Chain%20reactions

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Chain reactions

• Tamás Turányi
• Institute of Chemistry
• Eötvös University (ELTE)
• Budapest, Hungary

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Max Bodenstein (German, 1871-1942) Investigated
the H2?Cl2 photochemical reaction and observed
that single photon ? several million HCl product
species
Explanation of Bodenstein (1913) Primary
reaction Absorption of a single photon ?
single active molecule (maybe Cl2
???) Secondary reactions Single active molecule
? several million product species
The origin of term chain reactions
the gold watch chain of Bodenstein
This term was printed for the first time in 1921
in the PhD thesis of Jens Anton Christiansen
(Danish, 1988-1969)
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Bodenstein and Lind investigated (1907) the
production of hydrogen bromide in a thermal
reaction
Empirical rate equation
Bodenstein could not explain the origin of this
equation.
The proper mechanism was suggested (1919)
independently from each other by Jens A.
Christiansen, Karl F. Herzfeld and Michael
Polanyi
Karl F. Herzfeld (Austrian, 1892-1978) theory of
reaction rates, chain reactions
Michael Polanyi (Hungarian, 1891-1976) first
potential-energy surface, transition-state
theory, sociology
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Chain reactions
Chain carriers (also called chain centres, i.e.
reactive intermediates) are generated in the
initiation steps. In the chain propagation
steps the chain carriers react with the
reactants, produce products and regenerate the
chain carriers.
In the inhibition step the chain carriers react
with the product, reactants are reformed, and
there is no reduction in the number of chain
carriers.
In the branching step two or more chain carriers
are produced from a single chain carrier.
In the termination steps the chain carriers are
consumed.
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Mechanism of the H2?Br2 reaction
(a) initiation 1
(b) propagation 2
3
(c) inhibition 4
(d) termination 5
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Calculation of the concentration?time profiles
concentration?time profiles of the H2?Br2
reaction (stoichiometric mixture, T 600 K, p 1
atm)
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Relative rates at t 1 second (all rates are
normed with respect to v1)
rates of reaction steps rates of reaction steps
R1 Br2M?2 BrM 1.0
R2 BrH2?HBrH 100.2
R3 HBr2?HBrBr 100.1
R4 HHBr?H2Br 0.1
R5 2 BrM ? Br2M 1.0
rates of R1 and R5 ltlt rates of R2 and R3 rate of
R1 rate of R5 In the case of small HBr
rate of R2 rate of R3
production rates production rates
dH2/dt -100.1
dBr2/dt -100.1
dHBr/dt 200.2
dH/dt 0.0014
dBr/dt 0.0026
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Relation of reaction rates and production rates
200.2 100.2 100.1 0.1
0.0014 100.2 100.1 0.1
0.0026 2.0 100.2 100.1 0.1 2.0
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Calculation of Br

_________________________________________
 
1
5
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Calculation of H
Equation for Br is inserted
Algebraic equations for the calculation of H
and Br
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Calculation of the production rate of HBr
After insertion of the equations for Br and
H and rearrangement
This is identical to the empirical equation of
Bodenstein and Lind
HBr is almost zero at the beginning of the
reaction
Order for H2 and Br2 are 1 and 0.5,
respectively. The overall order of the reaction
is 1.5
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Chain length
Mean number of propagation steps which occur
before termination
consumption rate of the chain carrier in
the propagation step ?????????????????????????
??? consumption rate of the chain carrier
in the termination step
The chain length at t1 s in the H2?Br2 reaction
at the defined conditions
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The origin of explosions
Mixture H2Br2 cannot explode at isothermal
conditions.
Suggestion of Christiansen and Kramers (1923)
explosions are due to branching chain
reactions BUT it was a pure speculation
First experimental proof Nikolay Nikolaevich
Semenov (Russian, 1896-1986) Investigation (1926)
of the phosphorus vapour?oxygen
reacion. Explosion occurs, if the partial
pressure of O2 is between two limits.
Interpretation via a branching chain reaction.
Sir Cyril Norman Hinshelwood (English,
1897-1967) Investigation (1927) of the H2?O2
reaction discovery of the 1st and 2nd explosion
limits
The Nobel Prize in Chemistry 1956 Semenov and
Hinshelwood "for their researches into the
mechanism of chemical reactions"
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Explosion of hydrogen?oxygen mixtures 2 H2 O2
? 2 H2O
Observations? The 1st explosion limit depends on
the size of the vessel and the quality of the
wall. The 2nd and 3rd limits do not depend on
these
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1 H2 O2 ? .H .HO2 initiation 2 .OH H2 ?
.H H2O propagation 3 .H O2 ? .OH ?O
branching 4 ?O H2 ? .OH .H
branching 5 .H O2 M ? .HO2 M
termination 6 .H ? wall termination 7 O ?
wall termination 8 .OH ? wall
termination 9 .HO2 H2 ? .H H2O2
initiation 10 2 .HO2 ? H2O2 O2
termination 11 H2O2 ? 2 .OH initiation
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1 H2 O2 ? .H .HO2 initiation 2 .OH H2 ?
.H H2O propagation 3 .H O2 ? .OH ?O
branching 4 ?O H2 ? .OH .H
branching 5 .H O2 M ? .HO2 M
termination 6 .H ? wall termination 7 O ?
wall termination 8 .OH ? wall
termination 9 .HO2 H2 ? .H H2O2
initiation 10 2 .HO2 ? H2O2 O2
termination 11 H2O2 ? 2 .OH initiation
?
Below the 1st explosion limit
domination of the termination reactions at the
wall ? no explosion
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1 H2 O2 ? .H .HO2 initiation 2 .OH H2 ?
.H H2O propagation 3 .H O2 ? .OH ?O
branching 4 ?O H2 ? .OH .H
branching 5 .H O2 M ? .HO2 M
termination 6 .H ? wall termination 7 O ?
wall termination 8 .OH ? wall
termination 9 .HO2 H2 ? .H H2O2
initiation 10 2 .HO2 ? H2O2 O2
termination 11 H2O2 ? 2 .OH initiation
?
H.
H.
H.
Between the 1st and the 2nd explosion
limits Branching steps (2), (3) and (4).
  3              H O2 ? .OH
O 2              .OH H2 ? .H
H2O 4              O H2 ? .H
.OH 2              .OH H2 ? .H H2O
____________________ .H O2 3 H2 ? 3 .H 2
H2O ? explosion
H.
H.
H.
H.
H.
H.
H.
H.
H.
H.
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1 H2 O2 ? .H .HO2 initiation 2 .OH H2 ?
.H H2O propagation 3 .H O2 ? .OH ?O
branching 4 ?O H2 ? .OH .H
branching 5 .H O2 M ? .HO2 M
termination 6 .H ? wall termination 7 O ?
wall termination 8 .OH ? wall
termination 9 .HO2 H2 ? .H H2O2
initiation 10 2 .HO2 ? H2O2 O2
termination 11 H2O2 ? 2 .OH initiation
?
Between the 2nd and the 3rd explosion limits 5
.H O2 M ? .HO2 M termination   ? no
explosion
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1 H2 O2 ? .H .HO2 initiation 2 .OH H2 ?
.H H2O propagation 3 .H O2 ? .OH ?O
branching 4 ?O H2 ? .OH .H
branching 5 .H O2 M ? .HO2 M
termination 6 .H ? wall termination 7 O ?
wall termination 8 .OH ? wall
termination 9 .HO2 H2 ? .H H2O2
initiation 10 2 .HO2 ? H2O2 O2
termination 11 H2O2 ? 2 .OH initiation
?
above the 3rd explosion limit   Reactions (9),
(10), and (11) become important ? explosion  
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The two basic types of chain reactions
Open chain reactions Chain reactions without
branching steps Examples H2 Br2, reaction,,
alkane pyrolysis and polimerisation reactions
Branched chain reactions Chain reactions that
include branching reaction steps Examples H2O2
reaction, hydrocarbon?air explosions and flames
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Two types of explosions
Branched chain explosions rapid increase of the
concentration of chain carriers leads to the
increase of reaction rate and finally to explosion
Another possibility (i) exothermic
reaction, (ii) hindered dissipation of heat
and (iii) increased reaction rate with raising
temperature, then higher temperature ? faster
reactions ? increased heat production
? thermal explosion
Presence of a chain reaction is not needed for a
thermal explosion.

• Branched chain reactions are
• exothermic and fast
• dissipation of heat is frequently hindered
• most branched chain explosions are also thermal
  explosions

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Temperature dependence of the rate coefficient
Vant Hoffs equations (1884)
or
Theoretical considerations of Arrhenius (1889)
equilibrium between the normal and active
species activation energy E is T-independent
in small temperature range
Arrhenius equation
Jacobus Henricus Vant Hoff (Dutch, 1852-1911)
The first Nobel Prize in Chemistry (1901) in
recognition of the extraordinary services he has
rendered by the discovery of the laws of chemical
dynamics and osmotic pressure in solutions
Svante August Arrhenius (Swedish,
1859-1927) Nobel Prize in Chemistry (1903),
electrolytic theory of dissociation
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Arrhenius-plot
Arrhenius equation
or
A preexponential factor Ea activation energy
Plotting ln k against 1/T gives a line Slope
m  -Ea/R gives activation energy Ea
Arrhenius-plot
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Reaction CH4OH ? CH3 H2O
the most important methane consuming reaction in
the troposphere one of the most important
reactions of methane combustion
Arrhenius-plot between 220 K (?53 ?C )
and 320 K (47 ?C)
Arrhenius-plot between 300 K (27 ?C )
and 2200 K (?1930 ?C)
Arrhenius-equation is usually very accurate in a
narrow temperature range (solution phase
kinetics, atmospheric chemistry).
Arrhenius-equation is usually not applicable in
a wide temperature range (combustion,
explosions, pyrolysis).
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Extended Arrhenius-equation
Note that if n?0 ? A?B and Ea?C
General definition of activation energy
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Thank you allfor your attention
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Literature usedMichael J. Pilling Paul W.
SeakinsReaction KineticsOxford University
Press, 1995 Keith J. LaidlerThe World of
Physical ChemistryOxford University Press,
1995The Nobel Prize in Chemistry
1956Presentation speech by Professor A.
Ölanderhttp//nobelprize.org/chemistry/laureates/
1956/press.html H2?Br2 and H2?O2
concentration-time profileswere calculated by
Dr. István Gy. Zsély (Department of Physical
Chemistry, Eötvös University, Budapest)Comments
of Dr. Judit Zádor, Mr. János Daru, and Dr.Thomas
Condra are gratefully acknowledged. Special
thank to Prof. Preben G. Sørensen (University of
Copenhagen) for the photo of J. A. Christiansen
andto Prof. Ronald Imbihl (Universität Hannover)
for the photo of the gold watch of Bodenstein