Das System Atmosphärenchemie

1. katalytische Zyklen Reservoir Das System Atmosphärenchemie Transport Transport Reaktionen Quellen Abbau Dr. Martin Schultz - Max-Planck-Institut für Meteorologie, Hamburg

2. Reaction kinetics and photolysis • Atmospheric chemical reactions • Rate constants • UV/VIS light absorption • Photodissociation reactions

3. Chemical reactions • gas-phase reactionsA+B  C+DA+B  CC  A+BA+B+M  C+D+M • photodissociation reactionsA+h B+C • heterogeneous (aerosol-, liquid-phase) reactionssurface reactionsbulk reactions often A+B  C

4. (Homogeneous) gas-phase reactions Let us concentrate on a reaction of type A+B  C+D. Then k is called reaction rate constant. Note: k is often dependent on temperature and pressure.

5. Collision frequency Molecules need to collide before they can react.The collision frequency Zij is derived from gas kinetic theory: Time between collisions on the order of 10-9 s. Time, in which molecules are close enough to interact during a collision, typically 10-12..10-13 s. *2 corresponds to (rA+rB)2 [radii of hard spheres], but takes into account the requirement of a minimum energy required to break the bond. (see next slide)

6. Integrated over all total energies from 0 to, the frequency of reactive collisions becomes k Rate constant The collision cross section ij takes into account, that a minimum amount of energy E0 is needed in the collision to break the bonds.

7. Rate constant (2) Normally, k is written as where R is the gas constant R = k NA. If the activation energyE is sufficiently large, the temperature dependence of A is unimportant, and k follows the Arrhenius expression The theoretical maximum of k (every collision leads to a reaction) at room temperature is ~ 2·10-10 cm3 molecules s-1.

8. Examples • Ozone titration: O3+NO  O2+NO2A=2.0·10-12 cm3 molecules s-1E/R=1400 Krate constant@298K: k = 1.8 · 10-14 cm3 molecules s-1rate constant@230K: k = 4.5 · 10-15 cm3 molecules s-1 • Methane oxidation: OH+CH4 CH3+H2OA=2.8·10-14·T2/3 cm3 molecules s-1E/R=1575 Krate constant@298K: k = 6.33 · 10-15 cm3 molecules s-1rate constant@230K: k = 1.12 · 10-15 cm3 molecules s-1

9. A + B AB* C+D Order of a reaction • 1st order: A  products • 2nd order: A+B  products • 3rd order: A+B+M  products+M M is a “third body”, which is not chemically transformed but is required to absorb the excess energy of an activated intermediate state. Example: thermal decomposition of a loosly bond molecule most of the relevant reactions in the atmosphere Example: OH+HNO3 +M

10. Thus 4 (or 5) parameters: The Troe formula In the range of temperatures and pressures encountered throughout the troposphere and stratosphere, many reactions are in the falloff region between second order and third order reactions. Commonly, the rate constants for such reactions are expressed with the Troe formula: FC 0.6

11. „transition state theory“ (Theorie des Übergangszustandes) As molecules approach each other, they have to overcome an energy barrier (electronic repulsion). The energy they absorb leads to a loosening of the intramolecular bonds until a transition state is reached, which can then either fall back into the original molecules or proceed to yield the products of the reaction. Hr is the reaction enthalpy.

12. Quasi steady state approximation Several reactions proceed via the formation of an activated complex, which needs to get rid of excess energy in order to stabilize („quenching“). Example: O+O2 O3* O3*+M O3 The rate equation for the intermediate complex is: If the lifetime of the complex O3* is sufficiently short, then thus

13. k High pressure limit: Low pressure limit: Quasi steady state approximation (2) The formation rate of O3 is Using the QSSA expression for O3* just obtained, we get

14. Measuring rate constants OH + SO2 + M  HOSO2 + M 1. measurements of the OH decay rate for different pressures and SO2 initial concentrations 2. the slope of the decay rate gives the rate constant. Shown here: rate constant versus pressure

15. Reaction rate compilations • JPL report ‚Kinetic data for use in stratospheric modeling‘ (DeMore et al., 1997, 2000) • IUPAC recommendations (Atkinson et al., 1997) [for details on hydrocarbon reactions] These compilations involve laboratory kineticists from around the world and are generally considered the state-of-the-art description of atmospheric chemical reactions. Rate constants for a number of reaction rates are still very uncertain (e.g. HO2+CH3O2 CH3OOH+O2), and there is no guarantee for completeness. Nevertheless, data from these sources form the basis of all chemical models.

16. Photodissociation reactions The energy of a photon absorbed by an atmospheric molecule is transformed into rotational, vibrational, or electronic activation. This can lead to the breaking of a chemical bond, so that the molecule is dissociated. For most molecules, photodissociation requires radiation in the UV wavelength range (< 380 nm).

17. Absorption and quantum yield Absorption by molecules, aerosols, or cloud droplets is governed by Lambert-Beer‘s law: The absorption coefficient (absorption cross section)  depends on the wavelength . Only photons above a certain energy threshold will lead to dissociation of the molecule. This is expressed by the quantum yield (). () is reaction-dependent and also used to distinguish between two reaction channels. Example: (a) NO3 + h  NO2 + O yield 1 (b) NO3 + h  NO + O2 yield 2

18. Spectroscopic methods microwave far IR Raman IR UV absorption Electromagnetic spectrum rotation of heavy molecules rotation of light molecules/vibration of heavy molecules vibration of light molecules

19. Energy, wavelength, wave number, and frequency The wavelength and frequency of light are related through the speed of light (in vacuum):c =  Considered as a particle, the energy of a photon is: E = h = hc/ In spectroscopy, people like to use the wavenumber:  = 1/  For atmospheric chemistry (in the troposphere), wavelengths between 290 nm and 700 nm are relevant. Rotational spectra involve wavelengths into the microwave region (~cm). wavelength wave number frequency energy temperature* 290 nm 34500 cm-1 1.0·1015 s-1 400 kJ mol-1 ¤ 500 nm 20000 cm-1 6·1014 s-1 239 kJ mol-1 6000 K ‡ 20 m 500 cm-1 1.5 ·1013 s-1 6 kJ mol-1 285 K 1 cm 1 cm-1 3 ·1010 s-1 12 J mol-1 ¤ maximum intensity of solar radiation, ‡maximum intensity of terrestrial radiation, * maximum of Planck radiation

20. Radiation in the (lower) atmosphere (~280 K) (6000 K)

21. O2 O3 The solar spectrum

22. Energy levels and molecular absorption spectra For many molecules in the atmosphere, the energy of a molecule (quantum state) can be expressed as: E = Eelectronic + Evibrational + Erotational Absorption of a photon implies a transition of the electronic, vibrational, or rotational state (depending on the photon energy) Time scales: electronic transition: ~10-15 s vibrational and rotational transition: ~10-13 s lifetime of electronically excited state: 10-6 - 10-9 s (fluorescence) typical time between collisions: ~10-9 s

23. Structure of simple molecules

24. Re m2 m1 Rotational transitions Molecules with a permanent dipole moment produce an oscillating electric field when rotating (rigid rotator). The inertia (Drehmoment) of a rigid rotator is given by Quantum mechanics yields discrete energy levels for the rotation:

25. Rotational transitions (2) Molecules are not ideal rigid (starr) rotators, but in fact the atomic distance (Bindungslänge) increases with increasing rotational energy. This is expressed with a correction term: typical energy gap between states 10 cm-1  excited states are generaly populated under atmospheric conditions

26. Rotational transitions (3) Example: The CO molecule:Re = 1.1282 Å, m1=12 a.u., m2 = 16 a.u. Theoretical energy levels: J J(J+1) rot[cm-1] 0 0 0 1 2 3.86 2 6 11.6 ... State transitions: J J+1theory[cm-1] obs.[cm-1] 3 4 83.06 83.03 4 5 103.75 104.10 5 6 124.39 124.30 6 7 144.98 145.03 7 8 165.50 165.51 ...

27. Vibrational modes of di- and triatomic molecules 1 mode 3 modes 3 modes degrees of freedom: 3n-6 (3n-5 for linear molecules)

28. harmonic oscillator Evib = hvib(+½),  = 0, 1, 2, ... allowed transitions:  = 1 anharmonic oscillator Evib = hvib(+½)-hvibxe(+½)2 + ...,  = 0, 1, 2, ... allowed transitions:  = 1, 2, 3, ... Vibrational transitions typical energy gap between states 1000 cm-1  in atmosphere most molecules in ground state

29. P branch (J = -1) R branch (J = +1) P branch R branch 3 J‘ v‘ = 1 2 1 0 3 J‘‘ 2 v‘‘ = 0 1 0 Vibrational-Rotational transitions Vibration and rotation occur simultaneously. For a hypothetical vibrational transition =1, several rotational transitions with J = +1 or J = -1 are possible. In polatomic molecules, J = 0 may also occur. Spectrum of HCl

30. heteroatomic molecule homoatomic molecule a a 1sA 1sA 1sB 1sB E b b Electronic states of molecules The electronic state of a molecule is often described with the LCAO (linear combination of atomic orbitals) approximation. non bound bound

31. Electronic states of molecules (2) A diatomic molecule can be described by the following quantum numbers:  = component of total electronic angular momentum L along internuclear axis allowed values of  (0, 1, 2, 3) correspond to electronic states designated as , , , and , respectively S = spin quantum number (integral or zero for even number of electrons, 1/2 integral for odd number of electrons. 2S+1 is the multiplicity (singlet, doublet, triplet state)  = |  +  |, where  is the spin component along internuclear axis (-S, -S+1, ..., S-1, S) Furthermore, one must specify the symmetry of the wave function: g, u denote the symmetry with respect to reflection through the center of symmetry of the molecule („gerade“, „ungerade“) +, - distinguish two types of  states (symmetry upon reflection of the wave function through a plane passing through the two nuclei)

32. repulsive state triplet „“ ground state symmetry Energy diagram of O2

33. Electronic transitions Quantum mechanical selection rules:  = 0, ±1; S = 0 Hence, transitions between states with different multiplicity are „forbidden“ (but may still occur as weak lines). u  g allowed; u  u, g  g forbidden +  +, -  -, allowed, +  - forbidden Franck-Condon principle: time for electronic transition is much shorter than time for vibration, thus electronic transitions occur „vertically“

34. Electronic transitions (2) Example: „Fourth positive bands“ of CO Transition X1+, ‘‘=0  A1, ‘=0, 1, 2, 3, ... The potential energy curves are only slightly displaced, so that  = 1 gives the strongest absorption

35. Basic radiative transfer The basic radiation equation describes the amount of light (radiance) crossing a (plain) surface from all directions (irradiance): For chemical reactions, the direction of incidence does not matter, therefore one needs to consider the actinic flux instead:

36. jA Rate of photodissociation Putting it all together, the change in number density of a molecule A due to photolysis is given by Typical j-values for midlatitude noontime equinox conditions range from ~1 · 10-5 s-1 for jO(1D) to ~0.2 s-1 for jNO3. The actinic flux under these conditions is about 2·1014 photons cm-2 s-1 at 315-320 nm, and 7·1014 photons cm-2 s-1 at 360-365 nm.

37. O(1D) quantum yield Ozone photolysis O3+h O(3P)+O2, l<800 nm O3+h O(1D)+O2, l<320 nm O(1D) formation is important for the formation of OH, which is the cleansing agent of the atmosphere: O(1D)+H2O  2 OH Only a fraction of the O(1D) radicals react with water vapour, because: O(1D)+M  O(3P) and O(3P)+O2  O3

38. Physical constants and units Konstanten: Lichtgeschwindigkeit in Vakuum c = 2.9979·108 m/s Planck Konstante h = 6.626 ·10-34 J s Boltzmann Konstante k = R/NA = 1.381 ·10-23 J K-1 Einheiten: 1 cal = 4.184 J

39. Bibliographie Compilations of Rate constants: • Finnlayson-Pitts & Pitts, 1986. • Sander, S.P. et al., Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, NASA/JPL Evaluation, JPL Publication 02-25, 2002. Only online: http://jpldataeval.jpl.nasa.gov Other literature: • Engelke, F., Aufbau der Materie, Teubner Studienbücher Chemie, Stuttgart, 1992. • Herzberg, G. (Huber, K.P., and G. Herzberg), Molecular Spectra and molecular structure, Van Nostrand, New York, 1950 (1979).