1. CHBE 452 Lecture 31 Mass Transfer & Kinetics In Catalysis 1

2. Key Ideas For Today Generic mechanics of catalytic reactions Measure rate as a turnover number Rate equations complex Langmuir Hinshelwood kinetics 2

3. Generic Mechanisms Of Catalytic Reactions 3 Figure 5.20 Schematic of a) Langmuir-Hinshelwood, b) Rideal-Eley, c) precursor mechanism for the reaction A+B  AB and AB  A+B.

4. Turnover Number: Number Of Times Goes Around The Catalytic Cycle Per Second 4 Figure 12.1 A schematic of the catalytic cycle for Acetic acid production via the Monsanto process. Printing press analogy Reactants bind to sites on the catalyst surface Transformation occurs Reactants desorb

5. Typical Catalytic Cycle 5 Figure 5.10 Catalytic cycles for the production of water a) via disproportion of OH groups, b) via the reaction OH (ad) +H )ad)  H 2 O

6. Definition Of Turnover Number 6 (12.119) Physically, turnover number is the rate that the catalyst prints product per unit sec.

7. Typical Turnover Numbers 7

8. Next Topic Why Catalytic Kinetics Different Than Gas Phase Kinetics 8 Figure 2.15 The influence of the CO pressure on the rate of CO oxidation on Rh(111). Data of Schwartz, Schmidt, and Fisher.

9. Temperature Nonlinear 9 Figure 2.18 The rate of the reaction CO + ½ O 2  CO 2 on Rh(111). Data of Schwartz, Schmidt and Fisher[1986]. A) = 2.5  10 -8 torr, = 2.5  10 -8 torr, B) = 1  10 -7 torr, = 2.5  10 -8 torr, C) = 8  10 -7 torr, = 2.5  10 -8 torr, D) = 2  10 -7 torr, = 4  10 -7 torr, E) = 2  10 -7 torr, = 2.5  10 -8 torr, F) = 2.5  10 -8 torr, = 2.5  10 -8 torr,

10. Derivation Of Rate Law For A  C Mechanism 10 S+B  B ad 7 8 Also have a species B (12.122) 1 S + A A ad 2 3 A Ad C ad 4  5 C  C + S 6 (12.121)

11. Derivation: Next uses the steady state approximation to derive an equation for the production rate of C ad (this must be equal to the production rate of C). 11

12. Derivation Continued 12 People usually ignore reactions 3 and 4 since their rates very low rates compared to the other reactions.

13. Dropping The k 3 And k 4 Terms In Equations 12.124 And 12.125 And Rearranging Yields: 13

14. Rearranging Equations (12.126), (12.127) And (12.128) Yields: 14

15. Derivation Continued Equations (12.129) and (12.130) imply that there is an equilibrium in the reactions: 15   

16. Site Balance To Complete The Analysis If we define S 0 as the total number as sites n the catalyst, one can show: Pages of Algebra 16 (12.133)

17. Substituting Equations (12.140) And (12.141) Into Equation (12.123) Yields: 17 (12.142) In the catalysis literature, Equation (12.142) is called the Langmuir- Hinshelwood expression for the rate of the reaction A  C, also called Michaele’s Menton Equation.

18. Qualitative Behavior For Bimolecular Reactions (A+B  products) 18 Figure 12.32 A plot of the rate calculated from equation (12.161) with K B P B =10.

19. Physical Interpretation Of Maximum Rate For A+B  AB Catalysts have finite number of sites. Initially rates increase because surface concentration increases. Eventually A takes up so many sites that no B can adsorb. Further increases in A decrease rate. 19

20. Qualitative Behavior For Unimolecular Reactions (A  C) 20

21. Langmuir-Hinshelwood-Hougan-Watson Rate Laws: Trick To Simplify The Algebra Hougan and Watson’s Method: Identify rate determining step (RDS). Assume all steps before RDS in equilibrium with reactants. All steps after RDS in equilibrium with products. Plug into site balance to calculate rate equation. 21

22. Example: 22

23. Solution 23

24. Solution Continued 24 Need S to complete solution: get it from a site balance. S o = S + [A ad ] + [B ad ] (5) Combining (2), (3) and (5) S o = S + SK 1 P A + SK 2 P B (6) Solving (6) for S B2A1 o PKPK1 S S   (7)

25. Background: Mass Transfer Critical to Catalyst Design 25 Figure 12.27 An interconnecting pore structure which is selective for the formation of paraxylene.

26. Introduction In a supported catalyst reactants first diffuse into the catalyst, then they react The products diffuse out Gives opportunity for catalyst design 26

27. Reactant Concentration Drops Moving Into the Solid 27 Reactant Concentration Distance

28. Thiele Derivation for Diffusion In Catalysis Assume: Constant effective diffusivity First Order reaction per unit volume Irreversible reaction – Rate of diffusion of products out of catalyst does not affect rate 28 Reactant Concentration Distance

29. Define “Effectiveness Factor” 29

30. Derivation: Mass Balance On Differential Slice 30 Taking the limit as Δy → 0 Y Spherical pellet

31. Long Derivation 31

32. Thiele Plot 32

33. Issues With “Effectiveness Factor” Best catalysts have low “effectiveness factors” Effectiveness goes down as rate goes up High rate implies low selectivity Often want mass transfer limitations for selectivity I prefer “mass transfer factor” not “effectiveness factor” 33

34. Issues, Continued: Effective Diffusivity, D e, Unknown 34 Figure 14.3 A cross sectional diagram of a typical catalyst support.

35. Knudsen Diffusion Diffusion rate in gas phase controlled by gas – gas collisions Diffusion rate in small poles controlled by gas – surface collisions 35

36. Knudsen Diffusion From kinetic theory applies when 36

37. Knudsen Diffusion compared to 0.86 in the gas phase 37

38. Simple Models Never Work 38 Notice one molecule interferes with diffusion of second molecule

39. Summary Catalytic reactions follow a catalytic cycle reactants + S  adsorbed reactants Adsorbed reactants  products + S Different types of reactions Langmuir Hinshelwood Rideal-Eley 39

40. Summary Calculate kinetics via Hougan and Watson; Identify rate determining step (RDS) Assume all steps before RDS in equilibrium with reactants All steps after RDS in equilibrium with products Plug into site balance Predicts non-linear behavior also seen experimentally 40

41. Query What did you learn new in this lecture? 41