06523 Kinetics' Lecture 7 Kinetics and Mechanism IV' Chain reactions Rate laws revisited Unimolecula

1
06523 Kinetics. Lecture 7Kinetics and
Mechanism IV. Chain reactionsRate laws
revisitedUnimolecular reactionsChain
reactionsPolymerizationExplosions

• Dr John J. Birtill

2
Rate laws revisited (lectures 1 and 5)

• Consider two similar looking bromination
  reactions, both in aqueous solution

(1) C6H5NH2 Br2 ? BrC6H4NH2 H Br- (2)
CH2(CN)2 Br2 ? BrCH(CN)2 H Br-

• Similar reaction stoichiometries but very
  different rate laws.
• Reaction 1 has a simple rate expression that is
  similar to the reaction stoichiometry.
• The mechanism really does have single bimolecular
  reaction step
• Bimolecular electrophilic substitution
• Reaction 2 has a complex rate expression (lecture
  5). The initial forward step is unimolecular
  dissociation to a carbanion but the overall rate
  is the defined by the overall mechanism.
• When Br2 is gtgt k3H then rate expression
  simplifies to 1st order.

3
Rate laws revisited (lectures 1 and 5)

• The reaction stoichiometry
• defines the overall proportions of reactants and
  products.
• is equivalent to the sum of all the elementary
  steps in the reaction mechanism
• does not define the reaction mechanism unless
  there is only one elementary step.
• The rate law and reaction order for the overall
  reaction is made up of the combined rate laws for
  all the elementary reaction steps
• In other words it derives from the fundamental
  reaction mechanism
• For this reason the rate law for the overall
  reaction is empirical (determined by experiment)
  and cannot be predicted automatically from the
  reaction stoichiometry.
• The rate law of an elementary reaction step can
  be deduced directly from its stoichiometry.

Rate 1 forward k1CH2(CN)2 unimolecularRate
1 reverse k-1CH(CN)2- H bimolecular Rate 2
k2CH(CN)2- Br2 bimolecular Overall rate
complex (previous slide)
Step 1 CH2(CN)2 CH(CN)2-
H Step 2 CH(CN)2- Br2
CHBr(CN)2 Br- Overall CH2(CN)2
Br2 ? BrCH(CN)2 H Br-
4
Unimolecular reactions

• Some reactions are 1st order because an initial
  fast step is unimolecular but the overall
  reaction involves more than one molecule
• SN2 and SE1 reactions involve initial
  dissociation to carbocations and carbanions.
• Some gas phase reactions are 1st order and but
  again they are not truly unimolecular overall
• The overall mechanism is multi-step (e.g.,
  decomposition of N2O5) or catalysed by the
  surface of the vessel.
• Example 2N2O5 2N2O4 O2
  multi-step mechanism
• Some gas phase reactions are 1st order and can be
  described as unimolecular overall but even here
  the situation is a little more complex and the
  rate laws are pressure-dependent.
• Example isomerization of cyclopropane (strained
  molecule)

Rate kcyclo-C3H6
5
Unimolecular reactions Lindemann (-Christiansen)
mechanism

• Consider the unimolecular reaction A ? B
• Step (1) A reactant molecule A gains energy by
  collision with any other molecule M.
• Reverse step (1) The excited molecule A can lose
  energy by collision with another molecule
• Step (2) A decomposes by unimolecular decay

• Can apply the quasi-equilibrium approximation to
  step (1) but more general solution is to apply
  the steady state approximation to A and
  rearrange to solve for A (Hinshelwood).
• At high pressure k-1M gtgt k2 and the 1st order
  rate law applies (step 1 at quasi-equilibrium).

6
Unimolecular reactions Lindemann mechanism contd

• The overall rate law can be re-expressed in terms
  of a rate constant k that varies with pressure.
• The Lindemann theory predicts that k is constant
  at high pressure but decreases at low pressure.
• This is observed in practice. See plot for
  azomethane. k8 k1k2/k-1

Decomposition of azomethane at 603KCH3N2CH3 ?
C2H6 N2

• The Lindemann theory gives a qualitative fit to
  experimental data but
• estimates of k1 by simple collision theory did
  not agree with experiment
• plots of 1/k vs 1/M not linear.
• More sophisticated theories (Hinshelwood, RRK
  etc) consider the distribution of vibrational
  energy within the molecule.

log (k8)
Ref Reaction Kinetics M.J. Pilling P.W.
Seakins
7
Chain reactions

• Many gas-phase and liquid-phase reactions are
  chain reactions including many of industrial
  importance such as polymerizations.
• The chain carrier is commonly a free radical
  intermediate I but can also be an ion.
• Usually designate radical intermediate with in
  order to distinguish from non-radical species.
• The initiation step is slow but a reactive
  intermediate I (the chain carrier) forms the
  the product and another reactive intermediate and
  so the reaction keeps on going (propagation) over
  many cycles (the chain length) until the chain
  carrier is destroyed somehow (termination).
• A ? I initiation (slow)
• I A ? C I propagation (fast)
• I I ? D termination (slow)
• A branching step increases the number of chain
  carriers.
• I B ? 2 I'

8
Chain reactions continued

• An inhibition step removes chain carriers by
  reaction with the vessel walls or with foreign
  radicals.
• Nitric oxide NO has an unpaired electron. It is a
  weak chain initiator but a very efficient chain
  terninator.
• CH3 NO ? CH3NO ? H2O HCN
• If a reaction is inhibited by NO then this is
  evidence for a radical chain mechanism
• The initiation step may be caused by collisions
  of energetic molecules (thermolysis reactions) or
  absorption of a photon (photolysis reactions).
• Br2 h? ? 2Br
• In polymerization processes a small amount of an
  unstable molecule such as benzoyl peroxide may be
  used as a radical initiator to start off a chain
  reaction.
• Note that in nuclear fission the chain carrier is
  a neutron.

9
The hydrogen bromine reaction

• Overall reaction H2 Br2 ? 2HBr
• Complex rate law suggests a complex mechanism.

• Generally accepted mechanism
• (1) Br2 ? 2Br Initiation
• (2) Br H2 ? HBr H Propagation
• (3) H Br2 ? HBr Br Propagation
• (-2) HBr H ? Br H2 Retardation
• (-1) 2Br ? Br2 Termination
• Note that there are 2 radical intermediates H
  and Br (the chain carriers).
• Apply the steady state hypothesis to both of them.

10
The hydrogen bromine reaction contd.

• Eq (i) Overall rate
• Eq (ii) and Eq (iii)apply steady state approxm
  to H and Br.
• Eq (iv) add Eq (ii) and Eq (iii).
• Hence Eq (v) for Br.
• Eq (vi) substitute for Br in Eq (ii) and
  solve for H.
• Eq (vii) substitute for H and Br in Eq
  (i), cancel out terms and rearrange.

11
Free radical polymerization reactions

• Radical adds to an alkene to form a larger
  radical which then adds to another alkene and so
  on.

• Polyethylene R1 H ? Polyvinylchloride R1
  Cl ? Polystyrene R1 C6H5

• The base alkene is termed the monomer. Growing
  radicals are oligomers
• Reaction proceeds via initiation step then
  propagation steps until any two radicals react
  together in the termination reaction
• Use of radical initiator such as benzoyl
  peroxide
• Multiple propagation steps very similar and so k
  is approximately constant with size
• Average polymer chain length depends on average
  number of propagation steps before termination.
• Polymerization reactions are of world scale
  industrial importance

12
Gas-phase combustion explosions

• Thermal explosion energy released in thermal
  reaction causes temperature to rise and reaction
  rate to increase.and so temperature rises faster
  ... and so the rate accelerates catastrophically.
• Chain-branching explosion thermal explosion in
  which chain-branching occurs.
• Number of chain carriers grows exponentially as
  the reaction proceeds.
• Hydrogen-oxygen reaction has both characteristics
  and is explosive over wide range of conditions
• 2 H2 (g) O2 (g) ? 2 H2O (g)
• Simple stoichiometry but complex mechanism.
  Chain carriers include H, O, OH, and O2H
• Some steps include
• Initiation H2 O2 ? O2H H
• Propagation O2 H ? O OH branching
• O H2 ? OH H branching
• H2 OH ? H H2O
• Consider reaction at 460 600 ºC
• Reaction occurs smoothly at low pressure because
  sufficient number of chain carriers can reach
  container walls and recombine before reacting
• At higher pressure (above lower explosion limit)
  explosion will occur.
• At still higher pressure reaction (above higher
  explosion limit ) occurs smoothly because rate of
  radical recombination reactions (termination)
  becomes significant.