Catalysis and Catalytic Reactions - Spada UNS

Catalysis and Catalytic Reactions

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Scope:

• Catalyst & Catalysis

• Limited to gas phase reactions catalyzed by solids

• Mechanism & rate laws

• Interpretation of data – estimation of rate law parameters

• Physical properties of catalysts – estimation

• Catalytic reactors

• Design of Fixed bed reactor

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What is a catalyst ??

• Alters the rate of reaction

• Highly selective

• Does it participate in the reaction ??

• How does it change the rate ?? – Offers an alternate path with low E.

• Does it affect ∆H_R, ∆G_R, and Eq. constant ??

• Does it affect yield & selectivity ??

• Does it initiate a reaction ??

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Every catalytic reaction is a sequence of elementary steps, in which reactant molecules bind to the catalyst, where they react, after which the product detaches from the catalyst, liberating the latter for the next cycle

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Potential energy diagram of a heterogeneous catalytic reaction, with gaseous reactants and products and a solid catalyst. Note that the uncatalyzed reaction has to overcome a substantial energy barrier, whereas the barriers in the catalytic route are much lower.

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Homogeneous:

Catalytic:

At 600 K the ratio of catalytic to homogeneous rate is 1.44x10¹¹

Example: Boudart compared the homogeneous versus catalytic rates of ethylene hydrogenation.

2

43000 exp

10²⁷ p_H

r RT 



 



−

=

2

13000 exp

10

2 ²⁷ p_H

x RT

r 



 



−

=

8

What is a catalyst ??

• Were in use for making wine, cheese etc.

• Small amounts of catalyst

• Efficiency depends on activity, properties &

life of the catalyst

• Examples:

• Ammonia synthesis – Promoted iron

• SO₂ oxidation – Venadium Pentaoxide

• Cracking – Sylica, alumina

• Dehydrogenation – Platinum, Molybdenum

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Classification:

• Homogenous catalysis

• Heterogeneous catalysis

Catalysts are generally used to:

• Speedup reactions

• Change the operating temperature level

• Influence the product distribution

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Promoter: is an additive which has no catalytic properties of its own but enhances the activity of a catalyst

Promoter results in:

• Increase of available surface area

• Stabilization against crystal growth and sintering

• Improvement of mechanical strength

Examples: Alumina, Asbestos

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Carrier: principally serve as a framework on which catalyst is deposited - no catalytic properties of its own

Carrier results in:

• Highly porous nature - increase of available surface area

• Improve stability

• Improves the heat transfer characteristics

Examples: Alumina, Asbestos, Carborundum, Iron oxide, Manganese, Activated carbon, Zinc oxide

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Accelerator: are substances which can be added to a reacting system to maintain the activity of a catalyst by nullifying the effects of poisons

Poisons: substances which reduce the activity of a catalyst. They are not deliberately added but are unavoidably deposited during the reaction.

Examples: Sulfur, Lead, Metal ions such as Hg, Pd, Bi, Sn, Cu, Fe etc.

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Inhibitor: substances added to the catalyst during its manufacture to reduce its activity.

Coking/Fouling: deposition of carbonaceous material on the surface of the catalyst - Common to reactions involving hydrocarbons

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Activity: of a catalyst depends on the texture and electronic structure. Activity of a catalyst can be explained by:

• Active centers on the surface of the catalyst

• Geometry of surface

• Electronic structure

• Formation of surface intermediates

Efficiency of a catalyst depends on :

Activity, Selectivity and Life

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Active site: is a point on the catalyst surface that can form strong chemical bonds with an adsorbed atom/molecule.

These sites are unsaturated atoms in the solid resulting from:

• Surface irregularities

• Dislocations

• Edges of crystals

• Cracks along grain boundaries

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Mechanism of Heterogeneous Catalysis:

1. Bulk Diffusion of reacting molecules to the surface of the catalyst

2. Pore Diffusion of reacting molecules into the interior pores of the catalyst

3. Adsorption of reactants (chemisorption) on the surface of the catalyst

4. Reaction on the surface of the catalyst between adsorbed molecules

5. Desorption of products

6. Pore Diffusion of product molecules to the surface of the catalyst

7. Bulk Diffusion of product molecules

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Mechanism of Heterogeneous Catalysis:

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Mechanism of Heterogeneous Catalysis:

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Pore and film resistances in a catalyst particle

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Rate-Determining Step (rds)

In a kinetics scheme involving more than one step, it may be that one change occurs much faster or much slower than the others (as determined by relative magnitudes of rate constants).

In such a case, the overall rate, may be determined almost entirely by the slowest step, called the rate- determining step (rds).

The rate of the rds is infinitesimal when compared to the rates of other steps.

Alternately the rates of other steps are infinite compared to the rate of rds.

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Bulk Diffusion:

• Diffusion controlled reactions are usually fast

• Design of reactors – design of mass transfer equipment

• Increase in mass velocity increases the rate

• High L/D ratio reactors (narrow) are favored

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Pore Diffusion:

• Pore diffusion controlled reactions are few

• Design of reactors – most complicated

• Approaches bulk diffusion if the pore size is large

• Approaches Knudsen diffusion if the pore size is small.

• No effect of temperature or mass velocity

• Low L/D ratio reactors (wide) may be used with consequent reduction in pressure drop

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Chemisorption:

• Chemisorption controlled reactions are usually fast

• Rate increases rapidly with increase in temp.

• Permits the use of wide reactors Surface reaction:

• 70% of the reactions which are not controlled by diffusion falls under this case

• Rate increases rapidly with increase in temp.

• Permits the use of wide reactors

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Desorption:

• Desorption of a product could also be rate controlling in a few cases

Complexities:

• Theoretically more than one step can be rate controlling

• Too many possible mechanisms

• Experimental data is normally fitted to any single rate controlling step, which is then called the most plausible mechanism

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Item Physical Adsorption Chemisorption

Forces of attraction

Weak – VanderWaals forces Strong valency forces

Specificity Low High

Quantity Large Small

Heat Effects Exothermic, 1-15 kCal/mol Exothermic, 10-100 kCal/mol

Activation energy

Low High

Effect of Temp. Rapid at low temperatures &

reach equilibrium quickly.

Beyond T_Cof the gas, no ads.

Slow at low temp., Rate increases with temp.

Effect of Pressure

Increases with increase in pressure

Little effect

Surface Whole surface active Fraction of surface only Layers Multi-layer adsorption Mono-layer adsorption

Physical Adsorption Vs. Chemisorption

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Chemisorption rates:

• Adsorption data is reported in the form of isotherms

• Chemisorption may be considered as a

reaction between a reactant molecule and an active site resulting in an adsorbed molecule

A + σ ⇔ Aσ (or) A + S ⇔AS Turnover Frequency (N): defined as the

number of molecules reacting per active site per second at the conditions of the

experiment – a measure for the activity of the catalyst

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Langmuir Isotherm - Assumptions:

• Surface is uniformly active

• All sites are identical

• Amounts of adsorbed molecules will not interfere with further adsorption

• Uniform layer of adsorption Site balance:

t v

v total sites

sites vacant of

sites No vacant of

Fraction

σ

θ = = . =σ

t A

A total sites

sites occupied of

A No by occupied sites

of Fraction

σ

θ = = . =σ

=1 + A v θ θ

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Alternately:

number s

Avogadro

mass unit sites active of

sites No active of

conc Molar C_t

' /

. = .

=

number s

Avogadro

mass unit sites vacant of

sites No vacant of

conc Molar C_v

' /

. = .

=

number s

Avogadro

mass unit A by sites of A No

by sites of conc Molar C_AS

' /

. = .

=

t AS

v C C

C + =

Though other isotherms account for non-uniform surfaces, they have primarily been developed for single adsorbing components.

Thus, the extensions to interactions in multi-component systems is not yet possible, as with the Langmuir isotherm. Langmuir isotherms are only used for developing kinetic rate expressions. However, not all adsorption data can be represented by a Langmuir isotherm.

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Chemisorption rates (molecular adsorption):

A + σ ⇔ Aσ Forward rate = k₁p_Aθ_v Backward rate = k₂θ_A

At equilibrium: k₁p_Aθ_v = k₂θ_A (k₁/k₂)p_Aθ_v = θ_A

A A

A A

A K p

p K

= + 1 θ

A A

t A A

AS K p

C p C K

= + 1

=1 + A v θ θ

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Chemisorption rates (Atomic adsorption):

A₂+ 2σ ⇔ 2Aσ Forward rate = k_Ap_Aθ_v² Backward rate = k_-Aθ_A²

At equilibrium: k_Ap_Aθ_v²= k_-Aθ_A² (k_A/k_-A)p_Aθ_v²= θ_A²

A A

A A

A K p

p K

= + 1 θ

t A A

A A

AS C

p K

p C K

= + 1

What would be θ_A if chemisorption does not reach equilibrium ??

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Effect of increasing temperature

Volume of gas adsorbed

How to check for Molecular Adsorption / Atomic adsorption ??

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Langmuir adsorption isotherm for associative adsorption for three values of the equilibrium constant, K

A A

A A

A K p

p K

= + 1 θ

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Surface Reaction: reaction between the adsorbed molecules on the surface of the catalyst may proceed in a number of ways:

Single site mechanism: Aσ ⇔ Rσ

Dual site mechanism: Aσ + σ ⇔ Rσ + σ Aσ + Bσ ⇔ Rσ + Sσ Aσ+ Bσ ⇔ Rσ + σ

Langmuir-Hinshelwood kinetics

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Aσ + B(g) ⇔ Rσ Aσ ⇔ Rσ + S(g) Aσ+ B(g) ⇔ Rσ + S(g)

Aσ + Bσ ⇔ Rσ + σ + S(g)

Eley Riedel Mechanism

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Surface reaction rates:

(1) Aσ ⇔ Rσ

Forward rate = k_Sθ_A Backward rate = k_-Sθ_R At equilibrium: k_Sθ_A = k_-Sθ_R

A R

KS =θ _/θ (2) Aσ + σ ⇔ Rσ+ Sσ KS =θRθS_/θAθV

(3) Aσ + Bσ ⇔ Rσ+ Sσ KS =θRθS_/θAθB B A S R

S p p

K =θ _/θ (4) Aσ + B(g) ⇔ Rσ+ S(g)

(5) Aσ ⇔ Rσ+ S(g) ^{KS =θRpS /θA}

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Desorption rates:

Rσ ⇔ R + σ

(Desorption of R is the Reversal of adsorption of R)

Forward rate = k_Dθ_R Backward rate = k_-Dp_Rθ_V At equilibrium: k_Dθ_R = k_-Dp_Rθ_V

V R R D V R

R p θ K K p θ

θ = / =

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Synthesizing a rate law – Algorithm (Langmuir-Hinshelwood Approah) 1. Assume a sequence of steps

2. Write rate laws for each step assuming all steps to be reversible

3. Assume a rate limiting step

4. Equate the rate of rds to the overall rate 5. The rates of other steps are equated to zero

(equilibrium)

6. Using the rates of other steps eliminate all coverage dependent terms

7. If the derived rate law does not agree with expt., goto (3)

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• Approach is similar to non-elementary reactions

• In the case of non-elementary reactions there is only one rate law for a given mechanism

• But in the case of solid catalyzed gas phase reactions, there could be many (equal to the number of steps) rate laws for a given

mechanism

• In a given mechanism, even after assuming each of the steps as rds, and none of them satisfy the experimental data, start with a new

mechanism and repeat

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Example: C₆H₅CH(CH₃)₂→ C₆H₆ + C₃H₆ Cumene → Benzene + Propylene Suggested Mechanism:

C + σ ⇔ Cσ (Adsorption of cumene) Cσ ⇔ Bσ + P(g) (Surface reaction) Bσ ⇔ B + σ (Desorption of Benzene) Rate laws for each of the steps:

C A V C

Ap k

k Adsorption of

rate

Net = θ − ₋ θ

P B S C

S k p

k reaction Surface

of rate

Net = θ − ₋ θ

V B D B

D k p

k Desorption of

rate

Net = θ − ₋ θ

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Case-I: Adsorption is Rate limiting step

C A V C A

C Net rateof Adsorption k p k

r = = θ − ₋ θ

−

) /

( _{C V C A}

A

C k p K

r = θ −θ

−

0

Re = − ₋ =

P B S C

S k p

k action Surface

of rate

Net θ θ

=0

−

= ₋

V B D B

D k p

k Desorption of

rate

Net θ θ

S P B

C θ p /K

θ =

D V B B p θ /K θ =

V D S

B P

C K K

p

p θ

θ =

Site balance: θ_C + θ_B + θ_V = 1

D B D S

B P V

K p K K

p

p +

+

= 1 θ 1

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) /

( _{C V C A}

A

C k p K

r = θ −θ

−

) (

) (

eq B P C V A V D S A

B P V

C A

C K

p p p

K k K K

p p p

k

r = − = −

− θ θ θ

D B D S

B P

eq B P C A C

K p K K

p p

K p p p

k r

+ +

−

=

− 1

) (

Final rate law for Case-1

Case-II: Surface reaction is rate limiting step

C A V C

Ap k

k Adsorption of

rate

Net = θ − ₋ θ

P B S C

S k p

k reaction Surface

of rate

Net = θ − ₋ θ

V B D B

D k p

k Desorption of

rate

Net = θ − ₋ θ

46 V C A C C

A V C

Ap k K p

k Adsorption of

rate

Net = θ − ₋ θ =0⇒θ = θ

P B S C S

C Netrateof Surfacereaction k k p

r = = θ − ₋ θ

−

D V B B V

B D B

D k p p K

k Desorption of

rate

Net = θ − ₋ θ =0⇒θ = θ /

) /

( _{C B P S}

S

C k p K

r = θ −θ

−

Site balance: θ_C + θ_B + θ_V = 1

D B C A V

K p p

K +

+

= 1 θ 1

) /

( )

/

( _{A C V B P V D S S A V C B P A D S}

S

C k K p p p K K k K p p p K K K

r = − = −

− θ θ θ

D B C A

eq B P C A S C

K p p K

K p p p

K k r

+ +

−

=

−

1

) (

Final rate law for Case-2

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Case-III: Desorption is rate limiting step

P C S B P

B S C

S k p K p

k reaction Surface

of rate

Net = θ − ₋ θ =0⇒θ = θ /

) /

( _{B B V D}

D V B D B D

C Net rateof Desorption k k p k p K

r = = θ − θ = θ − θ

− ₋

V C A C C

A V C

Ap k K p

k Adsorption of

rate

Net = θ − ₋ θ =0⇒θ = θ

Site balance: θ_C + θ_B + θ_V = 1

P C S A C A

V 1 K p K K p /p

1 +

= + θ

P V C A S

B K K p θ / p

θ =

) / /

( _{S A C V P B V D}

D

C k K K p p p K

r = θ − θ

−

) /

/

( _{C P B A S D}

V A S D

C k K K p p p K K K

r = −

− θ

C S A C P A P

eq B P C S A D

P C S A C A

eq B P C S A D

C p K p p K K p

K p p p

K K k p

p K K p K

K p p p K K k

r + +

− + =

+

−

=

−

) (

/ 1

) /

(

48 D

B D S

B P

eq B P C A C

K p K K

p p

K p p p

k r

+ +

−

=

− 1

) (

D B C A

eq B P C A S C

K p p K

K p p p

K k r

+ +

−

=

−

1

) (

C S A C P A P

eq B P C S A D

C p K p p K K p

K p p p

K K k

r + +

−

=

−

) (

Case-1

Case-2

Case-3

) (

) (

term Adsorption

Force Driving term

Kinetic Rate=

What would be the effect of an inert ??

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Effect of increasing reactant concentration:

Increasing the reactant concentration increases both the driving force and adsorption inhibition terms.

C_A rate

Volcano shape results from a competition between kinetic driving force and adsorption inhibition terms.

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Term Case-1 Case-2 Case-3

Kinetic ^{kA kSKA kDKAKS}

Driving Force

Adsorption

eq B P

C K

p p − p

eq B P

C K

p p − p

eq B P

C K

p p − p

D B D S

B P

K p K K

p p + 1+

D B C

A K

p p K +

1+ pP+KApPpC+KAKSpC

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V C Ap K

θ

V C Ap K θ

V D S

B P

K K

p p θ

P V C A

SK p p K θ /

D V

B

K

p θ /

D V

B

K

p θ /

Coverage Case-1 Case-2 Case-3

θ

C

θ

_B

52

53

54

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• For a given mechanism, the driving force is unique, irrespective of RDS

• The product of equilibrium constant of all steps in the mechanism yield the overall eq. constant

• In the kinetic term, the rate constant of RDS will appear

• If adsorption of A is not RDS, then K_Ap_A will appear in the adsorption term

• If desorption of B is not rate limiting, then p_B/K_D will appear in the adsorption term

• If SR is RDS, then the adsorption term will be raised to the power equal to the number of sites involved in the SR step.

Remarks:

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Exercise: ^Al2O₃

N-pentane ⇔ I-Pentane

Suggested Mechanism:

N + σ ⇔ Nσ Nσ + σ ⇔ Iσ + σ Iσ ⇔ I + σ

Rate laws for each of the steps:

N A V N

Ap k

k Adsorption of

rate

Net = θ − ₋ θ

v I S v N

S k

k reaction Surface

of rate

Net = θ θ − ₋ θ θ

V I D I

D k p

k Desorption of

rate

Net = θ − ₋ θ

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Case-I: Adsorption is Rate limiting step

N A V N A

N Netrateof Adsorption k p k

r = = θ − ₋ θ

−

) /

( _{N V N A}

A

N k p K

r = θ −θ

−

0

Re = − ₋ =

v I S v N

S k

k action Surface

of rate

Net θ θ θ θ

=0

−

= ₋

V I D I

D k p

k Desorption of

rate

Net θ θ

S I

N θ /K

θ =

D V I I pθ /K θ =

V D S

I

N K K

p θ θ =

Site balance: θ_C + θ_B + θ_V = 1

D I D S

I V

K p K K

p +

+

= 1 θ 1

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) /

( _{N V N A}

A

N k p K

r = θ −θ

−

) (

) (

eq I N V A V D S A

I V

N A

N K

p p K k

K K p p

k

r = − = −

− θ θ θ

D I D S

I

Eq I N A N

K p K K

p K p p r k

+ +

= −

−

1

) / (

Rate law for Case-1

Case-II: Surface reaction is rate limiting step

N A V N

Ap k

k Adsorption of

rate

Net = θ − ₋ θ

v I S v N

S k

k reaction Surface

of rate

Net = θ θ − ₋ θ θ

V I D I

D k p

k Desorption of

rate

Net = θ − ₋ θ

59 V N A N N

A V N

Ap k K p

k Adsorption of

rate

Net = θ − ₋ θ =0⇒θ = θ

v I S v N S

N Netrateof Surfacereaction k k

r = = θ θ − ₋ θ θ

−

D V I I V

I D I

D k p p K

k Desorption of

rate

Net = θ − ₋ θ =0⇒θ = θ /

) /

( _{N I S}

v S

N k K

r = θ θ −θ

−

Site balance: θ_C + θ_B + θ_V = 1

D I N A

V 1 K p p /K

1 +

= + θ

) /

( )

/

( _{A N V I V D S S A v}² _{N I A D S}

V S

N k K p p K K k K p p K K K

r = − = −

− θ θ θ θ

)2

/ 1

(

) / (

D I N A

Eq I N A S

N K p p K

K p p K r k

+ +

= −

− Rate law for Case-2

60

Case-III: Desorption is rate limiting step

N S I v

I S v N

S k K

k reaction Surface

of rate

Net = θ θ − ₋ θ θ =0⇒θ = θ

) /

( _{I I V D}

D V I D I D

N Net rateof Desorption k k p k p K

r = = θ − θ = θ − θ

− ₋

V N A N N

A V N

Ap k K p

k Adsorption of

rate

Net = θ − ₋ θ =0⇒θ = θ

Site balance: θ_C + θ_B + θ_V = 1

N S A N A

V = +K p +K K p

1 θ 1

V N A S

I K K p θ

θ =

) / ( _{S A N V I V D}

D

N k K K p p K

r = θ − θ

−

) /

( _{N I A S D}

V A S D

N k K K p p K K K

r = −

− θ

N S A N A

Eq I N S A D

N K p K K p

K p p K K r k

+ +

= −

−

1

) / (

Rate law for Case-3

61

• How to verify which one is rate limiting step ??

• For this initial rate data is normally used

D B C A

eq B P C A S C

K p p K

K p p p

K k r

+ +

−

=

−

1

) (

C C C

A C A S

bp ap p

K p K r k

= +

= +

−

1

0 1

• In the absence of any products initially, the rate law simplifies to:

62

Case-1

Case-2

N S A N A

eq I N S A D

N K p K K p

K p p K K k

r + +

−

=

− 1

) (

)2

/ 1

(

) (

D I N A

eq I N A S

N K p p K

K p p K k

r + +

−

=

−

D I D S

I eq

I N A N

K p K K

p K p p k r

+ +

−

=

− 1

) (

N Ap k r =

− 0

0 2

) 1

( _{A N}

N A S

p K

p K r k

= +

−

Case-3

N S A N A

N S A D

p K K p K

p K K r k

+

= +

−

0 1