Chapter 25 Summary:

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• Chapter 25 Summary
• 1. Experimental techniques flow method,
  stopped-flow method, flash photolysis, quenching.
• The rates of reaction rate laws, rate constants,
  reaction order.
• Integrated rate laws first and second order,
  half lives.
• Reactions near equilibrium
• Temperature dependence of reaction rates The
  Arrhenius equation, transition states, activation
  energy
• Accounting for the rate laws Elementary
  reactions, molecularity, rate determining step,
  steady state approximation.

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Chapter 26 The Kinetics of Complex Reactions
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Chapter 26 Outline 26.1 The Rate Laws of Chain
Reactions 26.2 Explosions 26.5 Features of
Homogeneous Catalysis 26.6 Enzymes 26.11
Kinetics of Photophysical and Photochemical
Processes 26.12 Complex Photochemical
Processes Homework 26.1, 26.2, , 26.5, 26.6,
26.7, 26.8, 26.10, 26.12 parts (a) only.
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The Rate Laws of Chain Reactions
Many gas-phase reactions and liquid phase
polymerizations are chain reactions. In a chain
reaction a reaction intermediate (or chain
carrier) produced in one step generates an
intermediate in a subsequent step and so on. In
a radical chain reaction the chain carriers are
radicals i.e. chemical species with unpaired
electrons. Chain reactions can have simple or
complicated rate laws.
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The Rate Laws of Chain Reactions A Simple
Example
The pyrolysis of ethanal
CH3CHO(g) ? CH4(g) CO(g) ( a little bit of
C2H6 (g))
v kCH3CO3/2
Mechanism Initiation CH3CHO ?
CH3 CHO v kiCH3CHO Propagation CH3CHO
CH3 ? CH4 CH3CO v kpCH3CHOCH3 Propagati
on CH3CO ? CH3 CO v
kp'CH3CO Termination CH3 CH3 ?
CH3CH3 v ktCH32
We can test the proposed mechanism by showing
that it gives the observed rate law. Lets do
this using the steady state approximation.
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The Rate Laws of Chain Reactions A
Complicated Example
The hydrogen-bromine reaction H2(g) Br2(g) ?
2 HBr(g)
Mechanism Initiation Br2 M ?
Br Br M v kiBr2M Propagation
Br H2 ? HBr H v kpBrH2
H Br2 ? HBr Br v kp'
HBr2 Retardation H HBr ?
H2 Br v krHHBr Termination Br
Br M ? Br2 M v ktBr2M
See Example 26.1
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The Rate Laws of Chain Reactions A
Complicated Example
How did we select Br2 M ? Br Br M as
initiation over, say H2 M ? H H M?
Because of the lower bond energy. Similarly for
termination.
You have to play around with different
"chemically reasonable" steps until the predicted
v is in accord with experiment. There is not
necessarily a unique solution!
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Chain Reactions - Explosions
Solid-state explosions (e.g. the explosion of
ammonium nitrate or TNT) are very rapid
decomposition reactions that produce large
amounts of gas-phase molecules.
Some explosions are due to chain reactions.
There are two types Thermal Explosions and
Chain-Branching Explosions.
Both types of explosion may be illustrated using
the reaction of hydrogen and water. H2(g)
O2(g) ? 2H2O(g)
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Chain Reactions - Explosions
H2(g) O2(g) ? 2H2O(g)
Partial Mechanism Initiation
H2 ? H H v constant
(vinit) Propagation H2 OH
? H2O H v kpOHH2 Branching
O2 H ? O OH v kb
HO2 O H2 ? H OH v
kbOH2 Termination H wall
? ½H2 v ktH H O2 M ? HO2 M v
ktHO2M
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Chain Reactions - Explosions
EXPLOSION LIMITS for the H2/O2 system. At very
low pressures chain carriers quickly diffuse to
the container walls (H wall ? ½H2) and there
is no explosion. At moderate pressures
diffusion is slowed and branching is explosively
efficient. e.g. O2 H ? O OH and O H2
? H OH At high pressures H atoms are lost
via H O2 M ? HO2 M. At very high
pressures a thermal explosion occurs.
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Example 26.2 For the reaction of hydrogen and
oxygen described above, show that an explosion
occurs when the rate of chain branching exceeds
that of chain termination.
Partial Mechanism Initiation
H2 ? H H v constant
(vinit) Propagation H2 OH
? H2O H v kpOHH2 Branching
O2 H ? O OH v kb
HO2 O H2 ? H OH v
kbOH2 Termination H wall
? ½H2 v ktH H O2 M ? HO2 M v
ktHO2M
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Introduction to Polymerization Kinetics

• Briefly, we consider two types of polymerization
  process
• Stepwise polymerization
• Any two monomers in the reaction mixture can link
  together at any time.
• Growth of the polymer is not confined to chains
  already forming.
• Monomers removed early during the reaction.
• Molar mass of product grows with time.
• Condensation type processes are common second
  order rate law.
• Chain polmerization
• Activated monomer attacks another monomer,
  resulting dimer attacks another monomer,
  resulting trimer attacks another monomer etc.
• Monomer used up as it adds to growing chain.
• Rate is proportional to square root of the
  initiator concentration.

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Homogeneous Catalysis
Introduction Pre-equilibria
In chapter 25 we considered the progression of a
reaction through the formation of an
intermediate A? I ? P Now lets consider a
slightly more complicated situation
I reaches equilibrium with A and B
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Homogeneous Catalysis
Introduction Pre-equilibria
We may show that
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Homogeneous Catalysis
Catalysts provide alternative routes through
which reactions may proceed. In this way
catalysts speed up reaction rates. A homogenous
catalyst is a catalyst that exists in the same
phase as the reaction mixture. A heterogeneous
catalyst is in a different phase to the reaction
mixture.
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Homogeneous Catalysis
Fast!
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Homogeneous Catalysis
Enzymes

• For any given initial concentration of substrate,
  S0, the initial rate of product formation is
  proportional to the total concentration of
  enzyme, E0.
• For any given E0 and low values of S0, the
  rate of product formation is proportional to
  S0.
• For any given E0 and high values of S0, the
  rate of product formation becomes independent of
  S0 reaching a maximum velocity vmax.

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Homogeneous Catalysis
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Homogeneous Catalysis
The Michaelis-Menten Mechanism

• For any given initial concentration of substrate,
  S0, the initial rate of product formation is
  proportional to the total concentration of
  enzyme, E0.
• For any given E0 and low values of S0, the
  rate of product formation is proportional to
  S0.
• For any given E0 and high values of S0, the
  rate of product formation becomes independent of
  S0 reaching a maximum velocity vmax.

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Homogeneous Catalysis
The Michaelis-Menten Mechanism
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Homogeneous Catalysis
The Michaelis-Menten Mechanism
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Homogeneous Catalysis
The catalytic efficiency of enzymes
kcat is the number of catalytic cycles
(turnovers) performed by the active site in a
given interval divide by the duration of the
interval.
The catalytic efficiency, ?, of an enzyme is
given by
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Homogeneous Catalysis
Example 26.3 Determining the catalytic efficiency
of an enzyme. The enzyme carbonic anhydrase
catalyses the hydration of CO2 in red blood cells
to give bicarbonate ion CO2
H2O ? HCO3- H The following data were
obtained for the reaction at pH 7.1, 273.5 K
and an enzyme concentration of 2.3 nmol
L-1 CO2 / (mmol L-1) 1.25 2.5 5.0 20.0 Rate
/ (mol L-1 s-1) ? 105 2.78 5.00 8.33 16.7
1/CO2 / (mol L-1) ? 10-2 8.0 4.0 2.0 0.5 1/Rate
/ (mol L-1 s-1) ? 10-4 3.6 2.0 1.2 0.6
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Homogeneous Catalysis
Example 26.3 contd
y-intercept 4.0 ? 103 L-1 mol s-1 Slope 40 s
vmax 1/(y-intercept) KM vmax ? slope
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Oscillating Reactions
The concentrations of reactants, intermediates,
and products of certain chemical reactions can
vary periodically in either in space or time. If
we make up a mixture of potassium bromate,
malonic acid and a cerium (IV) salt in acidic
solution and watch we see
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Oscillating Reactions
This is an example of autocatalysis. The
Belousov-Zhabotinski reaction BrO3- HBrO2
H3O ? 2BrO2? 2H2O 2BrO2? 2Ce(III) 2H3O ?
2HBrO2 2Ce(IV) 2H2O
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Oscillating Reactions

• The Belousov-Zhabotinski reaction mechanism.
• 18 elementary steps!
• 21 different chemical species involved!
• The main features of the reaction can be
  reproduced using a model called the oregonator.
• A Y ? X C
• X Y ? 2C
• A X ? 2X 2Z
• 2X ? A C
• B Z ? Y P

A BrO3- B Malonic Acid C HOBr P
additional products X HBrO2 Y Br - Z Ce4
v k1AY v k2XY v k3AX v k4X2
v k5BZ
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Oscillating Reactions
The Belousov-Zhabotinski reaction mechanism.

• Just as we have done before we
• Play spot the intermediate
• Create Steady State equations
• Set up a rate expression in which the
  concentrations of the intermediates have been
  substituted out.
• Then if we want to track the concentrations of
  the reactants or products with time we must
  integrate the rate law (differential equation).
• We may then make plots of concentrations of
  species and see how they change with time. (See
  movie).

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Photochemistry
Examination of the Arrhenius Parameters show us
that chemical reactions need an energy source to
get going. Many reactions can be initiated by
the absorption of electromagnetic
radiation. The earth is constantly bathed in
electromagnetic radiation.
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Photochemistry
The electromagnetic spectrum

• Planks Equation
• E hv
• h Planks constant
• v frequency
• wavelength
• c / v
• c speed of light

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Photochemistry
What chemicals exist in the earths atmosphere and
what chemical processes can occur?
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Photochemistry
The Chemistry of the Earths Atmosphere.
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Photochemistry
The Chapman Model
O2 hv ? O O O3 hv ? O2 O O O2 M
? O3 M O O3 ? 2O2 O O M ? O2 M
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Photochemistry
The Chapman Model predicts a net formation of
trace amounts ozone. However, it overestimates
the amount of ozone in the stratosphere. Other
species contribute to the termination step O O3
? 2O2 according to X O3 ? XO O2 XO O ?
X O2 X can be H, OH, NO or Cl.
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Photochemistry
A cause of concern is the effect of anthropogenic
pollutants on the ozone concentration. CFCs may
be photolysed CF2Cl2 hv ? CF2Cl Cl A
reduction in stratospheric ozone will cause an
increase in the amount of UV radiation reaching
the earths surface.
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Photochemistry

• Global warming (for)
• Rise in CO2 and other greenhouse gases is human
  caused.
• Historical temp. record shows an increase of 0.4
  0.8 oC over the last 100 years.
• Unusual warmth over last 1000 years.
• CO2 conc. is the most important indicator of
  climate change.

• Climate models can reproduce warming trend but
  only when greenhouse gases are included.
• The theory has scientific consensus.

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Photochemistry

• Global Warming (Against)
• The Earth has been colder and warmer than it is
  today.
• The overwhelming majority of greenhouse gases are
  not produced by humans.
• Climate models can be made which predict global
  warming without considering human activity.
• Solar and Volcanic activity is much more
  important than global warming supporters would
  like to admit.

• Atmospheric chemistry is more complicated than
  the global warming supporters would like to admit
  (Undiscovered feedback mechanisms).
• A majority argument doesnt make it fact.

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Photochemistry some background
What happens when UV light strikes a
molecule? Molecules, just like atoms, consist of
nuclei surrounded by orbiting electrons. To
displace an electron from one molecular orbital
to a different orbital requires energy. It so
happens that for many molecules the energy
required for an electronic transition is of a
similar magnitude to the energy of UV radiation
(E2 E1 400 kJ mol-1)
(Check using Planks Equation).
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Photochemistry
The electromagnetic spectrum

• Planks Equation
• E hv
• h Planks constant
• v frequency
• wavelength
• c / v
• c speed of light

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Photochemistry some background
Just like atomic orbitals, each molecular orbital
may contain two electrons, one of which is
spin-up and one is spin-down
The vast majority of molecules possess even
numbers of electrons in which each electron is
paired up. If each electron is paired up the
molecule is referred to as being in a singlet
state. When UV light strikes a singlet molecule
it can promote an electron into a higher energy,
unoccupied molecular orbital
(Forbidden transition)
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Photochemistry some background
Now lets construct a potential energy plot for a
diatomic molecule, AB, for a given electronic
configuration, say a singlet state
No! Only discrete (quantized) energy levels are
allowed.
Within the potential energy plot can the molecule
possess any energy we choose?
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Photochemistry some background
What happens when IR light strikes a molecule?
Molecules are constantly vibrating at discrete
frequencies. The difference in energy between a
molecule vibrating at one frequency compared to
the same molecule vibrating at a higher frequency
corresponds to the energy of electromagnetic
radiation from the Infra-red region. When a
molecule interacts with light of IR frequencies a
vibrational excitation may be induced.
What happens when microwave light strikes a
molecule?
Molecules are constantly rotating at discrete
frequencies. The difference in energy between a
molecule rotating at one frequency compared to
the same molecule rotating at a higher frequency
corresponds to the energy of electromagnetic
radiation from the microwave region.
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Photochemistry some background
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Photochemistry The fates of electronically
excited states
Scenario 1.
Absorption AB (singlet, S) UV radiation ? AB
(higher energy singlet, S)
Fluorescence
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Photochemistry The fates of electronically
excited states
Scenario 2.
Absorption AB (singlet, S) UV radiation ? AB
(higher energy singlet, S)
Phosphorescence
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The Timescales of Photophysical Processes

• It takes about 10-16 seconds for absorption of UV
  and visible radiation to take place.
• So, the upper limit for a rate constant for a
  first-order photochemical reaction is about 1016
  s-1.
• Fluorescence is slower than absorption but still
  very fast and can be used to initiate very fast
  reactions

hv ?

• Phosphorescence is typically much slower than
  fluorescence.

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The Fluorescent Light
Sealed glass tube, electrodes at each end, filled
with argon and a little mercury at very low
pressure. Glass coated with a phosphor
powder. When we turn on the AC power electrons
flow from one electrode to the other electrode.
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Photochemistry The Primary Quantum Yield
In keeping with the timescales of photochemical
events there are two processes classifications P
rimary processes Products formed directly from
excited state (photoisomerization of
retinal) Secondary processes Products formed
from intermediates which have been formed
directly from the excited state of the reactant.
For a primary process we may define the primary
quantum yield as
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The Mechanism of Decay of Excited Singlet States.
Consider the formation and decay of an excited
singlet state
Rate Law Absorption S hvi ? S vabs
Iabs Fluorescence S ? S hvf vf
kfS Internal Conversion S ? S vic
kicS Intersystem Crossing S ? T visc
kiscS
We find that the quantum yield of fluorescence is