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Kinetics

Kinetics. What is Kinetics ?. Analysis of reaction mechanisms on the molecular scale Derivation of rate expressions Design and analysis of experiments to test rate equations and derive kinetic parameters Theoretical prediction of rate constants How can we improve it?.

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Kinetics

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  1. Kinetics

  2. What is Kinetics ? • Analysis of reaction mechanisms on the molecular scale • Derivation of rate expressions • Design and analysis of experiments to test rate equations and derive kinetic parameters • Theoretical prediction of rate constants • How can we improve it?

  3. Basic surface interactions CO2 CO Molecular adsorption Dissociativ adsorption O Diffusion Reaction Desorption • Reactions take place on the metal surface

  4. Reaction Scheme Reaction O2 CO CO2 + catalyst Adsorption Reaction Desorption Energy adsorption reaction desorption reaction coordinate

  5. Heterogeneous Catalysis Adsorption Reaction Desorption

  6. The ‘Mean-Field’Approximation A A B A A B B B B B A A B B B B A B A B random ordered r = N k AB r < N k AB N=total number of sites NA=Number of sites occuppied by A NB=Number of sites occuppied by B N*=Number of free sites A=NA/N B=NB/N *=(N-NA-NB)/N

  7. Monte Carlo Simulations r << N k AB

  8. Experimental Evidence by STM Scanning Tunneling Microscopy of Oxygen Atoms on Ruthenium Joost WintterlinFHI - Berlin a b 8x8 nm

  9. The Heat of Adsorption is Always …… G = H - T S Negative !!!! Negative !!!!

  10. Reaction Scheme Reaction O2 CO CO2 + catalyst Adsorption Reaction Desorption Energy adsorption reaction desorption reaction coordinate

  11. Adsorption Associative Adsorption: CO, N2, Ar, He, etc At equilibrium:

  12. Langmuir Isotherm KA pA A = 1 + KA pA

  13. Irving Langmuir(1881 - 1957) • worked at General Electrics • oxygen adsorption on tungsten • filaments of light bulbs • 1932: Nobel Prize in Chemistry • Langmuir Adsorption Isotherm: KA pA A = 1 + KA pA

  14. Adsorption Dissociative Adsorption: N2, O2, CO, H2 etc. For equilibrium =0

  15. Adsorption Competitive Adsorption:

  16. The Fuel Cell

  17. Pt electrode H2 H2/25 ppm CO H2/250 ppm CO H.-F. Oetjen et al. (1996) CO severely reduces efficiency

  18. Langmuir - Hinshelwood Kinetics 1915 Langmuir Isotherm 1927 Kinetics of Catalytic Reactions Irving Langmuir 1881 - 1957 Nobel Prize 1932 Cyril Norman Hinshelwood 1897 - 1967 Nobel Prize 1956

  19. Eley - Rideal Mechanism direct reaction between gas phase and adsorbed species Unlikely !!

  20. The Langmuir-Hinselwood (LH) mechanism Net reaction over catalyst Elementary steps

  21. The Complete Solution

  22. The Steady State Approximation Interesting solution for many processes, but we lose time dependence Last eq. not independent, i.e. n-1 eq. for n elementary steps

  23. The Quasi-equilibrium Approximation Notice Assumes one step is rate limiting while the rest are in Quasi-equilibrium RLS

  24. The Quasi-equilibrium Approximation Notice only valid when step 3 is rate limiting!

  25. Steps with Similar Rates rls rls Assume step 1 and 3 are slow i.e. rate limiting steps (rls) while step 2 and 4 are in quasi-equilibrium Resulting in a reduced problem as comparred to the complete solution

  26. Simplifications to the Quasi-equilibrium Approximation: Irreversible steps Irreversible steps: Assume for example that step 4 is irreversible k4-=0 K4-1=0 qAB=0r3-=0 How does this approximation describe the approach towards equilibrium?

  27. Simplifications to the Quasi-equilibrium Approximation:The MARI Approximation The Most Abundent Reaction Intermediate approximation (MARI) Assume for example that specie A bonds much stronger than B and AB- A will then become MARI What are examples of MARI??

  28. Simplifications to the Quasi-equilibrium Approximation: Nearly empty Surface Typical for high temperatures In that case is it simple to find the maximum of the rate as a function of gas-composition:

  29. Reaction order What is the reaction order nAB?

  30. Apparent activation energy as function of molefraction

  31. Apparent activation energy as function of molefraction Eapp The rate constant can be written as The equilibrium constants as Asumptions: p are assumed independent of T, i.e. we keep the pressure fixed. Notice that n+3and DSx both depends on T, but in a more weak manner than exponential. It can give problems in an Arrhenius plot.

  32. Coverage and reaction order and apparent activation energy as function of molefraction Notice: nA, nB, and Eapp varies with pressure for fixed temperature

  33. CO Oxidation Reaction Scheme The overall reaction is: The elementary step on a surface are:

  34. CO Oxidation the mechanics For the 3 elementary steps in Quasi equilibrium we easily obtain the langmuir equation for adsorption and desorption

  35. CO Oxidation- the rate The rate limiting step: From equilibrium we have

  36. CO Oxidation- Temperature limits ~ ~ ~ The CO2 interacts so weakly that step 4 can be considered irreversible Low Temperature limit: CO will become MARI Find reaction orders in this limit. nO2=0.5, nCO=-1

  37. CO Oxidation- Temperature limits ~1 ~ The CO2 interacts so weakly that step 4 can be considered irreversible High Temperature limit: Very low concentration of surface species Find reaction orders in this limit. nO2=0.5, nCO=1

  38. CO Oxidation-Results

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