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
Dec 21, 2015
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