10-21
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)
10-22
10-23
P10-10 (c)
10-24
P10-10 (d)
10-25
10-26
10-27
10-28
P10-11 (a)
10-29
P10-11 (b)
P10-11 (c)
The estimates of the rate law parameters were given to simplify the search techniques to
10-30
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
=
10-31
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
=
10-32
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
10-33
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
10-34
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
10-35
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)
10-36
P10-17 (b)
10-37
P10-17 (c)
10-38
P10-17 (d)
P10-17 (e)
10-39
P10-18 (a)
10-40
P10-18 (b)