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Thermodynamics. Modern Methods in Heterogeneous Catalysis F.C. Jentoft, November 1, 2002. Outline. Part I: Reaction + Catalyst Thermodynamics of the target reaction Thermodynamics of catalyst: bulk (see classes on solids and defects) and surface
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Thermodynamics Modern Methods in Heterogeneous Catalysis F.C. Jentoft, November 1, 2002
Outline Part I: Reaction + Catalyst • Thermodynamics of the target reaction • Thermodynamics of catalyst: bulk (see classes on solids and defects) and surface • Thermodynamics of interaction between reactant and catalyst (see class on adsorption) Part II: Practical Matters • Vapor pressure
What Thermodynamics Will Deliver… Gives “big picture”, essence, useful for estimates
Target Reaction - Motivation • Why look at TD? …can’t change it anyway by catalysis E E without catalyst with catalyst Must look at TD because we can’t change it! EA EA Reactants Reactants Products Products Reaction coordinate Reaction coordinate
Target Reaction – Quantities to Look at • Enthalpy of reaction ΔrHexothermic / endothermicΔrH of side reactions • Free Enthalpy (Gibbs Energy) ΔrGexergonic / endergonic • Equilibrium Constant K: Equilibrium Limitations • Change of Temperature and Pressure (variables)
Enthalpy of Reaction • Determines reactor setup (see classes on catalyst testing and reaction engineering)catalyst formulation / dilution“hot spots” / heating powerisothermal operation in the lab • Enthalpy of side reactionsparallel / secondary reactions
Enthalpy of Reaction, ΔrH • Reaction enthalpy needs a reaction equation!!! • Calculate from enthalpies of formation of products and reactants ΔrH°: standard enthalpy of reaction ΔfH°: standard enthalpies of formation vi: stoichiometric factors, positive for products, negative for reactants
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, ΔcH° )
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
Standard Conditions (IUPAC) • „Standard state pressure“(IUPAC 1982) p° = 105 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“ ??
Standard Conditions (Textbooks) • AtkinsSTP „Standard temperature and pressure““p = 101 325 Pa = 1 atm, T° = 273,15 K SATP „Standard ambient temperature and pressure“p° = 105 Pa = 1 bar, T° = 298,15 K • Wedler „Standarddruck“p = 1.013 bar = 1 atm = 101.325 kPa„Standardtemperatur“T° = 298,15 K
Standard Conditions (Other) • Catalysis Literature NTP „Normal temperature and pressure““20°C and 760 torr70 degrees F and 14.7 psia (1 atmosphere) ALWAYS CHECK / SPECIFY THE CONDITIONS !!
Sources for Thermodynamic Data • CRC Handbook of Thermophysical and Thermochemical DataEds. 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
Some Examples: Combustion • Combustion of hydrogen (Knallgasreaktion) ΔcH° = -286 kJ mol-1 • Combustion of carbonΔcH° = -394 kJ mol-1 Reactions with CO2, H2O or other very stable molecules as products are usually strongly exothermic, however….
Steam Reforming of Methanol ΔcH° = 93 kJ mol-1
ΔfH° = 49.0 kJ mol-1 State of the Matter • Formation of benzene at 298.15 K ΔfH° = 82.93 kJ mol-1 • Enthalpy of evaporation of benzene?ΔvapH° = 30.8 kJ mol-1 at 80°C
Partial Oxidation of Propene • Oxidation of propene to acroleinΔrH° = ??? kJ mol-1
Partial Oxidation • Only enthalpy of combustion, ΔcH°, of acrolein is given ΔcH° = -1633 kJ mol-1 Enthalpies of combustion are easily determined quantities (e.g. from quantitative combustion in a bomb calorimeter)
ΔcH° = -1754 kJ mol-1 ΔcH° = -1633 kJ mol-1 ΔfH° = -121 kJ mol-1 Use Hess’s Law Enthalpy is a State Function
E EA EA Reactants Partial Oxidation Product Total Oxidation Products • Oxidation of acrolein to CO2 ΔcH° = -1633 kJ mol-1 Reaction coordinate Partial vs. Total Oxidation • Oxidation of propene to acroleinΔrH° = -427 kJ mol-1
Oxidative dehydrogenation of isobutane to isobuteneΔrH° = -124 kJ mol-1 Dehydrogenation vs. Oxidative Dehydrogenation • Dehydrogenation of isobutane to isobuteneΔrH° = 117 kJ mol-1
Oxidative Dehydrogenation:Thermodynamic Traps • Combustion of isobuteneΔcH° = - 2525 kJ mol-1 Nevertheless, the oxidative dehydrogenation of isobutene is in commercial operation (CrO3/Al2O3 or supported Pt catalyst)
Dehydrogenation • Dehydrogenation of ethylbenzene to styreneΔrH° = 117 kJ mol-1
Enthalpy Products, T2 Products, T1 ΔrH2 ΔrH1 Reactants, T2 Reactants, T1 Reaction coordinate Change of ΔrH with Temperature • Most of the time, we are not interested in room temperature
How to Calculate ΔrH as Function of T • Each enthalpy in the reaction equation changes according to Kirchhoff’s law • And, if Cp = constant over the temperature range of interest
How to Calculate ΔrH as Function of T • Cp as a function of temperature is usually a polynomial expression such as • If there is a phase transition within the temperature range, it must be accounted for
Isomerization • Isomerization of butane ΔrH° = - 7 kJ mol-1 ΔrS° = -15 J mol-1 ΔrG°= - 2.3 kJ mol-1 • Consistency check....
Free Enthalpy ΔrG, and Equilibrium Constant K • Relation between ΔrG° and K in equilibrium, ΔrG=0 • Composition dependence of ΔrG • Thermodynamic equilibrium constant (dimensionless)
Different Equilibrium Constants K • Kp • correlation between Kth and Kp [Pai] For low pressures (a few bars and less), the fugacity coefficients are about 1 All pressures, including po should be in the same units.
at 298 K 28 % 72 % Isomerization Equilibrium • Isomerization of butane ΔrG°= - 2.3 kJ mol-1 • With and
Indefinite integration Definite integration Equilibrium Constant Temperature Dependence van’t Hoff’s Equation
Equilibrium Temperature Dependence Start your research by calculating the thermodynamics of your reaction!
Part II: Practical Matters • Vapor pressure and saturators Gas in Gas out Saturator, 100 ml Methanol 79.17 g, is 2.47 mol
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, Cp of liquid MeOH is 81.6 J mol-1 K-1 • The temperature of the methanol would theoretically drop by 108 K
For sublimation and evaporation assumes ideal behavior of the gas phase August’s vapor pressure formula assumes enthalpy is constant within given temperature range The Clausius-Clapeyron Equation General differential form of the Clausius-Clapeyron Equation
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 • T1 = 337.6 K, p = 100.66 kPa • The carrier gas will dissolve in the liquid and the vapor pressure will be lowered
Methanol Vapor Pressure Small temperature changes can cause significant changes in vapor pressure