0. Introduction 0.1 Concept The air / environment (geosphere): Is it a reactor? It s a matter of reactions and transports and mixing!

Transcription

1 0. Introduction 0.1 Concept The air / environment (geosphere): Is it a reactor? It s a matter of reactions and transports and mixing! mixing times: vertically lower few kilometers (boundary layer) 1h-1d, mixing with free troposphere 2-10 days around the globe on the same latitude (zonal transport) within a few weeks from mid latitudes to the pole (meridional transport) within days to weeks, hemispheric mixing 2-6 months Between hemispheres about 1 year troposphere-stratosphere 1-3 years Conceptually / knowledge to understand: (chemical) reactions (meteorological) transports and mixing Tools to understand: 3D transport models model parameters isolated in laboratory experiments significant ingredients identified in the field Idealized situations of atmospheric transport and mixing

2 0.2 Atmospheric pressure and composition Pressure and temperature profiles in the atmosphere Pressure [hpa] Height above sea level [km]

3 Pressure decline with altitude p = -g ρ z ρ = mg/cm, g = 981 cm/s², R = Pa cm³/mol/k z/ p = 8 m/hpa at ground 16 m/hpa in 6km altitude barometric step p(h) = p 0 e -hg/rt ( T/ h = 0) p(h,t) p 0 e -hg/rt Standard atmosphere(us Std 1962) km T[ C] p[hpa] M g [g/mol] N Lu /V[molec/cm³] x x x x x x x x10 12

4 0.3 Units for quantification of atmospheric trace substances Ideal gas law: pv = nrt = mrt/m g Universal gas constant R = 8206 Pa L/(mol K) = J/(mol K) = N a k B Avogadro s number N A = 6.023x10 23 Boltzmann constant k B = 1.38x Pa = N/m² = J/m³ J/K Molar mass M g air 28.8 g/mol Molar volume at T 0 =273 K and p 0 = Pa: V = L/mol Concentration c i = m i /V [µg/m³] (for gases: = density) Mass mixing ratio µ m i = c i /c [, %, ppmm, ppbm] Partial pressure p i = n i RT/V i [Pa] Volume mixing ratio µ V i = p i /p = V i /V [, %, ppmv, ppbv] Number density N i /V = n i N A /V = p i N A /RT [molec/cm³] Avogadro s number N A = 6.022x10 23 molec/mol More details: Schwartz & Warneck (1995): Units for use in atmospheric chemistry, Pure Appl. Chem. 67,

5 TROPOSPHERE - COMPOSITION (sum) _1!

6 1 Reaction types, kinetics 1.1 Reaction rate coefficient k (dt.: Reaktionsgeschwindigkeitskoeffizient) Temperature dependence: -dc i /dt = k T c i k T = A(T) e [ E/(RT)] Universal gas constant R = k B N A = 1.38x10-23 J/K x 6.023x10 23 /mol Providing the energy is sufficiently large, the temperature dependence of A is unimportant, and k T follows the Arrhenius expression: k T = A e [E a /(RT)] with activation energy E a Frequently used, too: van t Hoff expression: k T = B e [- E a /R (1/T 1/T ref )], The two expressions are equal via: A = B e [E a /(RT ref )]

7 Rate coefficient from gas kinetic theory = effective reactions per unit of time = = collision frequency x likelyhood of reaction per collision 1) Molecules need to collide ( 10 9 /s at 10 5 Pa). They are close enough to collide during ( )x 10 9 /s Collision frequency

8 Speed, collisions in absolute terms: from Maxwell-Boltzmann distribution function of molecular velocities (gas kinetic theory): dn/n = c (m <v i>² / 2kT) ; with c = (m / 2πkT) 0.5 <v i > = mean absolute velocity of molecules corresponding mean free path λ with regard to collisions λ i = 1 / [(N A /V)( 2 πσ i2 )], N A /V = 6.022x10 23 / = 2.46 x molec/m 3 N 2 : <v> = 0.51 m/s = 1840 km/h, λ = 65 nm CO 2 : <v> = 0.41 m/s = 1490 km/h, λ = 44 nm

9 2) Extra energy is needed to overcome the transition state As molecules approach each other they have to overcome an energy barrier because of 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. Reaction enthalpy H r.

10 Theoretical maximum at 1000 hpa, 293 K (for r i, r j = 0.2 nm, E 0 = 0 and no steric hindrance): k 2x10-10 cm³/molec/s Likelyhood: collision cross section, σ ij In the transition state, usually the energy provided from bond formation is less than the energy consumption from bond breaking. The collision cross section takes into account that a minimum amount of energy is needed. It is not necessarily provided with every orientation of the molecules during approach (steric factor).,

11 1.2 Homogeneous gas-phase reactions Reactions can be unimolecular, bi- or termolecular. The rate law of a reaction of the general form Is defined as aa + bb cc + dd Rate (dt.: Rate) = -dc A /dt/a = -dc B /dt/b = dc C /dt/c = dc D /dt/d example: 2 NO + O 2 2 NO 2 Rate = -dc NO /dt/2 = -dc O2 /dt = dc NO2 /dt/2

12 Second order Usually: bimolecular A + B C+ D A + B C ; A, B, C, D molecules or radicals example: O + O 2 O 3 NO + O 3 NO 2 + O 2 dc C /dt = -dc A /dt = -dc B /dt = k (2) c A1 c 1 B Reaction rate: second order (1+1=2) Reaction rate coefficient (denoting the order): k (2) The reaction order is given by the sum of the exponentials, n+m+..., of the concentration terms in the rate law of the form -dc A /dt = k c An c B m (n = zero or integer or fraction*) It is determined empirically. * overall reactions only

13 k T Example NO + O 3 NO 2 + O 2 k = A e [-(E a /R)T] Arrhenius expression, preexponential factor A, activation energy E a k(t -1 ) slope m = E a /R, intercept ln A, E a /R > 0 faster at higher T A = 2x10-12 cm³/molec/s E/R = K k 298 K = 1.8 x10-14 cm³/molec/s Steil, Crutzen, et al., 1998 k 230 K = 0.45x10-14 cm³/molec/s

14 2. Exception: First order (but not unimolecular): A + M C + D + M or if c B >> c A A + B + M C + D + M Here, M stands for any molecule or atom (i.e. N 2, O 2,...), not transformed but required to absorb excess energy, e.g. of an activated intermediate state: A + B = AB* +M C + D A +M C + D Example: thermic dissociation HOONO 2 HO 2 + NO 2 Reaction rate dc C /dt = -dc A /dt = k (1) c 1 A k (1) = k (2) c M1 (c M1 constant) Steil et al., 1998

15 Reaction orders A + B C + D is 2 nd order or in case dc B /dt 0 - pseudo-1 st order A + B + M C + D + M is 2 nd order or in case dc B /dt 0 - pseudo-1st order or if p << 1000 hpa - between 2 nd and 3 rd order The unit of a homogeneous gas-phase rate is [molec/cm 3 /s]. A 1 st or pseudo-1 st order rate law reads: -dc A /dt = dc C /dt = k (1) c C, with k (1) [1/s]. A 2 nd order rate law reads: -dc A /dt = dc C /dt = k (2) c C c D, with k (2) [cm 3 /molec/s]. A 3 rd order rate law reads e.g.: -dc A /dt = k (3) c C 2 c D, with k (3) [cm 6 /molec 2 /s].

16 3. between 2 nd and 3 rd order: In the range of pressures and temperatures in the upper troposphere and stratosphere (c M small) many reactions are in the region between 2 nd and 3 rd order reactions: k 0, k = low, high pressure limiting rate constant (Troe, 1979) F C = broadening factor of falloff curve between 2 nd and 3 rd order in the range of atmospheric pressures NO 2 + HO 2 + M HO 2 NO 2 + M K 0 = k 0 (T)c M, n = 3.2 K = k (T), m = 1.4 k 288 K/1000 hpa = 1.9 x10-12 cm³/molec/s k 288 K/500 hpa = 1.5 x10-12 cm³/molec/s k 230 K/500 hpa = 2.3 x10-12 cm³/molec/s k 230 K/1000 hpa = 3.0 x10-12 cm³/molec/s

17 1.3 Combinations of thermic reactions- Quasi steady state approximation Second order Usually: bimolecular A + B C+ D A + B C A, B, C, D molecules or radicals example: O + O 2 O 3 NO + O 3 NO 2 + O 2 Reaction rate: second order (1+1=2) dc C /dt = -dc A /dt = -dc B /dt = k c A1 c B 1 Reaction rate coefficient: k (2) k = A exp [-(E a /R)T] Arrhenius expression, preexponential factor A, activation energy E a k(t -1 ) slope E a /R, intercept ln A, E a /R > 0 faster at higher T

18 1.3 Combinations of thermic reactions- Quasi steady state approximation Second order Usually: bimolecular A + B C+ D A + B C A, B, C, D molecules or radicals example: O + O 2 O 3 NO + O 3 NO 2 + O 2 Reaction rate: second order (1+1=2) Very frequent: (1) A + B C* (-1) C* A + B (2) C* + M C Intermediate C*: dc C* /dt = k 1 c A c B k -1 c C* -k 2 c C* c M Lifetime of C* short dc C* /dt = 0 Hence: k 1 c A c B = k -1 c C* + k 2 c C* c M k dc C /dt = -dc A /dt = -dc B /dt = k c 1 c A1 c A c 1 B = c C* (k -1 +k 2 c M ) c B C* = k 1 c A c B /(k -1 +k 2 c M ) Reaction rate coefficient: k (2) Example k = A exp [-(E a /R)T] (1) O + O Arrhenius expression, preexponential factor A, activation 2 =O 3 * energy E (2) O a 3 * + M O 3 k(t -1 ) slope E a /R, intercept ln A, E a /R > 0 faster at higher T

19 Example (1) O + O 2 =O 3 * (2) O 3 * + M O 3 c O3* = k 1 c O c O2 /(k -1 + k 2 c M ) dc O3 /dt = k 2 c O3* c M dc O3 /dt = k 1 k 2 c O c O2 c M /(k -1 + k 2 c M )= [k 1 k 2 c M /(k -1 + k 2 c M )] c O c O2 High pressure limit: k -1 0 k = k 1 k Low pressure limit: c M 0 k 0 = k 1 k 2 / k -1

20 Reaction rate compilations Compilations are considered the state-of-the-art description of atmospheric chemistry, because complete knowledge is summarized and assessed, and laboratory kineticists from around the world are involved However, there is no guarantee for completeness, and some rate constants are very uncertain, but uncertainty is quantified Chemical kinetics and photochemical data for use in stratospheric modeling Eval. No. 12 (JPL-Publ-97-4; NAS ; NASA CR ), 1997 (updated 2005, Hydrocarbon reactions: Atkinson et al., Atmos. Chem. Phys. 6 (2006)

21 Chemical kinetics and photochemical data for use in stratospheric modeling Eval. No. 12 (JPL-Publ-97-4; NAS ; NASA CR ), 1997 (updated 2005) k = A exp (-E a / RT) Arrhenius expression

22 1.4 Photochemical reactions Radiation absorption in the atmosphere Gaseous molecules absorb ultraviolet, visible and infrared light: O 3 Consequences: photophysical and photochemical molecular processes change of spectrum:

23 Specific because of vibrational-rotational and electronic transitions: A series of vibrational-rotational states are populated (temperature dependent, Boltzmann) within electronic states. Vibrational-rotational (P, Q, R branches of change of J) and electronic transitions follow quantum rules (selection rules, allowed or not allowed). These correspond to characteristic spectroscopic patterns. Therefore, emission and absorption spectroscopy allows for unambiguous identification of molecules.

24 Electronic excitation: A B + C The energy barrier will be smaller and the distance between atoms will be larger for the excited molecule. B C B + C* A* B + C A

25 Fates of electronically excited molecules: Photophysical primary processes: emission (fluorescence, phosphorescence), nonradiative energy transition into heat Photochemical primary processes: dissociation, isomerization, re-arrangement, reaction Example for photophysical process: A* + B A + B*: SO 2 ( 3 B 1 ) + O 2 ( 3 Σ g ) SO 2 ( 1 A 1 ) + O 2 ( 1 Σ g ) Example for photochemical process: NO 2 (X 2 A) + hν (290 < λ < 430 nm) NO (X 2 Π) + O ( 3 P) Def.: Efficiency of a primary photochemical process i is given by ist quantum yield φ i := number of excited molecules by process i divided by total number of photons absorbed. The sum of the φ i of all the photochemical primary processes = 1.

26 Photodissociations Unimolecular A + hν B + C A, B, C, D molecules or radicals example: O 3 + hν O 2 + O ( 3 P) Reaction rate coefficient j (photolysis rate): dc C /dt = -dc A /dt = j c A Ground state, A /excitation state, A*: A + hν A* Example: O + hν O* i.e. O( 3 P) + hν O( 1 D)

27 Energy ranges, correspondence between energy and wavelength λ = c/ν with frequency ν E = hc/λ = hcω Planck relationship (wavelength λ, wavenumber ω, Planck s constant h = x Js) Commonly used energy units:

28 Energy ranges, correspondence between energy and wavelength λ= c/ν E = hc/λ = hcω Planck relationship (wavelength λ, wavenumber ω, Planck s constant h = x Js)

29 The rate of photochemical reactions Absorption ln(i 0 /I) = σnd I/I 0 = e (-σnd) Beer-Lambert law absorption cross section σ (cm², default: base e) molecule concentration N (cm -3 ), depth of absorptive layer d (cm) optical depth OD = σnd Caution: Most measurements are made to the base 10 (log(i 0 /I) = σ 10 Nd) x to reach base e

30 The photolysis rate The photolysis rate, j (s -1 ), is given by: j = λ φ(λ) σ(λ) L(λ) dλ quantum yield φ(λ) ( ), absorption cross section σ (cm²), actinic flux, L(λ) (cm -2 s -1 ) L is the total intensity of effective light (direct + scattered + reflected, spherically integrated).

31 The photolysis rate * L(λ) is a function of the solar zenith angle, cloudiness, aerosol concentration, and surface albedo*.

32 The photolysis rate L is measured using a (2π) radiometer or by measuring the photolytic decay (so-called chemical actinometry). Its value can be estimated via tabulated values of φ and σ for intervals of λ and estimates of L(λ) for given conditions. (Calvert, 1985)

33 Example j O3 : Quantum yield φ i (λ) for i = O 3 + hν O ( 1 D) + O 2 ( 3 Σ g- ) φ O3 O( 1 D) ( nm) 0.2 Data src.: Finlayson-Pitts & Pitts, 1998

34 Example j O3 : Absorption cross section σ(λ,t) of O 3 Example: σ O3 ( nm) 60 x cm²/molecule for T = 298 K Data src.: Finlayson-Pitts & Pitts, 1998

35 Radiation absorption in the atmosphere Actinic flux L(λ) - Example: For z = 15 km and solar zenith angle of 40 : L( nm)=( )x10 14v cm -2 s -1 Order of magnitude estimate of j O3 O( 1 D) for a selected wavelength interval: j O3 O( 1 D) ( nm) 0.2 x 60 x x 12 x s s -1