26 The kinetics of complex reactions

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26 The kinetics of complex reactions

• Chain reactions
• 26.1 The rate laws of chain reactions
• 26.2 Explosions
• Polymerization kinetics
• 26.3 Stepwise polymerization
• 26.4 Chain polymerization

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• Homogeneous catalysis
• 26.5 Features of homogeneous
• 26.6 Enzymes
• Oscillating reactions
• 26.7 Autocatalysis
• 26.8 Autocatalytic mechanisms
• 26.9 Bistabili
• 26.10 Chemical chaos
• Photochemistry

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• 26.11 Kinetics of photophysical and photochemical
  processes
• 26.12 Complex photochemical process
• Checklist of key ideas
• Further reading
• Exercises
• problem

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Chain reactions

• Chain reaction, a reaction in which an
  intermediate produced in one step generates an
  intermediate in a subsequent step, and so on.
• Chain carrier, the intermediates in a chain
  reaction.
• Radical chain, a chain reaction in which the
  chain carriers are radicals.

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26.1 The rate laws of chain reactions

• Pyrolysis, thermal decomposition in the absence
  of air.
• CH3CHO(g) CH4 CO(g)
• 
  VKCH3CHO3/2

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• In many cases,a chain reaction leads to a
  complicated rate law. An example is the
  hydrogen-bromine reaction

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26.2 Explosions

• A thermal explosion is a very rapid reaction
  arising from a rapid increase of reaction rate
  with increasing temperature.
• An example of both types of explosion is the
  reaction between hydrogen and oxygen

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• Although the net reaction is very simple,the
  mechanism is very complex and has not been fully
  elucidated.

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Polymerization kinetics

• In stepwise polymerization any two monomers
  present in the reaction mixture can link together
  at any time and growth of the polymer is not
  confined to chains that are already forming.As a
  result,monomers are removed early in the reaction
  and, as we shall see,the average molar mass of
  the product grows with time.
• In chain polymerization an activated
  monomer,M,attacks another monomer,links to
  it,then that unit attacks another monomer,and so
  on .High polymers are formed rapidly and only the
  yield, not the average molar mass,of the polymer
  is increased by allowing long reaction times.

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26.5 Features of homogeneous catalysis

• We can obtain some idea of the mode of action
  of homogeneous catalysts by examing the kinetics
  of the bromide-catalysed decomposition of
  hydrogen peroxide
• The reaction is believed to proceed through
  the following pre-equilibrium

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26.3 Stepwise polymerization

• Stepwise polymerization commonly proceeds by a
  condensation reaction,in which a small molecule
  is eliminated in each step.Stepwise
  polymerization is the mechanism of production of
  polyamides,as in the formation of nylon-66

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26.4 Chain polymerization

• Chain polymerization occurs by addition of
  monomers to a growing polymer,often by a radical
  chain process.It results in the rapid growth of
  an individual polymer chain for each activated
  monomer.Example include the addition
  polymerizations of ethene,methyl methacrylate,and
  styrene,as in

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Homogeneous catalysis

• A catalyst is a substance that accelerates a
  reaction but undergoes no net chemical change.The
  catalyst lowers the activation energyof the
  reaction by providing an alternative paththat
  avoids the slow,rate-determining step of the
  uncatalysed reaction(Fig26.8)
• A homogeneous catalyst is a catalyst in the
  same phase as the reaction mixture.

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26.5 Features of homogeneous catalysis

• We can obtain some idea of the mode of action
  of homogeneous catalysts by examing the kinetics
  of the bromide-catalysed decomposition of
  hydrogen peroxide.
• The reaction is believed to proceed through the
  follow pre-equilibrium

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• The second step is rate determining.Therefore,we
  can obtain the rate law of the overall reaction
  by setting the overall rate equal to the rate of
  the second step and using the equilibrium
  constant to express the concentration of H3O2in
  terms of the reaction.The result is

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• with in agreement with the observed
  dependence of the rate on the Br-concentration
  and the pH of the solution. The observed
  activation energy is that of the effective rate
  constant

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26.6 Enzymes

• (a)The Michaelis-menten mechanism of enzyme
  catalysis
• According to the Michaelis-menten mechanism,an
  enzyme-substrate complex is formed in the first
  step and either the substrate is released
  unchanged or after modification to form products

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• The rate of product formation is
• We can obtain the concentration of the
  enzyme-substrate comples by invoking the
  steady-state approximation and writing
• It follows that

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• By substituting this result into the rate
  ,we obtain the Michaelis-Menten
• equation for the rate of an enzyme-catalysed
  reaction

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• The constant(kakb)/ka is characteristic of a
  given enzyme acting on a given substrateit is
  called the Michaelis constant and written KM ,and
  KMES/ES.

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(b)The catalytic efficiency of enzymes

• The turnover number,or catalytic constant,
  of an enzyme,is the number of catalytic cycles
  performed by the active site in a given interval
  divided by the duration of the interval.This
  quantity has units of a first-order rate constant
  and ,in terms of

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• the Michaelis-Menten machanism, is numerically
  equivalent to kb ,the rate constant for release
  of product from the enzyme-substrate complex.It
  follows from the identification of kcat with kb
  and from
• that

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26.11 Kinetics of photophysical and photochemical
processes
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Comparative to singlet and triplet

• Energy

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Probability from So to S1 or T1
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vibration relaxation
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internal conversion
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intersystem crossing
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fluorescence
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phosphorescence
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(b) The primary quantum yield

• ?number of events/number of photos absorbed
• ?rate of process/intensity of light absorbed
  ?/Iabs

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Exercises

• Discussion questions
• Identify any initiation, propagation,
  retardation, inhibition,and termination steps in
  the following chain mechanisms

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• (b)Bearing in mind distinctions between the
  mechanism of stepwise and chain polymerization,
  describe ways in which it is possible to control
  the molar mass of a polymer by mainpulating the
  kinetic parameters of polymerization.
• (c)Discuss the features,advantages, and
  limitations of the Michaelis-Menten mechanism of
  enzyme action.
• (d)Consider the following chain mechanism

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• Use the steady-state approximation to deduce that
  the decomposion of AH is first-order in AH.

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Further reading

• Articles of general interest