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Break Link between Thermodynamics and Kinetics

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

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Outline 1.Motivation and Strategy 2.Some Important Concepts 3.Rate Equations 4.Mechanisms and Kinetics 5.Temperature Dependence of Rate Constant 6.Compensation Effect

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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….

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Motivation Reactants Products E EAEA Catalyst A Reaction coordinate Reactants Products E EAEA Catalyst B Reaction coordinate Design Parameters for Setup Compare catalysts: Activation energy E A

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Equilibrium conditions Microscopic Reversibility A* + B ABA + B k1k1 k -1 k2k2 k -2 k3k3 k -3 Unidirectional reaction with identical rates is not an option

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Steady State Approximation Bodenstein’s approximation for consecutive reactions If k 1 *>>k 1, then ABCABC k1k1 k1*k1* Simplifies Rate Equations

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Rate Equations I 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 Typical rate equation:

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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

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Catalysis in Solution: Specific Acid / Base Catalysis Rate constant a linear function of pH pseudo 1 st order Proton donor: H 3 O + (solvated protons) Proton acceptor:OH - Rate equation (analogous for base catalysis)

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

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Catalysis in Solution: General Acid Base Catalysis Proton donorHA, H 2 O... Proton acceptorB, H 2 O Rate equation 2 nd order H + + A - HA

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General Acid Catalysis

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

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Turn Over Frequency Rate with respect to number of active sites low site densityhigh 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)

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TOF, TON, Catalysis TON Total number of product formed molecules per active site TON= TOF*catalyst life time TON = 1stoichiometric reaction TON 10 2 catalytic reaction TON = 10 6 -10 7 industrial application TON origins from enzyme kinetics, definitions vary

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Examples for TOFs

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Reaction Steps in Heterogeneous Catalysis 1.Diffusion of reactant to catalyst 2.Adsorption of reactant on catalyst surface 3.Reaction 4.Desorption of products from catalyst surface 5.Diffusion of products away from catalyst We want to know the reaction kinetics. Diffusion should thus not be a rate limiting step.

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

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

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

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

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How to Derive a Rate Equation I 2 C 2 H 5 OH C 2 H 5 -O-C 2 H 5 + H 2 O H+H+

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How to Derive a Rate Equation II

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How to Derive a Rate Equation III

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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 + H 2

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Structure Insensitivity

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Structure Sensitivity also: ammonia synthesis (reactions involving C-C, N-N bond breaking) C 2 H 6 + H 2 2 CH 4 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

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Structure Sensitivity

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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 Theory Collision Theory Transition State Theory (Eyring)

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Arrhenius Theory BA k1k1 k -1 van’t Hoff’s Equation

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

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Collision Theory According to the simple collision theory, the preexponential factor is dependent on T 1/2 with N A Avogadro’s number, σ cross section, μ reduced mass, k Boltzmann’s constant

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

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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

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Example for Arrhenius Plot 2 different slopes may indicate change in mechanism or change from reaction to diffusion control

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

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

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Compensation Effect Observed for similar reactions on the same catalyst

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Compensation Effect: Explanations “Apparent” activation energy E A,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 E A,app is a weighted sum of the E A,true and the enthalpy of adsorption

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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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