CHBE 551 Lecture 31
description
Transcript of CHBE 551 Lecture 31
![Page 1: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/1.jpg)
CHBE 551 Lecture 31 Mass Transfer & Kinetics In Catalysis
1
![Page 2: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/2.jpg)
Key Ideas For Today
Generic mechanics of catalytic reactions
Measure rate as a turnover number Rate equations complex Langmuir Hinshelwood kinetics
2
![Page 3: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/3.jpg)
Generic Mechanisms Of Catalytic Reactions
3
B
Langmuir-Hinshelwood Rideal-Eley Precursor
A
B A
A B
A
A B
AB
B AB
AAB
ABA
B
AB
ABA
B
AB
ABA
B
AB
Figure 5.20 Schematic of a) Langmuir-Hinshelwood, b) Rideal-Eley, c) precursor mechanism for the reaction A+BAB and ABA+B.
![Page 4: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/4.jpg)
Turnover Number: Number Of Times Goes Around The Catalytic Cycle Per
Second
4
HI
H O2
CH OH3
CH I3
CH COOH3
CH COI3[Rh(CO) I ]2 2
-
RhI
H C3C I
I
O
RhI
CH3
CO I
I
C
O
CO
CO
CO
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
![Page 5: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/5.jpg)
Typical Catalytic Cycle
5
2
2
2
O O O O O O O O O O
+ H
H H
O O O O O O O O OH H
- H O
+ 1
/2 O
A 2
2
2
O
+1/2 O
H OH
- H
O
B
+ H
H OH
Figure 5.10 Catalytic cycles for the production of water a) via disproportion of OH groups, b) via the reaction OH(ad)+H)ad)H2O
![Page 6: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/6.jpg)
Definition Of Turnover Number
6
S
AN N
RT
(12.119)
Physically, turnover number is the rate that the catalyst prints product per unit sec.
![Page 7: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/7.jpg)
Typical Turnover Numbers
200 400 600 800 1000 1200
Reaction Temperature, K
10-6
10-4
10-2
100
102
Tur
nove
r N
umb
er, s
ec-1 Hydrogenation
OlefinIsomerization
Dehydrogenation
AlkaneHydrogenolysis
Cyclization
SiliconDeposition
GaAsDeposition
1400
7
![Page 8: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/8.jpg)
Next Topic Why Catalytic Kinetics Different Than Gas Phase Kinetics
1012
1013
10-6
Ra
te, M
ole
cule
s/cm
-se
c2
1011
10-7
10-8
10-6
CO pressure, torr10
-710
-8
O pressure, torr2
390 K
410 K415 K
450 K450 K
440 K440 K
425 K
8
Figure 2.15 The influence of the CO pressure on the rate of CO oxidation on Rh(111). Data of Schwartz, Schmidt, and Fisher.
![Page 9: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/9.jpg)
Temperature Nonlinear
9
Rat
e, M
olec
ules
/cm
-se
c2
Temperature, KTemperature, K
1E+13
1E+12
1E+11
600400 800600 800400
P =2.E-7 torrCO
A
B
C
2P =2.5E-8 torrO
DEF
Figure 2.18 The rate of the reaction CO + ½ O2 CO2 on Rh(111). Data of Schwartz, Schmidt and
Fisher[1986]. A) = 2.510-8 torr, = 2.510-8 torr, B) = 110-7 torr, = 2.510-8 torr, C) = 810-7 torr, = 2.510-8 torr, D) = 210-7 torr, = 410-7 torr, E) = 210-7 torr, = 2.510-8 torr, F) = 2.510-8 torr, = 2.510-8 torr,
![Page 10: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/10.jpg)
Derivation Of Rate Law For AC
Mechanism
10
S+BBad
7
8
Also have a species B
(12.122)
1 S + A Aad 2
3 AAd Cad 4
5 Cad C + S
6
(12.121)
![Page 11: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/11.jpg)
Derivation:
Next uses the steady state approximation to derive an equation for the production rate of Cad (this must be equal to the production rate of C).
11
![Page 12: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/12.jpg)
Derivation Continued
rC k3[Aad ] k4[Cad ]
(12.123)
SS on [Aad] and [Cad] 0 rAad k1PA[S] k2[Aad ] k3[Aad ] k4[Cad ]
(12.124) 0 rCad k6PC[S] k5[Cad ] k4[Cad ] k3[Aad ]
(12.125)
12
People usually ignore reactions 3 and 4 since their rates very low rates compared to the other reactions.
![Page 13: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/13.jpg)
Dropping The k3 And k4 Terms In Equations 12.124 And 12.125 And
Rearranging Yields:
[Aad ]k1k2
PA [S]
(12.126)
[ ]Cad ]k6k5
PC[S
(12.127)
13
Similarly for B
Badk8k
PB S7
(12.128)
![Page 14: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/14.jpg)
Rearranging Equations (12.126), (12.127) And (12.128) Yields:
[Aad ]
PA[S]
k1k2
(12.129)
[Bad ]
PB[S]
k8k7
(12.130)
CadPc S
k6k5
(12.131)
14
![Page 15: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/15.jpg)
Derivation Continued
Equations (12.129) and (12.130) imply that there is an equilibrium in the reactions:
15
1 A + S Aad 2 8 B + S Bad 7
6 C + S Cad 5
(12.132)
B
[Aad ]
PA[S]
k1k2
(12.129)
[Bad ]
PB[S]
k8k7
(12.130)
CadPc S
k6k5
(12.131)
![Page 16: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/16.jpg)
Site Balance To Complete The Analysis
If we define S0 as the total number as sites n the catalyst, one can show:
Pages of Algebra
16
(12.133)
S0 [S] [Aad ] [Bad Cad ]
[Aad ]KA PAS0
1 KA PA KBPB KCPC
(12.140)
[Cad ]KCPCS0
1 KA PA KBPB KCPC
(12.141)
![Page 17: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/17.jpg)
Substituting Equations (12.140) And (12.141) Into Equation (12.123) Yields:
rk3KA PAS0 k4KCPCS0
1 KA PA KBPB KCPC
17
(12.142)
In the catalysis literature, Equation (12.142) is called the Langmuir-Hinshelwood expression for the rate of the reaction AC, also called Michaele’s Menton Equation.
![Page 18: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/18.jpg)
Qualitative Behavior For Bimolecular Reactions (A+Bproducts)
PA
0 10 20 30 40 500.0E+0
5.0E+13
1.0E+14
1.5E+14
2.0E+14
2.5E+14
Rat
e, M
olec
ules
/cm
/se
c 2
18
Figure 12.32 A plot of the rate calculated from equation (12.161) with KBPB=10.
1012
1013
Rat
e, M
olec
ules
/cm
-se
c2
1011
10-6
CO pressure, torr10
-710
-8
390 K
410 K
450 K
440 K
![Page 19: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/19.jpg)
Physical Interpretation Of Maximum Rate For A+BAB
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.
19
![Page 20: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/20.jpg)
Qualitative Behavior For Unimolecular Reactions (AC)
P =25B
PA
0 10 20 30 40 500.0E+0
5.0E-9
1.0E-8
1.5E-8
2.0E-8
Rat
e, M
oles
/cm
/se
c 2
P =0B
20
0.01 0.1 1 10 1001E+16
1E+17
1E+18
1E+19
1E+20
770 K
1070 K
870 K
1270 K1670 K
Ammonia pressure, torr
Rat
e, M
olec
ules
/cm
-se
c2
![Page 21: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/21.jpg)
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
![Page 22: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/22.jpg)
Example:
The reaction A + B C obeys:
S A Aad (1)
S B Bad (2)
Aad Bad C 2S (3)
(12.157)
Derive an equation for the rate of formation of C as a function of the partial pressures of A and B. Assume that reaction (3) is rate determining.
22
![Page 23: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/23.jpg)
Solution
rC = k3[Aad][Bad] (1) Assume reaction 1 in equilibrium
1A
ad KPS
]A[ (2)
Similarly on reaction 2
2B
ad KPS
]B[ (3)
Combining 1,2 and 3 2
BA321C SPPkKKr (4)
23
![Page 24: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/24.jpg)
Solution Continued
24
Need S to complete solution: get it from a site balance. So= S + [Aad] + [Bad] (5) Combining (2), (3) and (5) So= S + SK1PA + K2PB (6) Solving (6) for S
B2A1
o
PKPK1S
S
(7)
Combining equations (4) and (7)
2B2A1
2oBA321
CPKPK1
SPPkKKr
(8)
![Page 25: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/25.jpg)
Background: Mass Transfer Critical to Catalyst Design
C HH
HCH
HH
DiffusionChannel
Cavity
25
Figure 12.27 An interconnecting pore structure which is selective for the formation of paraxylene.
![Page 26: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/26.jpg)
Introduction
In a supported catalyst reactants first diffuse into the catalyst, then they react The products diffuse out
Gives opportunity for catalyst design
26
![Page 27: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/27.jpg)
Reactant Concentration Drops Moving Into the Solid
27
Reactant Concentration
Dis
tan
ce
0 0.2 0.4 0.6 0.8 1 1.2 1.40
0.2
0.4
0.6
0.8
1
Distance from the center of the pellet
Con
cent
ratio
n
Edge of Pellet
Center of Pellet
GasPhase
Gas Phase Conc
Avg conc in pellet
Conc in pellet
![Page 28: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/28.jpg)
Thiele Derivation for Diffusion In Catalysis
Assume: Constant effective diffusivity First Order reaction per unit volume Irreversible reaction – Rate of diffusion of
products out of catalyst does not affect rate
28Reactant Concentration
Dis
tan
ce
![Page 29: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/29.jpg)
Define “Effectiveness Factor”
29
e
Actual rate for a catalyst pellet with mass transfer limitations
Rate in the absence of mass transfer limitations
![Page 30: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/30.jpg)
Derivation: Mass Balance On Differential Slice
30
Taking the limit as Δy → 0
Y
4 4
4
y DdC
dYy D
dC
dy
y y r
2 A
y y
2e
S
y
2A
e
d C
dy
2
y
dC
dy
r
D
2A A A
e
0
Spherical pellet
![Page 31: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/31.jpg)
Long Derivation
31
C Cy
y
Sinh 3 y/y
Sinh 3A A0 P P
P
PP A
e
y
3
k
D
e
P P P
1 1
3
1
3 tanh
![Page 32: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/32.jpg)
Thiele Plot
32
1.0
0.0
0.8
0.6
0.4
0.2
Mas
s T
rans
fer
Fac
tor
0 2 4 6 8 10Thele Parameter
Zero Order
First Order
Second Order
![Page 33: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/33.jpg)
Issues With “Effectiveness Factor”
Best catalysts have low “effectiveness factors” Effectiveness goes down as rate goes
up High rate implies low selectivity
Often want mass transfer limitations for selectivity
I prefer “mass transfer factor” not “effectiveness factor”
33
![Page 34: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/34.jpg)
Issues, Continued: Effective Diffusivity, De,
Unknown
34
Figure 14.3 A cross sectional diagram of a typical catalyst support.
![Page 35: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/35.jpg)
Knudsen Diffusion
Diffusion rate in gas phase controlled by gas – gas collisions
Diffusion rate in small poles controlled by gas – surface collisions
35
![Page 36: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/36.jpg)
Knudsen Diffusion
From kinetic theory
applies when
36
)pathfreemeanλ(λv3
1Dgas
diameterporeaa2V3
1Dk
gasa2
![Page 37: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/37.jpg)
Knudsen Diffusion
compared to 0.86 in the gas phase
37
21
212
3K M
AMU
K300
T
R1
a
sec
CM10x68.1D
22120100 Hforsec/cm.D poreÅ K
![Page 38: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/38.jpg)
Simple Models Never Work
38
Notice one molecule interferes with diffusion of second molecule
![Page 39: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/39.jpg)
Summary
Catalytic reactions follow a catalytic cycle reactants + S adsorbed reactantsAdsorbed reactants products + S
Different types of reactionsLangmuir HinshelwoodRideal-Eley
39
![Page 40: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/40.jpg)
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
Predicts non-linear behavior also seen experimentally
40
![Page 41: CHBE 551 Lecture 31](https://reader030.fdocuments.in/reader030/viewer/2022033104/568147a4550346895db4e139/html5/thumbnails/41.jpg)
Query
What did you learn new in this lecture?
41