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Chain reactions. Tamás Turányi Institute of Chemistry Eötvös University (ELTE) Budapest, Hungary. Max Bodenstein ( German, 1871-1942) Investigated the H 2  Cl 2 photochemical reaction and observed that single photon  several million HCl product species.

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Chain reactions l.jpg

Chain reactions

Tamás Turányi

Institute of Chemistry

Eötvös University (ELTE)

Budapest, Hungary

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Max Bodenstein (German, 1871-1942)

Investigated the H2Cl2photochemical 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 stepthe 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 thetermination stepsthe chain carriers are consumed.

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Mechanism of the H2Br2 reaction

(a) initiation:


(b) propagation:



(c) inhibition:


(d) termination:


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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 R1 and R5 << rates of R2 and R3

rate of R1 = rate of R5

In the case of small [HBr] :

rate of R2 = rate of R3

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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]





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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 and0.5, 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 t=1 s

in the H2Br2 reaction

at the defined conditions

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The origin of explosions

Mixture H2+Br2cannot 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


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 + .HO2initiation

2 .OH + H2  .H + H2O propagation

3 .H + O2  .OH + Obranching

4 O + H2  .OH + .Hbranching

5 .H + O2 + M  .HO2 + M termination*

6 .H wall termination

7 :O wall termination

8 .OH walltermination

9 .HO2 + H2  .H + H2O2 initiation *

10 2 .HO2  H2O2 + O2termination

11 H2O2  2 .OH initiation

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1 H2 + O2 .H + .HO2initiation

2 .OH + H2  .H + H2O propagation

3 .H + O2  .OH + Obranching

4 O + H2  .OH + .Hbranching

5 .H + O2 + M  .HO2 + M termination*

6 .H wall termination

7 :O wall termination

8 .OH walltermination

9 .HO2 + H2  .H + H2O2 initiation *

10 2 .HO2  H2O2 + O2termination

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 + .HO2initiation

2 .OH + H2  .H + H2O propagation

3 .H + O2  .OH + Obranching

4 O + H2  .OH + .Hbranching

5 .H + O2 + M  .HO2 + M termination*

6 .H wall termination

7 :O wall termination

8 .OH walltermination

9 .HO2 + H2  .H + H2O2 initiation *

10 2 .HO2  H2O2 + O2termination

11 H2O2  2 .OH initiation




Between the 1st and the 2nd explosion limits:

Branching steps (2), (3) and (4).

3H + 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












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1 H2 + O2 .H + .HO2initiation

2 .OH + H2  .H + H2O propagation

3 .H + O2  .OH + Obranching

4 O + H2  .OH + .Hbranching

5 .H + O2 + M  .HO2 + M termination*

6 .H wall termination

7 :O wall termination

8 .OH walltermination

9 .HO2 + H2  .H + H2O2 initiation *

10 2 .HO2  H2O2 + O2termination

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 + .HO2initiation

2 .OH + H2  .H + H2O propagation

3 .H + O2  .OH + Obranching

4 O + H2  .OH + .Hbranching

5 .H + O2 + M  .HO2 + M termination*

6 .H wall termination

7 :O wall termination

8 .OH walltermination

9 .HO2 + H2  .H + H2O2 initiation *

10 2 .HO2  H2O2 + O2termination

11 H2O2  2 .OH initiation

above the 3rd explosion limit

Reactions (9), (10), and (11) become important


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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: H2+O2 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 alsothermal explosions

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Temperature dependence of the rate coefficient

Van’t Hoff’s 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 Van’t 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 equation:


Apreexponential factor

Ea activation energy

Plotting ln kagainst 1/Tgives a line

Slope: m = -Ea/Rgives activation energy Ea


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Reaction CH4+OH  CH3 + H2O

the most important methane consuming reaction in the troposphere

one of the most important reactions of methane combustion

Arrhenius-plot between220 K (53 C )

and 320 K (+47 C)

Arrhenius-plot between300 K (27C )

and2200 K (1930 C)


is usually very accurate in a

narrow temperature range (solution phase kinetics, atmospheric chemistry).


is usually not applicable

in a wide temperature range

(combustion, explosions, pyrolysis).

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Extended Arrhenius-equation

Note that ifn0 ABandEaC

General definition of activation energy:

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Thank you allfor your attention

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Literature used:Michael J. Pilling – Paul W. SeakinsReaction KineticsOxford University Press, 1995 Keith J. LaidlerThe World of Physical ChemistryOxford University Press, 1995‘The Nobel Prize in Chemistry 1956’Presentation speech by Professor A. Ölander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