Lecture 12
Chemical Reaction Engineering (CRE) is the
field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in
which they take place.
Lecture 12 – Tuesday 2/19/2013
 Multiple Reactions
A
 Selectivity and Yield
 Series Reactions
 Complex Reactions
2
A
A
kD
kU
D
U
B
C
A +B
C+D
A +C
E
4 Types of Multiple Reactions
 Series:
A→B→C
 Parallel:
A→D
A→U
 Independent:
A→B
C→D
 Complex:
A + B →C + D
A+C→E
With multiple reactors, either molar flow or number of
moles must be used (no conversion!)
3
Selectivity and Yield
There are two types of selectivity and yield:
Instantaneous and Overall.
Instantaneous
Selectivity
Yield
4
S DU
rD

rU
rD
YD 
 rA
Overall
F
~
S DU  D
FU
~
YD 
FD
FA0  FA
Selectivity and Yield
k1
D
Example: A  B 
k2
A  B 
U
SD U
Desired Product:
rD  k1CA2CB
Undesired Product: rU  k2CACB
rD k1CA2CB k1
 
 CA
rU k2C ACB k2
To maximize the selectivity of D with respect to U run
at high concentration of A and use PFR.
5
Gas Phase
Multiple Reactions
6
Multiple Reactions
A) Mole Balance of each and every species
Flow
dFA
 rA
dV
dFB
 rB
dV
7
Batch
dN A
 rAV
dt
dNB
 rBV
dt
Multiple Reactions
B) Rates
a) Rate Law for each reaction:
b) Net Rates:
 r1 A  k1 AC AC B
 r2 A  k2 ACC C A
rA   riA  r1A  r2 A
i 1
c) Relative Rates:
8
riA
riB riC riD
=
=
=
-ai -bi ci di
Multiple Reactions
C) Stoichiometry
Gas:
FA  P  T0 
  
C A  CT 0
FA0  P0  T 
Liquid:
CA  FA 0
Example:
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A→B→C
(1) A → B
k1
(2) B → C
k2
Batch Series Reactions
1) Mole Balances
dN A
 rA V
dt
dN B
 rB V
dt
dN C
 rC V
dt
V=V0 (constant batch)
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dC A
 rA
dt
dC B
 rA
dt
dC C
 rA
dt
Batch Series Reactions
2) Rate Laws
 r1A  k1A C A
 r1B  k1B C B
Laws
rA  r1A
rB  r1B  r2 B
r1A r1B

1 1
r2 B r2C

1 1
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Net rates
Relative rates
Example: Batch Series Reactions
A→B→C
(1)
A→B
(2)
B→C
Ci
A
topt
1) Mole Balances V  VO
dC A
 rA
dt
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dC B
 rB
dt
B
dC C
 rC
dt
C
t
Example: Batch Series Reactions
2) Rate Laws
Laws:
r1A  k1CA
r2 B  k 2CB
Relative:
13
r1A r1B

1 1
r2 B r2 C

1 1
Example: Batch Series Reactions
3) Combine
Species A:
dC A

 rA  k1C A
dt
CA  CA0 exp  k1t 
Species B:
dC B
 rB
dt
rB  rB NET  r1B  r2B  k1CA  k 2CB
dC B
 k 2 C B  k1C A 0 exp  k1t 
dt
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Example: Batch Series Reactions


Using the integrating factor, I .F .  exp  k 2 dt  expk 2t 
d
CB expk2t   k C
1
dt
A0
expk 2  k1 t
at t = 0, CB=0
k1CA0
éëexp ( -k1t ) - exp ( -k2t )ùû
CB =
k2 - k1
CC  C A 0  C A  C B
 
15
 
C A0
CC 
k 2 1  e  k1t  k1 1  e  k2t
k 2  k1

Example: CSTR Series Reactions
ABC
What is the optimal  ?
1) Mole Balances
A:
FA0  FA  rAV  0
C A0 v0  C A v0  rAV  0
CA0  CA  rA  0
B:
0  v0 C B  rBV  0
 C B  rB  0
16
Example: CSTR Series Reactions
ABC
2) Rate Laws
Laws:
r1A  k1CA
r2 B  k 2CB
Relative:
Net:
r1A r1B

1 1
r2 B r2 C

1 1
rA  r1 A  0  k1C A
rB  r1 A  r2 B  k1C A  k2CB
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Example: CSTR Series Reactions
ABC
3) Combine
CA 0 - CA - k1CAt = 0
CA 0
CA =
1+ k1t
-CB + ( k1CA - k 2CB )t = 0
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k1CAt
CB =
1+ k2t
k1CA 0t
CB =
(1+ k2t )(1+ k1t )
Example: CSTR Series Reactions
ABC
Find
 that gives maximum concentration of B
k1C A0
CB 
1  k2 1  k1 
 max
dCB
0
d
19

1

k1k2
20
End of Lecture 12
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Supplementary Slides
22
Blood Coagulation
23
24
Notations
25
Notations
26
Mole Balances
27
Mole Balances
28
Mole Balances
29
Results
30
Blood Coagulation
Many metabolic reactions involve a large number of
sequential reactions, such as those that occur in the
coagulation of blood.
Cut → Blood → Clotting
Figure A. Normal Clot Coagulation of blood
31
(picture courtesy of: Mebs, Venomous and Poisonous
Animals, Medpharm, Stugart 2002, Page 305)
Schematic of Blood Coagulation
32
Cut
A+B
C
D
E
F
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Clot