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Lecture 10
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 10 – Tuesday 2/12/2013
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Block 1:
Block 2:
Block 3:
Block 4:
Mole Balances
Rate Laws
Stoichiometry
Combine
 Definition of Selectivity
 Semibatch Reactors
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Selectivity in Multiple Reactions
kD
A  B 
D
rD  k DC A2CB
(Desired)
kU
A  B 
U
rU  kU C ACB2
(Undesired )
Selectivity
Instantaneous
SD/U = rD/rU
YD  rD /  rA
Overall
ŜD/U = FD/FU
YˆD  FD /( FA0  FA )
S D /U
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Yield
rD k DC A2CB k DC A
 

2
rU ku C ACB kU CB
Keep CA high and CB low.
Semibatch Reactors
 Semibatch reactors can be very effective in
maximizing selectivity in liquid phase reactions.
 The reactant that starts in the reactor is always
the limiting reactant.
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Semibatch Reactors
Semibatch reactors
A+B→C+D
B, v0

m
Initial V
A
Liquid level and volume increase
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Semibatch Reactors
1) Mass Balance:
dm
 m
dt
m  0 0
and
dm
dV
 0
  00
dt
dt
dV
 0
dt
t  0 V  V0
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V  V0  0t
m  V0
Semibatch Reactors
1) Mole Balance on Species A:
[in] – [out] + [gen] = [acc]
dN A
0  0  rAV 
dt
dN A d [C AV ]
dC A
dV

V
 CA
dt
dt
dt
dt
dV
 0
dt
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 0C A
dC A
 rA 
dt
V
Semibatch Reactors
1) Mole Balance on Species B:
dN B
FB 0  0  rBV 
dt
dN B d [CBV ]
dCB
dV

V
 CB
dt
dt
dt
dt
FB 0  CB 00
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dV
 0
dt

C B 0  C B 0
dC B
 rB 
dt
V
Semibatch Reactors
1) Mass and Mole Balance Summary
1
2
3
4
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5
 0C A
dC A
 rA 
dt
V
 0 (C B 0  C B )
dC B
 rB 
dt
V
dCC
 0 CC
 rC 
dt
V
 0C D
dC D
 rD 
dt
V
V  V0   0t
Semibatch Reactors
6 rA  kCACB
2) Rate Laws
3) Stoichiometry
 rA  rB rC rD

 
1
1
1
1
7
rB  rA
8
rC  rA
9
rD  rA
10
N A0  N A
X
N A0
11
12
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4) Parameters
N A0  C A0V0
N A  CAV
C A0 , V0 , 0 , k , CB 0
Semibatch Reactors
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Semibatch Reactors
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Equilibrium Conversion in Semibatch
Reactors with Reversible Reactions
Consider the following reaction:


A  B
 C  D
Everything is the same as for the irreversible case,
except for the rate law:


CC CD 
 rA  k A C ACB 

K
C 

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Equilibrium Conversion in Semibatch
Reactors with Reversible Reactions
Where:
N A0 1  X 
V
F t  N A 0 X 
C B  B0
V
N A0 X
C C  CD 
V
C A
At equilibrium,  rA  0 then
CCe CDe N Ce N De
N A0 X e2
K C


C AeCBe N Ae N Be 1  X e FB 0t  N A0 X e 
Xe changes with time.
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P6-6B - Semibatch Reactors
Sodium Bicarbonate + Ethylene Chlorohydrin  Ethylene Glycol + NaCl + CO2
NaCHO3 + CH2OHCH2Cl  (CH2OH)2 + NaCl + CO2 
A + B  C + D + CO2 
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P6-6B - Semibatch Reactors
Semibatch Reactors in terms of Moles
A + B  C + D + CO2
Mole Balances
A
B
C
D
dN a
(1)
 rAV
dt
dN b
( 2)
 FB 0  rBV
dt
dN c
(3)
 rCV
dt
( 4) N D  N C
0   FCO2  rCO2V
CO2
(5)
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Stoichiometry
FCO2  rCO2V
 rA   rB  rC  r D  rCO2
(8)
dV
  0  CO2
dt
FCO2 MWCO2
CO2 
RHO
MW  44
(9)
RHO  1000
( 6)
(7 )
(10) Ca  N A V
(11) C B  N B V
Rate Laws
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(12) rA  kCAC B
N a0  N a
(13) X 
N a0
(14) N a 0  V0Ca 0
Rest of the Polymath Statements
Similar to Concentration Program
P6-6 Semibatch: Moles, Na, Nb, etc.
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P6-6 Semibatch: Concentrations CA, CB, CC
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Semibatch Reactors
Three Forms of the Mole Balances applied to Semibatch Reactors:
1. Molar Basis
dN A
 rAV
dt
dN B
 FB 0  rBV
dt
0
dC A
 rA  C A
2. Concentration
dt
V
Basis
0
dC B
 rB  C B 0  C B 
dt
V
3. Conversion
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dX  rAV

dt
N A0
dN A
 rAV
dt
dN B
 FB 0  rBV
dt
Semibatch Reactors
Consider the following elementary reaction:
A+B  C+D
-rA=kCACB
The combined Mole Balance, Rate Law, and
Stoichiometry may be written in terms of number
of moles, conversion, and/or concentration:
Conversion
dX k 1  X N Bi  FB 0t  N A0 X 

dt
V0  0t
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Concentration
No. of Moles

dC A
 rA  C A 0
dt
V
dN A
 rAV
dt

dC B
 rA  C B 0  C B  0
dt
V
dN B
 FA0  rBV
dt
Polymath Equations
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End of Lecture 10
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