ERT 208/4 REACTION
ENGINEERING:
Catalysis & Catalytic Reaction
Mechanism
Part B: The Rate Limiting Step…..
By; Mrs Hafiza Binti Shukor
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Rate Limiting Step??
When heterogeneous reactions are carried out at STEADY
STATE….the rate of each of the 3 reaction step in series (adsorption,
surface reaction & desorption) are equal to one another.
rA '  rAD  rs  rD
only ONE particular step in the series is usually found to be RATE
LIMITING @ RATE CONTROLLING
If we could make this particular step GO FASTER, the entire reaction
would proceed at accelerated rate.
It consist of first assuming a sequence of steps in the reaction.
In writing sequence choice, must made some;
a)mechanism (molecular @ atomic)
b)single @ dual sites reaction
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Rate Limiting Step??.....cont….
ASSUMPTION…..
All the steps are reversible reaction.
Activity of the surface towards adsorption, desorption @ surface
reaction is INDEPENDENT of coverage.
The surface is essentially uniform as far as the various steps in the
reaction are concerned.
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Rate Limiting Step??......cont…
EXAMPLE 1: ADSORPTION LIMITED REACTION
Synthesis of Ammonia
3H 2  N 2  2 NH 3
Over an iron catalyst that proceeds by the following mechanism;
H 2  2S  2 H  S
Rapid
N2  S  N2  S
N 2  S  S  2N  S
N  S  H  S  HN  S  S
NH  S  H  S  H 2 N  S  S
H 2 N  S  H  S  NH 3  S  S
Rate-Limiting
(adsorption of N2
molecules as an N
atom)
Rapid
NH 3  S  NH 3  S
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Rate Limiting Step??......cont…
EXAMPLE 2: SURFACE- LIMITED REACTION
Reactions between 2 noxious automobile
products, CO & NO
Cu
CO  NO 
CO2 
1
N2
2
Over an Copper catalyst that proceeds by the following mechanism;
CO  S  CO  S
Rapid
NO  S  NO  S
NO  S  CO  S  CO2  N  S  S
N  S  N  S  N2  S
N2  S  N2  S
Rate-Limiting (CO2 & N2
are weakly adsorbed)
Rapid
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Rate Limiting Step??......cont…
Synthesizing a Rate Law, Mechanism, and Rate Limiting Step
EXAMPLE 3:
DECOMPOSITION OF CUMENE TO FORM
BENZENE & PROPYLENE USING PLATINUM
CATALYZED
C6 H 5 CH CH 3 2  C3 H 6  C3 H 6
C
B
P
3 STEPS REPRESENT THE MECHANISME FOR CUMENE DECOMPOSITION
CS  BS  P
C
C S  CS
P
B
C
catalyst
catalyst
Adsorption of
cumene on the
surface
BS  B S
B
catalyst
Surface reaction to form
adsorbed benzene &
propylene in the gas phase
P
catalyst
Desorption of
benzene from
surface
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Which step is Rate Limiting Step???
Adsorption
rAD  k A PC CV  k ACCS
C S  CS

C C S 
kA

rAD  k A  PC CV 
Kc 

K
kA
C 

Surface Reaction
CS  BS  P
Desorption
BS  B S
rS  k S CCS  kS PP CBS
kS
KS 
k S

PP C BS
rS  k S  CCS 
KS





rD  k D PBS  kD PB CV
1
KB 
rD  k D CBS  K B PB CV 
K DB
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
1) Is the ADSORPTION of cumene is Rate Limiting Step???
C S  CS
The rate of adsorption :
rAD

C C S 

 k A  PC CV 

K
C 

Assumption For Adsorption Limited Reaction ;
Rate constant for this step (kA) is SMALL with respect to the specific
rates of other steps (kS and kD).
Ratio rS/kS and rD/kD very SMALL (approximately 0)
Ratio rAD/kA is LARGE
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
The rate of adsorption :
rAD

CCS  ….(1)

 k A  PC CV 

K
C 

For steady state operation : rC '  rAD  rS  rD ….(2)

PP C BS  ….(3)
The surface reaction rate expression is : rS  k S  CCS 



K
S


For adsorption limited reaction, kS is large…..so, we set ; rS
 0 ….(4)
kS
So,
rS 
PP C BS 
0
  CCS 
kS 
K S 
PP C BS
We evaluate CB.S to express CC.S
….(5)
C C S 
in term of partial pressure
KS
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
The desorption rate expression is :
rD  k D CBS  K B PB CV 
For adsorption limited reaction, kD is large…..so, we set ;
rD
 C BS  K B PB CV   0
So,
kD
C BS  K B PB CV
….(8)
Combine (5) and (8),
C C S
K B PB PP CV

KS
….(9)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
….(6)
rD
 0 ….(7)
kD
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
We know that ,,
rAD

C C S 

 k A  PC CV 

K
C 

Put (9) in above equation;
rAD
rAD
rAD

K B PB CV PP
 k A  PC CV 
KS KC


K B PB PP
 k A CV  PC 
K S KC


PB PP
 k A CV  PC 
KP












This terms is simply the overall partial
pressure equilibrium constant for this
reaction.
C  BP
Where…
….(10)
KS KC
….(11)
KP 
KB
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
To eliminate Cv, we use SITE BALANCE,
Total sites ,Ct =
Cv + CC.S. + CB.S
Vacant
Site
Put (8) and (9) in (12)……..
K B PB CV PP
Ct  CV 
 K B PB CV
KS
Occupied Site
(cumene &
benzene adsorb
on the surface)
Solving for Cv,
K B PB PP
Ct  CV 1 
 K B PB 
KS
Ct
So… CV 
K B P B PP
1
 K B PB
KS
….(13)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
….(12)
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
Now, we put (13) in (10)……..
rAD

PB PP
 k A CV  PC 
KP




rAD


Ct

 kA

K B PB PP
 K B PB
1
KS



 P  PB PP
 C
KP






So…
 rc '  rAD
k ACt ( PC  PS PP / K P )

1  K B PB PP / K S  K B PB
….(14)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
Now, we wish to sketch a plot of the initial rate as a function of partial
pressure of cumene,Pco
Initially, no product are present, so… Pp  PB  0
So…the initial rate,
 rc '  rAD
k ACt ( PC  PS PP / K P )

1  K B PB PP / K S  K B PB
rCO '  k ACt PCO  kPCO
If the cumene
decomposition is
ADSORPTION LIMITED,
then the initial rate will be
linear with the initial partial
pressure of cumene
initial rate,
 rCO '
initial partial pressure of cumene,Pco
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
2) Is the SURFACE REACTION of cumene is Rate Limiting
Step???
CS  BS  P
The rate of SURFACE REACTION :

PP C BS
rS  k S  CCS 
KS


 ….(1)


Since we cannot readily measure the conc of the adsorbed species, we must utilize the adsorption
& desorption step to eliminate CC.S and CB.S from this equation.
Assumption For SURFACE REACTION Limited Reaction ;
Rate constant for kA is LARGE (rAD)
Rate constant for kD is LARGE (rD)
Rate constant for kS is SMALL (rAD)
Ratio rAD/kA and rD/kD very SMALL (approximately 0)
Ratio rS/kS is LARGE
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..

CCS  ….(2)

The adsorption rate expression is : rAD  k A  PC CV 


K
C 

For adsorption limited reaction, kA is large…..so,; rAD
kA
So,
CC .S
rAD
 PC CV 
kA
KC
CC .S
0  PC CV 
KC
CC . S  K C PC CV ….(4)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
 0 ….(3)
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
The desorption rate expression is :
rD  k D CBS  K B PB CV 
….(5)
For SURFACE REACTION limited reaction, kD is large…..so, we set ;
rD
 0 ….(6)
kD
rD
 C BS  K B PB CV   0
So,
kD
C BS  K B PB CV ….(7)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
Now, put (4) and (7) in (1)….

PP C BS
rS  k S  CCS 
KS






PP K B PB CV
rS  k S  K C PC CV 
KS


PP K B PB
rS  k S CV  K C PC 
KS


PP PB
rS  k S K C CV  PC 
KP










 ….(8)

We know that,,
K S KC
 K P ….(9)
KB
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
Site Balance….
Ct  CV  CBS  CCS ….(10)
Ct  CV  K P PB CV  K C PC CV
Ct  CV (1  K B PB  K C PC )
Ct
….(11)
CV 
1  K B PB  K C PC
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
Put (11) in (8)….

Ct
rS  k S K C 
 1  K B PB  K C PC

PP PB
 PC 

KP

k S K C Ct ( PC  PP PB / K P )
 r 'c  rS 
1  K B PB  K C PC
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)



Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
Now, we wish to sketch a plot of the initial rate as a function of partial
pressure of cumene,Pco
Initially, no product are present, so… Pp  PB  0
So…the initial rate,
k S K C Ct ( PC  PP K B / K P )
 r 'c  rS 
1  K B PB  K C PC
 r 'c  rCO
 r 'c  rCO
k S K C Ct PCO

1  K C PCO
kPCO

1  K C PCO
where,
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
k  k S K C Ct
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
At low partial pressure of cumene,
K C PCO  1
kPCO

1  K C PCO
We observed that the initial rate will  r 'c  rCO
increase linearly with the initial
pressure of cumene.
rCO '  kPCO
At high partial pressure of cumene,
We observed that the initial rate will
independent with the initial pressure
of cumene.
K C PCO  1
 r 'c  rCO
kPCO

1  K C PCO
 r 'c  rCO
kPCO
k


K C PCO K C
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the SURFACE REACTION of cumene is Rate Limiting
Step???..cont..
Figure show that the initial rate of reaction as a function of initial partial
pressure of cumene for the case of surface reaction controlling..
initial rate,
 rCO '
initial partial pressure of cumene,Pco
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
3) Is the DESORPTIONof cumene is Rate Limiting Step???
BS  B S
The rate of DESORPTION:
rD  k D CBS  K B PB CV 
….(1)
Assumption For DESORPTION Limited Reaction ;
Rate constant for kA is LARGE (rAD)
Rate constant for kS is LARGE (rS)
Rate constant for kD is SMALL (rD)
Ratio rAD/kA and rS/kS very SMALL (approximately 0)
Ratio rD/kD is LARGE
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the DESORPTIONof cumene is Rate Limiting Step???..cont..
The adsorption rate expression is : rAD

CCS  ….(2)

 k A  PC CV 

K
C 

For adsorption limited reaction, kA is large…..so,; rAD
kA
So,
CC .S
rAD
 PC CV 
kA
KC
CC .S
0  PC CV 
KC
CC . S  K C PC CV ….(4)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
 0 ….(3)
Is the DESORPTION of cumene is Rate Limiting Step???..cont..
The SURFACE REACTION rate expression is :

PP C BS
rS  k S  CCS 
KS





….(5)
For DESORPTION limited reaction, kS is large…..so, we set ;
rS
 0 ….(6)
kS
So,

rS
PP C BS
  C C S 
KS 
KS
C B S
K S C C S

PP

0


….(7)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the DESORPTION of cumene is Rate Limiting Step???..cont..
Now, put (4) and (7) in (1)….
rD  k D C BS  K B PB CV 
 K S C C S

rD  k D 
 K B PB CV 
 PP

 K S K C Pc CV

rD  k D 
 K B PB CV 
PP


 Pc PB 
CV ….(8)
rD  k D K S K C  
 PP K P 
We know that,,
K S KC
Gas phase
 K P equilibrium
KB
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
constant
Is the DESORPTION of cumene is Rate Limiting Step???..cont..
Site Balance….
Ct  CV  CBS  CCS ….(9)
K S C C S
C t  CV  K c Pc CV 
PP
K S K C PC
C t  CV (1  K C PC 
)
PP
CV 
Ct
K S K C PC
1  K C PC 
PP
….(10)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the DESORPTION of cumene is Rate Limiting Step???..cont..
Put (10) in (8)….


 PC PB 
Ct

rD  k D K C K S  

K C K S PC
P
K
P 
 P
 1  K C PC 
PP







 PC PB 
K C K S PC
 / 1  K C PC 
rD  k D Ct K C K S  
PP
 PP K P 

PB PP 

k D Ct K C K S  PC 
KP 

 rC '  rD 
PP  K C PC PP  K C K S PC
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
….(11)
Is the DESORPTION of cumene is Rate Limiting Step???..cont..
To determine the dependence of the initial rate on partial pressure of
cumene, we again set:
Initially, no product are present, so… Pp  PB  0

PB PP 

k D Ct K C K S  PC 
So…the initial rate,
KP 

 rCO '  rD 
PP  K C PC PP  K C K S PC
initial rate,
 rCO '
rCO '  rD  k D Ct
Initial rate independent of the
initial partial pressure of
cumene
initial partial pressure of cumene,Pco
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
SUMMARY OF THE CUMENE DECOMPOSITION…
The experimental observation of –rco as a function of Pco are shown in
figure..from that, we clearly can see that either adsorption nor desorption
is RATE LIMITING…
C H CH CH   C H  C H
initial rate,
 rCO '
6
5
3
2
C
3
B
6
3
6
P
initial partial pressure of cumene,Pco
The rate law derived by assuming that SURFACE REACTION is RATE
LIMITING agrees with experimental data.
k S K C Ct ( PC  PP K B / K P )
 r 'c  rS 
1  K P PB  K C PC
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Eley-Rideal
Mechanism-reaction
between adsorbed
molecule & a molecule
in the gas phase.
ALGORITHM FOR DETERMINING REACTION
MECHANISM & RATE LIMITING STEP…
1) Select a mechanism for adsorption, surface reaction & desorption
(treat each reaction step as an elementary reaction when writing rate
law)
2) Assume a rate limiting step. Choose the SURFACE REACTION
first since >than 75% of all heterogeneous reactions that are not
diffusion limited are surface reaction limited.
3) Write down the rate law for surface reaction step
4) Solve concentration of adsorbed species using other step that are not
limiting reaction. (expression for adsorption & desorption rate law)
5) Assume, ratio rAD/kA and rD/kD very SMALL (approximately 0)
6) Write a site balance
7) Derive the rate law by combining step (2,3,4,5,6)
8) Compare with data experiment- if they agree, its mean you have
found the correct mechanism & rate limiting step. If not, assume a
different rate limiting step and different mechanism.
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
End of Part B
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)