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