Chapter 19: Spontaneous Change: Entropy and Free Energy Chemistry 140 Fall 2002 CHEMISTRY Ninth Edition GENERAL Principles and Modern Applications Petrucci • Harwood • Herring • Madura Chapter 19: Spontaneous Change: Entropy and Free Energy Philip Dutton University of Windsor, Canada Prentice-Hall © 2007 General Chemistry: Chapter 19 Prentice-Hall © 2007

Contents 19-1 Spontaneity: The Meaning of Spontaneous Change Chemistry 140 Fall 2002 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 19-7 ΔG° and Keq as Functions of Temperature 19-8 Coupled Reactions Focus On Coupled Reactions in Biological Systems General Chemistry: Chapter 19 Prentice-Hall © 2007

19-1 Spontaneity: The Meaning of Spontaneous Change General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 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 Prentice-Hall © 2007

General Chemistry: Chapter 19 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. General Chemistry: Chapter 19 Prentice-Hall © 2007

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 Prentice-Hall © 2007

The Boltzmann Equation for Entropy Chemistry 140 Fall 2002 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. Ludwig Boltzmann. Associated the number of energy levels in a system with the number of ways of arranging the particles in these levels. General Chemistry: Chapter 19 Prentice-Hall © 2007

Boltzmann Distribution General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Entropy Change ΔS = qrev T For changes occurring at constant temperature General Chemistry: Chapter 19 Prentice-Hall © 2007

19-3 Evaluating Entropy and Entropy Changes Phase transitions. Exchange of heat can be carried out reversibly. ΔS = ΔH Ttr H2O(s, 1 atm) H2O(l, 1 atm) ΔHfus = 6.02 kJ at 273.15 K ΔSfus = ΔHfus Ttr ° = 6.02 kJ mol-1 273.15 K = 2.2010-2 kJ mol-1 K-1 General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Chemistry 140 Fall 2002 Trouton’s Rule ΔS = ΔHvap Tbp  87 kJ mol-1 K-1 Failures of this rule are understandable: Water and hydrogen bonding. Sliquid is lower than expected so ΔS is larger than 87. General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Raoult’s Law PA =  APA ° General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Chemistry 140 Fall 2002 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 Prentice-Hall © 2007

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

Vibrational Energy and Entropy General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 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 Prentice-Hall © 2007

Free Energy and Free Energy Change Chemistry 140 Fall 2002 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 Prentice-Hall © 2007

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 Prentice-Hall © 2007

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 Prentice-Hall © 2007

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

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 Prentice-Hall © 2007

19-6 Free Energy Change and Equilibrium General Chemistry: Chapter 19 Prentice-Hall © 2007

Free Energy Change and Equilibrium Condensation Equilibrium Vaporization General Chemistry: Chapter 19 Prentice-Hall © 2007

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 Prentice-Hall © 2007

Relationship Between S and S° Vf qrev = -w = RT ln Vi ΔS = qrev T = R ln Vf Vi ΔS = Sf – Si = R ln Vf Vi Pi Pf = -R ln S = S° - R ln P P° = S° 1 = S° - R ln P General Chemistry: Chapter 19 Prentice-Hall © 2007

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) ΔSrxn = 2 SNH3 – SN2 –3SH2+ Rln PN2PH2 PNH3 2 3 ΔSrxn = ΔS°rxn + Rln PN2PH2 PNH3 2 3 General Chemistry: Chapter 19 Prentice-Hall © 2007

ΔG Under Non-standard Conditions ΔSrxn = ΔS°rxn + Rln PN2PH2 PNH3 2 3 ΔG = ΔH° - TΔS ΔG = ΔH° - TΔS°rxn – TR ln PN2PH2 PNH3 2 3 ΔG = ΔG° + RT ln PN2PH2 2 PNH3 3 ΔG = ΔG° + RT ln Q General Chemistry: Chapter 19 Prentice-Hall © 2007

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

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 Prentice-Hall © 2007

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

The Thermodynamic Equilibrium Constant: Activities. Chemistry 140 Fall 2002 The Thermodynamic Equilibrium Constant: Activities. For ideal gases at 1.0 bar: S = S° - R ln P P° = S° 1 PV=nRT or P=(n/V)RT, pressure is an effective concentration Therefore, in solution: S = S° - R ln c c° = S° - R ln a The effective concentration in the standard state for an ideal solution is c° = 1 M. General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Activities For pure solids and liquids: a = 1 For ideal gases: a = P (in bars, 1 bar = 0.987 atm) For ideal solutes in aqueous solution: a = c (in mol L-1) General Chemistry: Chapter 19 Prentice-Hall © 2007

The Thermodynamic Equilibrium Constant, Keq A dimensionless equilibrium constant expressed in terms of activities. Often Keq = Kc or KP, but not always. Must be used to determine ΔG. ΔG = ΔG° + RT ln agah… aaab… General Chemistry: Chapter 19 Prentice-Hall © 2007

19-7 ΔG° and Keq as Functions of Temperature ΔG° = ΔH° -TΔS° ΔG° = -RT ln Keq ln Keq = -ΔG° RT = -ΔH° TΔS° + ln Keq = -ΔH° RT ΔS° R + General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Van’t Hoff Equation If we evaluate this equation for a change in temperature: Keq2 -ΔH° ΔS° -ΔH° ΔS° ln = + - + Keq1 RT2 R RT1 R Keq2 -ΔH° 1 1 = - ln Keq1 R T2 T1 General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Prentice-Hall © 2007

Temperature Dependence of Keq Assume ΔH° and ΔS° do not vary significantly with temperature. ln Keq = -ΔH° RT ΔS° R + slope = -ΔH° R -ΔH° = R  slope = -8.3145 J mol-1 K-1  2.2104 K = -1.8102 kJ mol-1 General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 19-8 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. General Chemistry: Chapter 19 Prentice-Hall © 2007

General Chemistry: Chapter 19 Smelting Copper Ore Cu2O(s) → 2 Cu(s) + ½ O2(g) ΔG°673K = +125 kJ Δ Cu2O(s) → 2 Cu(s) + ½ O2(g) Non-spontaneous reaction: +125 kJ C(s) + ½ O2(g) → CO(g) Spontaneous reaction: -175 kJ Cu2O(s) + C(s) → 2 Cu(s) + CO(g) -50 kJ Spontaneous reaction! General Chemistry: Chapter 19 Prentice-Hall © 2007

Focus On Coupled Reactions in Biological Systems General Chemistry: Chapter 19 Prentice-Hall © 2007

The Biological Standard State ADP3- + HPO42- + H+ → ATP4- + H2O ΔG° = -9.2 kJ mol-1 ΔG = ΔG° + RT ln aATPaH2O aADPaPiaH3O+ But [H3O+] = 10-7 M not 1.0 M. ΔG = -9.2 kJ mol-1 + 41.6 kJ mol-1 = +32.4 kJ mol-1 = ΔG°' ADP to ATP is not spontaneous and biological systems use glucose. General Chemistry: Chapter 19 Prentice-Hall © 2007

Focus On Coupled Reactions in Biological Systems Glucose → 2 lactate + 2 H+ -218 kJ 2 ADP3- + 2 HPO42- + 2 H+ → 2 ATP4- + 2 H2O +64 kJ 2 ADP3- + 2 HPO42- + glucose → 2 ATP4- + 2 H2O + 2 lactate -153 kJ General Chemistry: Chapter 19 Prentice-Hall © 2007

End of Chapter Questions Work a problem from both ends to find the key log. a b c d d? e? e f Answer General Chemistry: Chapter 19 Prentice-Hall © 2007

End of Chapter Questions Work a problem from both ends to find the key log. a b c d d? e? e f Answer General Chemistry: Chapter 19 Prentice-Hall © 2007