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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
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
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.
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
Between the 2nd and the 3rd explosion limits:
5 .H + O2 + M .HO2 + M termination* no explosion
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
above the 3rd explosion limit Reactions (9), (10), and (11) become important
explosion
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
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