H 2 O(s, 1 atm) ΔHtr (13. 3) Ttr H 2 O(l,

Heating or Cooling at Constant Pressure Slide 13 - 17 General Chemistry: Chapter 13

Changes in State for an Ideal Gas Slide 13 - 18 General Chemistry: Chapter

Slide 13 - 19 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Slide 13 - 20 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

13 -3 Combining Boltzmann’s and Clausius’s Ideas: Absolute Entropies Third law of thermodynamics The

Slide 13 - 22 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

FIGURE 13 -5 Molar entropy as a function of temperature Slide 13 - 23

Standard molar entropy, Sº Tabulated in Appendix D. Slide 13 - 24 General Chemistry:

Standard molar entropy, Sº, increases as molecular complexity increases (i. e. , as the

13 -4 Criterion for Spontaneous Change: The Second Law of Thermodynamics. ΔSuniverse = ΔSsystem

Slide 13 - 27 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Slide 13 - 28 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Slide 13 - 29 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

(13. 11) Slide 13 - 30 General Chemistry: Chapter 13 Copyright © 2017 Pearson

Ideas about entropy can be summarized as follows. ΔSuniv > 0, the process is

Gibbs Energy and Gibbs Energy Change Hypothetical process: only pressure-volume work, at constant T

For the universe: TΔSuniv = TΔSsys – ΔHsys = –(ΔHsys – TΔSsys) –TΔSuniv =

Criteria for Spontaneous Change ΔGsys < 0 (negative) the process is spontaneous. ΔGsys >

Slide 13 - 35 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Applying the Gibbs Energy Criteria for Spontaneous Change Slide 13 - 36 General Chemistry:

Gibbs Energy and Work The second law guarantees that ∆G ≤ wnon-PV if wnon-PV

13 -5 Gibbs Energy Change of a System of Variable Composition: Δr. Gº and

The standard free energy of formation, Δf. Gº. The change in free energy for

Gibbs Energy of Reaction for Nonstandard Conditions, Δr. G Slide 13 - 40 General

Slide 13 - 41 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

FIGURE 13 -8 Variation of G at constant T and constant P Slide 13

1. If ∆r. G < 0, then G decreases as ξ increases. 2. If

The Thermodynamic Reaction Quotient, Q N 2(g) + 3 H 2(g) Slide 13 -

Relationship of Δr. Gº to the Equilibrium Constant K If the reaction is at

Δ r G = RT ln(Q/K) Slide 13 - 47 General Chemistry: Chapter 13

Different Forms of the Equilibrium Constant a. A + b. B + … c.

For reactions involving gases define (13. 20) (13. 21) Slide 13 - 49 General

In aqueous solutions (13. 22) (13. 23) Slide 13 - 50 General Chemistry: Chapter

In heterogeneous solutions 2 Al(s) + 6 H+(aq) Slide 13 - 51 2 Al

Interpreting the values of ∆r. Gº and K Δ r Gº = –RT ln

Slide 13 - 53 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Consider the implications on the position of the equilibrium for large or small values

FIGURE 13 -19 The position of equilibrium for small, large, and intermediate values of

13 -6 Δr. Gº and K as Functions of Temperature Δr. Gº = ΔHº–TΔSº

Slide 13 - 57 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

2 SO 2(g) 2 SO 3(g) ln Keq = slope = –ΔHº RT +

Van’t Hoff Equation evaluate –ΔHº ΔSº for a change in temperature: ln K =

13 -7 Coupled Reactions In order to drive a non-spontaneous reactions we changed the

Smelting Copper Ore Cu 2 O(s) Δ Non-spontaneous reaction: Spontaneous reaction: 2 Cu(s) +

13 -8 Chemical Potential and Thermodynamics of Spontaneous Chemical Change Gibbs Energy of an

use Gº and G to represent initial and final states (13. 28) molar Gibbs

Gibbs Energy of an Ideal Gas Mixture (13. 30) If we change the amount

Chemical Potential and Activity (13. 29) (13. 31) (13. 30) (13. 32) (13. 33)

The concept of activity was introduced by Lewis to ensure that the chemical potential

Expressing ∆r. Gº in Terms of Chemical Potentials Initial State Pure A at 1

Criterion for Predicting the Direction of Spontaneous Chemical Change a. A Initial: Change: Final:

(13. 35) where Slide 13 - 69 (13. 36) General Chemistry: Chapter 13 Copyright

recall (13. 31) (13. 36) (13. 15) Slide 13 - 70 General Chemistry: Chapter

End of Chapter Slide 13 - 71 General Chemistry: Chapter 13 Copyright © 2017

Slides: 71

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GENERAL CHEMISTRY PRINCIPLES AND MODERN APPLICATIONS ELEVENTH EDITION PETRUCCI HERRING MADURA BISSONNETTE Spontaneous Change: Entropy and Gibbs Energy 13 PHILIP DUTTON UNIVERSITY OF WINDSOR DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY Slide 13 - 1 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Spontaneous Change: Entropy and Gibbs Energy Slide 13 - 2 CONTENTS 13 -1 Spontaneity: The Meaning of Spontaneous Change 13 -2 The Concept of Entropy 13 -3 Evaluating Entropy and entropy Changes 13 -4 Criteria for Spontaneous Change: The Second Law of Thermodynamics 13 -5 Standard Gibbs Energy Change, ΔG 13 -6 Gibbs Energy Change and Equilibrium 13 -7 ΔG° and K as Functions of Temperature 13 -8 Coupled Reactions General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

13 -1 Entropy: Boltzmann’s View Microstates Macroscopic systems are made up of many particles. System is easily characterized (n, T, V, P) Microscopic systems are not easily characterized. positions, velocity and energy of individual molecules change from one instant to the next. According to quantum mechanics a microstate is a specific microscopic configuration describing how the particles of a system are distributed among the available energy levels. Slide 13 - 4 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

The Boltzmann Equation for Entropy S = k. B ln. W Entropy, S, is a thermodynamic property related to the way in which the energy of a system is distributed among the available energy levels. States. The microscopic energy levels available in a system. Microstates, W. The particular way in which particles are distributed amongst the states. Number of microstates = W. The Boltzmann constant, k. Effectively the gas constant per molecule = R/NA. Slide 13 - 6 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

• When the space available to the particles of a system is fixed, W and S increase as the total energy, U, increases or as T increases. • When the total energy of a system is fixed, W and S increase as the space available to the particles increases Slide 13 - 7 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Four situations generally produce an increase in entropy: • Pure liquids or liquid solutions are formed from solids. • Gases are formed from either solids or liquids. • The number of molecules of gas increases as a result of a chemical reaction. • The temperature of a substance increases. Slide 13 - 13 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

ΔStr = H 2 O(s, 1 atm) ΔHtr (13. 3) Ttr H 2 O(l, 1 atm) Δfus. H° = 6. 02 k. J at 273. 15 K Δfus. H ° 6. 02 k. J mol− 1 = 22. 0 J mol − 1 K − 1 Δ fus. S° = = Tmp 273. 15 K Trouton’s Rule: For many liquids at their boiling points, Δvap. H° ≈ 87 J mol − 1 K − 1 Δvap. S° = Tbp Slide 13 - 16 General Chemistry: Chapter 13 (13. 4) Copyright © 2017 Pearson Canada Inc.

13 -3 Combining Boltzmann’s and Clausius’s Ideas: Absolute Entropies Third law of thermodynamics The entropy of a pure perfect crystal at 0 K is zero. Standard molar entropy, Sº Tabulated in Appendix D. ΔS = [ ∆p. Sº(products) − ∆r. Sº (reactants)] Slide 13 - 21 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Standard molar entropy, Sº, increases as molecular complexity increases (i. e. , as the number of atoms per molecule increases). FIGURE 13 -6 Vibrational energy and entropy Slide 13 - 25 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

13 -4 Criterion for Spontaneous Change: The Second Law of Thermodynamics. ΔSuniverse = ΔSsystem + ΔSsurroundings > 0 (13. 10) All spontaneous processes produce an increase in the entropy of the universe. Slide 13 - 26 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Ideas about entropy can be summarized as follows. ΔSuniv > 0, the process is spontaneous. ΔGuniv < 0, the process is nonspontaneous. ΔGuniv = 0, the process is at reversible. Slide 13 - 31 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Gibbs Energy and Gibbs Energy Change Hypothetical process: only pressure-volume work, at constant T and P. qsurr = –qp = –ΔHsys Make the enthalpy change reversible. large surroundings, infinitesimal change in temperature. Under these conditions we can calculate entropy. Slide 13 - 32 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

For the universe: TΔSuniv = TΔSsys – ΔHsys = –(ΔHsys – TΔSsys) –TΔSuniv = ΔHsys – TΔSsys For the system: G = H – TS (13. 12) ΔG = ΔH – TΔS (13. 13) ΔGsys = –TΔSuniv. Slide 13 - 33 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Criteria for Spontaneous Change ΔGsys < 0 (negative) the process is spontaneous. ΔGsys > 0 (positive) the process is nonspontaneous. ΔGsys = 0 (zero) the process is at reversible and the system has reached equilibrium. J. Willard Gibbs (1839– 1903) —a great “unknown” scientist Slide 13 - 34 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Gibbs Energy and Work The second law guarantees that ∆G ≤ wnon-PV if wnon-PV = 0, then ∆G ≤ 0 Considering sign conventions ( w > 0 when work is done on the system, w < 0 when work is done by the system) wnon-PV = – | wnon-PV | when the system does non-PV work | wnon-PV | ≤ –∆G Slide 13 - 37 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

13 -5 Gibbs Energy Change of a System of Variable Composition: Δr. Gº and Δr. G Pure, unmixed reactants (each in its standard state) a. A + b. B + … Slide 13 - 38 Pure, unmixed products (each in its standard state) c. C + d. D + … General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

The standard free energy of formation, Δf. Gº. The change in free energy for a reaction in which a substance in its standard state is formed from its elements in reference forms in their standard states. The standard free energy of reaction, ΔGº. Δr. Gº = Δ r Hº – T r ΔSº Δr. Gº = [∑ Δf. Gº (products) − ∑Δf. Gº (reactants)] Slide 13 - 39 General Chemistry: Chapter 13 (13. 14) Copyright © 2017 Pearson Canada Inc.

1. If ∆r. G < 0, then G decreases as ξ increases. 2. If ∆r. G > 0, then G increases as ξ increases. 3. If ∆r. G = 0, then the system has attained the minimum possible value of G. Slide 13 - 43 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Relationship of Δr. Gº to the Equilibrium Constant K If the reaction is at equilibrium then: 0 = Δ r G° + RT ln Qeq = Δ r G° + RT ln K Δ r G° = –RT ln K (13. 17) If the reaction is not at equilibrium then: Δ r G = Δ r G° + RT ln Q = –RT ln K + RT ln Q (13. 18) Δ r G = RT ln(Q/K) we can predict the direction of spontaneous change Slide 13 - 46 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Consider the implications on the position of the equilibrium for large or small values of K. Without loss of generality, we can think about a gas phase equilibrium a. A(g) + b. B(g) + … Slide 13 - 54 c. C(g) + d. D(g) + … General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

13 -6 Δr. Gº and K as Functions of Temperature Δr. Gº = ΔHº–TΔSº Δ r Gº = –RT ln Keq –ΔGº –ΔHº TΔSº ln Keq = = + RT RT RT –ΔHº ΔSº ln K = + RT R Slide 13 - 56 General Chemistry: Chapter 13 (13. 24) Copyright © 2017 Pearson Canada Inc.

2 SO 2(g) 2 SO 3(g) ln Keq = slope = –ΔHº RT + ΔSº R –ΔHº = R×slope = – 8. 3145 J mol − 1 K − 1× 2. 2× 104 K = – 1. 8× 102 k. J mol − 1 FIGURE 13 -12 Temperature dependence of the equilibrium constant K for the reaction 2 SO 2(g)+O 2(g) 2 SO 3(g) Slide 13 - 58 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Van’t Hoff Equation evaluate –ΔHº ΔSº for a change in temperature: ln K = + RT R K 2 –ΔHº ΔSº – ln = + + RT 2 R RT 1 R K 1 ln Slide 13 - 59 K 2 K 1 1 –ΔHº 1 – = T 2 T 1 R General Chemistry: Chapter 13 (13. 25) Copyright © 2017 Pearson Canada Inc.

13 -7 Coupled Reactions In order to drive a non-spontaneous reactions we changed the conditions (i. e. temperature or electrolysis). Another method is to couple two reactions. One with a positive ΔG and one with a negative ΔG. Overall spontaneous process. Slide 13 - 60 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Smelting Copper Ore Cu 2 O(s) Δ Non-spontaneous reaction: Spontaneous reaction: 2 Cu(s) + ½ O 2(g) Cu 2 O(s) ΔGº 673 K = +125 k. J mol– 1 2 Cu(s) + ½ O 2(g) CO(g) Cu 2 O(s) + C(s) 2 Cu(s) + CO(g) +125 k. J mol– 1 − 175 k. J mol– 1 − 50 k. J mol– 1 Spontaneous reaction! Slide 13 - 61 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

13 -8 Chemical Potential and Thermodynamics of Spontaneous Chemical Change Gibbs Energy of an Ideal Gas for an isothermal process, ∆H = 0 Slide 13 - 62 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Gibbs Energy of an Ideal Gas Mixture (13. 30) If we change the amount of A by ∆n. A moles relates the change in Gibbs energy to the change in amount of gas A Slide 13 - 64 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

The concept of activity was introduced by Lewis to ensure that the chemical potential of a substance always has the form given by equation (13. 31) It is not particularly helpful to think of activity as an effective pressure or an effective concentration. It is much better to think of pressure and concentration as providing a measure of activity. Slide 13 - 66 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Expressing ∆r. Gº in Terms of Chemical Potentials Initial State Pure A at 1 bar, n. A = a mol Pure B at 1 bar, n. B = b mol Initial State Pure C at 1 bar, n. C = c mol Pure D at 1 bar, n. D = d mol (13. 34) Weighted sum of µ° values for products Slide 13 - 67 Weighted sum of µ° values for reactants General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.

Criterion for Predicting the Direction of Spontaneous Chemical Change a. A Initial: Change: Final: + dξ > 0 b. B dξ < 0 c. C + d. D n. A n. B n. C n. D Gi –a dξ –b dξ +c dξ +d. G n. A –a dξ n. B –b dξ n. C +c dξ n. D +d dξ Gf = Gi+d. G =Gf – Gi Slide 13 - 68 General Chemistry: Chapter 13 Copyright © 2017 Pearson Canada Inc.