Thermodynamic Aspects Of Heterogeneous Catalysis
Modern Methods in Heterogeneous Catalysis Research WS 2012/2013Thermodynamic Aspects of Heterogeneous CatalysisResearchRaimund HornFritz Haber Institute of the Max Planck Society BerlinEmmy Noether Research Group „High Temperature Catalysis“10/26/20121
IntroductionOne way of dealingwith thermodynamics!or2
Content1. Why does Thermodynamics matters in Catalysis?2. Thermodynamic Quantities, Concepts and Tools3. Chemical Equilibrium: Reactor Conversion for a Single Reaction4. Chemical Equilibrium: Conversion and Selectivity Calculations forMultiple Reactions3
1. Why does Thermodynamics matters in Catalysis?The best-known „catalytic reactor“:One reaction catalyzed bythe catalytic converter:CO ½ O2 CO2 rHo (298K) -283 kJ mol-1 CO2 OCO O M CO2 M CO2On PtCO O 2 OC O OC OIn the gas phaseCO O2CO2COO C OPtO O C 4
1. Why does Thermodynamics matter in Catalysis?Energetics of CO oxidationTemperatureE E r exp RT In the gas phaseE On PtTaken from: G. Ertl, Catalysis: Science and Technology Vol. 4 1983 p.245ff, all enthalpies in kJ mol-15
1. Why does Thermodynamics matter in Catalysis?Kinetics rA k T C A T Equilibrium RG 0ln K RTK ads A 0A 1 K ads A T TransportJA D AB T C A T v v0FT p 0 TFT 0 p T 06
1. Why does Thermodynamics matters in Catalysis?Thermodynamics matters in Catalysis because Thermodynamics determines the maximum extentof any given reaction C The reaction rate decreases with A B rA k f C A BKC approach to thermodynamic equilibrium macroscopic Heat release or uptake by chemical reactions leads tocomplex non-isothermal reactor behavior Adsorption/Desorption thermodynamics determines theconcentration of adsorbed species and in turn the rate ofsurface reactions (e.g. Langmuir Hinshelwood rateexpressions)microscopic The kinetics of elementary steps are related to theirthermodynamics7
1. Why does Thermodynamics matter in Catalysis?Taken from: M. Salciccioli et al. Chem. Eng. Sci. 66 (2011) 43198
Equilibrium Conversion and SelectivityCalculations for Multiple Reactions(Examples)Consequences for Reactor Design (Examples)Chemical Conversion for a Single Reaction (Example)Chemical Equilibrium and Law of Mass ActionChemical Potential µClausius Inequality and Gibbs Free Energy GEntropy S and Second Law of TDFirst Law of TD, U, H, CV, CpQuantities, Concepts and Tools9
2. Thermodynamic Quantities, Concepts and Tools?2.1) Systems in Thermodynamicsopen systemSystemclosed systemSurroundingse.g. a heatedflow reactorisolated systemExchange ofMattere.g. anautoclaveExchange ofEnergye.g. a thermos bottleor the universe10
2. Thermodynamic Quantities, Concepts and Tools?2.2) ProcessesIrreversible Processes11
2. Thermodynamic Quantities, Concepts and Tools?2.2) ProcessesReversible Processes12
2. Thermodynamic Quantities, Concepts and Tools?2.3) Important QuantitiesThermodynamic QuantitySymbol Intensive or Extensive?SI Unitmassmextensivekgmolar massMintensivekg mol-1temperatureTintensiveKpressureP, pintensivePafugacityfintensivePadensity intensivekg m-3volumeVextensivem3molar volumeVm, v, intensivem3 mol-1heatQextensiveJworkWextensiveJinner energyUextensiveJenthalpyHextensiveJfree energy, Helmholtz free energyF, AextensiveJfree enthalpy, Gibbs free energyGextensiveJ 13
2. Thermodynamic Quantities, Concepts and Tools?2.4) Important QuantitiesThermodynamic QuantitySymbolIntensive orExtensiveSI UnitentropySextensiveJ K-1molare inner energyUm,uintensiveJ mol-1molar enthalpyHm,hintensiveJ mol-1molar free energyAm, a, Fm, fintensiveJ mol-1molar free enthalpyGm, gintensiveJ mol-1chemical potentialµintensiveJ mol-1molar entropySm,sintensiveJ K-1 mol-1heat capacity at constant volumeCVextensiveJ K-1heat capacity at constant pressureCPextensiveJ K-1specific heat capacityc(V,p)intensiveJ kg-1 K-1molar heat capacityCm(V,p), cm(V,p)intensiveJ mol-1 K-114
2. Thermodynamic Quantities, Concepts and Tools?2.4.1) Internal Energy U in JU U trans U vib U rot U chem U nuc U el U magn .CV(internal pressure )0 for ideal gasesFirst Law of Thermodynamics: U Q W15
2. Thermodynamic Quantities, Concepts and Tools?2.4.2) Internal Energy U in JThe First Law of Thermodynamics is important for describing non-isothermalreactors (energy balance) but says nothing about the direction of a physical orchemical process! U Q W16
2. Thermodynamic Quantities, Concepts and Tools?2.4.3) Enthalpy H in JweightareaH H (T , p, n1 , n2 ,., nk ) H H H dp dH dn1 . dT T p ,n j p T ,n j n1 p ,T ,n j 1Cp(isothermer drosseleffekt in m3) 0 for ideal gases17
2. Thermodynamic Quantities, Concepts and Tools?2.4.3) Enthalpy H in J1 A A B B C C D D d dni ni ni ,0 i i H H p,Texample:enthalpy of reaction H i H iextent ofreactionHess Lawi13N 2 H 2 NH 3221 3 H H N 2 H H 2 1 H NH 32 2 The standard enthalpy of formation Hf or standard heat of formation of acompound is the change of enthalpy that accompanies the formation of 1mole of the compound from its elements, with all substances in their standardstates. The standard state of a gas is the (hypothetical) ideal gas at 1bar and298.15K. For liquids and solids it is the pure substance at 1bar and 298.15K.H NH 31 3 H ( NH 3 ) H N 2 H H 2 1 H NH 32 2 f18
2. Thermodynamic Quantities, Concepts and Tools?2.4.4) Heat capacities CV, Cp in J/Kfor ideal gasesC p ,m CV ,m R19
2. Thermodynamic Quantities, Concepts and Tools?2.4.4) Heat capacities CV, Cp in J/K13kJJ N 2 H 2 NH 3 r H 45.9 r C p i C pi 22.18622molmol KiKirchhoff‘s lawT 298.15 Kp 1bar13N2 H222T 298.15 Kp 1bar1NH 3kJ45.9mol r H r Cp T pT2T 400 Kp 1bar13N2 H222 r H (T2 ) r H (T1 ) r C p dTT1T 400 Kp 1bar1NH 3 48.2kJmol20
2. Thermodynamic Quantities, Concepts and Tools?2.4.5) EntropyExample: 3 Molecules (A,B,C) distributed among 4 energy states( 0 0, 1 1, 2 2 1, 3 3 1) with a total energy of total 3 1 (isolated system)Energy StateEnergyMacrostateS k ln WI3 1 22 1CBCABA 11 1BCACAB 00 1AABBCCBCBIII 3# of Microstates(statistical weight W)AIIAC3CAB6ABC121
2. Thermodynamic Quantities, Concepts and Tools?2.4.5) EntropySecond Law of Thermodynamics22
2. Thermodynamic Quantities, Concepts and Tools?2.4.5) Entropyirreversibleprocess 1 TlowThighSadiCarnotreversibleprocess23
2. Thermodynamic Quantities, Concepts and Tools?2.4.5) EntropyClausius InequalityRudolph ClausiusdQdS T24
2. Thermodynamic Quantities, Concepts and Tools?2.4.6) Helmholtz Free Energy (Free Energy) andGibbs Free Energy (Free Enthalpy)Clausius InequalitydQdS 0 dQ TdST Q V dU Q p dHspontaneous process at constant volumedU TdS 0spontaneous process at constant pressuredH TdS 0Helmholtz Free Energy (Free Energy):Gibbs Free Energy (Free Enthalpy):25
2. Thermodynamic Quantities, Concepts and Tools?2.4.7) Dependencies of G by Combining the First and Second Law ofThermodynamicsdU Q W Qrev Wrev TdS pdVH U pV dH dU pdV VdpdH TdS pdV pdV Vdp TdS VdpdG dH TdS SdT TdS Vdp TdS SdT VdP SdT G G V S T p p T26
2. Thermodynamic Quantities, Concepts and Tools?2.4.8) Gibbs Free Energy in Mixtures and the Chemical Potential G G G dG VdP SdT dn1 dn2 . dni n1 p ,T ,n j 1 n2 p ,T ,n j 2 ni p ,T ,n j i G i ni p,T ,n j iT,p const.chemical potential of idG i , Adni , A i , B dni , B i , B i , A dni , B 027
2. Thermodynamic Quantities, Concepts and Tools?2.4.8) Gibbs Free Energy in Mixtures and the Chemical Potential S i S m ,i T p ni p ,T ,n j i i p V T ni Vm ,i p ,T ,n j iExample: pure ideal gaspV nRT Vm V RT np28
2. Thermodynamic Quantities, Concepts and Tools?2.4.8) Gibbs Free Energy in Mixtures and the Chemical PotentialMembrane permeable for i(e.g. Pd and i H2)for ideal gaseous andliquid mixturesfor real systemsin any case29
2. Thermodynamic Quantities, Concepts and Tools?2.5)Chemical Equilibrium A A B B C C D D ni ni ,0 i extent ofreactionin equilibrium30
2. Thermodynamic Quantities, Concepts and Tools?2.5)Chemical EquilibriumGGTT const. k o n s t.pp const. k o n s t.d G 0G 0 R e a k tio n s k o o r d in a te31
2. Thermodynamic Quantities, Concepts and Tools?2.5)Chemical Equilibriumlaw of mass actionstandard state for all gases is the pure ideal gas at 1baractivity ofan ideal gasKp32
2. Thermodynamic Quantities, Concepts and Tools?2.5)Chemical EquilibriumK f ( p)Kp i i K x i p p x i ii i K p f ( p) i i p p K x p p K x f ( p)piV ni RT pi ci RTK c i RT ii i i RT p ci i p i p K c p K c f ( p) i33
2. Thermodynamic Quantities, Concepts and Tools?2.5)Chemical EquilibriumTemperature Dependance of K:Gibbs Helmholtz Equationvan‘t Hoff Equation34
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionExample: Calculate the maximum NH3 yield of the Haber-Bosch-Process for25 C 600 C and 1bar p 500 bar! Assume a stoichiometric feed andideal gases for simplicity!13N 2 g H 2 ( g ) NH 3 ( g )Equation:22Thermodynamic Data (NIST Chemistry Webbook, CRC Handbook, PC books.):Species Hf / kJ mol-1S / J mol-1 K-1Cp / J mol-1 K-1AB / 10-3 K-1C / 10-6 012NH3-45.9192.825.9332.58-3.046C p / J K 1 mol 1 A B T C T 235
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction G H T S Calculate K for 25 C:Species i Hf / kJ mol-1 S / J mol-1 K-1Cp / J mol-1 K-1AB / 10-3 K-1C / 10-6 0.83682.012NH31-45.9192.825.9332.58-3.046kJkJ H 1 / 2 0 ( 3 / 2) 0 1 ( 45.9) 45.9molmolJJ S 1 / 2 191.6 ( 3 / 2) 130.7 1 192.8 99.05mol Kmol KkJkJkJ G 45.9 298.15 K 99.05 10 3 16.37molmol Kmol G 16.37 103 J mol K exp 738K exp RT mol 8.314J 298.15 K 36
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionniCalculate X from K:Species ini0/molni/molxiN2-1/21/21/2-1/2 (1/2-1/2 )/(2- )H2-3/23/23/2-3/2 (3/2-3/2 )/(2- )NH310 /(2- )22- 1 1K a i i i 1d dni dni i d ni ni 0 i ini 00n N 2, 0 n N 2X n N 2, 0 N 2 ( 1 / 2) nN 2,01/ 21 p NH 3 p p 2 p 1/ 23/ 21/ 23/ 2 1 / 2 1 / 2 p 3 / 2 3 / 2 p p N 2 pH 2 p p p 2 p 2 37
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction1 p 2 p 738 1/ 23/ 2 1 / 2 1 / 2 p 3 / 2 3 / 2 p p 2 p 2 T 298.15 K and p 1 barSolution: Graphical Solution(e.g. with Excel, Origin.)38
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionT dependance of K: lnK H H T ln K T ln K T1 dT 22RT T p RTT1TT H T H T1 C p T dT T1Species i Hf /kJ mol-1Cp / J mol-1 K-1S /J mol-1 07-0.83682.012NH31-45.9192.825.9332.58-3.046 C 0p T A B T C T 2 A i Ai .i C T 30.17 30.9 10 T 5.90 10 T0p 3 6239
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionT H T H T1 C p T dT T dependance of K:T1 C 0p T A B T C T 2T H T H T1 A B T C T 2 dT T1 B 2 C 323 H T1 A T T1 T T1 T T123 B 2 C 3 B 2 C 3 H T1 A T1 T1 T1 A T T T2323 lnK H H T ln K T ln K T1 dT 22RT T p RTT1T40
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionT dependance of K: B 2 C 3 B 2 C 3 H T H T1 A T1 T1 T1 A T T T2323 H T const. A B C T22RTRTRT 2 R 3 R B 2 C 3 const. H T1 A T1 T1 T123 T const . A B C ln K T ln K T1 T dT2RT RT 2 R 3 R T1 const . 1 1 A T B C 22 ln K T ln K T1 ln T T T T11 R T1 T R T1 2 R6R 41
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionT dependance of K:const . 1 1 A T B C 22 ln K T ln K T1 ln T T T T11 R T1 T R T1 2 R6R Solve1 p 2 p exp ln K (T ) 1/ 23/ 2 1 / 2 1 / 2 p 3 / 2 3 / 2 p p 2 p 2 numerically or graphically with p and T as parameters gives (p,T)!42
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionSolution: Numerical Solution (e.g. with Matlab, Mathematica.) T/Kp / bartypical process conditions forindustrial ammonia synthesis43
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionThermodynamics says nothing about the rate at which a process proceeds!44
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionTeSO 2 1 / 2O2 V SO32 O5 , K 2 SO4 400 600 C r H 99kJ / molTa45
3. Chemical Equilibrium: Reactor Conversion for a Single ReactionCO 2 H 2 CH 3OH r H 300 K 90.8 kJ / molLinde Isothermal Reactor, e.g. formethanol synthesis46
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.1 Theory G T , p G n1 , n2 ,., nN minbut the ni cannot vary independently because they have to fulfill thematerials balancesmoles of species i inthe reaction mixtureN aki ni bki 1total moles of atoms of elementk in the reaction mixturesnumber of atoms ofelement k in species iN N a ki ni bk 0 k a ki ni bk 0 i 1 i 1 M N k a ki ni bk 0 k 1 i 1 Lagrange Multipliers47
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.1 TheoryM N F G T , p k a ki ni bk k 1 i 1 Lagrange Function F niMM G k a ki i k a ki 0k 1 T , p ,n j i ni T , p ,n j i k 1MGi0 RT ln a i k a ki 0k 1 N k a ki ni bk 0 i 1 set of N equations(1 for each of the N species)set of M equations(1 for each of the M elements)N M unknowns (n - mole numbers m - lambdas)48
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.2 Example: Calculate the equilibrium composition of a steam reformingmixture consisting of CH4, H2O, CO, CO2 and H2 at T 1000K and p 1bar.n0,CH4 2mol, n0,H2O 3mol. Ideal gases can be assumed.From thermodynamic tables (e.g. CRC Handbook) we extract:SpeciesCH4H2OCOCO2H2 Gf (1000K) / J mol-119475-192603-200281-3958650From the species formulas we obtain:SpeciesCH4H2OCOCO2H2# of C atomsaC,CH4 1aC,H2O 0aC,CO 1aC,CO2 1aC,H2 0# of O atomsaO,CH4 0aO,H2O 1aO,CO 1aO,CO2 2aO,H2 0# of H atomsaH,CH4 4aH,H2O 2aH,CO 0aH,CO2 0aH,H2 249
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.2 Example: Formulating the equations G 0f ,iRTM kaki 0k 1 RT ln a i ai pini 1barnip x ip p ni 1bar ni n19475 ln CH 4CH4:8.314 1000 ni i C4 H 0 8.314 10008.314 1000 nH 2O 192603 lnH2O: 8.314 1000 ni i nCO 200281 lnCO: 8.314 1000 ni i O2 H 0 8.314 10008.314 1000 C O 0 8.314 1000 8.314 1000 n 395865 ln CO 2CO2:8.314 1000 ni i C2 O 0 8.314 10008.314 1000 H2: nln H 2 ni i 2 H 0 8.314 1000 iistarting valuesn0,CH4 2 moln0,H2O 3 mol.atom balance on CnCH 4 nCO nCO 2 2 0atom balance on OnH 2O nCO 2nCO 2 3 0atom balance on H4nCH 4 2nH 2 O 2nH 2 14 050
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.2 Example: Solving the system of nonlinear equations e.g in Matlab (fsolve)nCH 4 0.175xCH 4 0.0202nH 2O 0.856x H 2O 0.0990nCO 1.507xCO 0.1742nCO 2 0.319xCO 2 0.0368nH 2 5.795x H 2 0.6698 n xii 8.651i 1iThe most difficult thing is to find starting values that work. Make educatedguesses based on physical or chemical knowledge (0 xi 1), e.g. nH 2ln ni i 2 H 8.314 1000 ln 0.5 0 H ,0 2881 2 8.314 1000 51
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.3 Another Example: Equilibrium Calculations with CHEMKINMethan Oxidation on Rh and Pt Coated Foam Catalysts(T 1000 C)CH4 O2 10-3 sp, H const.H2, CO, H2O, CO252
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.3 Another Example: Equilibrium Calculations with CHEMKIN5 wt% Rh on 80ppi -Al2O3 foam, feed 5 ln/min, C/O 1.0, Ar/O2 79/21, 1 barR. Horn*, K. A. Williams, N. J. Degenstein, A. Bitsch-Larsen, D. Dalle Nogare, S. A. Tupy, L. D. Schmidt J. Catal. 249 (2007) 380-393
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.4 Take home message: Some months in the Lab can save you one day inthe Library!!!typical transient experiment
4. Chemical Equilibrium: Conversion and Selectivity Calculations for MultipleReactions?4.4 Take home message: Some months in the Lab can save you one day inthe Library!!!tr/ss 98%tr/ss 99%
Thermodynamics matters in Catalysis!!!Kinetics rA k T C A T Equilibrium RG 0ln K RTK ads A 0A 1 K ads A T TransportJA D AB T C A T v v0FT p 0 TFT 0 p T 056
Maybe the better way to deal with Thermodynamics?Thank you very much for your attention!!!57
mass m extensive kg molar mass M intensive kg mol-1 temperature T intensive K pressure P, p intensive Pa fugacity f intensive Pa density intensive kg m-3 volume V extensive m3 molar volume V m, v, intensive m3 mol-1 heat Q extensive J work W extensive J inner energy U extensive J enthalpy H extensi
catalysis, spanning from asymmetric catalysis in organic synthesis to conversion of syngas into hydrocarbons and alcohols. Dr. Jones is the founding Editor-in-Chief of the journal, ACS Catalysis, and is Vice-President of the North American Catalysis Society.
biphasic catalysis is asymmetric phase - transfer catalysis ( PTC ), where a nonrace-mic chiral additive is applied to increase the mobility of a given catalyst or reactant into a favored phase and furthermore control the stereochemical outcome. Although, in general, catalyst recycling is somewhat diffi cult in PTC systems, it
The Handbook of Heterogeneous Catalysis? Industrial & Recent processes (1980 – 199x) Environmental Catalysis. F.C. Jentoft Dept. AC / FHI Berlin Early Catalytic Processes-6000 Beer brewing by malting procedure
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Handbook of Green Chemistry ISBN (12 volumes): 978-3-527-31404-1 Set 1 Green Catalysis 978-3-527-31577-2 Volume 1: Homogeneous Catalysis Set 2 Green Solvents 978-3-527-31574-1 Volume 2: Heterogeneous Catalysis Set 3 Green Processes 978-3-527-31576-5 Volume 3: Biocatalysis Set 4 Green Product
Acid-Base Catalysis Application of Solid Acid-Base Catalysts Annette Trunschke 18 February 2005. Modern Methods in Heterogeneous Catalysis Research : 18/02/2005 2 Outline 1. Introduction - basic principles 2. Substrates and products 3. Kinds of acid / base catalysts - examples 4. Characterization of surface acidity / basicity - examples .
basic principles of catalysis with special reference to homogeneous and heterogeneous catalysis, enzyme catalysis, and industrially important catalyzed reactions. 3. Surface chemistry and Interfacial phenomenon: Basic concepts of adsorption isotherm, sols, gels, emulsions, micro-emulsions, miscelles, aerosols. 4. Distribution Law:
The mechanistic ideas developed in homogeneous catalysis are also becoming more influential in the field of classical heterogeneous catalysis by suggesting structures for intermediatesandmechanismsfor reaction steps. By bringing about a reaction at lower temperature, a catalyst can save energy in commercial applications. It often gives higher selectivity for the desired product .
