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The liquid phase reaction
A + B C
follows an elementary rate law and is carried out isothermally in a flow system. The concentrations of A & B feed streams are 2 M before mixing. The volumetric flow rate of each stream is 5 dm3/min, and the entering temperature is 300 K. The streams are mixed immediately before entering. Two reactors are available. One is gray 200 dm3 CSTR that can be heated to 77°C or cooled to 0°C, and the other is a white 800 dm3 PFR operated at 300 K that cannot be heated or cooled but can be painted red or black. Note k = 0.07 dm3/mol.min at 300 K and E = 20 kcal/mol.
(a) Select type of reactor that could be used by showing appropriate calculations.
(b) Calculate time taken to achieve 90% conversion in a 200 dm3 batch reactor with CA0 = CB0 = 1 M after mixing at a temperature of 77°C.
(c) Repeat part (b) if the reactor were cooled to 0°C
(d) Calculate the conversion if the CSTR and PFR were operated at 300 K and connected in series. The entering volumetric flow rate is 10 dm3/h.
(e) Repeat part (d) if CSTR and PFR are connected in parallel with an entering flow rate of 5 mol/min to each of the reactor.
QUESTIONS
A
A
r
XFV
0
(a)Select type of reactor that could be used by showing appropriate calculations.
1. Design equation:
2. Rate Law:
3. Stoichiometry:
4. Combine:
CSTR
BAA CkCr
XCC AOA 1 XCC AOB 1
220
0
1 XkC
XFV
A
A
min/10min5min5/1 333000 moldmdmdmmolvCF AA
3200dmVCSTR 30 1 dmmolCA
?350 KTk
Using Arrhenius eq, find k at T=350K
Solving for X,
350
1
300
1
987.1
20000exp07.0)350( Kk
min45.8)350( 3 moldmKk
(a)Select type of reactor that could be used by showing appropriate calculations.
CSTR
220
0
1 XkC
XFV
A
A
2233
2
11min45.8
min10200
Xdmmolmoldm
Xmoldm
925.0X
X
AA r
dXFV
0
0
(a)Select type of reactor that could be used by showing appropriate calculations.
1. Design equation:
2. Rate Law:
3. Stoichiometry:
4. Combine:
5. Solving for X: X= 0.85
PFR
BAA CkCr
XCC AOA 1 XCC AOB 1
X
A
A
X
dX
kC
FV
022
0
0
1min/100 molFA
3800dmVPFR 3
0 1 dmmolCA
min07.0 3 moldmk
XX
F
VkC
A
A
10
20
200dm3 CSTR gives higher conversion than 800dm3 PFR
Thus, CSTR is chosen.
(a)Select type of reactor that could be used by showing appropriate calculations.
(b) Calculate time taken to achieve 90% conversion in a 200 dm3 batch reactor with CA0 = CB0 = 1 M after mixing at a temperature of 77°C.
1. Design equation:
2. Rate Law:
3. Stoichiometry:
4. Combine:
5. Solving for t:
Batch
Vrdt
dXN A
RA 0
BAA CkCr
XCC AOA 1 XCC AOB 1
VXkCdt
dXN AO
RA
220 1 22
0 1 XkCdt
dXC AO
RA
21 XkCdt
dXAO
R
Rt
RAO
X
dtkCX
dX
0021
(b) Calculate time taken to achieve 90% conversion in a 200 dm3 batch reactor with CA0 = CB0 = 1 M after mixing at a temperature of 77°C.
5. Solving for t:
21 XkCdt
dXAO
R
Rt
RAO
X
dtkCX
dX
0021
AOR kCX
Xt
1
33 1min45.89.01
9.0
dmmolmoldm
min065.1
Using the same equation in part (b), except the value of k is used at T= 273K.
From Arrhenius eq,
Thus,
(c) Repeat part (b) if the reactor were cooled to 0°C
dayskCX
Xt
AOR 5.2min3543
1
273
1
350
1
987.1
20000exp45.8)273( Kk
min1054.2 33 moldm
AOR kCX
Xt
1
(d) Calculate the conversion if the CSTR and PFR were operated at 300 K and connected in series. The entering volumetric flow rate is 10 dm3/h.
v0=10 dm3/h.
220
0
1 XkC
XFV
A
ACSTR
00
220
0
220 11
vC
XkCV
F
XkCVX
A
ACSTR
A
ACSTR
min10
11min07.02003
2333
dm
XdmmolmoldmdmX
44.0X
?X
(d) Calculate the conversion if the CSTR and PFR were operated at 300 K and connected in series. The entering volumetric flow rate is 10 dm3/h.
v0=10 dm3/h.
44.0X?X
X
A
A
X
dX
kC
FV
44.022
0
0
1
44.01
1
1
120
0
XkC
FV
A
A
7857.1
1
1800
20
003
XkC
vCdm
A
A
7857.1
1
1
1min07.0
min10800
33
33
Xdmmolmoldm
dmdm
865.0X
(e) Repeat part (d) if CSTR and PFR are connected in parallel with an entering flow rate of 5 dm3/h to each of the reactor.
5 dm3/h.
5 dm3/h.
10 dm3/h.
00
220
0
220 11
vC
XkCV
F
XkCVX
A
ACSTR
A
ACSTR
min5
11min07.02003
2333
dm
XdmmolmoldmdmX
56.0X
?X
(e) Repeat part (d) if CSTR and PFR are connected in parallel with an entering flow rate of 5 dm3/h to each of the reactor.
5 dm3/h.
5 dm3/h.
10 dm3/h. 56.0X
?X
X
A
A
X
dX
kC
FV
022
0
0
1
XX
F
VkC
A
A
10
20
XX
dm
dmmolmoldmdm
1min5
1min07.08003
333
91.0X
