Chapter 6 (P2-3) (Note)

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CHAPTER 6

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Contents1. Catalysts and their characterizations

2. Steps in gas-solid catalytic reactions

3. Rate law, mechanisms and RDS

4. Design of reactors for gas-solid catalytic reactions

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5. Heterogeneous data analysis for reactor design

6. Catalyst deactivation

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6.2 Steps in gas-solid catalytic reactions

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Bulk fluid

Pore mouth

4

Catalyst surface

Active site

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SEVEN steps involved in a gas-solid catalytic reaction:

1. Diffusion of the reactant(s) from the bulk fluid to the external

surface of the catalytic pellet2. Diffusion of the reactant(s) from the pore mouth through the

catalyst pores to the internal catalytic surface

3. Adsor tion of the reactant s onto the catal st surface

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4. Reaction on the surface of the catalyst

5. Desorption of the product(s) from the surface

6. Diffusion of the products from the interior of the pellet to thepore mouth at the external surface

7. Diffusion of the products from the external surface to the bulkfluid.

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Step 1: Diffusion from bulk to external surface

Rate (mass transfer) =Mass transfer coefficient

( )AsAbc CCk

/ABc Dk =

6

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Step 2: Internal diffusion

Rate (mass transfer) = AsrCk(The concentration at the interior surface is CA, which is small compared to CAS.

kr is overall rate constant is a function of particle size)

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Step 3: Adsorption isotherms

Adsorption of A on an active site S,SASA +

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The population balance of active sites is

SAvt CCC +=

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Two types of adsorption:

i) Molecular adsorption (nondissociated adsorption)

-Ni-Ni-Ni-Ni- -Ni-Ni-Ni-Ni-

CO CO

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ii) Dissociative adsorption

-Fe-Fe-Fe-Fe- -Fe-Fe-Fe-Fe-

COC O

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For molecular adsorption

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Adsorption equilibrium constantKA = kA/k-A

SCOvt CCC +=

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For dissociative adsorption

C.SSOvt CCCC ++=

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At equilibrium rAD = 0 and for CC.S = CO.S

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Step 4: Surface reaction

a) Single-site reaction: AS BS

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b) Dual-site reaction: AS + S BS + S

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Dual-site reaction: AS + BS CS + DS

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Dual-site reaction: AS + BS CS + DS

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c) Eley-Rideal: AS + B(g) CS +D(g)

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Reaction between an adsorbed molecule and a molecule in the gas phase

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Step 5: Desorption

Desorption equilibrium constant

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Steps 6 and 7: The rates of mass transfer are similar to Steps 1 and 2, except the reactant

concentration is replaced by the product concentration.

KD = 1/KC

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166.3 Rate law, mechanisms and RDS

Rate limiting step (Rate determining step, RDS)

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Sometimes, the overall reaction rate is controlled by one of thesteps RDS. If we could make this particular step to gofaster, the entire reaction would proceed at an accelerated rate.

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Conversion of the automobile exhaust products over Cu-catalyst

22 2

1

NCONOCO++

The mechanism is as follows:

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Adsorption

Surface reaction

Desorption

SNOSNO +

+

SlowestSSNCOSNOSCO +++ 2

Rapid

SNSNSNSNSN

+

+

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2

Rapid

Rapid

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( )

PBC

HCHCCHCHHC

+

+

+

PropyleneBnzeneCumene

63662356

How to determine RDS??

??rorrorrr DSAD'

C ===

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Langmuir-Hinshelwood kinetic mechanism (Propose):

Adsorption

Surface reaction

Desorption

PSBSC+

SCSC +

SBSB +

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SCSC + SBSB +

1. Adsorption of cumene

=

C

SCvCADAD

K

CCPkr

3. Desorption of benzene

DB

vBSBDD

K

CPCkr

=

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PSBSC +

2. Surface reaction

=

S

SBP

SCSSK

CPCkr

vBBSBD CPKCk=

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=

S

SBP

SCSS K

CP

Ckr

PSB

SC

PCC

=

0

S

S

k

r

i) If the Adsorption of Cumene is rate-Limiting

(1)

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S

( )vBBSBDD CPKCkr =

vBBSB CPKC =

0D

D

k

r(2)

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=

C

SCvCADAD

K

C

CPkr S

PSB

SC K

PCC

=

vBBSB CPKC =


(3)

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v

p

PBCAv

CS

PBBCAAD C

KPPPkC

KKPPKPkr

=

=

B

CS

p K

KK

K=

CV = ??

(4)

Overall partial pressure equilibrium constant

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SBSCvt CCCC ++=

v

p

PBCAAD C

K

PPPkr

=

BBSBPB

tv

PKKKPP

CC

++

=

/1(5)

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( )BBSBPB

tpBPCAADc

PKKKPP

CKPPPkrr

++

==

/1/'

000

'

CCAtC kPPkCr ==

- ,

There are no products present initially, PP0, P

B0

(Initial rate)

(6)

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CPKC =

0A

AD

k

r

ii) If the Surface Reaction is rate-Limiting

=

C

SC

vCAAD K

C

CPkr(1)

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( )vBBSBDD CPKCkr =

vBBSB CPKC =

0D

D

k

r(2)

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vBBSB CPKC =

VCCSC CPKC =

=

S

SBP

SCSS K

CPCkr


(3)

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V

P

PB

CCSv

S

PBB

CCSS CKPKkCKKPkr =

=

B

CSp

K

KKK =

CV = ??

(4)

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SBSCvt CCCC ++=CCBB

tv

PKPK

CC

++

=

1

V

P

PBCCSS C

K

PPPKkr

=


(5)

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( ))1(

/'

CCBB

tpBPCCSSc

PKPK

CKPPPKkrr

++

==

If surface reaction is the rate-limiting step, then

(6)

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There are no products present initially, PP0, PB0


00' CCtCskPPCKk

( ))1(

/'

CCBB

tpBPCCSSc

PKPK

CKPPPKkrr

++

==

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00

0

11 CCCCC

PKPK ++

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iii) If the Desorption of Benzene is rate-Limiting

( )vBBSBDD CPKCkr =

0// AADSS krkr VCCSC CPKC =P

SSCSB

PKCC

=

tC

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( )

PCCCSCP

PBPCCStD

DCPPKPKKP

KPPPKKCkrr

++

==

/'

tDC Ckr ='

0

vBBPCCSDD

CCPCSC

v

PKPPKK ++ /1

There are no products present initially, PP

0, PB

0

B

CSp

K

KKK =

(Initial rate)

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Adsorption is RDS

00

'

CC kPr =

Surface reaction is RDS

Summary

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tDC Ckr ='

0

0

0

0 1

'

CC

C

CPKr +

=

Desorption is RDS

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For this reaction, the experimental data follow the behaviour of the

surface reaction rate law.

Thus, surface reaction is the RDS

( )1

1/

'

pBPCScPKPK

KPPPkrr++

==

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( ) )1( 1/'

IICCBB

pBPCScPKPKPK

KPPPkrr+++

==

VIISI CPKC =

In the presence of inerts,

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Summary: Algorithm for Determining Reaction Mechanism andRate-Limiting Step

1. Write down the reaction equationfor adsorption, surface

reaction, and desorption steps.2. Assume arate-limiting step3. Find the expression for concentration of the adsorbed

s ecies intermediates b assumin the other two ste s are

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very fast.4. Write a site balancefor Ct5. Derive the rate law, rAD = ?? or rS = ?? or rD = ??6. Compare the derived rate law with experimental data.7. If the prediction is not correct, then assume other rate-limiting

step, and repeat (2) to (6).

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Derive rate law for RDS surface reaction

SISI

SISN

SNSN

+

+)(

A

SNVNAAD

K

CCPkr =

)(S

SISNSS

K

CCkr

=

Example 6.2

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VIDSIDD

VNASN

A

SNVN

A

AD

CPKC

K

CCPk

r

=

==

0

VIDSI

VIDSI

D

D

CPKC

CPKCk

r

=

==

0 V

S

IDNASS

S

VIDVNASS

CKPKPKkr

K

CPKCPKkr

)(

)(

=

=

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IDNA

tv

VIDVNAvt

SISNvt

PKPKCC

CPKCPKCC

CCCC

++

=

++=

++=

1

PK

IDNA

t

P

INASS

IDNA

t

S

IDNASS

V

S

NASS

PKPKC

KPPKkr

PKPK

C

K

PKPKkr

K

r

++

=

++

=

=

1)(

1)(

D

ASP

KKKK =

33

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Single-site versus Dual-site Mechanisms

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Single-site versus Dual-site Mechanisms

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If irreversible surface reaction is RDS

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Rate Law Derived from PSSH

Assume each species adsorbed on the surface is a reactive

intermediate, i.e. 0* =

Si

r

Example, consideration the isomerization of n-pentene to i-pentene

according to the following mechanism:

Alternative way to derive rate law

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If surface reaction limiting, the

SNSSN Ckrr =='

SISI

SISNSNSN

+

+

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0

0

*

*

=+=

==

vIISIISNSSI

SNSSNNvNNSN

CPkCkCkr

CkCkCPkr

SISNvt CCCC ++=

( )

+

+=

+

=

I

I

I

SNI

NNSvSI

SN

vNNSN

Pk

k

kkk

PkkCC

kk

CPkC

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I

II

SN

NNS

SN

NN

tv

k

Pk

kkk

Pkk

kk

PkCC

+

+

+

+

+

=

)(1

1

SNSSN Ckrr =='

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I

II

I

S

SN

NN

t

SN

NNSSN

k

Pk

k

k

kk

Pk

C

kk

Pkkrr

+++

+

++

==

]1[1

'

II

I

S

NS

NN

N

NS

tNSSN

PKk

k

kk

PKP

kkCKkrr

++

+

++

==

]1[/1

1/1

'

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NNN

III

NS

tSN

kkK

kkK

kk

CkKk

=

=

+

=

/

/

/1

NSkk

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Temperature Dependence of the Rate Law

Consider a surface-reaction limited irreversible isomerization

A B

BBAA

ASA

PKPK

kPrr

++

==

1

'

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Chapter 6 (P2-3) (Note)

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