chain reactions tamás turányi institute of chemistry eötvös university (elte) budapest, hungary

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]Br

BrH[HBr]

2

2/322

k

k

dt

d

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][H

d

Hd42242

2 kkvvt

252321531

2 [Br]][H][BrMBrd

Brdkkkvvv

t

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

d

Hd42322432 kkkvvv

t

][[Br]2Br][H][][H][Br][Br][H][Br222d

Brd 25423222154321 MkHkkkMkvvvvv

t

Br]H[H][H][Br][Br][Hd

HBrd42322432 kkkvvv

t

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 steps

R1 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

Hdvvv

t

54321 22

d

Brdvvvvv

t

0.0014 = +100.2 –100.1 –0.1

0.0026 = 2.0 – 100.2 + 100.1 + 0.1 – 2.0

432d

HBrdvvv

t

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]

0

d

Hd432 vvv

t

022d

Brd54321 vvvvv

t_________________________________________

022 51 vv

51 vv

M[Br]MBr 2521 kk

25

1 BrBrk

k

MBr2MBr2

MBrMBr2 2

1

5

+

Calculation of [H]

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

d

Hd42322 kkk

t

[HBr]k][Brk

Brkk

k][H

H423

25

122

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

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

122 kkk

kk

25

1 BrBrk

k

[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

Brkk

k][H

H423

25

122

[HBr]][Br

Br][H2

d

HBrd

3

42

2

3

225

12

kk

kk

k

t

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

21

225

12 Br][H2

d

HBrd

k

kk

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

The overall order of the reaction is 1.5

.

[HBr]Br

BrH[HBr]

2

2/322

k

k

dt

d

Br]H[H][H][Br][Br][Hd

HBrd42322432 kkkvvv

t

25

1 Brk

kBr

Mean number of propagation steps which occur before termination =

1.502

2.100

v2

v

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 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 termination7 :O wall termination8 .OH wall termination9 .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









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.

H.

H.

H.









Between the 2nd and the 3rd explosion limits:


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: RT

E

Ak

e

Van’t Hoff’s equations (1884): orRT

E

Ak

e RT

DTB

Ak

2

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 AE

RTa

exp

A preexponential factorEa activation energy

Arrhenius-plot:

ln lnk AE

RTa

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 + H2O

the 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)

RT

CnBTk

e

Extended Arrhenius-equation

Note that if n0 AB and EaC

General definition of activation energy:

p

a T

kRE

1

ln

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 tamás turányi institute of chemistry eötvös university (elte) budapest, hungary

Documents

chain propagation

chain centres

number of chain carriers

single chain carrier

origin of term chain

hungary slide

atm slide

thermal reaction