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10-21
Explicit equations as entered by the user
[1] e = 1
[2] Pao = 10
P10-10 (a)
10-22
P10-10 (b)
10-23
P10-10 (c)
10-24
P10-10 (d)
10-26
P10-11 (a)
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 low temperature and low pressure
2
Dep VTIPO
r kP=
2
Dep
VTIPO
rk
P=
At high pressure
1
2>>
VTIPO
KP
2
2
VTIPO
Dep
VTIPO
kP k
rKP K
= =
10-32
P10-14
P10-15 (a)
Using Polymath non-linear regression few can find the parameters for all models:
See Polymath program P10-15.pol.
(1)
POLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM^a*PH2^b
Variable Ini guess Value 95% confidence
10-33
Precision
(2)
POLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM/(1+KM*PM)
Variable Ini guess Value 95% confidence
(3)
OLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM*PH2/((1+KM*PM)^2)
Variable Ini guess Value 95% confidence
(4)
POLYMATH Results
Nonlinear regression (L-M)
Model: rT = k*PM*PH2/(1+KM*PM+KH2*PH2)
Variable Ini guess Value 95% confidence
10-34
Nonlinear regression settings
Max # iterations = 300
Precision
R^2 = -3.2021716
P10-15 (b)
We can see from the precision results from the Polymath regressions that rate law (2) best
describes the data.
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
k = 0.0031 KNO = 57.23 KH2 = 102
(2)
POLYMATH Results
Nonlinear regression (L-M)
10-35
Nonlinear regression settings
Max # iterations = 300
Precision
R^2 = -9.6842898
(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
k = 0.000519 KNO = 13.19 KH2 = 18.49
The third rate law best describes the data.
P10-17 (a)
10-36
P10-17 (b)
10-37
P10-17 (c)
P10-17 (d)
P10-17 (e)
P10-18 (a)
P10-18 (b)
