ChE 553 Lecture 14 Catalytic Kinetics 1

Objective Provide an overview of catalytic kinetics –How do rates vary with concentration –Simple modles: langmuir 2

Key Ideas For Today Generic mechanisms of catalytic reactions Measure rate as a turnover number Rate equations complex Langmuir Hinshelwood kinetics 3

Generic Mechanisms Of Catalytic Reactions 4 Figure 5.20 Schematic of a) Langmuir-Hinshelwood, b) Rideal-Eley, c) precursor mechanism for the reaction A+B  AB and AB  A+B.

Turnover Number: Number Of Times Goes Around The Catalytic Cycle Per Second 5 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

Typical Catalytic Cycle 6 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

Definition Of Turnover Number 7 (12.119) Physically, turnover number is the rate that the catalyst prints product per unit sec.

Typical Turnover Numbers 8

Next Topic Why Catalytic Kinetics Different Than Gas Phase Kinetics 9 Figure 2.15 The influence of the CO pressure on the rate of CO oxidation on Rh(111). Data of Schwartz, Schmidt, and Fisher.

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

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. 11

Derivation Of Rate Law For A  C Mechanism 12 1 S + A A ad 2 3 A Ad C ad 4 5 C C + S 6 (12.121)  Rate Determining Step   

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). 13

Derivation 14 People usually ignore reactions 3 and 4 since their rates very low rates compared to the other reactions. 1 S + A A ad 2 3 A Ad C ad 4 5 C C + S 6 (12.121) SS approximation on A ad and C ad   

Dropping The k 3 And k 4 Terms In Equations And And Rearranging Yields: 15

Rearranging Equations (12.126), (12.127) And (12.128) Yields: 16

Derivation Continued Equations (12.129) and (12.130) imply that there is an equilibrium in the reactions: 17 C + S C ad A + S A ad  

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 18

Substituting Equations (12.140) And (12.141) Into Equation (12.123) Yields: 19 (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.

Qualitative Behavior For Unimolecular Reactions (A  C) 20

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

Example: 22

Solution 23

Solution Continued 24

Qualitative Behavior For Bimolecular Reactions (A+B  products) 25 Figure A plot of the rate calculated from equation (12.161) with K B P B =10.

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. 26

Another Example: Consider a different reaction (12.120) 27 S + A A ad 2 3 A Ad C ad 4 5 C C + S 6 1 (12.121)   

Derivation The Same 28

What Does This Look Like? 29

Summary Catalytic reactions follow a catalytic cycle reactants + S  adsorbed reactants Adsorbed reactants  products + S Different types of reactions Langmuir Hinshelwood Rideal-Eley 30

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 31

Key Predictions Unimolecular reactions Rate increases with pressure, levels Rate always increases with temperature Very sensitive to poisons Bimolecular reactions Rate rises reaches a maximum at finite temp and pressure, then drops Sensitive to poisons 32