P8-25
Mole balance:
C
A B
A B C
dF
dF dF
r r r
dW dW dW
= = =
Rate Laws:
213
A B A A
r r r r
=!+ +
Stoichiometry:
0
0
A
A T
T
B
B T
T
F T
C C
F T
F T
C C
F T
=
=
Energy balance:
See Polymath program P8-25.pol.
Calculated values of DEQ variables
Variable
Initial value
Minimal value
Maximal value
Final value
1
w
0
0
100.
100.
2
fb
1.
0.9261241
1.368476
0.9261241
9
Dhr3a
-1100.
-1100.
-1100.
-1100.
10
cpa
100.
100.
100.
100.
11
cpb
100.
100.
100.
100.
12
cpc
100.
100.
100.
100.
20
ca
1.
0.5682599
1.
0.6892094
21
cb
1.
0.7341242
1.253213
0.7341242
22
r1a
-0.5312401
-0.5748799
-0.362406
-0.5473402
Differential equations
1
d(fb)/d(w) = rb
2
d(fa)/d(w) = ra
Explicit equations
1
Ua = 16
2
Ta = 500
3
Dhr1a = -1800
8-83
11
ft = 2
12
To = 330
13
Kc = 10 * exp(4.8 * (430 / T – 1.5))
P8-25 (a) As seen in the above table, the lowest concentration of o-xylene (A) = .568 mol/dm3
P8-25 (c) The maximum concentration of o-xylene = 1 mol/dm3
P8-25 (d) The same equations are used except that FB0 = 0.
P8-25 (e)
Decreasing the heat of reaction of reaction 1 slightly decreases the amount of E formed.
P8-26 (a)
A B C
!+
8-84
G
E F
E F G
dF
dF dF
r r r
dV dV dV
= = =
Rate Laws:
1 2 3A s B T
r r r r=! ! !
1B s
r r=
Stoichiometry:
0
A
A T
T
F
P P
F
=
Energy Balance:
( )
1 1 2 2 3 3
* 299 * 283 *30 * 201 *90 * 249 * 68 * 40
s R A B R A T R A
A B C D E F G I
r H r H r H
dT
dV F F F F F F F F
! “ +“+“
=+ + + + + + +
8-85
Calculated values of DEQ variables
Variable
Initial value
Minimal value
Maximal value
Final value
1
v
0
0
10.
10.
2
fa
0.00344
0.002496
0.00344
0.002496
3
fb
0
0
0.0008974
0.0008974
4
fc
0
0
0.0008615
0.0008615
13
p
2137.
2137.
2137.
2137.
14
phi
0.4
0.4
0.4
0.4
15
Kl
0.0459123
0.0196554
0.0459123
0.0196554
16
sr
14.5
14.5
14.5
14.5
17
fi
0.04988
0.04988
0.04988
0.04988
18
ft
0.05332
0.05332
0.0542282
0.0542282
19
Pa
0.1548387
0.1104652
0.1548387
0.1104652
20
Pb
0
0
0.0397155
0.0397155
Differential equations
1
d(fa)/d(v) = ra
2
d(fb)/d(v) = rb
8-86
Explicit equations
1
Hla = 118000
2
H2a = 105200
3
H3a = -53900
4
p = 2137
5
phi = .4
11
Pb = fb / ft * 2.4
Fstyrene = 0.0008974
Fbenzene = 1.078E-05
Ftoluene = 3.588E-05
SS/BT = 19.2
P8-26 (b)
T0 = 930K
P8-26 (c)
T0 = 1100 K
P8-26 (d)
Plotting the production of styrene as a function of To gives the following graph. The temperature
that is ideal is 995K
P8-26 (e)
Plotting the production of styrene as a function of the steam gives the following graph and the
ratio that is the ideal is 25:1
P8-26 (f)
When we add a heat exchanger to the reactor, the energy balance becomes:
( ) ( )
1 1 2 2 3 3
a s R A B R A T R A
Ua T T r H r H r H
dT
! ! “ +“+“
8-88
P8-26 (g) Individualized solution
P8-26 (h) Individualized solution
P8-27 (a)
P8-27 (b)
P8-27 (c)
Figure E8-5.3 shows a decrease in temperature while the reaction rate is large because the
reaction is endothermic. Once the reaction rate drops, the heat exchanger increases the
P8-27 (d)
In Figure E8-10.1, the temperature increases quickly until the reactants are used up. Then there is
P8-28 (a)
See Polymath program P8-28-a.pol.
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 10 10
T 675 675 715.55597 704.76882
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(T)/d(V) = (Ua*(Ta-T)+(-ra*(-dHr)))/(Fao*Cpa)
[2] d(X)/d(V) = -ra/Fao
Explicit equations as entered by the user
[1] Fao = 5
P8-28 (b)
P8-28 (c)
Again using the same POLYMATH program, we can vary the ambient temperature until the
reaciton runs away. As the following summary table will show the maximum temperature is 708K.
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 10 10
T 675 675 758.02032 712.2666
P8-28 (d)
POLYMATH Results
Calculated values of the DEQ variables
Variable initial value minimal value maximal value final value
V 0 0 10 10
X 0 0 0.0304837 0.0304837
Fao 5 5 5 5
ODE Report (RKF45)
Differential equations as entered by the user
[1] d(X)/d(V) = -ra/Fao
Explicit equations as entered by the user
[1] Fao = 5
[2] Ua = 5
8-92
P8-28 (e)
P8-28 (f) No solution will be given
8-93
P8-29
8-95