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Chemical Reaction EngineeringLecture 2: Review of Undergraduate Material
Jayant M. Modak
Department of Chemical Engineering
Indian Institute of Science, Bangalore
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Ethylene production by thermal cracking of ethane
!The thermal cracking of ethane is carried out inmultitubular reactor. Typical production capacity
of each tube is 10000 Tons per annum.
!Reactor specifications:" Feed to the reactor: ethane + steam (?)" Inlet pressure - 2.99 atm; temperature - 680C" Tube length 95 m, ethylene conversion 60%
Indian Institute of Science
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Cracking of ethane to ethylene
26 24CH
C!
Reactor Design
Stoichiometryconversionmolar flows
Rate ofreaction
Molebalances
Batch/CSTR/PFR
Conversion
Volume
Production rate
CSTR +PFR
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Indian Institute of Science
Topic 1: Basic concepts
!Representation of reaction!Extent of reaction and conversion!Thermodynamics and chemical reactions
" Heat of reaction" Condition of equilibrium
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Indian Institute of Science
Representation of chemical reaction single reaction
!Consider a single chemical reaction in N speciesA1, A2,., AN
!General representation:
!jAj
= 0
j=1
N
"
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Indian Institute of Science
Representation of chemical reaction multiple reactions
!Consider R chemical reactions in N species A1,A2,., AN
!General representation:!ijAj = 0
j=1
N
" , i = 1,!2,!.........,!R
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Indian Institute of Science
Representation of chemical reaction independent reactions
!Stoichiometric matrix
!Number of independent reaction
! =
!11 !
1N
! " !!R1
# !RN
"
#
$
$$
%
&
'
''
R!=!rank!! !"# $%
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Indian Institute of Science
Progress of chemical reaction single reaction
!Consider a reaction !!jAj = 0 taking place in aclosed system
nj0 = number of moles of speciesjpresent initially
nj = number of moles of speciesjat any time t
!Molar extent of reaction - "
! =
nj" n
j0
#j
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Indian Institute of Science
Molar extent of reaction
!Properties of"" defined for the reaction
" Extensive property in moles
"Always positive
! =
nj" n
j0
#j
! =
nj " nj0
#j
=n
k " nk0
#k
$!!nk = nk0 + #k#j
nj " nj0( )
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Indian Institute of Science
Conversion of species
!Conversion X
!Stoichiometrically limiting species k
X=n
j0! nj
nj0
min!! ! nj0"
j
#
$
%&
'
(
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Cracking of ethane to ethylene
26 24CHC!
Molar flow at
entry
Ethane, F10
Molar flow at
exit
Ethane, F1Ethylene, F2
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Stoichiometric tables Flow reactor
!
1
A1
+!
2
A2
+ !
3
A3
+!
4
A4
= 0
Species Entry(mol/
min)
Change(mol/
min)
Exit from the reactor(mol/min)
A1 F1O -(F10X) F1=F10- F10XAj j=2,3, 4 FjO - #j/#1
(F10X)Fj=Fj0- #j/#1 F10X
I (inerts) FI0 ----- FI= FI0
Total FT0 FT=FT0-(!#j/#1)F10XFT=FT0+!F10X
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Concentrations in terms of conversion
Pv = Z FT RTP
0v0= Z
0F
T0RT
0
!"#$#
v = v0
P0
P%&'
()*
ZZ
0
%&'
()*
TT0
%&'
()*
FT
FT0
%&'
()*
FT= F
T0+ +F
10X
FT
FT0
= 1+ +F10
FT0
X= 1+ +y10X= 1+ ,X
v=
v0
P0
P
%
&'
(
)*
Z
Z0
%
&'
(
)*
T
T0
%
&'
(
)*1+ ,
X( )
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Concentrations in terms of conversion
0
0
0
0 0
0 0
0
0 0
0 0
0
0 0
1
1
/
1
A
A
A AA
A
A A
B
B A
FC
v
F F XFC
v v
Z TX PC C
X P Z T
Z Tb aX P C C
X P Z T
!
!
=
"= =
# $ # $ " # $# $= % & % & % & % &
+' ( ' (' ( ' ( # $ #) " # $# $
= % & %% & % &+' ( ' (
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Summary Stoichiometry of reaction
!Keywords & concepts" Stoichiometric coefficients" Multiple reactions" Set of independent reactions" Extent of reaction" Conversion" Stoichiometric tables
Indian Institute of Science
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Ethylene production by thermal cracking of ethane
!The thermal cracking of ethane is carried out inmultitubular reactor. Typical production capacity
of each tube is 10000 Tons per annum.
!Reactor specifications:" Feed to the reactor: ethane + steam (?)" Inlet pressure - 2.99 atm; temperature - 680C" Tube length 95 m, ethylene conversion 60%
Indian Institute of Science
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Chemical Equilibrium
!Consider a reaction !!jAj = 0 taking place atconstant temperature T and pressure P. The
system will spontaneously change in the direction
of increasing entropy, reaching equilibrium when
entropy can not increase further.!Free energy and Gibbs equations
Indian Institute of Science
dG = Vdp ! SdT+ jdnjj=1
N
" ,
Chemical !Potential !j = #G#nj$%& '()T,P,nk
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Chemical Equilibrium
!Equilibrium condition
Indian Institute of Science
Gibb 's!Equation dG = Vdp ! SdT+ jdj=1
N
" nj
!!!G
!"#$%
&'(T,P
=
)jjj=1
N
*=
0
!!!!!dG
=
Vdp"SdT
+ #jjd
$
j=1
N
%
Progress!of!reaction nj = nj0 + !j"!!or !!dnj = !jd"!
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Chemical potential
!Solution
Indian Institute of Science
jT,P,x( ) = j0 T,P
r,x
r( ) + RTln!jxj
x = composition!,!T = temperature,!P = pressure
superscript!r !=!reference!= activity!coefficient
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Free energy change
j=
j0+RTln a
j( )
!
1
A1
+!2
A2
+ !3
A3
+ !4
A4
= 0
!j
j
j=1
N
" = !jj0j" +RT !j ln aj( )
j"
!G = !G0 +RTln "j
aj
#j
$
%&
'
()
!G = !G
0+RTlnK
a
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Equilibrium condition
!1A
1+!
2A
2+ !
3A
3+!
4A
4= 0
!G = !G0 + RTln "j
aj
#j
$%&
'()= 0
!G = !G0
+ RTlnKa = 0
Ka= "
j
aj
#j
$%&
'()= exp
*!G0
RT
$
%&'
()
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Equilibrium extent of reaction
!1A
1+!
2A
2+ !
3A
3+!
4A
4= 0
KP= !
j
Pj
"j
#$%
&'(
Pj= y
jP=
Nj
NT
P
Nj = Nj0 +"j)
KP= !
j
PN
j0+"
j#
NT0 +# "jj$
%
&
'''
(
)
***
"j+
,
---
.
/
000
=F #( )
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Extent of reaction and operating conditions
!
1
A1
+ !
2
A2
+!
3
A3
+!
4
A4
= 0
KP(T) = !
j
PN
j0+ "
j#
NT0
+# "
jj$
%
&
''
'
(
)
**
*
"j+
,
--
-
.
/
00
0
= F #,P,Nj0( )
d
dYlnK
P(T)!" #$ =
d
dYF %,P,N
j0( )!" #$ =&F
&Y+
&F
&%
d%
dY
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Extent of reaction and operating conditions
!
1
A1
+ !
2
A2
+!
3
A3
+!
4
A4
= 0
d!
dY= C
F !( )F' !( )
Temperature C="H
RT2 "H= heatofreaction
Pressure C= #
$j
j
%
P$
j=changeinno. ofmoles
j
%
Inerts C= ?
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Indian Institute of Science
Equilibrium conversion - Endothermic reaction
300 320 340 360 380 4000.0
0.2
0.4
0.6
0.8
1.0
Xe
q
T
Isothermal
Adiabatic
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Heat of reaction
!HR= "
jhj
j
#
hj (T) = hj0
+ CPj dT298
T
$!H
R= "
jhj
0
j
# + "jj
# CPj dT298T
$
!HR = !HR0 + "j
j# CPj dT298T
$
!
1
A1
+ !
2
A2
+!
3
A3
+!
4
A4
= 0
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Summary
!Free energy!Chemical potential!Condition of Equilibrium!Equilibrium constant!Equilibrium extent of reaction!Operating conditions
Indian Institute of Science
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Chemical Reaction EngineeringLecture 4: Review of Undergraduate Material
Jayant M. Modak
Department of Chemical Engineering
Indian Institute of Science, Bangalore
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Indian Institute of
Chemical Kinetics: Basic concepts
!Kinetics of irreversible and reversible reactions" Power law kinetics" Law of mass action kinetics
!Rate of simple reactions
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Classification of reactions
!Based on mechanism of the reaction" Elementary and nonelementary reactions
Example: chlorination of nitric oxide to give nitrosyl chloride
2NO + Cl2! 2NOCl
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Classification of reactions
!Based on the direction of the reaction" Irreversible and reversible reactions
cyclopropane! propylene
trans " butylene! cis " butylene
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Classification of reactions
!Based on number of phases present in the system" Homogenous and heterogeneous reactions
C2H
6(g)! C
2H
4(g) + H
2(g)
CO2 (g) + NaOH(l)! NaHCO3(l)
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Indian Institute of
Rate of chemical reaction single reaction
!Consider a reaction !!jAj = 0 taking place in aclosed, isothermal, constant pressure system
!Rate of reaction - rr =
1
Vd!
dt! =
nj" n
j0
#j
rj =1
V
dnj
dt
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Indian Institute of
Reaction rate
!Consider a reaction !!jAj = 0 taking place in aclosed, isothermal, constant pressure system
r = r(T,P,y1
,y2
...yN!
1
)
= r(T,P,C1,C2 ...CN!1)
= r(T,C1,C
2...CN!1,CN)
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Activation energy
0.0020 0.0025 0.0030 0.0035
-6
-4
-2
0
2
ln
(k)
1/T (K-1)
ln (k)
ln ln
E
RTk Ae
Ek A
R
! "#$ %& '=
= #
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Indian Institute of
Rate contours endothermic reaction
0
10
20
30
40
50
60
70
80
90
100
700 750 800 850 900 950 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Temperature
Ex
tent
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Indian Institute of
Rate contours exothermic reaction
0
50
100
150
200
250
300
350
400
450
500
450 500 550 600 650 700
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Temperature K
Extent
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Summary
!Rate of reaction!Power law kinetics!Law of mass action kinetics!Exothermic and endothermic reactions
Indian Institute of