2. Why heterogeneous catalysis
Design of catalytic processes
requires a knowledge reactor
design, operation optimization
and selection.
3. Heterogeneous
external mass transfer restrictions
Surface reactions
internal mass transfer restrictions
Different phases
Homogeneous
none
none
none
Similar phases
Advantages
Reduced energy requirements
Easy product-catalyst separation
Heterogeneous catalyst
Major Differences
4. Basic Properties of catalyst
A catalyst affects the rate of reaction but emerges from the process unchanged. A
catalyst usually changes a reaction rate by promoting a different molecular path for
a reaction and thereby lowering the activation energy.
Reaction examples
A small amount of catalyst is often sufficient to bring about a considerable extent of
reaction. (huge surface area)
The catalyst does not affect the equilibrium state
5. Steps in Heterogeneous Catalytic Reactions
Step 1: Transport of Reactants to the
Catalyst Surface
Step 2: Transport within the Porous
Catalyst
Step 3: Adsorption of Reactants
It is necessary that at least one of the
reactants attach itself (physical or
chemisorption) to the catalyst surface so
that the reaction proceeds
Step 4: Surface Reaction
Then chemical reaction occurs between adsorbed
species.
Step 5: Desorption of Products
The reverse of Step 3.
Step 6: Diffusion of the Products to the External
Catalyst Surface
This step is essentially the reverse of
Step 2.
Step 7: Transport of Products to the Bulk Fluid
The reverse of Step 1.
6. 1.1 THE RATE EQUATION FOR SURFACE KINETICS
Langmuir Mechanism
• Chemical bonds are formed
• Adsorption sites are
energetically uniform
• Monolayer coverage
• No interaction between
absorbed
• Molecules
• It assumes mass law
describes individual steps
Other adsorption isotherms
Freundlich Adsorption
Isotherm
BET adsorption Isotherm
7. Langmuir Mechanism
Adsorption
𝐴 + 𝑆 ↔ 𝐴. 𝑆
Rate expression
𝑟𝑎 = 𝑘𝑎𝐶𝐴𝐶𝑠 with rate coefficient ka
𝑟𝑑 = 𝑘𝑑𝐶𝐴.𝑠 with rate coefficient kd
Schematic
The catalyst sites are either covered or covered such that:
𝐶𝑇 = 𝐶𝑠 + 𝐶𝐴𝑠
Where: 𝐶𝑠 vacant sites, 𝐶𝐴𝑠 sites occupied by A
At equilibrium adsorption is equal to
desorption
𝑘𝑑𝐶𝐴.𝑠 = 𝑘𝑎𝐶𝐴𝐶𝑠
Eliminating species difficult to measure
𝑘𝑑𝐶𝐴.𝑠 = 𝑘𝑎𝐶𝐴(𝐶𝑇−𝐶𝐴.𝑠)
𝑘𝑑𝐶𝐴.𝑠 = 𝑘𝑎𝐶𝐴𝐶𝑇 − 𝑘𝑎𝐶𝐴𝐶𝐴.𝑠
𝑘𝑑𝐶𝐴.𝑠 + 𝑘𝑎𝐶𝐴𝐶𝐴.𝑠 = 𝑘𝑎𝐶𝐴𝐶𝑇
𝐶𝐴.𝑠 =
𝑘𝑎𝐶𝐴𝐶𝑇
𝑘𝑑 + 𝑘𝑎𝐶𝐴
Divide by kd
𝐶𝐴.𝑠 =
𝐾𝐴𝐶𝐴𝐶𝑇
1 + 𝐾𝐴𝐶𝐴
Where KA = ka/kd
𝜃 =
𝐶𝐴.𝑠
𝐶𝑇
=
𝐾𝐴𝐶𝐴
1 + 𝐾𝐴𝐶𝐴
8. Langmuir Mechanism- Two species adsorbing same site
Adsorption
𝐴 + 𝑆 ↔ 𝐴. 𝑆
𝐵 + 𝑆 ↔ 𝐵. 𝑆
Rate expression
𝑟𝐶𝐴𝑆 = 𝑘𝑎𝐴𝐶𝐴𝐶𝑠 −𝑘𝑑 𝐶𝐴.𝑠
𝑟𝐵𝑆 = 𝑘𝑎𝐵𝐶𝐵𝐶𝑠 −𝑘𝑑𝐵 𝐶𝐵.𝑠
The catalyst sites are either covered or covered
such that:
𝐶𝑇 = 𝐶𝑠 + 𝐶𝐵𝑠 + 𝐶𝐴𝑠
Where: 𝐶𝑠 vacant sites, 𝐶𝐴𝑠 sites occupied by A
@ equilibrium
𝐾𝐴 =
𝐶𝐴.𝑆
𝐶𝐴𝐶𝑆
=
𝑘𝑎𝐴
𝑘𝑑𝐴
𝐶𝐴.𝑠 = 𝐾𝐴𝐶𝐴𝐶𝑠
𝐶𝐵.𝑠 = 𝐾𝐵𝐶𝐵𝐶𝑠
𝐶𝑇 = 𝐶𝑠 + 𝐾𝐵𝐶𝐵𝐶𝑠 + 𝐾𝐴𝐶𝐴𝐶𝑠
𝐶𝑆 =
𝐶𝑇
1 + 𝐾𝐵𝐶𝐵 + 𝐾𝐴𝐶𝐴
The concentration of absorbed species is given by:
𝐶𝑖.𝑆 =
𝐶𝑇𝐾𝑖𝐶𝑖
1 + 𝐾𝐵𝐶𝐵 + 𝐾𝐴𝐶𝐴
9. Langmuir Mechanism- if a molecule dissociate upon adsorption
Adsorption
𝐴2 + 2𝑆 ↔ 2𝐴. 𝑆
Rate expression
𝑟𝐶𝐴𝑆 = 𝑘𝑎𝐴𝐶𝐴𝐶𝑠 −𝑘𝑑 𝐶𝐴.𝑠
The catalyst sites are either covered or covered
such that:
𝐶𝑇 = 𝐶𝑠 + 𝐶𝐴𝑠
Where: 𝐶𝑠 vacant sites, 𝐶𝐴𝑠 sites occupied by A
@ equilibrium
𝐾𝐴 =
𝐶𝐴.𝑆
2
𝐶𝐴2
𝐶𝑆
2
𝐶𝐴.𝑠
2
= 𝐾𝐴𝐶𝐴𝐶𝑠
2
𝐶𝑇 = 𝐶𝑠 + 𝐾𝐴𝐶𝐴𝐶𝑠
2
𝐶𝐴.𝑆 =
𝐶𝑇 𝐾𝐴𝐶𝐴2
𝐶𝑠
1 + 𝐾𝐴𝐶𝐴2
10. Summary
i) Adsorption
ii) Different systems
a) 𝐴 + 𝑆 ↔ 𝐴. 𝑆
b) 𝐴 + 𝑆 ↔ 𝐴. 𝑆
𝐵 + 𝑆 ↔ 𝐵. 𝑆
c) 𝐴2+2𝑆 ↔ 2𝐴. 𝑆
NB: One method of checking whether a model predicts the behavior of experimental
data is to linearize the model equation and then plot the indicated variables against one
another
11. Exercise
Come up with a Langmuir equation for
dissociative adsorption of carbon monoxide on
platinum.
12. Surface reactions
After the reactants have adsorbed onto the surface it is capable of reacting in a
number of ways to form a product: Langmuir-Hinshelwood kinetics
1) Single reaction
𝐴. 𝑆 ↔ 𝑆. 𝐵
this reaction represents a
isomerization/ decomposition
reaction.
𝑟𝑠𝑟 = 𝑘𝑠𝑟𝐶𝐴.𝑠 −𝑘−𝑠𝑟 𝐶𝑆.𝐵
𝑟𝑠𝑟 = 𝑘𝑠𝑟 𝐶𝐴.𝑠 −
𝐶𝑆.𝐵
𝐾𝑆𝑅
Where; 𝑘𝑠𝑟-surface reaction rate coefficient
𝐾𝑆𝑅-surface reaction equilibrium coefficient
2) Dual sites
𝐴. 𝑆 + 𝑆 ↔ 𝑆. 𝐵 + 𝑆
The adsorbed reactant interacts with
another site (occupied or unoccupied)
to form product.
𝑟𝑠𝑟 = 𝑘𝑠𝑟 𝐶𝐴.𝑠𝐶𝑆 −
𝐶𝑆.𝐵𝐶𝑆
𝐾𝑆𝑅
13. Surface reactions
Another types of dual-sites mechanism is the reaction between two adsorbed
species
2) Dual sites (ii)
𝐴. 𝑆 + 𝐵. 𝑆 ↔ 𝑆. 𝐶 + 𝑆. 𝐷
Two species adsorbed on the same
type of sites
𝑟𝑠𝑟 = 𝑘𝑠𝑟 𝐶𝐴.𝑠𝐶𝐵.𝑆 −
𝐶𝑆.𝐶𝐶𝑆.𝐷
𝐾𝑆𝑅
3) Dual sites (iii)
𝐴. 𝑆 + 𝐵. 𝑆` ↔ 𝑆. 𝐶` + 𝑆. 𝐷
Two species adsorbed on different
type of sites
𝑟𝑠𝑟 = 𝑘𝑠𝑟 𝐶𝐴.𝑠𝐶𝐵.𝑆` −
𝐶𝑆`.𝐶𝐶𝑆.𝐷
𝐾𝑆𝑅
14. 1.1 THE RATE EQUATION FOR SURFACE KINETICS
Eley-Rideal Mechanism
• Is for a reaction between an
absorbed molecule and a
molecule in the gas phase
𝐴. 𝑆 + 𝐵. (𝑔) ↔ 𝑆. 𝐶
Rate Law:
𝑟𝑠𝑟 = 𝑘𝑠𝑟 𝐶𝐴.𝑠𝑃𝐵 −
𝐶𝑆.𝐶
𝐾𝑆𝑅
15. Desorption
After the catalytic reactions the products subsequently have to desorb into the gas
phase
C. 𝑆 ↔ 𝑆 + 𝐶(𝑔)
Desorption rate:
𝑟𝐷𝑐 = 𝑘𝐷𝑐 𝐶𝐶.𝑠 −
𝐶𝑆𝑃𝐶
𝐾𝐷𝑐
Note that rate of desorption of C is opposite the rate of a adsorption of C
𝑟𝐷𝑐 = 𝑘𝐴𝐷𝑐
In addition the desorption equilibrium constant KDC is just the reciprocal of the
adsorption equilibrium constant.
𝑟𝐷𝑐 = 𝑘𝐷𝑐 𝐶𝐶.𝑠 − 𝐾𝐴𝑐𝐶𝑆𝑃𝐶
16. The Rate-limiting step
At steady state the rates of each of the three
reaction steps in series (adsorption, surface
reaction and desorption) are equal.
Usually one of the steps is rate limiting, the
process of coming with the rate is as follows:
i) Rates are written for individual steps assuming
they are reversible
ii) A rate limiting step is postulated and steps that
are not rate limiting are used to eliminate all
coverage-dependent terms
17. Adsorption controlling
C 𝑔 + 𝑆 𝑠 ↔ 𝑆. 𝐶(𝑠) adsorption
𝑟𝐴𝐷 = 𝑘𝐴𝐷 𝑃𝐶𝐶𝑠 −
𝐶𝐶𝐶.𝑆
𝐾𝐴𝐷
C. 𝑆 ↔ 𝐵. 𝑆 + 𝑃 surface reaction
𝑟𝑆 = 𝑘𝑆 𝐶𝐶.𝑆 −
𝑃𝑃𝐶𝐵.𝑆
𝐾𝑠
B. 𝑆 ↔ 𝑆 + 𝐵 desorption
𝑟𝐷 = 𝑘𝐷 𝐶𝐵.𝑆 −
𝑃𝐵𝐶𝑆
𝐾𝐷𝐵
But KDB is the reciprocal of KADB
𝑟𝐷 = 𝑘𝐷 𝐶𝐵.𝑆 − 𝐾𝐴𝐷𝐵𝑃𝐵𝐶𝑆
Assuming steady state
𝑟`𝑐 = 𝑟𝐴𝐷 = 𝑟𝑆 = 𝑟𝐷𝐷
If adsorption is controlling: kAD<<< Ks ,Kd
𝑟`𝑐 = 𝑟𝐴𝐷 = 𝑘𝐴𝐷 𝑃𝐶𝐶𝑠 −
𝐶𝐶𝐶.𝑆
𝐾𝐴𝐷
Since CS and CC.S can not be measured they need
to be replaced.Based on ealier assumption rs/ks &
rD/kD ̴ 0 while rAD/kAD is relative large.
𝑟𝑆 = 𝑘𝑆 𝐶𝐶.𝑆 −
𝑃𝑃𝐶𝐵.𝑆
𝐾𝑠
surface reaction
0 = 𝐶𝐶.𝑆 −
𝑃𝑃𝐶𝐵.𝑆
𝐾𝑠
20. Rate Law analysis
Dependence on the product if products are
adsorbed to the surface, they do appear as a
denominator on the rate equation
𝑟 =
1 + 𝐾𝐶𝑃𝐶 + ⋯
Dependence on reactant and leveling off : this
normal suggest an expression as shown below
𝑟 =
𝑃𝑐
1 + 𝐾𝐶𝑃𝐶 + ⋯
21. References
1. Calvin H. Bartholomew and Robert J. Farrauto,
“Fundamentals of industrial catalytic processes”
JOHN WILEY & SONS, INC., 2 nd edition, 2006.
2. Octave Levenspiel., Chemical Reaction
Engineering, 3rd Edition, John Wiley & Sons,New
York, 1999
3. J. R Richardson and D. G Peacock., Chemical
Engineering volume 3, 3 rd Edition, Pergamon ,
1994
4. H. Scott Fogler, Essentials of Chemical Reaction
Engineering, Pearson Education International, 2010
