Chemical RXN Eng I - (1) Exercises (B&W)
Chemical RXN Eng I - (1) Exercises (B&W)
Chemical RXN Eng I - (1) Exercises (B&W)
WS 2016/17
Chemical Reaction
Engineering I
Collection of Exercises
Content
Content
Content
offers to foot the bill, if the assumption of the group will be right.
that the cable car passenger will win the competition. The landlord is astonished and
taurant. They have a look at the data and claim after some tricks with the Excel file,
Accidentally a group of process engineering students from Graz is sitting in the res-
rupts the connection to all of the three transmitters after 3 minutes. By then the land-
Start and data transfer work out perfectly until out of the sudden a disturbance inter-
cross driver takes the forest road. Winner is the competitor, who first crosses the alti-
has entered the cable car. The mountain biker takes the ski lift trail and the moto-
biker and the motocross driver are allowed to start, when the cable car passenger
tervals of 10 seconds with the computer of the landlord. It is agreed that the mountain
referee of the competition. They decide to record the altitude via GPS in regular in-
of decent is also mentioned, which leads to a bet. The landlord is willing to be the
are discussing the state of the economy. During the lively discussion the fastest way
passenger, are sitting in a restaurant on top of a popular mountain at 1445 [m]. They
Three sportsman, a mountain biker, a motocross driver and a passionate cable car
1435
1425
1415
1405
1395
1385
1375
1365
1355
1345
1335
1325
1315
1305
1295
1285
1275
1265
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
1185
1200
1210
1225
1240
1250
1265
1280
1295
1310
1325
1340
1350
1370
1380
1400
1415
1430
1445
driver [m]
passenger [m]
1445
H motocross
H cable car
t [s]
915
930
945
965
980
1000
1020
1045
1070
1090
1120
1150
1180
1215
1250
1290
1340
1390
1445
biker [m]
H mountain
]) at
When does the passionate hiker arrive at the starting point of his adventure?
altitude.
along the forest road towards the starting point of his trip, the Trout Farm at 1200 [m]
Meanwhile the clock says half past one pm and the hiker is carrying his tired body
farmer with his tractor, who gives the poor hiker a ride to his farm at 1500 [m] altitude.
takes him down the ski arena at 1700 [m] within 10 minutes. By chance he meets a
recognizes hiking as very tiring and prefers the convenience of a cable car, which
About one and a half hours later he continues his journey down the mountain. He
Hut is famous for its own brewed beer. One can easily take up to 3 beers at one go.
tion, he says to himself, a short break has never done anybody any harm. The Zirben
[m]. Since he is not able to pass the Zirben Hut on his way down from the valley sta-
ski lift, which takes him within 20 minutes quickly down to the valley station at 2000
time goes by much quicker in the mountains than in the valley. He decides to take the
self a so called Jagertee Grande. After one hour and 3 Jagertees he recognizes, that
lift at 2504 [m] above sea level. In the Edelweiss Hut next to it the hiker allows him-
quently exceeded in this area. After 30 minutes he already reaches the top of the ski
which are open all the year round. Apparently the explosive limit of ethanol is fre-
mountain huts,
Refreshed after a mouthful of his hipflask he starts the descent over the eastern
Can he reach the summit before sunrise? When does he arrive on top?
he wants to reach the summit at 2741 [m] altitude before sunrise at 7:15 am. At 5:12
He starts well rested at 4:45 am at the western slope 1500 [m] above sea level, since
A passionate hiker decides very early in the morning to climb his favourite mountain.
0.086
0.138
0.166
0.189
0.216
0.250
0.267
0.275
600
1200
1800
2400
3600
7200
10800
14400
cIsobutylacetat [mol/l]
t [s]
reaction. The data analysis has to be carried out by the integral method.
table below. Determine the reaction order n and the reaction rate constant for this
was determined in a fixed setting of time intervals. The results are presented in the
Determine n and k.
Measurement data:
55.6
50.4
45.9
42.0
38.4
35.1
10
20
30
40
50
60
31.9
61.9
70
MnO4- [ml]
t [min]
equation is:
This reaction is carried out in a beaker at T = 25 [C], in which the progress of de-
of 100 [C]. The initial concentration of acetic anhydride and isobutanol is both
c0 = 0.304 [mol/l]. The concentration of isobutyl acetate in the contents of the reactor
1.000
0.935
0.846
0.688
0.468
12
20
20
12
0.175
0.435
0.650
0.84
1.000
c/c0
0.207
0.484
0.767
1.000
c/c0
12
t [min]
0.168
0.410
0.714
0.966
c/c0
50
0.267
10800
0.275
0.250
7200
14400
0.216
0.189
0.166
0.138
0.086
cIsobutylacetat [mol/l]
3600
2400
1800
1200
600
t [s]
d = -log k
k = 10-2.6407 = 0.0023 [l/(mol s)]
a=n=2
k[
12
t [min]
T = 50 [C]
38
0.099
0.358
0.624
0.874
1.000
c/c0
T = 38 [C]
y=ax+d
15
10
t [min]
T = 25 [C]
below. Determine the reaction order n and the reaction rate constant for this reaction.
determined in a fixed setting of time intervals. The results are presented in the table
0.304 [mol/l]. The concentration of isobutyl acetate in the contents of the reactor was
of 100 [C]. The initial concentration of acetic anhydride and isobutanol is both c0 =
25
20
10
T [C]
t [min]
T = 20 [C]
c/c0
t [min]
T = 10 [C]
the experiment Fe3+ was added to the solution in a molar ratio of Fe3+:EDTA of 1:2.
800 [ml] EDTA of c0 = 1 [mmol/l] has been treated with a ND-radiation emitter. Before
The investigation of the reaction in exercise Kin-1 (determination of n and k), has to
1.000
0.860
0.602
0.355
0.083
0.000
0.000
0.0
3.0
11.4
19.5
32.5
48.8
97.5
c [mmol/l]
t [min]
the following reduction in EDTA concentration can be observed. One after another
Data:
0.41
0.26
0.13
0.06
0.02
0.01
30
36
45
55
70
100
0.63
20
0.58
0.74
16
25
0.84
0.90
0.95
1.00
c [mmol/l]
12
time
acetate substitute is splits of from the EDTA molecules by the radiation treatment.
For the photolysis of EDTA by treating a 1 [mmol/l] EDTA solution with ND-radiation
Kin-6: Autocatalysis
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.2
2.0
2.8
3.8
5.0
6.6
8.8
12.7
The reaction order n, the pre-exponential (or frequency) factor A and the activation
11
0.9
0.6
25.0
716
11.6
700
XA
5.12
683
11
The reaction rate constant k is 0.182 [1/s] and the density is constant during the reac-
cA [mol/l]
2.20
666
+ I2,g
2,g
T [K]
2 HIg
t [s]
Chemical reaction:
10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
XA
V/FA,0 [l s/mol]
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
cA [mol/l]
XA
V/FA,0 [l s/mol]
PFR (continuous tubular reactor) of the same reactor volume as in exercise React-1?
cA [mol/l]
What is the permissible flow of component A (FA,0) to reach the same conversion in a
What is the permissible flow of component A (FA,0) to reach the same conversion in a
React-1?
The reaction rate constant k is 0,182 [1/s] and the density is constant during the reac-
13
The reaction rate constant k is 0.182 [1/s] and the density is constant during the reac-
12
14
20
40
60
V/FA,0-RR
10
12
14
Comparison of V/FA,0 for continuous tubular reactor (PFR) and continuous stirred-
V/FA,0-kRK
15
bB
aA
cC
CH3COOC4H9 +
dD
H2O
74 [g/mol]
116 [g/mol]
butanol
butyl acetate
Result:
time needed for manipulation, heating and cooling phase comes to 30 minutes.
Calculate the reactor volume for the production of 100 [kg/h] butyl acetate, when the
XA = 0.5.
60 [g/mol]
acetic acid
Molar mass
The density
tanol. A reaction rate constant of k = 2.9 10-4 [l/(mol s)] was found for the experiment.
sidered as 2nd-order reaction with regard to acetic acid, because of the excess of bu-
The molar ratio between butanol and acetic acid is 4.97:1. The reaction can be con-
C4H9OH
CH3COOH +
Chemical reaction:
ture of 100 [C] and with sulphuric acid (0.032 w%) as a catalyst.
Butanol is esterified to butyl acetate with acetic acid in a batch reactor at a tempera-
= constant
tTot = 1 [h]
XA = 0.35
cC
CH3COOC2H5 +
dD
H2O
c.
b.
a.
cD,0 = 0
cC,0 = 0
cB,0 = 10 [kmol/m3]
cD,0 = 0
cC,0 = 0
cD,0 = 17
cC,0 = 0
cB,0 = 10 [kmol/m3]
How much is the reactor volume Vreactor for different initial concentrations?
k2 cC cD
K = k1/k2 = 2.9
bB
aA
C2H5OH
CH3COOH +
from acetic acid and ethanol. The catalyst is aqueous hydrochloric acid, the tempera-
2 [t] of ethyl acetate (= 22.7 [kmol/h]) shall be produced in a isothermal batch reactor
B.
17
16
bB
aA
cC
CH3COOC4H9 +
dD
H2O
XA = 0.999
Data:
Result: V
with k in [1/s]
with k in [l/(mol h)]
rA = - 3 cA2
rA = -0.05
Rate laws:
116 [g/mol]
Butyl acetate
B.
The volumetric input flow (feed) FV,0 for a conversion of acetic acid of XA = 0.5 at a
74 [g/mol]
Butanol
with k in [1/s]
rA = -3 cA
VR = 1000 [l]
60 [g/mol]
Acetic acid
Molar mass
Calculate:
The density
rA = -0.0001cA
rA = -0.5
tanol. A reaction rate constant of k = 2.9 10-4 [l/(mol s)] was found for the experiment.
Rate laws:
XA = 0.99
Fv,0 = 10 [l/h]
FA,0 = 5 [mol/h]
sidered as 2nd-order reaction with regard to acetic acid, because of the excess of bu-
The molar ratio between butanol and acetic acid is 4.97:1. The reaction can be con-
C4H9OH
CH3COOH +
Chemical reaction:
Data:
perature of 100 [C] and with sulphuric acid (0.032 w%) as a catalyst.
Butanol is esterified to butyl acetate with acetic acid in a plug flow reactor at a tem-
18
B.
19
rA [mol/(m3 s)]
-0.45
-0.37
-0.3
-0.195
-0.113
-0.079
-0.05
XA
0.1
0.2
0.4
0.6
0.7
0.8
(1/-rA)
[m3]
[m3]
VCSTR, X=0.8 =
VPFR, X=0.8 =
Result:
XA = 0.8
P = 8.2 [bar]
T = 500 [K]
pure substance A.
20
(FA,0/-rA)
21
22
R+R
H2C2O4
H2SO4
KMnO4
2 [ml]
1 [ml]
2 [ml]
0.02
50
0.05
[mol/l]
[w%]
[mol/l]
= 546 [nm].
CEET: Permanganate and oxalic acid was mixed in a cuvette, then the absorption of
The following experiment was carried out by Mr. Gruber in the lab of the institute of
A+R
0.0079035
19.2
0.0005387
0.0001837
31.2
34.2
0.0000031
Determine k and compare the reactor volume for CSTR and PFR.
40.2
0.0000561
0.0018093
28.2
37.2
0.0047738
25.2
0.0074021
0.008
16.2
22.2
cA [mol/l]
t [s]
23
24
B is proceeded in the
How much are the volumes VPFR und VCSTR? (data and graphs see page 25)
How much are the volumes VCSTR und VPFR? (data and graphs see page 25)
in the first reactor (CTSR) is XA = 0.4 and in the second reactor (PFR) XA = 0.8.
A reaction A
How much are the volumes VPFR1 und VPFR2? (data and graphs see page 25)
PFR is XA = 0.4 and in the second PFR XA = 0.8. FA,0 = 0.4 [mol/s].
A reaction A
case of 4 CSTRs?
c) How much are the volume of each CSTR and the total volume of all reactors in
b) How much is the volume, if the reaction is carried out in one CSTR?
CSTR is XA = 0.4 and in the second CSTR XA = 0.8. FA,0 = 0.4 [mol/s].
A reaction A
0.0
0.1
0.2
0.4
0.6
0.7
0.8
React-14
React-12
React-15
React-13
XA
25
FA,0/-rA [m ]
st
Determine:
XA
39
53
0.2
59
0.4
38
0.6
25
0.65
887
triglyceride
921
1260
787
880
The reaction is isothermal and carried out at three different temperatures at lab scale.
calculated ideally.
cence. (A second step, in which the triglyceride would be exposed to further trans-
the product (RME) is separated from glycerine and the rest of methanol by coales-
further assumption is made, that in a first step the reaction is carried out until a 95%
A reactor for the production of 20 000 [t/year] biodiesel has to be designed and its
92
32
MeOH
glycerine
297
RME
glyceride. The properties of the reactants are listed in the table below.
This is a complex stepwise reaction with the intermediates diglyceride and mono-
Data:
To produce biodiesel (e.g. rapeseed methyl ester - RME) from plant oils, the catalytic
27
26
1.1116
0.2471
0.1593
0.1068
0.0874
0.0571
180
300
420
600
1200
0.0301
0.0525
0.0735
0.0919
0.1311
1.1167
T = 40 [C]
0.0165
0.0286
0.0398
0.0653
0.0822
1.1168
T = 55 [C]
28
PFRs in series?
d) How does it affect the total volume, if you split up the one PFR in b) into 2
separation is carried out continuously after the reactor. The factory operates in
of products are let out and reactor is filled again. The time of manipulation
of products after the reaction is carried out in the tank reactor. The two phases
T = 25 [C]
t [s]
triglyceride [mol/kg]
[m]
[m]
H-gesamt
[m]
[mol/l]
[m3/ batch]
ctri
glycerine
MeOH
triglyceride
RME
[kg/batch]
1.3
[m /batch]
Hgross CSTR
12.81
0.02985
9.34
[min]
[l/(mols)]
residence time
[C]
40
43 743.3
[J/mol]
EA
1.5
0.95
16
300
596 002
[h]
[days]
k0
manipulation
time of
Xtri
[kmol/batch]
20 000
[t per year]
29
[C]
[l/(mols)]
-rtri
Fn
[mol/l]
ctri
[mol/(ls)]
[m3]
[h]
-rtri
VR
Fn
Fm
[m3/h]
Fv
glycerine
20 000
[t per year]
MeOH
[kmol/batch]
Fm
ctri
Fv
glycerine
MeOH
triglyceride
RME
[h]
[m3]
[mol/(ls)]
[mol/l]
[m3/h]
[kg/ batch]
VR
[m /batch]
CSTR
0.02985
30
triglyceride
RME
43 743.3
[J/mol]
EA
[kg/ batch]
596 002
k0
40
0.95
Xtri
300
24
[days]
b) continuous reactors
[m3/ batch]
PFR
[kmol/ batch]
20 000
[t per year]
31
0.95
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Xtri
0.95
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Xtri
ctri [mol/l]
ctri [mol/l]
c) CSTR
-rtri [mol/(ls)]
d) PFR
-rtri [mol/(ls)]
-rtri [kmol/(m3h)]
-rtri [kmol/(m3h)]
1/(-rtri)
1/(-rtri)
32
4
20
50
1
6
24
n = _____, k = _____
cA [mmol/l]
Fv [l/min]
300
0.65
240
0.92
250
110
0.56
360
0.37
24
0.41
0,48
200
0.28
0,48
560
0.2
0,48
B is in-
b) How long is the residence time, if this reaction is carried out until 75% conver-
a) How long is the residence time, if this reaction is carried out until 75% conver-
[s]
cA,t [mol/l]
cA,0 [mol/l]
Data:
vestigated in a CSTR.
Data:
33
The reaction A
4 B.
cA(XA)
4 PH3,g
P4, g + 6 H2,g
carried out in a PFR at a pressure of 460 [kPa]. The flow shall be 2 [kmol/h]. Deter-
tion:
discuss the influence on the tubular reactor volume of the different reflux ratios R =
R+S
cB,t = 20 [kmol/m3]
cA,t = 20 [kmol/m3]
cA,t = 20 [kmol/m3]
5R
given: A + B
given: A + B
2R
given: A + 2B
given: A + B
cA,t = 20 [kmol/m3]
XA,t = 0.8
determine: cB,t, cA,t, XB,t
given: A + 2B
given: A + B
35
What is the activation energy EA of the reaction with the following experimental data?
34
r I)
e) Determine the reaction rate and plot it in a graph to find the ratio of V/FA.
conversion.
pressure P = 1485 [kPa] and temperature of T = 277 [C]. At this operation condition
The input flow consists of 28 % SO2 and 72 % air. The oxidation is carried out at the
rI
cC
(a A +
bB
SO3 + x N2
SO2 + 0,5 O2 + x N2
cA,t = 40 [kmol/m3]
given:
A+3B=6R
37
Result:
398
388
378
368
358
348
338
328
318
308
298
T [K]
KT
K298 = 426
= - 75 [kJ/mol]
= - 15 [kJ/mol]
gas I:
In a continuous reactor the following reaction of gases A and B is carried out in inert
36
25
25
25
H2(g)
NH3(g)
35.618
28.835
29.132
[J/(mol K)]
[C]
N2(g)
substance
CP
-45.94
38
3. stoichiometry:
2. reaction rate:
1. mole balance:
Solution:
the reactor.
Derive a function of the conversion XA and the temperature T against the length of
Hf
[kJ/mol]
Data:
or
apply:
special case
[kg/m3]
[kJ/kmol A];
[kJ/mol A]
CP [kJ/(molK)];
[kJ/mol A]
CP [kJ/(molK)];
c [kmol/m ];
CP [kJ/(kgK)];
39
40
2C
0.2
288
0.00134
T [K]
k [1/s]
0.00188
293
20
0.00263
298
25
0.00351
303
30
= 1070
= -210 [kJ/mol].
[kg/m ] and the specific heat capacity is CP = 3.8 [kJ/(kg K)]. It is also an exothermal
The reaction is carried out at T = 15 [C] in a batch reactor, with an initial concentra-
15
T [C]
0.8
0.7
0.6
0.5
0.4
0.1
reaction in terms of acetic acid anhydride (= A). The table below shows the tempera-
2 CH3COOH
0.3
(CH3CO)2O + H2O
Data:
T [K]
chemical reaction:
Acetic acid anhydride (acetic anhydride) is hydrolysed with water according to the
k [1/s]
1/(k (1-X))
41
42
EA = 65.7 [kJ/mol]
Reaction:
Input:
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
CSTR:
PFR:
Production scale:
reaction.
high pressure conditions. Compare the reactor volume of a CSTR and a PFR for this
Xe
Xe
(-rA)
(-rA)
FA,0/-rA
FA,0/-rA
43