Kinetics-Complex-Reactions.presentation g

kinetics complex

1. Chemistry 232
Kinetics of Complex
Reactions

2. Chain Reactions
Classifying steps in a chain reaction.
Initiation
C
2H
6 (g) 2 CH
3•
Propagation Steps
C
2H
6 + •CH
3  •C
2H
5 + CH
4
Branching Steps
H
2
O + •O•  2 •OH

3. Chain Reactions (Cont’d)
Retardation Step
HBr + H•  H
2 + Br•
Terminations Steps
2 CH
3
CH
2
•  CH
3
CH
2
CH
2
CH
3
Inhibition Steps
R• + CH
3
•  RCH
3

4. The H
2 + Br
2 Reaction
The overall rate for the reaction was
established in 1906 by Bodenstein and Lind

HBrkBr
BrHk
dt
HBrd
/
2
2
3
22



5. The Mechanism
The mechanism was proposed independently by
Christiansen and Herzfeld and by Michael Polyani.
Mechanism
Rate Laws
BrBr2
2
 HHBrHBr
2
 BrHBrBrH
2
 BrHHBrH
2
2BrBrBr 

211
Brkv

222 HBrkv 

 HBrkv
222
HBrHkv 
33

2
44 Brkv

6. Using the SSA
Using the SSA on the rates of
formation of Br• and H•


 HBr
k
k
Br
BrH
k
k
k
dt
HBrd
/
2
3
2
2
3
22
4
1
2
2









7. Hydrogenation of Ethane
The Rice-Herzfeld Mechanism
Mechanism

362 2CHHC
423362
CHCHCHCHHC 
 HCHCHCHCH
2223
22333 HCHCHHCHCH 
6223 HCHCHCH 

8. Rate Laws for the Rice-Herzfeld
Mechanism
The rate laws for the elementary
reactions are as follows.

6211 HCkv
 
36222
CHHCkv
 
 2322 CHCHkv
 
3322
// CHCHHkv 
 
2333 CHCHHkv

9. Explosions
Thermal explosions
Rapid increase in the reactions rate with
temperature.
Chain branching explosions
 chain branching steps in the mechanism
lead to a rapid (exponential) increase in
the number of chain carriers in the
system.

10. Photochemical Reactions
Many reactions are initiated by the
absorption of light.
Stark-Einstein Law – one photon is
absorbed by each molecule responsible for
the primary photochemical process.
Iv
I
I = Intensity of the absorbed radiation

11. Primary Quantum Yield
Define the primary quantum yield, 
absorbed photons of #
productsprimary of #

Define the overall quantum yield, 
absorbed photons of #
react that molecules reactant of #


12. Photosensitization
Transfer of excitation energy from one
molecule (the photosensitizer) to
another nonabsorbing species during a
collision..





HHgHHHg
HHgHHg
HgHg
nm
2
2
254
2

13. Polymerization Kinetics
Chain polymerization
Activated monomer attacks another
monomer, chemically bonds to the
monomer, and then the whole unit
proceeds to attack another monomer.
Stepwise polymerization
A reaction in which a small molecule
(e.g., H
2O) is eliminated in each step.

14. Chain Polymerization
The overall polymerization rate is first order
in monomer and ½ order in initiator.

The kinetic chain length, 
kcl
Measure of the efficiency of the chain
propagation reaction.
produced centres active of #
consumed units monomer of #

i
p
kcl
v
v


15. Mechanism
Initiation
I  2 R•
Or
M + R•  M
1 •
Propagation
M + M
1
•  M
2
•
M + M
2•  M
3 •
M + M
3
•  M
4
•
Etc.
Ikv
ii
Rate Laws
 
1npp MMkv

16. Mechanism (Cont’d)
Termination
M + M
3•  M
4 •

2
Mkv
tt
Note – Not all the initiator molecules produce chains
Define  = fraction of initiator molecules that produce chains

Ik
dt
Md
i
2



17. Return to Kinetic Chain Length
We can express the kinetic chain
length in terms of k
t
and k
p




2
1
2
1
2
2
2
ti
p
t
p
kcl
kk
IMk
Mk
MMk







18. Stepwise Polymerization
A classic example of a stepwise
polymerization – nylon production.
NH
2
-(CH
2
)
6
-NH
2
+ HOOC-(CH
2
)
4
COOH 
NH
2
-(CH
2
)
6
-NHOC-(CH
2
)
4
COOH + H
2
O
After many steps
H-(NH-(CH
2)
6-NHOC-(CH
2)
4CO)
n-OH

19. The Reaction Rate Law
Consider the condensation of a
generic hydroxyacid
OH-M-COOH
Expect the following rate law
 COOHOHkv
polypoly


20. The Reaction Rate Law (Cont’d)
Let [A] = [-COOH]
A can be taken as any generic end
group for the polymer undergoing
condensation.
Note 1 –OH for each –COOH


2
Ak
AOHkv
poly
polypoly



21. The Reaction Rate Law (Cont’d)
If the rate constant is independent of
the molar mass of the polymer
 
 
 


opoly
o
opoly
o
t
Atk
A
COOHtk
COOH
COOH





1
1

22. The Fraction of Polymerization
Denote p = the fraction of end groups
that have polymerized


o
to
A
AA
p




opoly
opoly
Atk
Atk
p


1

23. Statistics of Polymerization
Define P
n = total probability that a
polymer is composed of n-monomers
ppP
n
n


1
1

24. The Degree of Polymerization
Define <n> as the average number of
monomers in the chain


t
o
A
A
p
n 










1
1

25. Degree of Polymerization (cont’d)
The average polymer length in a
stepwise polymerization increases as
time increases.



opoly
opoly
opoly
Atk
Atk
Atk
p
n













1
1
1
1
1

26. Molar Masses of Polymers
The average molar mass of the
polymer also increases with time.
Two types of molar mass distributions.
<M>
n = the number averaged molar mass
of the polymer.
<M>
w
= the mass averaged molar mass
of the polymer.

27. Definitions of <M>
n
Two definitions!
 


J
JJ
o
n
Mn
n
MpM
1
11
M
o = molar mass of monomer
n = number of polymers of mass M
n
M
J
= molar mass of polymer of length n
J

28. Definitions of <M>
w
<M>
w is defined as follows
 





J
JJ
JJ
j
x
no
w
Mn
Mn
pxMpM
n
122
1
Note - x
n
the number of monomer
units in a polymer molecule

29. The Dispersity of a Polymer Mixture
Polymers consists of many molecules
of varying sizes.
Define the dispersity index () of the
mass distribution.
n
w
M
M

Note – monodisperse sample
ideally has <M>
w
=<M>
n

30. The Dispersity Index in a Stepwise
Polymerization
The dispersity index varies as follows
in a condensation polymerization
n
w
M
M
1
Note – as the polymerization
proceeds, the ratio of <M>
w/<M>
n
approaches 2!!!

31. Mass Distributions in Polymer
Samples
For a random polymer sample
0911131517192123 252729313335373941
Monodisperse Sample
Polydisperse Sample
Molar mass / (10000 g/mole)
P
n

32. Types of Catalyst
We will briefly discuss three types of
catalysts. The type of catalyst
depends on the phase of the catalyst
and the reacting species.
Homogeneous
Heterogeneous
Enzyme

33. Homogeneous Catalysis
The catalyst and the reactants are in the
same phase
e.g. Oxidation of SO
2
(g)

to SO
3
(g)
2 SO
2
(g) + O
2
(g)  2 SO
3
(g)SLOW
Presence of NO (g), the following occurs.
NO (g) + O
2
(g)  NO
2
(g)
NO
2 (g) + SO
2 (g)  SO
3 (g) + NO (g)FAST

34. 
SO
3 (g) is a potent acid rain gas
H
2O (l) + SO
3 (g)  H
2SO
4 (aq)

Note the rate of NO
2
(g) oxidizing
SO
2(g) to SO
3(g) is faster than the
direct oxidation.

NO
x(g) are produced from burning
fossil fuels such as gasoline, coal, oil!!

35. Heterogeneous Catalysis
The catalyst and the reactants are in
different phases
adsorption the binding of molecules on a
surface.
Adsorption on the surface occurs on active
sites
Places where reacting molecules are
adsorbed and physically bond to the metal
surface.

36. 
The hydrogenation of ethene (C
2H
4 (g))
to ethane
C
2
H
4
(g) + H
2
(g)  C
2
H
6
(g)
Reaction is energetically favourable


rxnH = -136.98 kJ/mole of ethane.
With a finely divided metal such as Ni
(s), Pt (s), or Pd(s), the reaction goes
very quickly .

37. There are four main steps in the process
the molecules approach the surface;
H
2 (g) and C
2H
4 (g) adsorb on the surface;
H
2
dissociates to form H(g) on the surface; the
adsorbed H atoms migrate to the adsorbed C
2H
4
and react to form the product (C
2H
6) on the
surface
the product desorbs from the surface and
diffuses back to the gas phase

39. Simplified Model for Enzyme Catalysis
E  enzyme; S  substrate; P 
product
E + S  ES
ES P + E
rate = k [ES]
The reaction rate depends directly on
the concentration of the substrate.

40. Enzyme Catalysis
Enzymes - proteins (M > 10000 g/mol)
High degree of specificity (i.e., they will
react with one substance and one
substance primarily
Living cell > 3000 different enzymes

42. The Lock and Key Hypothesis
Enzymes are large, usually floppy
molecules. Being proteins, they are
folded into fixed configuration.
According to Fischer, active site is
rigid, the substrate’s molecular
structure exactly fits the “lock” (hence,
the “key”).

43. The Lock and Key (II)