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Break. Link between Thermodynamics and Kinetics. Kinetics. Modern Methods in Heterogeneous Catalysis F.C. Jentoft, November 1, 2002. Outline. Motivation and Strategy Some Important Concepts Rate Equations Mechanisms and Kinetics Temperature Dependence of Rate Constant

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  1. Break • Link between Thermodynamics and Kinetics

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

  3. Outline • Motivation and Strategy • Some Important Concepts • Rate Equations • Mechanisms and Kinetics • Temperature Dependence of Rate Constant • Compensation Effect

  4. What Kinetics Will (Not) Deliver… • Reaction rates • Rate equation / reaction order • Rate constant • Apparent activation energies • Will not deliver a mechanism….. • But any mechanism we think of should be consistent with the kinetic data….

  5. E E Catalyst A Catalyst B EA EA Reactants Reactants Products Products Reaction coordinate Reaction coordinate Motivation • Compare catalysts: Activation energy EA • Design Parameters for Setup

  6. Microscopic Reversibility k1 A + B AB k-1 k2 k3 k-2 k-3 A* + B • Equilibrium conditions • Unidirectional reaction with identical rates is not an option

  7. Steady State Approximation • Bodenstein’s approximation for consecutive reactionsIf k1*>>k1, then k1 k1* A B C • Simplifies Rate Equations

  8. Rate Equations I • Typical rate equation: • With a,b,c, the individual reaction order with respect to a particular reactant and the total reaction order n the sum of the exponents • With r the reaction rate in units of mol/l per time

  9. Rate Equations II • Typical rate equation: • With k the rate constant in units of min-1 for a first order reaction, for higher orders in inverse units of concentration in different powers

  10. pseudo 1st order Catalysis in Solution:Specific Acid / Base Catalysis • Rate constant a linear function of pH • Proton donor: H3O+ (solvated protons)Proton acceptor: OH- • Rate equation (analogous for base catalysis)

  11. Specific Acid Catalysis • Dependence of the observed rate constant for oximation of acetone on pH at 25°C. The rate equation is r = kobs * Cacetone

  12. 2nd order HA H+ + A- Catalysis in Solution:General Acid Base Catalysis • Proton donor HA, H2O...Proton acceptor B, H2O • Rate equation

  13. General Acid Catalysis

  14. Rates in Heterogeneous Catalysis • Rate with respect to mass or surface area

  15. Turn Over Frequency • Rate with respect to number of active sites low site density high site density • Turnover frequency is the number of molecules formed per active site per second (in a stage of saturation with reactant, i.e. a zero order reaction with respect to the reactant)

  16. TOF, TON, Catalysis • TONTotal number of product formed molecules per active siteTON= TOF*catalyst life time • TON = 1 stoichiometric reactionTON  102 catalytic reactionTON = 106-107 industrial application • TON origins from enzyme kinetics, definitions vary

  17. Examples for TOFs

  18. Reaction Steps in Heterogeneous Catalysis • Diffusion of reactant to catalyst • Adsorption of reactant on catalyst surface • Reaction • Desorption of products from catalyst surface • Diffusion of products away from catalyst We want to know the reaction kinetics. Diffusion should thus not be a rate limiting step.

  19. Interfacial Gradient Effects • Mass transfer bulk of fluid to surface • Case 1: reaction at surface instantaneousglobal rate controlled through mass transfer“diffusion control”, favored at high T • Case 2: reactant concentration at surface same as in bulk fluidglobal rate controlled through reaction rate“reaction controlling”, favored at low T and high turbulence

  20. Intraparticle Gradient Effects • Mass transfer within the pores of a catalyst • Vary particle size!

  21. Langmuir Hinshelwood Mechanism • Both species are adsorbed, adsorption follows Langmuir isotherm (see class next week) B A

  22. Eley Rideal Mechanism B A • Only one species is adsorbed, adsorption follows Langmuir isotherm

  23. How to Derive a Rate Equation I H+ 2 C2H5OH C2H5-O-C2H5 + H2O

  24. How to Derive a Rate Equation II

  25. How to Derive a Rate Equation III

  26. + H2 Structure Insensitivity • rate per exposed metal surface area is NOT a function of the metal particle size • active site 1-2 atoms • Example: the hydrogenation of cyclohexene

  27. Structure Insensitivity

  28. C2H6 + H2 2 CH4 Structure Sensitivity • also: ammonia synthesis (reactions involving C-C, N-N bond breaking) • rate per exposed metal surface area is a function of the metal particle size / the exposed facet plane • active site an ensemble of atoms • Example: the hydrogenolysis of ethane

  29. Structure Sensitivity

  30. Temperature Dependence of Rate Constant • Once a rate equation has been established, a rate constant can be calculated • The rate constant is temperature dependent • There are three different ways to derive this relation:Arrhenius TheoryCollision Theory Transition State Theory (Eyring)

  31. k1 van’t Hoff’s Equation A B k-1 Arrhenius Theory

  32. Arrhenius Theory • With E the apparent activation energy in kJ mol-1A the frequency factor • Plot of ln k vs. 1/T gives a slope of -EA/R which allows the calculation of the activation energy • A rule of thumb: the rate doubles for 10 K rise in temperature

  33. Collision Theory • According to the simple collision theory, the preexponential factor is dependent on T1/2 • with NA Avogadro’s number, σ cross section, μ reduced mass, k Boltzmann’s constant

  34. Activated Complex Theory A + BC A B C AB + C • Evans/Polanyi, Eyring • based on statistical thermodynamics

  35. Results of Activated Complex Theory • Rate constant (based on number of moles) • Function of T • From the equilibrium constant for the activated complex, a standard free enthalpy of activation can be calculated

  36. Example for Arrhenius Plot 2 different slopes may indicate change in mechanismor change from reaction to diffusion control

  37. Compensation Effect • A “sympathetic variation of the activation energy with the ln of the pre-exponential factor” • ln A and EA/RT have the same order of magnitude but different signs • Change in EA may b compensated by change in A

  38. Compensation Effect • Observed for the same reaction on a family of catalysts

  39. Compensation Effect • Observed for similar reactions on the same catalyst

  40. Compensation Effect: Explanations • “Apparent” activation energy EA,app derived from measured rate and rate equation • With increasing temperature, the “true” reaction rate will increase • With increasing temperature the coverage decreases (exothermic adsorption), leading to a smaller measured rate • EA,app is a weighted sum of the EA,true and the enthalpy of adsorption

  41. Literature • Gabor A. Somorjai, Introduction to Surface Chemistry and Catalysis, John Wiley, New York, 1994 • Bruce C. Gates, Catalytic Chemistry, John Wiley, New York, 1992 • G Ertl, H. Knözinger, J. Weitkamp, Handbook of Heterogeneous Catalysis, Wiley-VCH, Weinheim 1997 • G. Wedler, Physikalische Chemie, Verlag Chemie Weinheim • G.F. Froment, K.B. Bischoff, Chemical Reactor Analysis and Design, Wiley 1990 • Compensation effect: G.C. Bond, Catal. Today 1993, J. Catal. 1996

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