Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 1 of 44 CHEMISTRY Ninth Edition GENERAL Principles and Modern Applications Petrucci Harwood Herring Madura Chapter 19: Spontaneous Change: Entropy and Free Energy

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 2 of 44 Contents 19-1Spontaneity: The Meaning of Spontaneous Change 19-2The Concept of Entropy 19-3Evaluating Entropy and Entropy Changes 19-4Criteria for Spontaneous Change: The Second Law of Thermodynamics 19-5Standard Free Energy Change, ΔG° 19-6Free Energy Change and Equilibrium 19-7ΔG° and K eq as Functions of Temperature

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 3 of Spontaneity: The Meaning of Spontaneous Change

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 4 of 44 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 O 2 (g) → 2 Fe 2 O 3 (s) H 2 O(s) H 2 O(l)

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 5 of 44 Spontaneous Process  Potential energy decreases.  For chemical systems the internal energy U is 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.

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 6 of 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

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 7 of 44 The Boltzmann Equation for Entropy  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/N A. S = k lnW

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 8 of 44 Entropy Change ΔS = q rev T For changes occurring at constant temperature

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 9 of Evaluating Entropy and Entropy Changes  Phase transitions.  Exchange of heat can be carried out reversibly. ΔS = ΔHΔH T tr H 2 O(s, 1 atm) H 2 O(l, 1 atm) ΔH fus  = 6.02 kJ at K ΔS fus = ΔH fus T tr ° = 6.02 kJ mol K = 2.20  kJ mol -1 K -1

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 10 of 44 Trouton’s Rule ΔS = ΔH vap T bp  87 kJ mol -1 K -1

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 11 of 44 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 = [  p S°(products) -  r S°(reactants)]

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 12 of 44 Entropy as a Function of Temperature

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 13 of 44 Vibrational Energy and Entropy

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 14 of Criteria for Spontaneous Change: The Second Law of Thermodynamics. ΔS total = ΔS universe = ΔS system + ΔS surroundings The Second Law of Thermodynamics: ΔS universe = ΔS system + ΔS surroundings > 0 All spontaneous processes produce an increase in the entropy of the universe.

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 15 of 44 Free Energy and Free Energy Change  Hypothetical process:  only pressure-volume work, at constant T and P. q surroundings = -q p = -ΔH sys  Make the enthalpy change reversible.  large surroundings, infinitesimal change in temperature.  Under these conditions we can calculate entropy.

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 16 of 44 Free Energy and Free Energy Change TΔS univ. = TΔS sys – ΔH sys = -(ΔH sys – TΔS sys ) -TΔS univ. = ΔH sys – TΔS sys G = H - TS ΔG = ΔH - TΔS For the universe: For the system: ΔG sys = - TΔS universe

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 17 of 44 Criteria for Spontaneous Change ΔG sys < 0 (negative), the process is spontaneous. ΔG sys = 0 (zero), the process is at equilibrium. ΔG sys > 0 (positive), the process is non-spontaneous. J. Willard Gibbs

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 18 of 44 Table 19.1 Criteria for Spontaneous Change

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 19 of Standard Free Energy Change, ΔG°  The standard free energy of formation, ΔG f °.  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 ΔG f °(products) -  r ΔG f °(reactants)]

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 20 of 44 Free Energy Change and Equilibrium CondensationEquilibriumVaporization

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 21 of 44 Relationship of ΔG° to ΔG for Non-standard Conditions 2 N 2 (g) + 3 H 2 (g) 2 NH 3 (g) ΔG = ΔH - TΔSΔG° = ΔH° - TΔS° For ideal gases ΔH = ΔH° ΔG = ΔH° - TΔS

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 22 of 44 Relationship Between S and S° q rev = -w = RT ln VfVf ViVi ΔS = q rev T = R ln VfVf ViVi ΔS = S f – S i = R ln VfVf ViVi PiPi PfPf = -R ln PfPf PiPi S = S° - R ln P P°P° = S° - R ln P 1 = S° - R ln P

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 23 of 44 N 2 (g) + 3 H 2 (g) 2 NH 3 (g) S NH 3 = S NH 3 – Rln P NH 3 S N 2 = S N 2 – Rln P N 2 S H 2 = S H 2 – Rln P H 2 ΔS rxn = 2  (S NH 3 – Rln P NH 3 ) – (S N 2 – Rln P N 2 ) –3  (S H 2 – Rln P H 2 ) ΔS rxn = 2 S NH 3 – S N 2 –3S H 2 + Rln PN2PH2PN2PH2 P NH ΔS rxn = ΔS° rxn + Rln PN2PH2PN2PH2 P NH 3 2 3

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 24 of 44 ΔG Under Non-standard Conditions ΔG = ΔH° - TΔS ΔS rxn = ΔS° rxn + Rln PN2PH2PN2PH2 P NH ΔG = ΔH° - TΔS° rxn – TR ln PN2PH2PN2PH2 P NH ΔG = ΔG° + RT ln PN2PH2PN2PH2 2 P NH ΔG = ΔG° + RT ln Q

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 25 of 44 ΔG and the Equilibrium Constant K eq ΔG = ΔG° + RT ln Q ΔG = ΔG° + RT ln K eq = 0 If the reaction is at equilibrium then: ΔG° = -RT ln K eq

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 26 of 44 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.

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 27 of 44 Significance of the Magnitude of ΔG

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 28 of ΔG° and K eq as Functions of Temperature ΔG° = ΔH° -TΔS°ΔG° = -RT ln K eq ln K eq = -ΔG° RT = -ΔH° RT TΔS° RT + ln K eq = -ΔH° RT ΔS° R +

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 29 of 44 Van’t Hoff Equation If we evaluate this equation for a change in temperature: ln = -ΔH° RT 2 ΔS° R + -ΔH° RT 1 ΔS° R + - = -ΔH° R 1 T2T2 1 T1T1 - K eq1 K eq2 ln K eq1 K eq2

Prentice-Hall © 2007 General Chemistry: Chapter 19 Slide 30 of 44