Transcript Document 7641420

Chemistry 232
Kinetics of Complex
Reactions
Chain Reactions

Classifying steps in a chain reaction.

Initiation


Propagation Steps


C2H6 (g) 2 CH3•
C2H6 + •CH3  •C2H5 + CH4
Branching Steps

H2O + •O•  2 •OH
Chain Reactions (Cont’d)

Retardation Step


Terminations Steps


HBr + H•  H2 + Br•
2 CH3CH2•  CH3CH2CH2CH3
Inhibition Steps

R• + CH3•  RCH3
The H2 + Br2 Reaction

The overall rate for the reaction was
established in 1906 by Bodenstein and Lind
d HBr 
k H 2 Br2  2

/
Br2   k HBr 
dt
3
The Mechanism

The mechanism was proposed
independently by Christiansen and Herzfeld
and by Michael Polyani.
Mechanism
Rate Laws
Br2  2Br 
v1  k1Br2 
Br  H2  HBr  H  v 2  k2 Br H2 
H  Br2  HBr  Br  v 2  k2 Br2 H 

H  HBr  H2  Br  v 3  k3 H HBr
2
v 4  k 4 Br 
Br  Br   Br2
Using the SSA

Using the SSA on the rates of
formation of Br• and H•
3
k


2k 2  1 H 2 Br2  2
k4 
d HBr 


k
dt
Br2   3 k / HBr 
2
Hydrogenation of Ethane

The Rice-Herzfeld Mechanism
Mechanism
C2H6  2CH3 
C2H6  CH3   CH3CH2  CH4
CH3CH2   CH2CH2  H 
CH3CH3  H   CH3CH2  H2
CH3CH2  H   C2H6
Rate Laws for the Rice-Herzfeld
Mechanism

The rate laws for the elementary
reactions are as follows.
v1  k1C2H6 
v 2  k 2 C2H6 CH3 
v 2  k 2 CH3CH2 
v 2 /  k 2 / H CH3CH3 
v 3  k3 H CH3CH2 
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.
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.
vI  I
I = Intensity of the absorbed radiation
Primary Quantum Yield

Define the primary quantum yield, 
# of primary products

# of photons absorbed
 Define the overall quantum yield, 
# of reactant molecules that react

# of photons absorbed
Photosensitization

Transfer of excitation energy from one
molecule (the photosensitizer) to
another nonabsorbing species during a
collision..
254 nm
Hg  Hg 
Hg  H 2  Hg  2H 
Hg   H 2  HgH  H 
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., H2O) is eliminated in each step.
Chain Polymerization


The overall polymerization rate is first order
in monomer and ½ order in initiator.
The kinetic chain length, kcl

 kcl
Measure of the efficiency of the chain
propagation reaction.
vp
# of monomer units consumed


vi
# of active centres produced
Mechanism

Initiation
I  2 R•
Or
M + R•  M1 •

Rate Laws
v i  ki I 
Propagation
M + M 1•  M 2 •
M + M 2•  M 3 •
M + M3•  M4 •
Etc.
v p  k p M M n 1 
Mechanism (Cont’d)

Termination
M + M3•  M4 •
v t  kt M 
2
Note – Not all the initiator molecules produce chains
Define  = fraction of initiator molecules that produce chains
d M 

 2k i I 
dt
Return to Kinetic Chain Length

We can express the kinetic chain
length in terms of kt and kp
 kcl 

k p M M 
2k t M 
2
k p M I 
1
2
2k i k t 
1
2
Stepwise Polymerization

A classic example of a stepwise
polymerization – nylon production.
NH2-(CH2)6-NH2 + HOOC-(CH2)4COOH 
NH2-(CH2)6-NHOC-(CH2)4COOH + H2O

After many steps
H-(NH-(CH2)6-NHOC-(CH2)4CO)n-OH
The Reaction Rate Law

Consider the condensation of a
generic hydroxyacid
OH-M-COOH

Expect the following rate law
v poly  k poly  OH  COOH 
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
v poly  k poly  OH A
 k poly A
2
The Reaction Rate Law (Cont’d)

If the rate constant is independent of
the molar mass of the polymer

 COOH o
 COOH t 
1  k poly t  COOH o

Ao

1  k poly t Ao
The Fraction of Polymerization

Denote p = the fraction of end groups
that have polymerized

Ao  At
p
Ao
p
k poly t Ao
1  k poly t Ao
Statistics of Polymerization

Define Pn = total probability that a
polymer is composed of n-monomers
Pn  p 
n 1
1  p 
The Degree of Polymerization

Define <n> as the average number of
monomers in the chain
 1  Ao
 
n  
 1  p  At
Degree of Polymerization (cont’d)

The average polymer length in a
stepwise polymerization increases as
time increases.
k poly t Ao
 1 
  1 
n  
1  k poly t Ao
 1 p 
 1  k poly t Ao
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.
Definitions of <M>n

Two definitions!
M
n
 1 1  p M o
1
 J nJ M J
n
Mo = molar mass of monomer
n = number of polymers of mass Mn
MJ = molar mass of polymer of length nJ
Definitions of <M>w

<M>w is defined as follows
M
 1  p  Mo  j x n  p
2
w
2
nJ M J

J nJ MJ
Note - xn the number of monomer
units in a polymer molecule
x n 1
The Dispersity of a Polymer Mixture


Polymers consists of many molecules
of varying sizes.
Define the dispersity index () of the
mass distribution.

M
M
w
n
Note – monodisperse sample
ideally has <M>w=<M>n
The Dispersity Index in a Stepwise
Polymerization

The dispersity index varies as follows
in a condensation polymerization
1  
M
M
w
n
Note – as the polymerization
proceeds, the ratio of <M>w/<M>n
approaches 2!!!
Mass Distributions in Polymer
Samples

For a random polymer sample
Monodisperse Sample
Polydisperse Sample
Pn
09
11
13
15
17
19
21
23
25
27
29
31
33
35
37
Molar mass / (10000 g/mole)
39
41
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
Homogeneous Catalysis


The catalyst and the reactants are in the
same phase
e.g. Oxidation of SO2 (g) to SO3 (g)
2 SO2(g) + O2(g)  2 SO3 (g) SLOW

Presence of NO (g), the following occurs.
NO (g) + O2 (g)  NO2 (g)
NO2 (g) + SO2 (g)  SO3 (g) + NO (g)
FAST



SO3 (g) is a potent acid rain gas
H2O (l) + SO3 (g)  H2SO4 (aq)
Note the rate of NO2(g) oxidizing
SO2(g) to SO3(g) is faster than the
direct oxidation.
NOx(g) are produced from burning
fossil fuels such as gasoline, coal, oil!!
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.

The hydrogenation of ethene (C2H4
(g)) to ethane
C2H4 (g) + H2(g)  C2H6 (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 .

There are four main steps in the process




the molecules approach the surface;
H2 (g) and C2H4 (g) adsorb on the surface;
H2 dissociates to form H(g) on the surface; the
adsorbed H atoms migrate to the adsorbed C2H4
and react to form the product (C2H6) on the
surface
the product desorbs from the surface and
diffuses back to the gas phase
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.
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
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”).
The Lock and Key (II)