Catalytic Kinetics: Cycles and the LHHW Formalism kinetics Physical adsorption Chemisorption From...
Transcript of Catalytic Kinetics: Cycles and the LHHW Formalism kinetics Physical adsorption Chemisorption From...
© Michael T. Klein Reactions 1
Catalytic Kinetics: Cycles and the LHHW Formalism
"A Catalyst is by definition a substance that increases the rateof approach to equilibrium of a chemical reaction without beingsubstantially consumed in the reaction; a catalyst works byforming chemical bonds to one or more reactants and therebyfacilitating their conversion. A catalyst does not significantlyaffect the reaction equilibrium."1
"The definition of a catalyst rests on the idea of reaction rateand therefore the subject of reaction kinetics is central,providing the quantitative framework."1
Gates, B.C. Catalytic Chemistry, Wiley (1990).1
Common theme: Catalysis ≡ Kinetics
© Michael T. Klein Reactions 2
Reaction Chemistry: The Practice of Catalysis
Reaction: A → B + C
Thermodynamics: ∆HoR = ∆Ho
f B + ∆Hof C - ∆Ho
f A
Role of Catalyst: Increase the rate
Implications: Smaller vesselsBetter selectivities (relative rates)
© Michael T. Klein Reactions 3
Reaction Coordinate Diagram Motivates and Explains Catalysis
EA
A poor catalyst
Homogeneous
A good catalyst
B + C
ξ
∆HR = EB + EC - EA is independent of catalyst
© Michael T. Klein Reactions 4
Kinetics of Heterogeneous Catalytic Reactions
External Transport Adsorption/Desorption Internal Transport Surface Reaction
© Michael T. Klein Reactions 5
Series and Parallel Events in Catalytic Reactions
1
2
34
5
6
7Steps 1,3,4,5,7 in series Steps 2,3,4,5,6 in parallel
Al
Bl
Bs
A
BA
A B
s
ss
ss
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SITES AND ACTIVE CENTERS
"|" USED TO INDICATE A CATALYTIC SITE
Single Site Dual Site
A R S A R S
Al Rl Sl Al1=Rl1 Rl2 Sl2
Surface Intermediates, Active Centers
=
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Adsorption
Adsorbent
Adsorbate
Temperature range
Heat of adsorption
Rate and activation energy
Coverage
Reversibility
Importance
All solids
All gases below critical point
Low T
Low, ~ ∆Hliq
Very rapid, low E
Multilayer
Highly reversible
For determination of surfacearea and pore size
Some solids
Some chemically reactivegases
Generally high temperature
High order, about enthalpyof reaction
Nonactivated, low E;activated, high E
Monolayer and less
Often irreversible
For determination of surfaceconcentration, rates ofadsorption and desorption,estimates of active centerarea, and elucidation ofsurface-reaction kinetics
Physical adsorption Chemisorption
From Carberry, J. J. , Chemical and Catalytic Reaction Engineering, McGraw Hill
© Michael T. Klein Reactions 8
Adsorption Isotherms
Langmuir Model:Homogeneous solid surface Energetics independent of coverage Adsorbed species don't interact
Mass Action Steps:
A + l = Al
ra = kaCACl rd = kdCAl
© Michael T. Klein Reactions 9
Adsorption Isotherms
The Equilibrium Isotherm:ra = rd kaCACl = kdCAl
or, withCt = constant = Cl + CAlΘA = CAl /C t = KACA/(1 + KACA)
1.0
01
order
1st order0
0ΘA
CA CA/ SAT
© Michael T. Klein Reactions 10
Extensions of Basic Idea
1. Multicomponent Systems
2. Dissociative Adsorption of "A"
ΘA = (K APA)1/2 /(1 + (K APA)1/2 + ΣKjPj)
Θi = C il/C t = KiCi/(1 + ΣKjCj)
© Michael T. Klein Reactions 11
Heterogeneous Rate Laws
Premises
Homogeneous Principles Valid
Surface Concentrations Relevant
Three Different Classes of (Equal) Rates
© Michael T. Klein Reactions 12
Heterogeneous Rate Laws
1. Adsorption A + l = Al
2. Surface Reaction Al = Rl
3. Desorption Rl = R + l
K = Adsorption Equilibrium Constant (used by convention)
ra = kA(C ACl-C Al/KA)
rsr = ksr(C Al-C Rl/Ksr)
rd = kR(C Rl/KR-C RCl)
Site Balance: C t = C l + C A + C B + …
i
© Michael T. Klein Reactions 13
Steady State Solution
This General Rate Expression Reduced for VariousRate Controlling Steps
Which May:Not ExistChange with TChange with P
© Michael T. Klein Reactions 14
Rate Determining Step
1. The Usual Procedure 2. Requires that all other steps be in virtual equilibrium
Two Common Cases:
1. Surface Reaction Controls 2. Adsorption/Desorption Controls
© Michael T. Klein Reactions 15
Surface Reaction Controlling
A R
r = k sr(C Al - CRl/Ksr)
Θi = C il/C t = KiCi/(1 + Σ KjCj)
r = ksrCtKA(C A-C R/K)/(1 + KACA + KRCR)
K = KsrKA/KR
© Michael T. Klein Reactions 16
Additional Examples
Bimolecular Reactions A + B R + S
r = k srCtKAKB(C ACB-C RCS/K)/(1 + ΣKJCJ)2
rinit1st
0
C A
-1
© Michael T. Klein Reactions 17
Additional Examples
Two-Site Mechanisms
A l1 + B l2 R l1 + S l2
r = k sr C Al1 C Bl2 =
k sr C t K A K B C A C B /(1 + Σ K i1 C i )(1 + Σ K i2 C i2 )
© Michael T. Klein Reactions 18
Additional Examples
Rideal Mechanism
Al + B (g) Rl + S (g)
r = k srCtKACACB/(1 + ΣKiCi)
© Michael T. Klein Reactions 19
Additional Examples
Mole Change
l + Al Bl + Cl
r = k srCtKA(C A-C BCC/K)/(1 + ΣKiCi)2
© Michael T. Klein Reactions 20
Kinetic Groups
Yang/Hougen tables from Froment, G. F. and K. B. Bischoff, Chemical Reactor Analysis and Design, Wiley
Adsorption of A controlling kAAdsorption of B controlling kBDesorption of R controlling kRKAdsorption of A controlling with dissociation kAImpact of A controlling kAKBHomogeneous reaction controlling k
Surface Reaction Controlling
A R A R + S A + B R A + B R + S
Without dissociation ksrKA ksrKA ksrKAKB ksrKAKBWith dissociation of A ksrKA ksrKA ksrKAKB ksrKAKBB not adsorbed ksrKA ksrKA ksrKA ksrKAB not adsorbed, A dissociated ksrKA ksrKA ksrKA ksrKA
© Michael T. Klein Reactions 21
Exponents of Adsorption Groups
Yang/Hougen tables from Froment, G. F. and K. B. Bischoff, Chemical Reactor Analysis and Design, Wiley
Adsorption of A controlling without dissociation n = 1Desorption of R controlling n = 1Adsorption of A controlling with dissociation n = 2Impact of A without dissociation A + B R n = 1Impact of A without dissociation A + B R + S n = 2Homogeneous reaction n = 0
Surface Reaction Controlling
A R A R + S A + B R A + B R + S
No dissociation of A 1 2 2 2Dissociation of A 2 2 3 3Dissociation of A(B not adsorbed) 2 2 2 2No dissociation of A(B not adsorbed) 1 2 1 2
© Michael T. Klein Reactions 22
Driving-Force Groups
Reaction A R A R + S A + B R A + B R + S
Adsorption of A controlling pA - pRK pA - pRpS
K pA - pRKpB
pA - pRpSKpB
Adsorption of B controlling 0 0 pB - pRKpA
pB - pRpSKpA
Desorption of R controlling pA - pRK
pApS
- pRk pApB- pR
KpApB
ps - pR
K
Surface reaction controlling pA - pRK pA - pRpS
K pApB - pRK pApB -
pRpSK
Impact of controlling 0 0 pApB - pRK pApB - pRpS
K(A not adsorbed)
Homogeneous reaction pA - pRK pA - pRpS
K pApB - pRK pApB - pRpS
Kcontrolling
Yang/Hougen tables from Froment, G. F. and K. B. Bischoff, Chemical Reactor Analysis and Design, Wiley
© Michael T. Klein Reactions 23
Replacement In the General Adsorption Groups
Yang/Hougen tables from Froment, G. F. and K. B. Bischoff, Chemical Reactor Analysis and Design, Wiley
(l + KApA + KBpB + KSpS + KRPR + KIpI )
Reaction A R A R + S A + B R A + B R + S
Where adsorption of A is rate KApRK
KApRpSK
KApRKpB
KApRpSKpBcontrolling, replace KApA by
Where adsorption of B is rate 0 0 KBpRKpA
KBpRpSKpAcontrolling, replace KSpS by
Where desorption of A is rate KKRpA KKRpApS
KKRpSpB KKRpApB
pscontrolling, replace KApA by
Where adsorption of A is rate KApRK
KApRpSK
KApRKpB
KApRpSKpBcontrolling with dissociation
of A, replace KApA by
Where equilibrium adsorptionof A takes place with dissociation of A, replace KApA KApA KApA KApAKApA byand similarly for other components adsorbed with dissociation
Where A is not adsorbedreplace KApA by 0 0 0 0and similarly for othercomponents that are notadsorbed
© Michael T. Klein Reactions 24
ADSORPTION/DESORPTION CONTROLLING
• SURFACE REACTION IN VIRTUAL EQUILIBRIUM
KSR = Πi Cil νil
1. Al + Bl Rl + Sl with Adsorption of "A" controlling
r = kaA CA Cl – kdA CAl = k 'A(CACl – CAl/KA)
CBl = KBCBCl
CRl = KRCRClCSl = KSCSClCAl = C RlCSl/(CBlKSR)
4 eqn, 4 unknowns
Used instead of final adsorption isotherm
r = kACt (CA - CRCS /CBK)
1+
CRCSCB
KAK + KBCB + K RCR + KS CS
© Michael T. Klein Reactions 25
Some Criteria for Parameter Estimation
1. Adsorption and Rate Constants be Statistically non-negative
2. E* > 0 ln k ↓ with 1/ T ↑ (Arrhenius)
3. Exothermic adsorption ln k ↑ with 1/ T ↑
Confidence intervals may make negative-value containingmodels acceptable.
© Michael T. Klein Reactions 26
Linearization of Model
rA = kr KA(pA - pR pS/K)(1+ KApA + KRpR + KSpS)2 y = a + bpA + c pR + dpS
y = pA - pRpS/KrA
a = 1/ kKAb = KA/ kKA
c = KR/ kKAd = KS/ kKA
This allows linear regression. However, this suffers from lack ostatistical rigor--y not truly dependent variable.
© Michael T. Klein Reactions 27
Catalysis in Series
A1 → A2 → A3
A1 strongly held, A2 weak, A3 not at all
r1 = k1K1A1/(1+ K1A1 –~ k1
r2 = k2K2A2 2 2 –~ k2K2A2
@ Max of A2 0 = r 1 - r2 ⇒ k1 = k2K2A2
or A2|Max = k1k2K2
r1 r2
Independent Rates:
)
/(1+ K )A
© Michael T. Klein Reactions 28
Coupled Rates
In reality, with coupling, r2 = k2K2A2/(1+K 2A2 + K1A1) –~ k2K2
K1 A2A1
A2 =
k1
k2
K1
K2 A1
orA2
C
A2I = K1A1 >>1
Gain in selectivity due to coupling• This is thermodynamic in nature
MAX
MAX
MAX
•
© Michael T. Klein Reactions 29
Analytical Rate Laws Derived from Mechanism BEFORE Use In Reactor Model
A Heterogeneous Chemistry (A B) Example
A + AA BB B +
l ll ll l
⇔⇔⇔
rA
A sr A B A sr
sr
BA
A sr
sr
AB
l A B K
K k k Kk K kK
KkK A
K kK
KkK B
=−
+ +
+ +
+
+ +
+
0
1 1 1 1 1 1 1( / )
rAsr A
A B
l k K A B KK A K B
=−
+ +0
1( / ) rA
B
A B
l k K A B KK A KK A
=−
+ +0
1( / ) rA
A
AB
l k A B KKK
B K B=
−
+ +
0
1
( / )
surface rxn control adsorption control
desorption control
© Michael T. Klein Reactions 30
Steady State Solution
A = R
Ksr
dCa/dt = r a
dCAl /dt = 0 = ra - rsr
dCRl/dt = 0 = rsr - rd
dCR/dt = r d
r = Ct (C A-CR/K)
1
KAksr + 1
kA + 1
KkR +
1KAksr
+ 1+KKkkR
ACA +
1
KAksr +
1+K srKsrkA
K RCR
A
© Michael T. Klein Reactions 31
Derivation of Rate Laws: Useful Tools The Steady State Approximation
k2
© Michael T. Klein Reactions 32
Derivation of Rate Laws: Useful Tools The Steady State Approximation