chain reactions

Chain reactions

Tamás TurányiInstitute of Chemistry

Eötvös University (ELTE)Budapest, Hungary

Max Bodenstein (German, 1871-1942)Investigated the H2Cl2 photochemical reaction and observed that single photon several million HCl product species

This term was printed for the first time in 1921 in the PhD thesis ofJens Anton Christiansen (Danish, 1988-1969)

The origin of term ‘chain reactions’ : the gold watch chain of Bodenstein

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

Bodenstein and Lind investigated (1907) the production of hydrogen bromide in a thermal reaction:

Karl F. Herzfeld (Austrian, 1892-1978) theory of reaction rates, chain reactions

The proper mechanism was suggested (1919) independently from each other by Jens A. Christiansen, Karl F. Herzfeld and Michael Polanyi :

HBr2BrH 22

.

[HBr]BrBrH[HBr]

2

2/322

kk

dtd

MBr2MBr2

Empirical rate equation:

HHBrHBr 2 BrHBrBrH 2 BrHHBrH 2MBrMBr2 2

Michael Polanyi (Hungarian, 1891-1976) first potential-energy surface, transition-state theory, sociology

Bodenstein could not explain the origin of this equation.

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.

Chain reactions

Mechanism of the H2Br2 reaction(a) initiation:

1 MBr2MBr2 MBr211 kv

(b) propagation:

2 HHBrHBr 2 ][Br][H222 kv BrHBrBrH 2 ][H][Br233 kv

(c) inhibition:

4 BrHHBrH 2 [H][HBr]kv 44

(d) termination:

5 MBrMBr2 2 M[Br]255 kv

3

Calculation of the concentrationtime profiles

concentrationtime profiles of the H2Br2 reaction (stoichiometric mixture, T= 600 K, p= 1 atm)

[H][HBr]][Br][HdHd

422422 kkvvt

252321531

2 [Br]][H][BrMBrdBrd kkkvvvt

[H][HBr]][H][Br][Br][HdHd

42322432 kkkvvvt

][[Br]2Br][H][][H][Br][Br][H][Br222dBrd 2

5423222154321 MkHkkkMkvvvvvt

Br]H[H][H][Br][Br][HdHBrd

42322432 kkkvvvt

MBr2MBr1 2 HHBrHBr2 2 BrHBrBrH3 2 BrHHBrH4 2MBrMBr25 2

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

production rates

d[H2]/dt -100.1

d[Br2]/dt -100.1

d[HBr]/dt +200.2

d[H]/dt +0.0014

d[Br]/dt +0.0026

rates of reaction stepsR1 Br2+M2 Br+M 1.0

R2 Br+H2HBr+H 100.2

R3 H+Br2HBr+Br 100.1

R4 H+HBrH2+Br 0.1

R5 2 Br+M Br2+M 1.0

Relative rates at t = 1 second(all rates are normed with respect to v1)

432d

Hd vvvt

54321 22

dBrd vvvvvt

0.0014 = +100.2 –100.1 –0.1

0.0026 = 2.0 – 100.2 + 100.1 + 0.1 – 2.0

432d

HBrd vvvt

200.2 = +100.2 +100.1 –0.1

Relation of reaction rates and production rates

MBr2MBr1 2 HHBrHBr2 2 BrHBrBrH3 2 BrHHBrH4 2MBrMBr25 2

Calculation of [Br]

0dHd

432 vvvt

022dBrd

54321 vvvvvt_________________________________________

022 51 vv

51 vv

M[Br]MBr 2521 kk

25

1 BrBrkk

MBr2MBr2

MBrMBr2 2

1

5

+

Calculation of [H]

[H][HBr]][H][Br][Br][HdHd

42322 kkkt

[HBr]k][Brk

Brkkk][H

H423

25

122

5121 ,,BrBr kkf 54321222 ,,,,,HBr,H,BrH kkkkkf

[H][HBr]][H][BrBr][H0 42325

122 kkkkk

25

1 BrBrkk

[H][HBr]][H][Br][Br][H0 42322 kkk

Equation for [Br] is inserted:

Algebraic equations for the calculation of [H] and [Br]:

Calculation of the production rate of HBr

This is identical to the empirical equation of Bodenstein and Lind:

After insertion of the equations for [Br] and [H] and rearrangement:

[HBr]k][Brk

Brkkk][H

H423

25

122

[HBr]][Br

Br][H2

dHBrd

3

42

23

225

12

kk

kkk

t

[HBr] is almost zero at the beginning of the reaction: 2

1

225

12 Br][H2

dHBrd

kkk

t Order for H2 and Br2 are 1 and 0.5, respectively.

The overall order of the reaction is 1.5

.

[HBr]BrBrH[HBr]

2

2/322

kk

dtd

Br]H[H][H][Br][Br][HdHBrd

42322432 kkkvvvt

25

1 BrkkBr

Mean number of propagation steps which occur before termination =

1.5022.100

v2v

5

2

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 H2Br2 reaction at the defined conditions

Chain length

The origin of explosions

The Nobel Prize in Chemistry 1956: Semenov and Hinshelwood: "for their researches into the mechanism of chemical reactions"

Sir Cyril Norman Hinshelwood (English, 1897-1967)

Investigation (1927) of the H2O2 reaction:discovery of the 1st and 2nd explosion limits

First experimental proof:Nikolay Nikolaevich Semenov (Russian, 1896-1986)Investigation (1926) of the phosphorus vapouroxygen reacion.Explosion occurs, if the partial pressure of O2 is between two limits. Interpretation via a branching chain reaction.

Mixture H2+Br2 cannot explode at isothermal conditions.

Suggestion of Christiansen and Kramers (1923): explosions are due to branching chain reactionsBUT: it was a pure speculation

Explosion of hydrogenoxygen mixtures 2 H2 + O2 2 H2O

ObservationsThe 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

1 H2 + O2 .H + .HO2 initiation2 .OH + H2 .H + H2O propagation3 .H + O2 .OH + O branching4 O + H2 .OH + .H branching5 .H + O2 + M .HO2 + M termination*6 .H wall termination7 :O wall termination8 .OH wall termination9 .HO2 + H2 .H + H2O2 initiation *10 2 .HO2 H2O2 + O2 termination11 H2O2 2 .OH initiation

Below the 1st explosion limit:

domination of the termination reactions at the wall

no explosion


Between the 1st and the 2nd explosion limits:

Branching steps (2), (3) and (4). 3 H + O2 .OH + :O2 .OH + H2 .H + H2O4 :O + H2 .H + .OH2 .OH + H2 .H + H2O+ ____________________.H + O2 + 3 H2 3 .H + 2 H2O explosion

H. H.

H.

H.

H.

H.

H.

H.

H.

H.

H.

H.

H.


Between the 2nd and the 3rd explosion limits:

5 .H + O2 + M .HO2 + M termination* no explosion


above the 3rd explosion limit Reactions (9), (10), and (11) become important

explosion


The two basic types of chain reactions

Open chain reactionsChain reactions without branching steps

Examples: H2 + Br2, reaction,, alkane pyrolysis and polimerisation reactions

Branched chain reactionsChain reactions that include branching reaction steps

Examples: H2+O2 reaction, hydrocarbonair explosions and flames

Two types of explosions

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

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

thermal explosion

Branched chain explosions: rapid increase of the concentration of chain carriers leads to the increase of reaction rate and finally to explosion

Svante August Arrhenius (Swedish, 1859-1927)Nobel Prize in Chemistry (1903), electrolytic theory of dissociation

Theoretical considerations of Arrhenius (1889):• equilibrium between the ‘normal’ and ‘active’ species • activation energy E is T-independent in small temperature range

Arrhenius equation: RTE

Ak

e

Van’t Hoff’s equations (1884): orRTE

Ak

e RTDTB

Ak2

e

Temperature dependence of the rate coefficient

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”

Arrhenius-plot

k A ERTa

exp

A preexponential factorEa activation energy

Arrhenius-plot:

ln lnk AERTa

Plotting ln k against 1/T gives a lineSlope: m = -Ea/R gives activation energy Ea

Arrhenius equation:

or

Arrhenius-plot between 220 K (53 C ) and 320 K (+47 C)

Reaction CH4+OH CH3 + H2Othe most important methane consuming reaction in the troposphereone of the most important reactions of methane combustion

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).

Arrhenius-plot between 300 K (27 C ) and 2200 K (1930 C)

RTC

nBTk

e

Extended Arrhenius-equation

Note that if n0 AB and EaC

General definition of activation energy:

pa T

kRE

1ln

Thank you allfor your attention

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. Ölanderhttp://nobelprize.org/chemistry/laureates/1956/press.html

H2Br2 and H2O2 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

chain reactions

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