ERT 208/4 REACTION
ENGINEERING:
Catalysis & Catalytic
Reaction Mechanism
Part B: The Rate
Limiting Step..
By; Mrs Hafiza Binti Shu
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;
ERT 208/4
ENGINEERING
a)mechanism (molecular
@REACTION
atomic)
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 m
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
CO NO
Cu
CO2
1
N2
2
Over an Copper catalyst that proceeds by the following
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 Rat
EXAMPLE 3:
FORM
PLATINUM
DECOMPOSITION OF CUMENE TO
BENZENE & PROPYLENE USING
CATALYZED
C 6 H 5 CH CH 3 2 C 3 H 6 C 3 H 6
C
3 STEPS REPRESENT THE MECHANISME FOR CUMENE
DECOMPOSITION
CS BS P
C
C S CS
P
B
catalyst
catalyst
Adsorption of
cumene on the
surface
BS BS
catalyst
Surface reaction to
form adsorbed
benzene & propylene
in the gas phase
catalyst
Desorption of
benzene from
surface
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Which step is Rate Limiting Step???
Adsorption r k P C k C
AD
A C V
A C S
C S CS
C C S
kA
rAD k A PC CV
Kc
KC
kA
rS k S CCS k S PP C BS
Surface Reaction
CS BS P
Desorption
BS BS
kS
KS
k S
rS k S CCS
PP C BS
KS
rD k D PBS k D PB CV
1
KB
rD k D C BS K B PB CV
K DB
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
1) Is the ADSORPTION of cumene is Rate Limi
C S CS
The rate of adsorption :
rAD
C C S
k A PC CV
KC
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 Limitin
C C S
The rate of adsorption :
rAD k A PC CV
K
.(1)
For steady state operation
rC ' rAD : rS rD .(2)
PP C BS .(3
The surface reaction rate expression
rS k S CCis
:
S
K
S
For adsorption limited reaction, kS is large..so,
we
rS
0 .(4)
kS
So, rS
PP C BS
0
CCS
kS
K S
PP C BS
.(5) We evaluate CB.S to
C C S
express CC.S in term of
KS
partial pressure
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the ADSORPTION of cumene is Rate Limitin
The desorption rate expression
C:BS K B PB CV
rD k Dis
.(6
For adsorption limited reaction, kD is large..so,
we
rD
0 .(7)
rD
C BS K B PB CV 0
So,
kD
C BS 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)
kD
Is the ADSORPTION of cumene is Rate Limitin
We know that ,,
rAD
C C S
k A PC CV
KC
Put (9) in above
equation;
rAD
rAD
rAD
K B PB CV PP
This terms is simply the
k A PC CV
overall partial pressure
K
K
S
C
equilibrium constant for
C BP
this
reaction.
K B PB PP
k A CV PC
K
K
S
C
Where
KS KC
PB PP
.(11)
.(10) K P
k A CV PC
KB
K
P
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
Is the ADSORPTION of cumene is Rate Limitin
To eliminate Cv, we use SITE
BALANCE,
Total sites ,Ct
Cv
=
Vaca
nt
Site
Put (8) and (9) in (12)
..
K B PB CV PP
Ct CV
KS
+ CC.S. + CB.S.(12)
K B PB CV
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)
Is the ADSORPTION of cumene is Rate Limitin
Now, we put (13) in
(10)..
rAD
rAD
PB PP
k A CV PC
KP
Ct
kA
K B PB PP
K B PB
1
KS
P PB PP
C
KP
So
rc ' rAD
k A Ct ( 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 Limitin
Now, we wish to sketch a plot of the initial rate as
a function of partial pressure of cumene,Pco
Pp PBso
0
Initially, no product are present,
Sothe initial rate,
rc ' rAD
k A Ct ( PC PS PP / K P )
1 K B PB PP / K S K B PB
rCO ' k A Ct PCO kPCO
If the cumene
decomposition is
ADSORPTION
LIMITED, then the
initial rate will be
linear with the
initial partial
rCO '
initial rate,
initial partial pressure of cum
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
2) Is the SURFACE REACTION of cumene is
Rate Limiting Step???
CS BS P
The rate of SURFACE REACTION :
rS k S CCS
PP C BS
KS
.(1)
Since we cannot readily measure the conc of the adsorbed species,
we must utilize the adsorption & desorption step to eliminate C C.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
ERT 208/4 REACTION ENGINEERING
(approximately 0)
SEM 2 (2009/2010)
Is the SURFACE REACTION of cumene is Rate
Limiting Step???..cont..
CCS .(2)
PC:CV
rAD k Ais
The adsorption rate expression
K
C
For adsorption limited reaction, kA isrADlarge..so,;
0 .(3)
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)
Is the SURFACE REACTION of cumene is Rate
Limiting Step???..cont..
The desorption rate expression
C:BS K B PB CV
rD k Dis
.(5
For SURFACE REACTION limited reaction, kD is large
rD
0 .(6)
kD
rD
C BS K B PB CV 0
So,
kD
C BS 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 BS
KS
rS k S CCS
PP K B PB CV
rS k S K C PC CV
K
S
PP K B PB
rS k S CV K C PC
K
S
PP PB
.(8)
rS k S K C CV PC
KP
We know that,,
KS 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 C BS CCS .(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
Pp PBso
0
Initially, no product are present,
k S K C Ct ( PC PP K B / K P )
r 'c rS
1 K B PB K C PC
Sothe initial rate,
r 'c rCO
k S K C Ct PCO
1 K C PCO
r 'c rCO
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,
We observed that the
initial rate will increase
linearly with the initial
pressure of cumene.
K C PCO 1
r 'c rCO
kPCO
1 K C PCO
rCO ' kPCO
At high partial pressure of K C PCO 1
kPCO
cumene,
r 'c rCO
We observed that the
1 K C PCO
initial rate will
kPCO
k
independent with the
r 'c rCO
K C PCO K C
initial pressure of
cumene.
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..
rCO '
initial rate,
initial partial pressure of cumene,Pco
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
3) Is the DESORPTIONof cumene is Rate
Limiting Step???
BS BS
The rate of DESORPTION:
rD k D C BS 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..
CCS .(2)
PC:CV
rAD k Ais
The adsorption rate expression
K
C
For adsorption limited reaction, kA isrADlarge..so,;
0 .(3)
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)
Is the DESORPTION of cumene is Rate
Limiting Step???..cont..
The SURFACE REACTION rate expression is :
rS k S CCS
PP C BS
KS
.(5)
For DESORPTION limited reaction, kS is large..so, w
rS
0 .(6)
kS
So,
rS
PP C BS
CCS
KS
KS
C B S
K S C C S
PP
.(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 BS 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
We know that,,
Pc PB
CV .(8)
rD k D K S K C
PP K P
K S KC
K P Gas
phase
KB
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
equilibri
um
constant
Is the DESORPTION of cumene is Rate
Limiting Step???..cont..
Site Balance.
Ct CV C BS CCS .(9)
K S C C S
Ct CV K c Pc CV
PP
K S K C PC
Ct 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
K
P
P
K
C
S
C
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
.(11)
rC ' rD
PP K C PC PP K C K S PC
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
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:
Pp PBso
0
Initially, no product are present,
PB PP
k D Ct K C K S PC
Sothe 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
ERT 208/4 REACTION ENGINEERING
initial partial pressure of cumene,Pco
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
desorption
CH 3 2 Cis
C 6 nor
H 5 CH
HRATE
C3 H 6
3
6
rCO '
C
B
P
initial rate,
LIMITING
initial partial pressure of cumene,Pco
The rate law derived by assuming that SURFACE
REACTION is RATE LIMITING agrees with
Eley-Rideal
experimental data.
Mechanism-
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)
reaction
between
adsorbed
molecule & a
molecule in the
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
208/4 REACTION ENGINEERING
(approximately 0) ERT
SEM 2 (2009/2010)
End of Part B
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)
