Catalytic Reaction Kinetics
 Why catalytic reaction kinetics
 Derivation rate expressions
 Simplifications
– Rate determining step
– Initial reaction rate
 Limiting cases
– Temperature dependency
– Pressure dependency
 Examples
Catalysis and Catalysts - Kinetics
Reactor design equation
conversion i
stoichiometric coefficient i
dx i
  i    r
d W Fi 
rate expression
‘space time’
catalyst effectiveness
Catalysis and Catalysts - Kinetics
Simple example: reversible reaction
A
B
‘Elementary processes’
A
B
1
3
k1
1.
A + *
k -1
2
A*
B*
2.
A*
A*
k2
B*
k -2
k3
3.
‘Langmuir adsorption’
Catalysis and Catalysts - Kinetics
B*
k -3
B + *
Elementary processes
 Rate expression follows from rate equation:
r1  r1  r1  k1 pA NT *  k1 NT A
r2  r2  r2  k2 NT A  k2 NT B
r3  r3  r3  k3 NT B  k3 pB NT *
 At steady state:
r  r1  r2  r3
Eliminate unknown surface occupancies
Catalysis and Catalysts - Kinetics
Elementary processes contd.
1  *  A  B
 Site balance:
(7.5)
 Steady-state assumption:
(7.6-7)
 Rate expression:
(7.9)
r
Catalysis and Catalysts - Kinetics
NTk1k2k3 ( pA  pB / Keq )
(.....)  (......)pA  (......)pB
d A
0
dt
dB
0
dt
with: Keq  K1K2K3
Quasi-equilibrium / rate-determining step
r+1
r-1
r +2
r-2
rate determining
r+3
r-3
‘quasi-equilibrium’
r
r = r+2 - r-2
Catalysis and Catalysts - Kinetics
Rate expression r.d.s.
Rate determining step:
r  r2  r2  k2 NT A  k2 NT B
Eliminate unknown occupancies
Quasi-equilibrium:
r1  r1
So:
A  K1pA  *
B 
Catalysis and Catalysts - Kinetics
pB
 *
K3
k1 pA NT *  k1 NT A
with: K1 
k1
k1
Rate expression, contd.
Substitution:
r  r2  r2  k2 NT K1pA *  k 2 NT pB * / K 3
r  k2 NT K1 *  pA  pB / K eq 
where:
Unknown still *
Catalysis and Catalysts - Kinetics
p 
K eq  K1K 2K 3   B 
 pA eq
Rate expression, contd.
Site balance:
1  *  A  B  *  1 K1pA  pB / K3 
1
* 
1  K1pA  pB / K3 
Finally:
r 
Catalysis and Catalysts - Kinetics
NT k 2K1  pA  pB / K eq 
1  K1pA  pB / K 3 
Other rate-determining steps
Adsorption r.d.s
r 
NT k1  pA  pB / K eq

1  1  1/ K 2  pB / K 3
Surface reaction r.d.s.
r 
NT k 2 K1  pA  pB / K eq 
1  K1pA  pB / K 3 
Desorption r.d.s.
r 
Catalysis and Catalysts - Kinetics
NT k3K1K 2  pA  pB / K eq 
1  1  K 2  K1pA
Langmuir adsorption




Uniform surface (no heterogeneity)
Constant number of identical sites
Only one molecule per site
No interaction between adsorbed species
A+*
1
A*
100
KA (bar-1)
0.8
10
A 
K A pA
1  K A pA
0.6
1
0.4
0.2
0
Catalysis and Catalysts - Kinetics
0.1
0
0.2
0.4
0.6
pA (bar)
0.8
1
Thermodynamics
Equilibrium constant
Reaction entropy
RT ln Keq  Go (T )  H o (T )  TSo
Reaction enthalpy
  i Gfo,i (T )
i
Adsorption constant
SA0 H A0
ln K A 

R
RT
atm-1
Catalysis and Catalysts - Kinetics
Adsorption entropy, <0
(J/mol K)
Adsorption enthalpy,<0
(J/mol)
Multicomponent adsorption / inhibition
Langmuir adsorption
A 
K A pA
1 KA pA   KIpI 
Inhibitors
Catalysis and Catalysts - Kinetics
Dissociative adsorption
H2 + 2*
H 
2H*
 KH2 pH2 
0.5
1   KH2 pH2 
0.5
Two adjacent sites needed
Catalysis and Catalysts - Kinetics
Langmuir-Hinshelwood/Hougen-Watson models
(LHHW)
For: A+B
includes NT, k(rds)
r 
C+D
pApB-pCpD/Keq
(kinetic factor )  (driving force )
(adsorption term )n
molecular: KApA
dissociative: (KApA)0.5
Catalysis and Catalysts - Kinetics
= 0, 1, 2
number of species in r.d.s.
Verwerking p. 11 t/m 13
Catalysis and Catalysts - Kinetics
Initial rate expressions
 Forward rates
 Product terms negligible
Adsorption
r0  NTk1pA0
T1
Surface reaction
NT k2K A pA0
r0 
1  K A pA0
T2
T2
T3
T3
pA0
Catalysis and Catalysts - Kinetics
pA0
(K2 and KApA0 >>1)
r0  NTk3
T1
T1
r0
Desorption
T2
T3
pA0
Ethanol dehydrogenation
Franckaerts &Froment
Cu-Co cat.
C2H5OH 
CH3CHO + H2
Model:
1.
2.
3.
4.
A+*
A* + *
R*
S*




A*
R* + S*
R+*
S+*
= Derive rate expression =
Catalysis and Catalysts - Kinetics
(r.d.s.)
Initial rates - linear transformation
Ethanol dehydrogenation
Full expression
Initial rate
r0 
r 
k2 s NT K A  pA  pR pS / K eq
1  K A pA  KR pR  K S pS 
k K A pA

2
with k  k2sNT
1 K A pA 
2
After rearrangement
pA

r0
1
k KA

KA
k KA
 pA
linear form: y  a  b  x
linear least squares fit
trends, positive parameters
Catalysis and Catalysts - Kinetics
Initial rates - CO hydrogenation over Rh
Van Santen et al.
Kinetic model
1. CO + *  CO*
2. CO* + *  C* + O*
(r.d.s.)
800
Initial rate
600
r0 
sk2NTKCO pCO
1 KCO pCO 
2
Rate
r0  sNTk2CO  *
400
200
0
0.2
600
0.4
550
0.6
500
450
0.8
Catalysis and Catalysts - Kinetics
1.0
400
Temperature and Pressure Dependence
Verwerking p. 18 t/m21
*A
k+#
k-#
Catalysis and Catalysts - Kinetics
*A#
kbarrier
*B
Limiting cases - forward rates
r
Surface reaction r.d.s.
k2 NT K A pA
1  K A pA  KB pB 
1. Strong adsorption A
r  k 2 NT
A* #
Eaobs  Ea2
Ea2
A*
B*
Catalysis and Catalysts - Kinetics
Limiting cases - forward rates
r
Surface reaction r.d.s.
k2 NT K A pA
1  K A pA  KB pB 
2. Weak adsorption
r  k2 NT K A pA
A* #
Eaobs  Ea2  HA
A(g) + *
Ea2
HA
A*
Catalysis and Catalysts - Kinetics
Limiting cases - forward rates
r
Surface reaction r.d.s.
k2 NT K A pA
1  K A pA  KB pB 
3. Strong adsorption B
r 
k 2 N T K A pA
KB pB
Eaobs  Ea2  HA  HB
A* #
B + *+ A
HA
- HB
A*
B* + A
Catalysis and Catalysts - Kinetics
Ea2
Cracking of n-alkanes over ZSM-5
J. Wei I&EC Res.33(1994)2467
r0  k2K A pA
Eaobs  Ea2  HA
200
Ea2
100
kJ/mol
0
-100
Eaobs
HA
-200
Carbon number
Catalysis and Catalysts - Kinetics
Observed temperature behaviour
•T higher
coverage lower
•Highest Ea most favoured
Change in r.d.s.
adsorption r.d.s.
ln robs
desorption r.d.s.
1/T
Catalysis and Catalysts - Kinetics
‘Kinetic Coupling’
two kinetically significant steps
Pt-catalysed dehydrogenation of methylcyclohexane:
M  T + H2
Two kinetic significant steps:
* + M  ....
T*
T+ *
mari
no inhibition by e.g. benzene
T* much higher than equilibrium with gas phase T
Catalysis and Catalysts - Kinetics
Sabatier principle - Volcano plot
Rate
Heat of adsorption
Catalysis and Catalysts - Kinetics
Summary
 Langmuir adsorption
– uniform sites
– no interaction adsorbed species
– constant number of sites
 Rate expression
– series of elementary steps
– steady state assumption
– site balance
– quasi-equilibrium / rate determining step(s)
– initial rates
mechanism
Catalysis and Catalysts - Kinetics
kinetics
Catalysed N2O decomposition over oxides
Winter, Cimino
Rate expressions:
r  k obs  pN 2O
r  k obs 
1st order
pN 2O
pO 
strong O2 inhibition
0.5
2
r 
k obs pN 2O
1 p
O2
K3
0.5
Also: orders 0.5-1
water inhibition
= Explain / derive =
Catalysis and Catalysts - Kinetics

moderate inhibition
N2O decomposition over Mn2O3
Vannice et al. 1995
2 N2O
2N2 + O2
Kinetic model
N2O + * 
N2O* 
2 O*

1.
2.
3.
N2O*
N2 + O*
2* + O2
Rate expression
r 
k 2 NT K 1 pN 2O
1 K p
1 N 2O
Catalysis and Catalysts - Kinetics
  pO 2 K 3 
0.5

N2O decomposition over Mn2O3
Vannice et al. 1995
order N2O ~0.78
Oxygen inhibition
0.4
pN2O = 10 kPa
r / 10-6 mol.s-1.g-1
Eaobs= 96 kJ/mol
0.3
648 K
0.2
638 K
623 K
608 K
0.1
0.0
0.0
598 K
2.0
4.0
6.0
pO2 / kPa
= Explain =
Catalysis and Catalysts - Kinetics
8.0
10.0
N2O decomposition over Mn2O3
Vannice et al. 1995
Kinetic model
H1  29 kJ/mol
Values
S1  38 J/mol K
Ea2  130 kJ / mol
1.
2.
3.
N2O + *  N2O*
N2O*

N2 + O*
2 O*
 2* + O2
Rate expression
r 
1 K p
H3  92 kJ/mol
S3  109 J/mol K
= Thermodynamically consistent =
Catalysis and Catalysts - Kinetics
k 2 NT K1pN 2O
1 N 2O
 pO 2 K 3 
0.5

N2O decomposition over ZSM-5 (Co,Cu,Fe)
Kapteijn et al. 11th ICC,1996
2 N2O
2N2 + O2
Kinetic model
1.
2.
N2O + *  N2 + O*
N2O + O* N2 + O2 + *
Rate expression
r
Catalysis and Catalysts - Kinetics
k1 NT pN 2O
1  k1 k2 
no oxygen inhibition
N2O decomposition over ZSM-5 (Co,Cu,Fe)
Kapteijn et al. 11th ICC,1996
1.0
743 K
0.8
X(N2O)
833 K
0.6
Oxygen inhibition model
793 K
Cu-ZSM-5
Fe-ZSM-5
0.4
Co-ZSM-5
1.
2.
3.
N2O + * 
N2O + O*
O2 + * 
0.2
N2 + O*
N2 + O2 + *
*O2
Rate expression
r
k1 NT pN 2O
1  k1 k2  K3 pO2 
Catalysis and Catalysts - Kinetics
733 K
688K
773 K
0.0
0
2
4
6
p(O2) / kPa
8
10
Effect of CO on N2O decomposition
1. 0
Cu -Z SM -5 (6 7 3 K)
CO + * 
CO2 + *
CO* (Cu+)
X(N2O)
CO + O*
0. 8
0. 6
F e -Z SM -5 (6 7 3 K)
0. 4
0. 2
Co -Z SM -5 (6 9 3 K)
0. 0
0. 0
0. 5
1. 0
1. 5
m o l a r CO/N
O ra ti o
2
CO removes oxygen from surface
so ‘enhances’ step 2, oxygen removal
now observed: rate of step 1
increase: ~2, >3, >100
Catalysis and Catalysts - Kinetics
r1 = k1 NT pN2O
2. 0
Effect of CO on N2O decomposition
rate without CO
r
k1NT pN 2O
1 k1 k2 
ratio = 1 + k1/k2
So k1/k2 = :
Catalysis and Catalysts - Kinetics
1
Co
>2
Cu
>100 Fe
rate with CO
r  k1 NT pN 2O
and: O* 
 O* 
k1 k 2
1  k1 k 2
0.7
>0.9
>0.99
Apparent activation energies N2O decomposition
CO/ N2O = 2
Apparent activation energies (kJ/mol)
only N2O
Co
110
115
Cu
138
187
Fe
165
78
Co,
Fe
r  k1 NT pN 2O
Cu
r
Catalysis and Catalysts - Kinetics
CO/N2O=2
k1 NT pN 2O
k N p
 1 T N 2O
1 k1 k2  KCO pCO  KCO pCO
Eaobs  Ea1
Eaobs  Ea1  HCO
Apparent activation energies N2O decomposition
CO/ N2O = 0
Apparent activation energies (kJ/mol)
only N2O
Co,
Cu
k N p
r  1 T N 2O
1  k1 k2 
Fe
r  k2 NT pN 2O
Catalysis and Catalysts - Kinetics
CO/N2O=2
Co
110
115
Cu
138
187
Fe
165
78
Eaobs  mix(Ea1, Ea2 )
Eaobs  Ea2
Complex kinetics
HDN of Quinone over NiMo/Al2O3 (Prins & Jian, Zurich)
Kinetic scheme
N
THQ1
Q
NH2
N
N
N
THQ5
DHQ
OPA
PB
NH2
PCHA
PCHE
Purpose: Kinetics of reaction
Effects functions Ni and Mo
Addition role of P
PCH
Catalysis and Catalysts - Kinetics
Complex kinetics
Subscheme research: HDN of OPA
NH2
OPA
PB
Not observed
intermediate,
not significant
NH2
PCHA
Catalysis and Catalysts - Kinetics
PCHE
PCH
Complex kinetics
HDN of OPA
Derived global scheme:
k1
NH2
OPA
PB
k6
k3
k5
PCHE
Catalysis and Catalysts - Kinetics
PCH
How can this ‘direct’ step
be rationalised?
Complex kinetics
HDN of OPA (Jiang & Prins)
Reaction modelling
OPA NiMo one site model 370C
strong adsorption
N-containg species
OPA
0.8
Partial pressure (kPa)
plug flow reactor
5
4
PCH
0.6
PCHE
0.4
3
PB
2
0.2
1
0.0
0
0
10
20
30
space time (cs)
excellent fit
Catalysis and Catalysts - Kinetics
40
50
60
Partial pressure (kPa)
1.0
Complex kinetics
HDN of OPA
Competitive parallel steps
Direct global
routes
OPA + *
HCs not adsorbed
(weakly compared to N-s)
kb
OPA*
PB + *
ka
Fast reaction
steps
PCHA*
slow
PCHE*
kd
The direct
route to PCH
Only traces found
PCHA + *
kc
PCHE + *
ke
PCH + *
Other hydrogenation
functional sites ?
Catalysis and Catalysts - Kinetics
Rate expressions
•Steady state assumption
•Site balance (one site)
•Strong adsorption N-species
parallel reactions
rOPA  
ka  kb KOPA pOPA

ka 
1  1 
 KOPA pOPA  KNH3 pNH3
kc  kd 

Q: explain zero order OPA
direct
route
rPCH
Catalysis and Catalysts - Kinetics
 ka kd 

 KOPA pOPA  ke pPCHE
 ka  kd 


ka 
1  1 
 KOPA pOPA  KNH3 pNH3
kc  kd 

from PCHE
Catalysis and Catalysts - Kinetics
‘Kinetic coupling’
two steps kinetically significant
Decomposition of ammonia over Mo (low p, high T)
2NH3 -> N2 + 3H2
Steps:
2NH3 + * -> 2N* + 3H2
2N*
-> N2
surface concentration N much higher than equilibrium
with N2 pressure
‘fugacity of N* corresponds with virtual fugacity N2
Catalysis and Catalysts - Kinetics
Virtual fugacity, kinetic coupling
Aromatization light alkanes over zeolite
Alkanes -> Aromatics + Hydrogen
• Cracking yields high H*, so high fugacity H*
• H* not in equilibrium with H2
-> low aromatics selectivity
Addition of Ga provides escape route for H*
zeolite:
Ga:
alkane
2H*
-> 2H* + .....
-> H2
Kinetic coupling used to increase reaction selectivity for aromatics
Catalysis and Catalysts - Kinetics
Kinetic coupling between catalytic cycles
effect on selectivity
Hydrogenation:
butyne -> butene -> butane
A1
A2
A3
butyne and butene compete for the same sites
but:
K1 >> K2
resulting high selectivity for butene (desired) possible
even when k2 > k1
since:
S1,2 
k1K1
k 2K 2
Meyer and Burwell (JACS 85(1963)2877) mol%:
2-butyne
22.0
cis-2-butene
77.2
trans-2-butene
0.7
1-butene
0.0
butane
0.1
Catalysis and Catalysts - Kinetics
Kinetic coupling between catalytic cycles
effect on selectivity
Bifunctional catalysis: Reforming
Isomerization n-pentane: n-C5 -> i-C5
Pt-function:
n-C5 -> n-C5=
surface diffusion
Acid function:
low concentration
close proximity
n-C5= -> i-C5=
surface diffusion
Pt-function:
i-C5= -> i-C5
Catalytic cycles on different catalysts
Affect selectivity:
• modify surface (change adsorption properties)
• modify fluid phase (change adsorption properties)
benzene hydrogenation M. Soede
Catalysis and Catalysts - Kinetics
Competitive adsorption
Selective hydrogenation aromatics
S.Toppinen,Thesis 1996
Ni-alumina trilobe catalyst
3 mm particles
40 bar H2
125oC
semi-batch reactor
CH3
CH2
CH3
CH3
•Consecutive conversion
behaviour
•rate constants ~ similar
•adsorption constants
decrease
co n ce n tra ti o n / wt.%
30
25
CH3
20
CH3
15
10
H3C
5
0
0
2
4
6
8
s p a c e ti m e / m i n .g .m l -1
Propose a rate expression to account for this effect
Catalysis and Catalysts - Kinetics
10
CH3
Partial benzene hydrogenation
 Ru-catalyst - clusters of crystallites
 Slurry reaction, elevated pressures
 Water-salt addition increases selectivity
+H
2
+ 2 H2
Ru
Salt-water
Adsorption / Desorption properties affected
Catalysis and Catalysts - Kinetics
Dual site models:
A+B
C

A + *

A*

B + *

B*

A* + B*

C* + *

C + *

C*
r
Catalysis and Catalysts - Kinetics
(r.d.s.)
k3 sNT K1K 2pA pB  pC / Keq 
1 K1pA  K2 pB  pC / K 4 2
Surface occupancies
Empty sites:
Occupied by A:
* 
1
1  K1pA  pB / K3 
A 
K1pA
1 K1pA  pB / K3 
B 
pB / K3
1 K1pA  pB / K3 
Occupied by B:
Catalysis and Catalysts - Kinetics
Dual site models, contd.
r  r3  r3  s  NT k3 A B  k3C * 
Number of neighbouring sites (here: 6)
Catalysis and Catalysts - Kinetics