CHBE 551 Lecture 31 Mass Transfer & Kinetics In Catalysis
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Key Ideas For Today
Generic mechanics of catalytic reactions
Measure rate as a turnover number Rate equations complex Langmuir Hinshelwood kinetics
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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.
Turnover Number: Number Of Times Goes Around The Catalytic Cycle Per
Second
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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
Typical Catalytic Cycle
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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
Definition Of Turnover Number
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S
AN N
RT
(12.119)
Physically, turnover number is the rate that the catalyst prints product per unit sec.
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
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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
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Figure 2.15 The influence of the CO pressure on the rate of CO oxidation on Rh(111). Data of Schwartz, Schmidt, and Fisher.
Temperature Nonlinear
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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,
Derivation Of Rate Law For AC
Mechanism
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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)
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).
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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)
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People usually ignore reactions 3 and 4 since their rates very low rates compared to the other reactions.
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)
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Similarly for B
Badk8k
PB S7
(12.128)
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)
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Derivation Continued
Equations (12.129) and (12.130) imply that there is an equilibrium in the reactions:
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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)
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
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(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)
Substituting Equations (12.140) And (12.141) Into Equation (12.123) Yields:
rk3KA PAS0 k4KCPCS0
1 KA PA KBPB KCPC
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(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.
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
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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
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.
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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
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.
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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.
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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)
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Solution Continued
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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)
Background: Mass Transfer Critical to Catalyst Design
C HH
HCH
HH
DiffusionChannel
Cavity
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Figure 12.27 An interconnecting pore structure which is selective for the formation of paraxylene.
Introduction
In a supported catalyst reactants first diffuse into the catalyst, then they react The products diffuse out
Gives opportunity for catalyst design
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Reactant Concentration Drops Moving Into the Solid
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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
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
Define “Effectiveness Factor”
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e
Actual rate for a catalyst pellet with mass transfer limitations
Rate in the absence of mass transfer limitations
Derivation: Mass Balance On Differential Slice
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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
Long Derivation
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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
Thiele Plot
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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
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”
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Issues, Continued: Effective Diffusivity, De,
Unknown
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Figure 14.3 A cross sectional diagram of a typical catalyst support.
Knudsen Diffusion
Diffusion rate in gas phase controlled by gas – gas collisions
Diffusion rate in small poles controlled by gas – surface collisions
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Knudsen Diffusion
From kinetic theory
applies when
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)pathfreemeanλ(λv3
1Dgas
diameterporeaa2V3
1Dk
gasa2
Knudsen Diffusion
compared to 0.86 in the gas phase
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21
212
3K M
AMU
K300
T
R1
a
sec
CM10x68.1D
22120100 Hforsec/cm.D poreÅ K
Simple Models Never Work
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Notice one molecule interferes with diffusion of second molecule
Summary
Catalytic reactions follow a catalytic cycle reactants + S adsorbed reactantsAdsorbed reactants products + S
Different types of reactionsLangmuir HinshelwoodRideal-Eley
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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
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Query
What did you learn new in this lecture?
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