ChE 320 CHEMICAL REACTION ENGINEERING
Final Examination Second Semester (1433/1434)
Answer All Questions
Time Allowed 3 Hours
QUESTION 1
The elementary gas phase reaction is given:
2𝐴 → 𝐵
Calculate the space time required for a CSTR and a PFR to achieve 90%
conversion using pure feed of A.
Additional Information
T0 = 500 K, P0 = 8.2 atm, CA0 = 0.2 mol/dm3, k = 0.5 mol/dm3/s,
𝜐0=2.5 fm3/s.
𝑑𝑚3 ∙ 𝑎𝑡𝑚
𝑅 = 0.082
𝑚𝑜𝑙 ∙ 𝐾
𝑥
(1 + 𝜀𝑥)2
(1 + 𝜀)2 𝑥
2
∫
𝑑𝑥 = 2𝜀(1 + 𝜀) ln(1 − 𝑥) + 𝜀 𝑥 +
2
1−𝑥
0 (1 − 𝑥)
QUESTION 2
The following reaction follows an elementary rate law
𝑁2 + 𝑂2 ⇌ 2𝑁𝑂
Initially 77% N2, 15% O2, 8% inerts are fed to a constant volume batch
reactor where 80% of the equilibrium conversion is reached in 151 µs.
What is the specific reaction rate constant kforward?
Additional Information
Xe = 0.02, V = 0.4 dm3, KC = 0.01, P0 = 20 atm, T0 = 2700 K
Simpson's one-third rule
ℎ
∫ 𝑓(𝑥)𝑑𝑥 = [𝑓(𝑥0 ) + 4𝑓(𝑥1 ) + 𝑓(𝑥2 )]
3
𝑥0
𝑥2 − 𝑥0
ℎ=
2
𝑥2
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QUESTION 3
Compound A undergoes a reversible isomerization reaction, 𝐴 ⇌ 𝐵, over
a supported metal catalyst. Under pertinent conditions, A and B are liquid,
miscible, and of nearly identical density; the equilibrium constant for the
reaction (in concentration units) is 8.5. In a fixed-bed isothermal flow
reactor in which backmixing is negligible (i.e., plug flow), a feed of pure A
undergoes a net conversion to B of 55%. The reaction is elementary. If a
second, identical flow reactor at the same temperature is placed
downstream from the first, what overall conversion of A would you expect
if:
(a) The reactors are directly connected in series?
(b) The products from the first reactor are separated by appropriate
processing and only the unconverted A is fed to the second reactor?
Additional Information
x
∫
0
dx
1
= − ln(1 − εx)
1 − εx
ε
QUESTION 4
The following reversible, elementary, liquid phase reaction occurs in
PFR:
𝐴⇌𝐵
The entering flow rate is 10 dm3/s with an entering concentration of 2
M of A and the feed temperature is 310 K.
a) What is the reactor volume to achieve 90% of the adiabatic
equilibrium conversion?
b) Now consider a series of reactors with interstage cooling so that
the temperature is cooled to 300 K in each interstage cooler. How
many reactors are necessary to achieve 95% total conversion?
Additional information:
𝑐𝑎𝑙
°
𝐶𝑃𝐴 = 𝐶𝑃𝐵 = 50
, ∆𝐻𝑟𝑥𝑛
= −10,000
𝑚𝑜𝑙∙𝐾
𝑐𝑎𝑙
𝑚𝑜𝑙 𝐴
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1
0.9
Equilibrium Conversion
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
300
320
340
360
380
400
420
440
460
480
500
Temperature (K)
Figure 4.1
6
1/-ra (s.dm3/mol)
5
4
3
2
1
0
0
0.1
0.2
X
0.3
0.4
0.5
Figure 4.2
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QUESTION 5
The irreversible liquid phase acid catalyzed isomerization reaction
𝐴→
𝐻2 𝑆𝑂4
𝐶
is carried out isothermally in a semibatch reactor.
H2SO4
A
A 2 molar solution of H2SO4 is fed at a constant rate of 5 dm3/min to a
reactor that initially contains no sulfuric acid. The initial volume of pure A
solution in the reactor is 100 dm3. The concentration of pure A is 10
mol/dm3. The reaction is first order in A and first order in catalyst
concentration and the specific reaction rate is 0.05 dm3/mol min. The
catalyst, of course, is not consumed during the reaction. Obtain an
analytical solution for the number of moles of A, NA and the concentration
of A, CA, as a function of time. What is the concentration of A and of H2SO4
after 30 minutes?
Additional information:
𝑧
𝑧
1
𝑎
∫(
]
) 𝑑𝑧 = ( 2 ) [𝑏𝑧 + 𝑎 ln
𝑎 + 𝑏𝑧
𝑏
𝑎 + 𝑏𝑧
0
S = H2SO4
FS = CS0*v0
CA0 = 10 mol/dm3
V0 = 100 dm3
dNA/dt=rA*V
dNS/dt=FS
V=V0+vot
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