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Lecture 11 Thursday 2/7/08. Determining the Rate Law from Experimental Data Integral Method Graphical Method Nonlinear Least Regression Multiple Reactions The Four Types What’s New to Our Algorithm Reactions in Series. Levenspiel Plot. - PowerPoint PPT Presentation
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Lecture 11 Thursday 2/7/08Determining the Rate Law from Experimental Data
Integral Method
Graphical Method
Nonlinear Least Regression
Multiple Reactions
The Four Types
What’s New to Our Algorithm
Reactions in Series
Levenspiel Plot
FA 0 rA
X
Two steps to get
Step 1: Rate Law
Step 2: Stoichiometry
Step 3: Combine to get
rA f X
rA g Ci
Ci h X
rA f X
Finding Rate Laws, Multiple Reactions
AA
AA
AAi
Ckdt
dC
kCdt
dC
ktCC
lnlnln
1 1
110
Slope = α
CA
dCA/dt
ln
ln
Ap
p
A
C
dtdC
k
t(min) 0 1 2 3
CA(mol/L) 1 0.7 0.5 0.35
0.3 0.2 0.15t
CA
Find the f(t) of using equal area differentiationt
CA
t
CA
.1
.2
.3
t1 2 3
Areas equal for both sides of the histogram
CA 1 0.7 0.5 0.35
-dCA/dt 0.35 0.25 0.175 0.12
Plot –dCA/dt as a function of CA
α = slope Ap
p
A
C
dtdC
k
ln
CA
Slope = αdCA/dt
Regression Method
Cmeas 1 0.7 0.5 0.35
CCalc 1 0.5 0.33 0.25
(Cc-Cm) 0 -0.2 -0.17 -0.10
(Cc-Cm)2 0 0.04 0.029 0.01
Guess values for α and k and solve for measured data points then sum squared differences
for α = 2, k = 1 → S2 = 0.079
for α = 2, k = 2 → S2 = 0.27
etc. until S2 is a minimum
4 Types of Multiple Reactions
• Series: A → B → C
• Parallel: A → D, A → U
• Independent: A → B, C → D
• Complex: A + B →C + D, A + C → E
With multiple reactors, either molar flow or number of moles must be used (no conversion!)
Flow Batch
Rates: rate law for each reaction
net rates:
the sum of rates for each reaction given
BB
AA
rdV
dF
rdV
dF
Vrdt
dN
Vrdt
dN
BB
AA
AAi
iAA rrrr 211
example: 1) A + B → C + D -r1A= k1ACACB -r2A= k1ACACC
2) A + B → E etc….
relative rates:
only applied to a given reaction
Stoich:
example: A → B → C (1) A → B k1
(2) B → C k2
1) mole balance: 2) rates:
i
iD
i
iC
i
iB
i
iA
d
r
c
r
b
r
a
r
T
T
P
P
F
FCC
A
ATA
0
000
AC
AB
AA
CC
BB
AA
rdt
dC
rdt
dC
rdt
dC
Vrdt
dN
Vrdt
dN
Vrdt
dN
V=V0 (constant batch) BBB
AA
BBB
AAA
rrr
rr
Ckr
Ckr
21
1
11
11
laws
net rates
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