Lecture 12 Tuesday 2/12/08 Multiple Reactions Selectivety and Yield Series Reactions Complex Reactions

Department of Chemical Engineering, University of Michigan, Ann Arbor

2 HSF, 04/22/23

Many metabolic reactions involve a large number of sequential reactions, such as those that occur in the coagulation of blood.

Cut → Blood → Clotting

Blood Coagulation

Figure A. Normal Clot Coagulation of blood

(picture courtesy of: Mebs, Venomous and Poisonous Animals, Medpharm, Stugart 2002, Page 305)

Department of Chemical Engineering, University of Michigan, Ann Arbor

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Schematic of Blood Coagulation

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Cut

A + B

C

D

E

F

Clot

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MODEL EQUATIONS:

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MODEL EQUATIONS:

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NOTATIONS

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NOTATIONS

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MOLE BALANCE

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MOLE BALANCE

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MOLE BALANCE

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RESULTS

Multiple Reactionsexample: A → B → C

(1) A → B

(2) B → C

1) Mole balances:

2) Rates: rate laws:

relative rates:

3) Combine:

CC

BB

AA r

dtdCr

dtdCr

dtdC

BB

AA

CkrCkr

22

11

11

11

2211 CBBA rrrr

BAAC

tktkAB

Btk

ABB

BABBB

tkAAAA

A

CCCC

eekk

CkC

C teCkCkdt

dC

CkCkrrdt

dC

eCCCkrdt

dC

0

12

01

012

2121

01

21

1

1

0 ,0at

When is CB the highest?

12

1

2

1

2

2112

01

ln

0

12

21

kkkk

tkke

ekekkk

Ckdt

dC

tkk

tktkAB

Example: CSTR multiple reactions A → B → C

what is the optimal ?

1) Mole Balance:

0000

00

0

0

000

0

BB

BB

AAA

AAA

AAA

rCVrCV

rCCVrVCVC

VrFF

2) Rates: laws: net:

relative:

3) Combine:

BB

AA

CkrCkr

22

11

BABBB

AAA

CkCkrrrCkrr

2121

11 0

11

112211 CBBA rrrr

21max

12

01

2

1

21

1

0

10

111

1

01

0

kk

kkCkC

kCkC

CkCkCk

CC

CkCC

AB

AB

BAB

AA

AAA

0d

dCB

Example: Liquid phase PFR

A + 2B → C (1)

2A + 3C → D (2)

1) Mole balances:

2) Rates: laws:

net:

relative:

3) Stoich:

overall selectivity:

parameters:

DD

CC

BB

AA r

dVdFr

dVdFr

dVdFr

dVdF

3222

211 CACCBAAA CCkrCCkr

DDCCC

BBAAA

rrrrrrrrrr

221

121

CDCADCA

ABACCBA

rrrrrrr

rrrrrrr

2222222

1111111

31

32

132

2 121

15 ,102 ,2 ,250 ,100

21

000

AA

BA

kkCCVV

00000

V VVFC

VFC

VFC

VFC D

DC

CB

BA

A

0

0 0000001.0

~

A

AA

D

C

D

C

FFFX

FF

FFS