Chemical Engineering Chapter 10 Explicit Equations Entered The User Pao Ypaoxex Fao Kpakpa Rate Alpha The

subject Type Homework Help
subject Pages 14
subject Words 123
subject Authors H. Scott Fogler

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Explicit equations as entered by the user
[1] e = 1
[2] Pao = 10
[3] Pa = y*Pao*(1-X)/(1+e*X)
P10-10 (a)
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P10-10 (c)
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P10-10 (d)
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P10-11 (a)
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P10-11 (b)
P10-11 (c)
The estimates of the rate law parameters were given to simplify the search techniques to
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P10-12 (a)
P10-12 (b)
P10-13
Assume the rate law is of the form
2
2
1
VTIPO
Dep
VTIPO
kP
rKP
=+
At high temperatures
K as T! "
and therefore
2
Dep
VTIPO
rk
P=
Run 1
( )2
0.028 11.2
0.05
=
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Run 2
( )2
0.45 11.28
0.2
=
Run 5
( )2
7.2 11.25
0.8
=
At low temperature and low pressure
Run 2
( )2
0.015 0.375
0.2
=
These fit the low pressure data
At high pressure
2
2
VTIPO
Dep
VTIPO
kP k
rKP K
= =
This fits the high pressure data
At PVTIPO = 1.5, r = 0.095 and at PVTIPO = 2, r = 0.1
Now find the activation energy
At low pressure and high temperature k = 11.2
At low pressure and low temperature k = 0.4
2 2 1
1 1 2 1 2
1 1
ln k T T
E E
k R T T R T T
! " ! " ! "
#
=#=
$ % $ % $ %
& ' & ' & '
( )( )
11.2 473 393
ln
0.4 473 393
E
R
! "
#
! " =$ %
$ % $ %
& ' & '
7738
E
R=
15375 cal
E
mol
=
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P10-14
P10-15 (a)
Using Polymath non-linear regression few can find the parameters for all models:
POLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM^a*PH2^b
Variable Ini guess Value 95% confidence
k 1 1.1481487 0.1078106
a 0.1 0.1843053 0.0873668
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Precision
R^2 = 0.7852809
R^2adj = 0.7375655
Rmsd = 0.0372861
(2)
POLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM/(1+KM*PM)
Variable Ini guess Value 95% confidence
k 1 12.256274 2.1574162
KM 2 9.0251862 1.8060287
Precision
R^2 = 0.9800096
R^2adj = 0.9780106
Rmsd = 0.0113769
k = 12.26 KM = 9.025
(3)
OLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM*PH2/((1+KM*PM)^2)
Variable Ini guess Value 95% confidence
k 1 8.4090333 18.516752
Precision
R^2 = -4.3638352
R^2adj = -4.9002187
Rmsd = 0.1863588
(4)
POLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM*PH2/(1+KM*PM+KH2*PH2)
Variable Ini guess Value 95% confidence
k 1 101.99929 4.614109
KM 2 83.608282 7.1561591
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Nonlinear regression settings
Max # iterations = 300
Precision
R^2 = -3.2021716
R^2adj = -4.1359875
k = 102 KM = 83.6 KH2 = 67.21
P10-15 (b)
We can see from the precision results from the Polymath regressions that rate law (2) best
P10-16
Using Polymath non-linear regression few can find the parameters for all models:
(1)
POLYMATH Results
Nonlinear regression (L-M)
Model: r = k*KNO*PNO*PH2/(1+KNO*PNO+KH2*PH2)
Variable Ini guess Value 95% confidence
k 1 0.0030965 3.702E-05
KNO 1 57.237884 1.0353031
Precision
R^2 = 0.9709596
R^2adj = 0.9645062
Rmsd = 5.265E-07
k = 0.0031 KNO = 57.23 KH2 = 102
(2)
POLYMATH Results
Nonlinear regression (L-M)
Variable Ini guess Value 95% confidence
k 0.1 -4.713E-06 1.297E-05
KNO 10 -108.42354 4.9334604
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Nonlinear regression settings
Max # iterations = 300
Precision
R^2 = -9.6842898
R^2adj = -12.058576
(3)
POLYMATH Results
Nonlinear regression (L-M)
Model: r = k*KNO*PNO*KH2*PH2/((1+KNO*PNO+KH2*PH2)^2)
Variable Ini guess Value 95% confidence
k 0.1 5.194E-04 2.242E-04
KNO 10 13.187119 7.659298
Nonlinear regression settings
Max # iterations = 300
Precision
R^2 = 0.9809761
The third rate law best describes the data.
P10-17 (a)
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P10-17 (b)
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P10-17 (c)
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P10-17 (d)
P10-17 (e)
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P10-18 (a)
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P10-18 (b)

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