2. IC-1/38 Lecture-3 16-09-2004 Kinetics

3. IC-2/38 Lecture-3 16-09-2004 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?

4. IC-3/38 Lecture-3 16-09-2004 Basic surface interactions Reactions take place on the metal surface Desorption Reaction Molecular adsorption Dissociativ adsorption Diffusion CO CO 2 O

5. IC-4/38 Lecture-3 16-09-2004 Reaction Scheme + AdsorptionDesorption CO O2O2 CO 2 catalyst adsorptionreactiondesorption reaction coordinate Energy Reaction

6. IC-5/38 Lecture-3 16-09-2004 Heterogeneous Catalysis Adsorption Reaction Desorption

7. IC-6/38 Lecture-3 16-09-2004 The ‘Mean-Field’Approximation B A A A A B B A A A A B BB B B B B B B randomordered r = N k  A  B r < N k  A  B N=total number of sites N A =Number of sites occuppied by A N B =Number of sites occuppied by B N * =Number of free sites  A =N A /N  B =N B /N  * =(N-N A -N B )/N

8. IC-7/38 Lecture-3 16-09-2004 Monte Carlo Simulations r << N k  A  B

9. IC-8/38 Lecture-3 16-09-2004 Experimental Evidence by STM 8x8 nm a b Scanning Tunneling Microscopy of Oxygen Atoms on Ruthenium Joost WintterlinFHI - Berlin

10. IC-9/38 Lecture-3 16-09-2004 The Heat of Adsorption is Always …… Negative !!!! G = H - T S

11. IC-10/38 Lecture-3 16-09-2004 Reaction Scheme + AdsorptionDesorption CO O2O2 CO 2 catalyst adsorptionreactiondesorption reaction coordinate Energy Reaction

12. IC-11/38 Lecture-3 16-09-2004 Adsorption Associative Adsorption: CO, N 2, Ar, He, etc At equilibrium:

13. IC-12/38 Lecture-3 16-09-2004 Langmuir Isotherm  A = K A p A 1 + K A p A

14. IC-13/38 Lecture-3 16-09-2004 Irving Langmuir (1881 - 1957) worked at General Electrics oxygen adsorption on tungsten filaments of light bulbs 1932: Nobel Prize in Chemistry Langmuir Adsorption Isotherm:  A = K A p A 1 + K A p A

15. IC-14/38 Lecture-3 16-09-2004 Adsorption Dissociative Adsorption: N 2, O 2, CO, H 2 etc. For equilibrium =0

16. IC-15/38 Lecture-3 16-09-2004 Adsorption Competitive Adsorption:

17. IC-16/38 Lecture-3 16-09-2004 The Fuel Cell

18. IC-17/38 Lecture-3 16-09-2004 H2H2 H 2 /25 ppm CO H 2 /250 ppm CO H.-F. Oetjen et al. (1996) Pt electrode CO severely reduces efficiency

19. IC-18/38 Lecture-3 16-09-2004 Langmuir - Hinshelwood Kinetics Irving Langmuir 1881 - 1957 Nobel Prize 1932 1915 Langmuir Isotherm 1927 Kinetics of Catalytic Reactions Cyril Norman Hinshelwood 1897 - 1967 Nobel Prize 1956

20. IC-19/38 Lecture-3 16-09-2004 Eley - Rideal Mechanism direct reaction between gas phase and adsorbed species Unlikely !!

21. IC-20/38 Lecture-3 16-09-2004 The Langmuir-Hinselwood (LH) mechanism Net reaction over catalyst Elementary steps

22. IC-21/38 Lecture-3 16-09-2004 The Complete Solution

23. IC-22/38 Lecture-3 16-09-2004 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

24. IC-23/38 Lecture-3 16-09-2004 The Quasi-equilibrium Approximation Assumes one step is rate limiting while the rest are in Quasi-equilibrium RLS Notice

25. IC-24/38 Lecture-3 16-09-2004 The Quasi-equilibrium Approximation Notice only valid when step 3 is rate limiting!

26. IC-25/38 Lecture-3 16-09-2004 Steps with Similar Rates while step 2 and 4 are in quasi-equilibrium Assume step 1 and 3 are slow i.e. rate limiting steps (rls) Resulting in a reduced problem as comparred to the complete solution rls

27. IC-26/38 Lecture-3 16-09-2004 Simplifications to the Quasi-equilibrium Approximation: Irreversible steps How does this approximation describe the approach towards equilibrium? Irreversible steps: Assume for example that step 4 is irreversible k 4 - =0 K 4 -1 =0    0  r 3 - =0

28. IC-27/38 Lecture-3 16-09-2004 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??

29. IC-28/38 Lecture-3 16-09-2004 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:

30. IC-29/38 Lecture-3 16-09-2004 Reaction order What is the reaction order n AB ?

31. IC-30/38 Lecture-3 16-09-2004 Apparent activation energy as function of molefraction

32. IC-31/38 Lecture-3 16-09-2004 Apparent activation energy as function of molefraction Notice that    and  S x both depends on T, but in a more weak manner than exponential. It can give problems in an Arrhenius plot. E app Asumptions: p are assumed independent of T, i.e. we keep the pressure fixed. The rate constant can be written as The equilibrium constants as

33. IC-32/38 Lecture-3 16-09-2004 Coverage and reaction order and apparent activation energy as function of molefraction Notice: n A, n B, and E app varies with pressure for fixed temperature

34. IC-33/38 Lecture-3 16-09-2004 CO Oxidation Reaction Scheme The overall reaction is: The elementary step on a surface are:

35. IC-34/38 Lecture-3 16-09-2004 CO Oxidation the mechanics For the 3 elementary steps in Quasi equilibrium we easily obtain the langmuir equation for adsorption and desorption

36. IC-35/38 Lecture-3 16-09-2004 CO Oxidation- the rate The rate limiting step: From equilibrium we have

37. IC-36/38 Lecture-3 16-09-2004 CO Oxidation- Temperature limits Low Temperature limit: CO will become MARI The CO 2 interacts so weakly that step 4 can be considered irreversible ~ ~ ~ Find reaction orders in this limit. n O2 =0.5, n CO =-1

38. IC-37/38 Lecture-3 16-09-2004 CO Oxidation- Temperature limits The CO 2 interacts so weakly that step 4 can be considered irreversible High Temperature limit: Very low concentration of surface species ~1~1 ~ Find reaction orders in this limit. n O2 =0.5, n CO =1

39. IC-38/38 Lecture-3 16-09-2004 CO Oxidation-Results