Chain reactions

Chain reactions: 

Chain reactions Tamás Turányi Department of Physical Chemistry Eötvös University (ELTE) Budapest, Hungary

Slide2: 

Max Bodenstein (German, 1871-1942) Investigated the H2Cl2 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 of Jens 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

Slide3: 

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 : Empirical rate equation: Michael Polanyi (Hungarian, 1891-1976) first potential-energy surface, transition-state theory, sociology Bodenstein could not explain the origin of this equation.

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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

Slide5: 

Mechanism of the H2Br2 reaction (a) initiation: 1 (b) propagation: 2 (c) inhibition: 4 (d) termination: 5 3

Slide6: 

Calculation of the concentrationtime profiles concentrationtime profiles of the H2Br2 reaction (stoichiometric mixture, T= 600 K, p= 1 atm)

Slide7: 

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

Slide8: 

0,0014 = +100,2 –100,1 –0,1 0,0026 = 2,0 – 100,2 + 100,1 + 0,1 – 2,0 200,2 = +100,2 +100,1 –0,1 Relation of reaction rates and production rates

Slide9: 

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 This is identical to the empirical equation of Bodenstein and Lind: After insertion of the equations for [Br] and [H] and rearrangement: [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

Slide12: 

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 Chain length

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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 H2O2 reaction: discovery of the 1st and 2nd explosion limits 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. Mixture H2+Br2 cannot explode at isothermal conditions. Suggestion of Christiansen and Kramers (1923): explosions are due to branching chain reactions BUT: it was a pure speculation

Slide14: 

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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Below the 1st explosion limit: domination of the termination reactions at the wall  no explosion  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

Slide17: 

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. 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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Between the 2nd and the 3rd explosion limits: 5 .H + O2 + M  .HO2 + M termination*    no explosion  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

Slide19: 

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

Slide20: 

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 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

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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: Van’t Hoff’s equations (1884): or 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”

Slide23: 

Arrhenius-plot A preexponential factor Ea activation energy Arrhenius-plot: Plotting ln k against 1/T gives a line Slope: m = -Ea/R gives activation energy Ea Arrhenius equation: or

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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 troposphere one 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)

Slide25: 

Extended Arrhenius-equation Note that if n0  AB and EaC General definition of activation energy:

Thank you allfor your attention: 

Thank you all for 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 H2Br2 and H2O2 concentration-time profileswere calculated by Dr. István Gy. Zsély (Department of Physical Chemistry, Eötvös University, Budapest)Comments of Ms. Judit Zádor 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 wrist watch of Bodenstein: 

Literature used: Michael J. Pilling – Paul W. Seakins Reaction Kinetics Oxford University Press, 1995 Keith J. Laidler The World of Physical Chemistry Oxford University Press, 1995 ‘The Nobel Prize in Chemistry 1956’ Presentation speech by Professor A. Ölander http://nobelprize.org/chemistry/laureates/1956/press.html H2Br2 and H2O2 concentration-time profiles were calculated by Dr. István Gy. Zsély (Department of Physical Chemistry, Eötvös University, Budapest) Comments of Ms. Judit Zádor are gratefully acknowledged. Special thank to Prof. Preben G. Sørensen (University of Copenhagen) for the photo of J. A. Christiansen and to Prof. Ronald Imbihl (Universität Hannover) for the photo of the gold wrist watch of Bodenstein