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Chapter 19: Spontaneous Change: Entropy and Free Energy

Petrucci • Harwood • Herring • Madura. GENERAL. Ninth Edition. CHEMISTRY. Principles and Modern Applications. Chapter 19: Spontaneous Change: Entropy and Free Energy. Contents. 19-1 Spontaneity: The Meaning of Spontaneous Change 19-2 The Concept of Entropy

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Chapter 19: Spontaneous Change: Entropy and Free Energy

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  1. Petrucci • Harwood • Herring • Madura GENERAL Ninth Edition CHEMISTRY Principles and Modern Applications Chapter 19: Spontaneous Change: Entropy and Free Energy General Chemistry: Chapter 19

  2. Contents 19-1 Spontaneity: The Meaning of Spontaneous Change 19-2 The Concept of Entropy 19-3 Evaluating Entropy and Entropy Changes 19-4 Criteria for Spontaneous Change: The Second Law of Thermodynamics 19-5 Standard Free Energy Change, ΔG° 19-6 Free Energy Change and Equilibrium 19-7ΔG° and Keqas Functions of Temperature General Chemistry: Chapter 19

  3. 19-1 Spontaneity: The Meaning of Spontaneous Change General Chemistry: Chapter 19

  4. Spontaneous Process • A process that occurs in a system left to itself. • Once started, no external actions is necessary to make the process continue. • A non-spontaneous process will not occur without external action continuously applied. 4 Fe(s) + 3 O2(g) → 2 Fe2O3(s) H2O(s) H2O(l) General Chemistry: Chapter 19

  5. Spontaneous Process • Potential energy decreases. • For chemical systems the internal energy Uis equivalent to potential energy. • Berthelot and Thomsen 1870’s. • Spontaneous change occurs in the direction in which the enthalpy of a system decreases. • Mainly true but there are exceptions. General Chemistry: Chapter 19

  6. 19-2 The Concept of Entropy • Entropy, S. • The greater the number of configurations of the microscopic particles among the energy levels in a particular system, the greater the entropy of the system. ΔS > 0 spontaneous ΔU = ΔH = 0 General Chemistry: Chapter 19

  7. The Boltzmann Equation for Entropy S = k lnW • Entropy, S • 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. General Chemistry: Chapter 19

  8. qrev ΔS = T Entropy Change For changes occurring at constant temperature General Chemistry: Chapter 19

  9. ΔH ΔS = Ttr ° ΔHfus 6.02 kJ mol-1 ΔSfus = = = 2.2010-2 kJ mol-1 K-1 Ttr 273.15 K 19-3 Evaluating Entropy and Entropy Changes • Phase transitions. • Exchange of heat can be carried out reversibly. H2O(s, 1 atm) H2O(l, 1 atm) ΔHfus = 6.02 kJ at 273.15 K General Chemistry: Chapter 19

  10. ΔHvap  87 kJ mol-1 K-1 ΔS = Tbp Trouton’s Rule General Chemistry: Chapter 19

  11. Absolute Entropies • Third law of thermodynamics. • The entropy of a pure perfect crystal at 0 K is zero. • Standard molar entropy. • Tabulated in Appendix D. ΔS = [ pS°(products) -rS°(reactants)] General Chemistry: Chapter 19

  12. Entropy as a Function of Temperature General Chemistry: Chapter 19

  13. Vibrational Energy and Entropy General Chemistry: Chapter 19

  14. 19-4 Criteria for Spontaneous Change:The Second Law of Thermodynamics. ΔStotal = ΔSuniverse = ΔSsystem + ΔSsurroundings The Second Law of Thermodynamics: ΔSuniverse = ΔSsystem + ΔSsurroundings > 0 All spontaneous processes produce an increase in the entropy of the universe. General Chemistry: Chapter 19

  15. Free Energy and Free Energy Change • Hypothetical process: • only pressure-volume work, at constant T and P. qsurroundings = -qp = -ΔHsys • Make the enthalpy change reversible. • large surroundings, infinitesimal change in temperature. • Under these conditions we can calculate entropy. General Chemistry: Chapter 19

  16. Free Energy and Free Energy Change For the universe: TΔSuniv. = TΔSsys – ΔHsys = -(ΔHsys – TΔSsys) -TΔSuniv. = ΔHsys – TΔSsys For the system: G = H - TS ΔG = ΔH - TΔS ΔGsys = - TΔSuniverse General Chemistry: Chapter 19

  17. Criteria for Spontaneous Change ΔGsys < 0 (negative), the process is spontaneous. ΔGsys = 0 (zero), the process is at equilibrium. ΔGsys > 0 (positive), the process is non-spontaneous. J. Willard Gibbs 1839-1903 General Chemistry: Chapter 19

  18. Table 19.1 Criteria for Spontaneous Change General Chemistry: Chapter 19

  19. 19-5 Standard Free Energy Change, ΔG° • The standard free energy of formation, ΔGf°. • 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, ΔG°. ΔG° = [ p ΔGf°(products) -r ΔGf°(reactants)] General Chemistry: Chapter 19

  20. Free Energy Change and Equilibrium Condensation Equilibrium Vaporization General Chemistry: Chapter 19

  21. Relationship of ΔG° to ΔG for Non-standard Conditions 2 N2(g) + 3 H2(g) 2 NH3(g) ΔG = ΔH - TΔS ΔG° = ΔH° - TΔS° For ideal gases ΔH = ΔH° ΔG = ΔH° - TΔS General Chemistry: Chapter 19

  22. qrev Vf = R ln ΔS = T Vi Pf Pi Vf = R ln = -R ln = R ln ΔS = Sf – Si Pi Pf Vi P P - R ln - R ln = S° - R ln P = S° S = S° 1 P° Relationship Between S and S° Vf qrev = -w = RT ln Vi General Chemistry: Chapter 19

  23. 3 PN2PH2 ΔSrxn = 2 SNH3 – SN2 –3SH2+ Rln 2 PNH3 3 PN2PH2 ΔSrxn = ΔS°rxn + Rln 2 PNH3 N2(g) + 3 H2(g) 2 NH3(g) SN2= SN2 – Rln PN2 SH2 =SH2 – Rln PH2 SNH3 = SNH3 – Rln PNH3 ΔSrxn = 2(SNH3 – Rln PNH3) – (SN2 – Rln PN2) –3(SH2 – Rln PH2) General Chemistry: Chapter 19

  24. 3 2 PN2PH2 ΔG = ΔH° - TΔS°rxn – TR ln 2 PNH3 2 PNH3 ΔG = ΔG° + RT ln 3 2 PN2PH2 3 2 PN2PH2 ΔSrxn = ΔS°rxn + Rln 2 PNH3 ΔG Under Non-standard Conditions ΔG = ΔH° - TΔS ΔG = ΔG° + RT ln Q General Chemistry: Chapter 19

  25. If the reaction is at equilibrium then: ΔG = ΔG° + RT ln Keq= 0 ΔG and the Equilibrium Constant Keq ΔG = ΔG° + RT ln Q ΔG° = -RT ln Keq General Chemistry: Chapter 19

  26. Criteria for Spontaneous Change Every chemical reaction consists of both a forward and a reverse reaction. The direction of spontaneous change is the direction in which the free energy decreases. General Chemistry: Chapter 19

  27. Significance of the Magnitude of ΔG General Chemistry: Chapter 19

  28. -ΔG° -ΔH° TΔS° ln Keq = = + RT RT RT -ΔH° ΔS° ln Keq = + RT R 19-7 ΔG° and Keq as Functions of Temperature ΔG° = ΔH° -TΔS° ΔG° = -RT ln Keq General Chemistry: Chapter 19

  29. Van’t Hoff Equation If we evaluate this equation for a change in temperature: Keq2 -ΔH° ΔS° -ΔH° ΔS° - ln = + + RT2 R RT1 R Keq1 Keq2 1 1 -ΔH° - = ln T2 T1 R Keq1 General Chemistry: Chapter 19

  30. General Chemistry: Chapter 19

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