1. Thermodynamics Modern Methods in Heterogeneous Catalysis F.C. Jentoft, November 1, 2002

2. Outline Part I: Reaction + Catalyst 1.Thermodynamics of the target reaction 2.Thermodynamics of catalyst: bulk (see classes on solids and defects) and surface 3.Thermodynamics of interaction between reactant and catalyst (see class on adsorption) Part II: Practical Matters 1.Vapor pressure

3. What Thermodynamics Will Deliver… Gives “big picture”, essence, useful for estimates

4. Target Reaction - Motivation  Why look at TD? …can’t change it anyway by catalysis Reactants Products E EAEA without catalyst Reaction coordinate Reactants Products E EAEA with catalyst Reaction coordinate Must look at TD because we can’t change it!

5. Target Reaction – Quantities to Look at  Enthalpy of reaction Δ r H exothermic / endothermic Δ r H of side reactions  Free Enthalpy (Gibbs Energy) Δ r G exergonic / endergonic  Equilibrium Constant K: Equilibrium Limitations  Change of Temperature and Pressure (variables)

6. Enthalpy of Reaction  Determines reactor setup (see classes on catalyst testing and reaction engineering) catalyst formulation / dilution “hot spots” / heating power isothermal operation in the lab  Enthalpy of side reactions parallel / secondary reactions

7. Enthalpy of Reaction, Δ r H  Reaction enthalpy needs a reaction equation!!!  Calculate from enthalpies of formation of products and reactants Δ r H°:standard enthalpy of reaction Δ f H°:standard enthalpies of formation v i :stoichiometric factors, positive for products, negative for reactants

8. Things to Watch in Calculations…..  Stoichiometric factors  Standard conditions  State of the matter (solid, liquid, gaseous)  Which data are available (sometimes only enthalpy of combustion, Δ c H° )

9. Standard Conditions (IUPAC)  International Union of Pure and Applied Chemistry (IUPAC) Größen, Einheiten und Symbole in der Physikalischen Chemie VCH, Weinheim 1996 FHI library 50 E 49 (English version: 50 E 48)  Standard state indicated by superscript ,° www.iupac.org

10. Standard Conditions (IUPAC)  „Standard state pressure“(IUPAC 1982) p° = 10 5 Pa „Standard atmosphere“ (before 1982) p° = 101 325 Pa = 1 atm  „Standard concentration“c° = 1 mol dm -3  „Standard molality“m° = 1 mol kg -1  „Standard temperature“??

11. Standard Conditions (Textbooks)  Atkins STP „Standard temperature and pressure““ p = 101 325 Pa = 1 atm, T° = 273,15 K SATP „Standard ambient temperature and pressure“ p° = 10 5 Pa = 1 bar, T° = 298,15 K  Wedler „Standarddruck“ p = 1.013 bar = 1 atm = 101.325 kPa „Standardtemperatur“ T° = 298,15 K

12. Standard Conditions (Other)  Catalysis Literature NTP „Normal temperature and pressure““ 20°C and 760 torr 70 degrees F and 14.7 psia (1 atmosphere) ALWAYS CHECK / SPECIFY THE CONDITIONS !!

13. Sources for Thermodynamic Data  CRC Handbook of Thermophysical and Thermochemical Data Eds. David R. Lide, Henry V. Kehiaian CRC Press Boca Raton New York 1994 FHI library 50 E 55  D'Ans Lax Taschenbuch für Chemiker und Physiker Ed. C. Synowietz Springer Verlag 1983 FHI library 50 E 54

14. Some Examples: Combustion  Combustion of hydrogen (Knallgasreaktion) Δ c H° = -286 kJ mol -1  Combustion of carbon Δ c H° = -394 kJ mol -1 Reactions with CO 2, H 2 O or other very stable molecules as products are usually strongly exothermic, however….

15. Steam Reforming of Methanol Δ c H° = 93 kJ mol -1

16. State of the Matter  Formation of benzene at 298.15 K Δ f H° = 49.0 kJ mol -1  Enthalpy of evaporation of benzene? Δ vap H° = 30.8 kJ mol -1 at 80°C Δ f H° = 82.93 kJ mol -1

17. Partial Oxidation of Propene  Oxidation of propene to acrolein Δ r H° = ??? kJ mol -1

18. Examples for Sources

20. Partial Oxidation  Only enthalpy of combustion, Δ c H °, of acrolein is given Δ c H° = -1633 kJ mol -1 Enthalpies of combustion are easily determined quantities (e.g. from quantitative combustion in a bomb calorimeter)

21. Use Hess’s Law Δ c H° = -1754 kJ mol -1 Δ c H° = -1633 kJ mol -1 Δ f H° = -121 kJ mol -1 Enthalpy is a State Function

22. Partial vs. Total Oxidation  Oxidation of propene to acrolein Δ r H° = -427 kJ mol -1  Oxidation of acrolein to CO 2 Δ c H° = -1633 kJ mol -1 Reactants Partial Oxidation Product E EAEA Reaction coordinate Total Oxidation Products EAEA

23. Dehydrogenation vs. Oxidative Dehydrogenation  Oxidative dehydrogenation of isobutane to isobutene Δ r H ° = -124 kJ mol -1  Dehydrogenation of isobutane to isobutene Δ r H ° = 117 kJ mol -1

24.  Combustion of isobutene Δ c H° = - 2525 kJ mol -1 Oxidative Dehydrogenation: Thermodynamic Traps Nevertheless, the oxidative dehydrogenation of isobutene is in commercial operation (CrO 3 /Al 2 O 3 or supported Pt catalyst)

25.  Dehydrogenation of ethylbenzene to styrene Δ r H° = 117 kJ mol -1 Dehydrogenation

26. Change of Δ r H with Temperature  Most of the time, we are not interested in room temperature Reactants, T 1 Products, T 1 Enthalpy Reaction coordinate Products, T 2 Reactants, T 2 ΔrH1ΔrH1 ΔrH2ΔrH2

27. How to Calculate Δ r H as Function of T  Each enthalpy in the reaction equation changes according to Kirchhoff’s law  And, if C p = constant over the temperature range of interest

28. Heat Capacity as a Function of T, Condensed Phases

29. Heat Capacity as a Function of T, Gases

30. How to Calculate Δ r H as Function of T  If there is a phase transition within the temperature range, it must be accounted for  C p as a function of temperature is usually a polynomial expression such as

31.  Consistency check....  Isomerization of butane Δ r H° = - 7 kJ mol -1 Δ r S° = -15 J mol -1 Δ r G°= - 2.3 kJ mol -1 Isomerization

32. Free Enthalpy Δ r G, and Equilibrium Constant K  Relation between Δ r G° and K in equilibrium, Δ r G=0 (dimensionless)  Thermodynamic equilibrium constant  Composition dependence of Δ r G

33.  correlation between K th and K p Different Equilibrium Constants K For low pressures (a few bars and less), the fugacity coefficients are about 1 All pressures, including p o should be in the same units. [Pa  i ] KpKp

34.  With and  Isomerization of butane Δ r G°= - 2.3 kJ mol -1 Isomerization Equilibrium at 298 K 28 %72 %

35. Equilibrium Constant Temperature Dependence van’t Hoff’s Equation Indefinite integration Definite integration

36. Equilibrium Temperature Dependence Start your research by calculating the thermodynamics of your reaction!

37. Part II: Practical Matters  Vapor pressure and saturators Saturator, 100 ml Methanol 79.17 g, is 2.47 mol Gas outGas in

38. Methanol Thermodynamic Data

39. Heat Consumed by Evaporation  Assumption: saturator is adiabatic, evaporate 20 ml of methanol, all energy for evaporation taken from remaining 80 ml methanol  20 ml is about 0.5 mol, need about 17.7 kJ for evaporation  80 ml is about 2 mol, C p of liquid MeOH is 81.6 J mol -1 K -1  The temperature of the methanol would theoretically drop by 108 K

40. The Clausius-Clapeyron Equation General differential form of the Clausius-Clapeyron Equation For sublimation and evaporation assumes ideal behavior of the gas phase August’s vapor pressure formula assumes enthalpy is constant within given temperature range

41. Vapor Pressure and Temperature  At 64.4°C, the vapor pressure of methanol is 755 torr and the enthalpy of evaporation is 35.4 kJ mol -1  T 1 = 337.6 K, p = 100.66 kPa  The carrier gas will dissolve in the liquid and the vapor pressure will be lowered

42. Methanol Vapor Pressure Small temperature changes can cause significant changes in vapor pressure