ATM 507 Lecture 4. Text reading Chapters 3 and 4 Today s topics Chemistry, Radiation and Photochemistry review. Problem Set 1: due Sept.

Transcription

1 ATM 507 Lecture 4 Text reading Chapters 3 and 4 Today s topics Chemistry, Radiation and Photochemistry review Problem Set 1: due Sept. 11

2 Temperature Dependence of Rate Constants Reaction rates change with temperature for two reasons: - encounter frequencies (EF) increase with temperature (T) at constant density - a relatively slow increase ( EF ~ T ½ ) - the probability of high energy encounters increase with T Probability (HEE) varies rapidly as ~ e -(Constant/T) This T dep term generally dominates ( the functional form is derivable from thermodynamics) In 1889 Arrhenius derived the following empirical expression based on experimental rate measurements: k(t) = A e - Ea/RT where: A (the steric or Arrhenius factor) is related to the encounter frequency and geometry of the encounter. E a (the activation energy or energy barrier) is related to the energy needed in simultaneous bond breaking and formation along the reaction coordinate. R is the gas constant for these calculations use the following units R = J mole -1 K -1 = calorie mole -1 K -1

3 Maxwell-Boltzmann distribution of molecular speed (i.e., kinetic energy)

4 Reaction Diagram (Potential Energy Surface along the reaction coordinate) E A

5 More on Temperature Dependence Typical values for E a : Radical-molecule reaction: E a 2-5 kcal/mole Radical- radical reaction: E a 0 kcal/mole (Recall that H rxn values were generally larger than that.) How much does a 2 kcal/mole barrier affect the rate constant? Set E a = 2000 cal/mole; R 2 cal mole -1 K -1 ; T = 300 K. Exp(-E a /RT) = exp (-2000/600) = (~ 30-fold decrease in rate constant) Small barrier (2 kcal/mole) has a large influence Most reactions (abstractions - driven by collision energy) have positive T-dependence: T increases, k increases Some reactions (associations driven by complex formation; things stick together better at lower temps) have negative T-dependence: T decreases, k increases

6 Experimental Techniques for Determination of Rate Constants Plasma discharge flow tube reactor Species A is a radical, formed in a plasma discharge Key concept for this type of experiment is the plug flow approximation, which allows reaction time to be measured by distance along the tube, i.e., t = d/v.

7 Typical Experimental Kinetics Results The termolecular reaction of OH + SO 2 + M HOSO 2 + M as a function of M (i.e., pressure of Argon) Each point in this plot is a measured decay of OH for a fixed [SO 2 ]. Each line is a rate constant determination at a given pressure from measured decays as [SO 2 ] is changed. This plot is the effective second order rate constants (slopes of lines in left hand plot) versus the total pressure. Notice linear pressure dependence at low p, fall off region, and high pressure limit.

8 Indoor Smog Chambers

9 Outdoor Smog Chambers

10 UNC Outdoor Smog Chamber

11 EUPHORE Chamber The European Photoreactor The construction completed in September Each simulation chamber consists of a half-spherical Teflon bag, volume ~ 204 m 3. The chambers are made of a fluorineethene-propene (FEP -DuPont) foil with a thickness of mm. The foil has a transmission of more than 80 % in the wavelength range between 280 and 640 nm.

12 Typical Smog Chamber Results

13 Atmospheric Radiation and Photochemistry Solar energy (radiation) drives the chemistry of the earth s atmosphere. This photochemistry begins with the absorption of a photon - usually a UV (ultraviolet) or visible photon. A + h A* ( A* = A in an electronically excited quantum state) At least four processes are then possible 1. A* B + C dissociation 2. A* + B C + D direct reaction 3. A* A + h fluorescence 4. A* + M A + M collisional deactivation Dissociation is the most important of these processes to atmospheric chemistry, but notice that not every absorbed photon leads to dissociation. (Just like not every collision leads to reaction.)

14 Relation between wavelength and bond (dissociation) energy Does the absorbed photon carry enough energy to cause photolysis of the molecule? (and what wavelength of light is the threshold for dissociation?) Molecule Bond Energy in kj/mole O 3 ~ 25 kcal/mole ~ 104 kj/mole NO 2 ~ 72 kcal/mole ~ 301 kj/mole O 2 ~ 119 kcal/mole ~ 498 kcal/mole Planck Relationship: E = h = hc/λ

15 Planck Constant h = Planck constant 6.63x10-27 erg sec photon -1 (quanta -1 ) 6.63x10-34 J sec photon x10-37 kcal sec photon x10-14 kcal sec mole x10-13 kj sec mole -1 c = speed of light = 3x10 10 cm s -1 = 3x10 8 m s -1 = 3x10 17 nm s -1 Wavelength: 1 cm = 10 4 µm = 10 7 nm = 10 8 Å Power: 1 Watt = 1 J s -1 Energy: 1 calorie = J

16 Dissociation Wavelength Use the energy to wavelength relation, and the bond energies to calculate the wavelength at which dissociation is energetically possible. Quite often one must go to much shorter (more energetic) wavelengths before dissociation actually occurs. E = hc/λ λ DISS hc/e BOND

17 Use h = 3.99x10-13 kj sec mole -1 Or hc = 1.197x10 5 kj nm mole -1 λ DISS (O 3 ) = hc/e BOND = 1.197x10 5 /104 = 1163 nm λ DISS (NO 2 ) = hc/e BOND = 398 nm λ DISS (O 2 ) = hc/e BOND = 240 nm Mole cule BE (kj/mole) Wavelength for which dissociation is possible Wavelength range for maximum dissociation O nm ~600 nm NO nm ~ nm O nm ~240 nm

18 Solar Radiation and Its Absorption How do the solar photons get to the molecules? 1. Direct from sun 2. Diffuse (scattered off other molecules, clusters, aerosols, etc.) 3. Reflected from ground or cloud (albedo) Ultimate source in all cases is the sun. TOA = Top of Atmosphere: Benchmark point for Solar spectral irradiance SL = Sea Level: Solar Spectral irradiance after atmospheric influences

19 Solar Radiation at Top of Atmosphere (yellow shading)

20 This altitude is a 1/e depth the altitude at which I/I 0 = 1/e.

21 Solar Radiation Note that the solar spectrum is often approximated by a 6000 (or 5250) K black body. (solar energy at the TOA) (energy absorbed in the atmosphere) = (solar energy at SL) Each absorption event involves one photon. Not all photons have the same energy. Consider (quantify) solar input in two ways: 1. Energy units (e.g. Watts m -2 ) energy time -1 area Quanta photons time -1 area -1

22 Energy peaks at nm. # of photons peaks at a slightly longer wavelength of ~ 600 nm X-ray and UV photons have the highest energy and strongest absorptions they are most effective at dissociation (and ionization in the case of x-rays). Most UV photons are absorbed in the upper atmosphere.

23 Describing Actinic Flux and other Fundamental Quantities Associated with Solar Radiation Solar Zenith Angle (SZA) θ is the angle of incident solar radiation measured from the vertical θ = 0 - sun is directly overhead θ = 90 - sunrise or sunset General formula for calculating the solar zenith angle cos sin sin d cos cos d cos h Vertical θ l = latitude, d = declination angle (day of year), and h = hour angle (at local noon h = 0)

24 Zenith Angle as a Function of Latitude and Season

25 Air mass m Intuitively, the air mass factor is a correction factor which takes into account the additional air a ray of light passes through when it has a SZA other than 0. Formally, the air mass is the ratio of the length of the atmospheric path at θ = SZA to the vertical path (SZA = 0 ). V θ L L / V m 1/ cos sec For θ < 60, this simple geometric relation is fine. At larger angles (and especially near 90 ), corrections for refraction and the curvature of the atmosphere must be included.

26 Quantities which express Incident Radiation Spherical co-ordinate system R = radial distance θ = SZA (zenith angle or elevation) φ = angle of rotation about θ = 0 (azimuth) Solid angle = Ω = A/R 2 ; dω = sinθ dθ dφ; units are steradians Solar Radiance L(λ, θ, φ) is the amount of light passing across a surface per unit area per unit solid angle (of the emitter) per unit time per unit wavelength interval. Units of L: (Energy) Joule m -2 s -1 st -1 nm -1 (Quanta) photons cm -2 s -1 st -1 nm -1 (we don t use this quantity)

27 Irradiance E(λ) also called the spectral irradiance, net flux, or energy flux is the amount of radiative energy impinging on a surface E(λ) = = L(λ, θ, φ) cosθ sinθ dθ dφ Actinic Flux F(λ) is the flux of photons appropriate for photochemical calculations. (includes scattered light, which means there is no normalizing cosθ term) F(λ) = L(λ, θ, φ) d Ω = L(λ, θ, φ) sinθ dθ dφ The actinic flux is the quantity we are most interested in. Typically, one uses tables of fluxes.

28 Ground Level Actinic Fluxes at 40 N Lat.

29 Transmission of radiation through the atmosphere Transmitted radiation I t = I o e -tm m = air mass Radiation is absorbed and scattered by gases and particles t is the total extinction of radiation (dimensionless) t = t (λ) = t sg + t ag + t sp + t ap s = scattering a = absorption g = gases p = particles Transmissivity - T (λ) = I t (λ)/i 0 (λ) = e -tm

30 Individual Radiation-Affecting Processes Scattering by gases Rayleigh or molecular scattering t sg ~ λ -4 t sg (1.044x10-5 )(n 0λ - 1) 2 / λ 4 n 0λ = index of refraction of air at temperature and pressure of interest Absorption by gases consider O 3 as an example t ag = σ n l = σ N col σ = σ(λ) = absorption cross-section N col = column density = # molecules cm -2 I/I 0 = exp (-σn col m) = exp(- σm [O 3 ]dz) O 3 is the dominant absorber in UVA and UVB regions Scattering and absorption by particles Aerosol extinction = t ap + t sp These quantities depend on size, wavelength, and composition

31 Light and the Laws of Photochemistry First law: Only light which is absorbed by a molecule can be effective in producing photochemical changes in a molecule. Quantum yield of the reaction: A + h A* B + C number of molecules of A* that undergo the processproducingb & C number of photons absorbed bya 0 Φ i 1 for each process i Second Law: The absorption of light by a molecule is a one quantum process for low to moderate light intensities (e.g quanta s -1 ) so that the sum of the primary process quantum yields i must be unity.

32 Photochemical Reaction Pathways (review) A + h A* Absorption Followed by 1. A* B + C dissociation 2. A* + B C + D direct reaction 3. A* A + h fluorescence 4. A* + M A + M collisional deactivation or quenching 5. (A* A + + e - ionization)

33 Beer-Lambert Law (for the absorption of light) Used to describe the absorption of light passing through a moderately weak absorber. I(λ) = I 0 (λ) exp{-(abs. coeff.)(conc.)(path length)} Formulation from Chemistry textbooks log 10 (I 0 /I) = ε C l I 0 = incident monochromatic (or narrow) intensity I = transmitted intensity ε = molar extinction coefficient (base 10) = ε(λ, T, C) C = concentration (moles li -1 or M) l = absorption pathlength in cm

34 Beer-Lambert Law (cont.) Gas Phase Absorption (pressure units) I = I 0 exp (-k p l ) or ln(i 0 /I) = k p l k = absorption coefficient in atm -1 cm -1 p = absorber partial pressure in atm Gas Phase Absorption (absolute units) I = I 0 exp (-σ N l ) or ln(i 0 /I) = σ N l σ = absorption cross-section in cm 2 molecule -1 N = absorber density in molecules cm -3 For a mixture of gases I = I 0 exp [-(σ 1 N 1 + σ 2 N 2 + σ 3 N 3 + ) l ]