Physical Chemistry II “The mistress of the world and her shadow” Chemistry 402 L. G. Sobotka Department of Chemistry Washington University, St Louis, MO, 63130 January 3, 2012 Contents IIntroduction 7 1 Physical Chemistry II - 402 -Thermodynamics (mostly) 8 1.1Who,when,where.............................................. 8 1.2CourseContent/Logistics.......................................... 8 1.3Grading.................................................... 8 1.3.1 Exams................................................. 8 1.3.2 Quizzes................................................ 8 1.3.3 ProblemSets............................................. 8 1.3.4 Grading................................................ 8 2Constants 9 3 The Structure of Physical Science 10 3.1ClassicalMechanics.............................................. 10 3.2QuantumMechanics............................................. 11 3.3StatisticalMechanics............................................. 11 3.4Thermodynamics............................................... 12 3.5Kinetics.................................................... 13 4RequisiteMath 15 4.1 Exact differentials.............................................. 15 4.2Euler’sReciprocityrelation......................................... 15 4.2.1 Example................................................ 16 4.3Euler’sCyclicrelation............................................ 16 4.3.1 Example................................................ 16 4.4Integratingfactors.............................................. 17 4.5LegendreTransformations.......................................... 17 4.6Euler’stheoremforhomogeneousfunctions................................. 18 II Lecture Notes 19 1 Thermodynamics Concepts 20 1.1Whatisitgoodfor.............................................. 20 1.2 Definitions................................................... 20 1.2.1 systems................................................ 20 1.2.2 Greeklesson............................................. 20 1.2.3 Additionalterms........................................... 20 1.3Thermometry................................................. 20 1 1.4Pressure+ .................................................. 21 1.4.1 Pressureunits............................................. 21 1.4.2 gasconstant.............................................. 21 1.5EoS’s ................................................... 21 1.5.1 IGL.................................................. 21 1.5.2 Realgases............................................... 21 2FirstLaw 22 2.1TheInternalEnergy............................................. 22 2.1.1 Components............................................. 22 2.1.2 History................................................ 22 2.1.3 Statement............................................... 22 2.2Work...................................................... 23 2.3Heat...................................................... 23 2.4HeatCapacities................................................ 23 2.5StateFunctions................................................ 24 2.6 Reversibility . ................................................. 24 2.7 W vs W ................................................. 24 2.8DesignerfxnEnthalpyH........................................... 24 2.9dUvsdH................................................... 24 2.10AdiabaticExpansionandCompressionofanIG.............................. 25 3 U(T), H(T), and Heat Capacities (C)26 3.1Mathematicalpropertiesofstatefxns-Review.............................. 26 3.1.1 EulerexercisewithIGL....................................... 26 3.1.2 Some useful coefficients....................................... 26 3.1.3 Generalrelationships......................................... 26 3.2 ∆U(T,V)................................................... 27 3.3 Example ∆U(T,V).............................................. 27 3.4 ∆H(T,P)................................................... 27 3.5HeatCapacities-TheTincrementfunctionsforU&H.......................... 28 3.5.1 Overview............................................... 28 3.5.2 vs ............................................... 28 3.5.3 HeatCapacityData......................................... 29 3.6 ∆u(T) and ∆h(T).............................................. 29 3.7 Joule-Thomson effect............................................. 29 4 Thermochemistry 31 4.1EnergyStorageandReference........................................ 31 4.2ChemicalRxns................................................ 31 4.3Hess’slaw................................................... 31 4.3.1 Overview............................................... 31 4.3.2 BondEnthalpies(energies)..................................... 32 4.4 ∆( ) ................................................... 33 4.5 Experimental ∆ and ∆ ......................................... 34 4.5.1 Calorimetry.............................................. 34 5 SecondandThirdLaws 36 5.1SpontaneousProcesses............................................ 36 5.1.1 SecondLawStatements....................................... 36 2 5.2HeatEngines................................................. 37 5.2.1 Impossible (perpetual motion machines) engines of the 1 kind................. 37 5.2.2 Impossible engines of the 2 kind................................. 37 5.2.3 CarnotCycle-reversible...................................... 38 5.2.4 CarnotCycle-irreversible...................................... 38 5.2.5 ProofthatSisastatefunctionusingaGeneralizedCarnotcycle................ 39 5.3Another(formal)perspective........................................ 39 5.4S(T,P)andS(T,V).............................................. 40 5.4.1 ∆ (Micro/Macroinsight).................................... 40 5.5EntropychangesinHeatConduction.................................... 41 5.6SecondlawReview.............................................. 41 5.7Thirdlaw................................................... 41 5.7.1 Historyandstatements....................................... 41 5.7.2 ResidualEntropy........................................... 42 5.7.3 Adiabaticdemagnetization..................................... 43 5.8StandardEntropy.............................................. 43 5.9 ∆( ) ................................................... 43 6 Chemical Equilibrium 44 6.1 Equilibrium Criteria . .......................................... 44 6.1.1 Definitions.............................................. 44 6.1.2 Types of equilibrium ......................................... 44 6.1.3 Criteriawithvariousconstraints.................................. 44 6.2Maxwell’srelations.............................................. 45 6.3Curvaturerelations.............................................. 45 6.4Incrementfunctions............................................. 45 6.4.1 G (P)................................................. 46 6.4.2 G (T)................................................. 46 ∆ 6.4.3 Gibbs-Helmholtz ( )....................................... 46 6.5 FreeenergyandWork............................................ 46 6.5.1 Helmholtz work ......................................... 46 → 6.5.2 Gibbs work .......................................... 47 → 6.5.3 Summary............................................... 47 6.6 The Chemical potential .......................................... 47 6.7 ∆S and ∆G .............................................. 47 6.8ChemicalpotentialofanIG......................................... 48 6.9 Chemical equilibrium . .......................................... 49 7RealGases 50 7.1EquationsofState.............................................. 50 7.1.1 Criticalpoints............................................ 51 7.1.2 Correspondingstates......................................... 51 7.2FugacityofaRG............................................... 52 7.3 Compressibility Fugacity.......................................... 53 ⇒ 7.3.1 Gross Compressibilities ....................................... 53 7.3.2 f(P) or (Z).............................................. 53 ln 7.3.3 f(T) or ( ) ............................................ 53 7.4MixturesofRGs............................................... 54 3 8Phasechanges 55 8.1GibbsphaseRule............................................... 55 8.1.1 Whatcanyoucontrol?........................................ 55 8.1.2 Whatisacomponent?........................................ 55 8.1.3 TopologicalAside........................................... 56 8.2 Geometric interpretation of and ................................... 56 8.3First-orderphasetransition......................................... 58 8.4Clapeyronequation.............................................. 58 8.5Clausius-Clapeyronequation........................................ 59 8.6 P(inertgas)................................................. 59 8.7 H( ).................................................... 60 8.8 G( ).................................................... 60 8.9Surfacetension................................................ 60 9 Solutions and Multicomponent systems 61 9.1IdealSolution................................................. 61 9.1.1 The IS is like IG ....................................... 61 9.2 Equilibrium between a S-IS ......................................... 62 9.3RealSolutions................................................. 63 9.4 Solvent/Solute ref. states .......................................... 63 9.4.1 Non-idealities&AzeotropesSurvey................................ 64 9.5Gibbs-DuhemEquation..........................................