1. 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)
By; Mrs Hafiza Binti Shukor

2. 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.
only ONE particular step in the series is usually found to be RATE 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 atomic)
dual sites reaction
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

3. Rate Limiting Step??.....cont….
ASSUMPTION…..
All the steps are reversible reaction.
Activity of the surface towards adsorption, 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)

4. Rate Limiting Step??......cont…
EXAMPLE 1: ADSORPTION LIMITED REACTION
Synthesis of Ammonia
Over an iron catalyst that proceeds by the following mechanism;
Rapid
Rate-Limiting
(adsorption of N2 molecules as an N atom)
Rapid
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

5. Rate Limiting Step??......cont…
EXAMPLE 2: SURFACE- LIMITED REACTION
Reactions between 2 noxious automobile products, CO & NO
Over an Copper catalyst that proceeds by the following mechanism;
Rapid
Rate-Limiting (CO2 & N2 are weakly adsorbed)
Rapid
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

6. 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 C B P
3 STEPS REPRESENT THE MECHANISME FOR CUMENE DECOMPOSITION P P C B B C
catalyst
catalyst
catalyst
catalyst
Adsorption of
cumene on the
surface
Surface reaction to form adsorbed benzene & propylene in the gas phase
Desorption of benzene from surface
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

7. Which step is Rate Limiting Step???
Adsorption
Surface Reaction
Desorption
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

8. 1) Is the ADSORPTION of cumene is Rate Limiting Step???
The rate of adsorption :
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)

9. Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
The rate of adsorption :
….(1)
For steady state operation :
….(2)
….(3)
The surface reaction rate expression is :
For adsorption limited reaction, kS is large…..so, we set ;
….(4)
So,
We evaluate CB.S to express CC.S in term of partial pressure
….(5)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

10. Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
….(6)
The desorption rate expression is :
For adsorption limited reaction, kD is large…..so, we set ;
….(7)
So,
….(8)
Combine (5) and (8),
….(9)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

11. Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
We know that ,,
Put (9) in above equation;
This terms is simply the overall partial pressure equilibrium constant for this reaction.
Where…
….(11)
….(10)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

12. Occupied Site (cumene & benzene adsorb on the surface)
Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
To eliminate Cv, we use SITE BALANCE,
Cv + CC.S. + CB.S
Total sites ,Ct =
….(12)
Vacant Site
Occupied Site (cumene & benzene adsorb on the surface)
Put (8) and (9) in (12)……..
Solving for Cv,
So…
….(13)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

13. Is the ADSORPTION of cumene is Rate Limiting Step???..cont..
Now, we put (13) in (10)……..
So…
….(14)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

14. 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…
So…the initial rate,
If the cumene decomposition is ADSORPTION LIMITED, then the initial rate will be linear with the initial partial pressure of cumene
initial rate,
initial partial pressure of cumene,Pco
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

15. 2) Is the SURFACE REACTION of cumene is Rate Limiting Step???
The rate of SURFACE REACTION :
….(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)

16. Is the SURFACE REACTION of cumene is Rate Limiting Step???..cont..
….(2)
The adsorption rate expression is :
For adsorption limited reaction, kA is large…..so,;
….(3)
So,
….(4)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

17. Is the SURFACE REACTION of cumene is Rate Limiting Step???..cont..
….(5)
The desorption rate expression is :
For SURFACE REACTION limited reaction, kD is large…..so, we set ;
….(6)
So,
….(7)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

18. Is the SURFACE REACTION of cumene is Rate Limiting Step???..cont..
Now, put (4) and (7) in (1)….
We know that,,
….(8)
….(9)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

19. Is the SURFACE REACTION of cumene is Rate Limiting Step???..cont..
Site Balance….
….(10)
….(11)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

20. Is the SURFACE REACTION of cumene is Rate Limiting Step???..cont..
Put (11) in (8)….
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

21. 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…
So…the initial rate,
where,
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

22. 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.
At high partial pressure of cumene,
We observed that the initial rate will independent with the initial pressure of cumene.
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

23. 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,
initial partial pressure of cumene,Pco
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

24. 3) Is the DESORPTIONof cumene is Rate Limiting Step???
The rate of DESORPTION:
….(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)

25. Is the DESORPTIONof cumene is Rate Limiting Step???..cont..
….(2)
The adsorption rate expression is :
For adsorption limited reaction, kA is large…..so,;
….(3)
So,
….(4)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

26. Is the DESORPTION of cumene is Rate Limiting Step???..cont..
The SURFACE REACTION rate expression is :
….(5)
For DESORPTION limited reaction, kS is large…..so, we set ;
….(6)
So,
….(7)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

27. Is the DESORPTION of cumene is Rate Limiting Step???..cont..
Now, put (4) and (7) in (1)….
We know that,,
Gas phase equilibrium constant
….(8)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

28. Is the DESORPTION of cumene is Rate Limiting Step???..cont..
Site Balance….
….(9)
….(10)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

29. Is the DESORPTION of cumene is Rate Limiting Step???..cont..
Put (10) in (8)….
….(11)
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

30. 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…
So…the initial rate,
initial rate,
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)

31. 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…
initial rate, C B P
initial partial pressure of cumene,Pco
The rate law derived by assuming that SURFACE REACTION is RATE LIMITING agrees with experimental data.
Eley-Rideal Mechanism-reaction between adsorbed molecule & a molecule in the gas phase.
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)

32. ALGORITHM FOR DETERMINING REACTION MECHANISM & RATE LIMITING STEP…
Select a mechanism for adsorption, surface reaction & desorption (treat each reaction step as an elementary reaction when writing rate law)
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.
Write down the rate law for surface reaction step
Solve concentration of adsorbed species using other step that are not limiting reaction. (expression for adsorption & desorption rate law)
Assume, ratio rAD/kA and rD/kD very SMALL (approximately 0)
Write a site balance
Derive the rate law by combining step (2,3,4,5,6)
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)

33. End of Part B
ERT 208/4 REACTION ENGINEERING
SEM 2 (2009/2010)