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Fundamentals of air Pollution – Atmospheric Photochemistry - Part A

Fundamentals of air Pollution – Atmospheric Photochemistry - Part A. Yaacov Mamane Visiting Scientist NCR, Rome Dec 2006 - May 2007 CNR, Monterotondo, Italy. Reaction Kinetics. SOLAR IRRADIANCE SPECTRA. 1  m = 1000 nm = 10 -6 m. Note: 1 W = 1 J s -1. ENERGY TRANSITIONS.

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Fundamentals of air Pollution – Atmospheric Photochemistry - Part A

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  1. Fundamentals of air Pollution – Atmospheric Photochemistry - Part A Yaacov Mamane Visiting Scientist NCR, Rome Dec 2006 - May 2007 CNR, Monterotondo, Italy

  2. Reaction Kinetics

  3. SOLAR IRRADIANCE SPECTRA 1 m = 1000 nm = 10-6 m • Note: 1 W = 1 J s-1

  4. ENERGY TRANSITIONS • Gas molecules absorb radiation by increasing internal energy • Internal energy  electronic, vibrational, & rotational states • Energy requirements • Electronic transitions •  UV (< 0.4 m) • Vibrational transitions •  Near-IR (< 0.7-20 m) • Rotational transitions •  Far-IR (> 20 m) • Photochemical change • Breaking chemical bonds  energy requirements such that • atmospheric photochemical reactions typically occur only • when electronic energy levels are excited

  5. UV ABSORPTION AND PHOTOCHEMISTRY • Stratospheric photochemistry • ~100% absorption of UV<290nm • Electronic transitions of O2 and O3 in the stratosphere • Tropospheric photochemistry • Absorption of UV~290-400 nm

  6. WAVE CHARACTERISTICS OF LIGHT • Light = Ensemble of waves of different wavelengths • Speed of light (c) = 2.998 x 108 m s-1  • Wavelength () • Distance between successive crests or troughs • Frequency () • Number of crests or troughs that pass a point per second • c =  

  7. PARTICLE CHARACTERISTICS OF LIGHT • Light = flux of discrete units (i.e quanta) called photons • Energy per photon = h = hc/  • h = Planck’s constant = 6.6262 x 10-34 J s • Electron-volt (eV) is another commonly used energy unit • 1 eV = 1.6 x 10-19 J • Photochemical change occurs only by absorption of photons • No photochemcial change due to to light scattering and • reflection

  8. SCATTERING AND ABSORPTION OF SOLAR RADIATION Scattering by gases and particles SUN Scattered direct radiation Direct solar radiation ATMOSPHERIC SLAB Scattered reflected radiation Reflected solar radiation EARTH • Actinic flux (I) • Number of photons entering slab per unit area per unit time • from any direction (photons cm-2 s-1)

  9. PRINCIPLES OF PHOTOCHEMISTRY • Molecular energy levels • Higher energy levels of molecules are at discrete • displacements from ground-state energy level • Quantum requirement • Each molecule undergoing photochemical change absorbs • one photon, the energy of which is exactly equal to the • difference in energy between the ground-state energy • level and one of the higher energy levels of the molecule • Consequences of quantum requirement • Absorption of light by a molecule is wavelength dependent • because energy of a photon is wavelength dependent

  10. PHOTOCHEMICAL PROCESSES • Absorption of light leads to excited molecule • AB  AB* • Primary photochemical processes • Ionization: AB*  AB+ + e- • Luminescence: AB*  AB + h • Intermolecular energy transfer: AB* + CD  AB + CD* • Quenching: AB* + M  AB + M • Dissociation: AB*  A + B • Reaction: AB* + E  C + D • We are often interested in dissociation reactions • AB  A + B h h

  11. QUANTUM YIELD • Quantum yield for process • i = (number of excited molecules that proceed along • pathway i)/(number of excited molecules formed) • Quantum yield for product • A = (number of molecules of specis A formed)/(number • of excited molecules formed) • Note • i = 1, where summation is over all possible pathways A = i, where summation is over all pathways that yield A

  12. RATE OF PHOTOCHEMICAL PROCESSES h • AB  A + B • By definition, for an elementary reaction • Rate of reaction = -dnAB/dt = dnA/dt = dnB/dt = knAB • Quantum requirement • Rate of reaction = rate of absorption over all wavelengths • =  (rate of absorption() AB A + B() d, • where the integration is over all wavelengths • Rate of absorption • By definition, rate of absorption() = I() AB() nAB • where, • I() = photon flux of wavelength  • AB() = absorption cross-section of AB at wavelength  • nAB = number density of AB

  13. PHOTOCHEMICAL RATE CONSTANT h • AB  A + B • Rate of reaction = -dnAB/dt = dnA/dt = dnB/dt = knAB • =  I() AB() nAB AB A + B() d • Photochemical rate constant (k) • k =  I() AB() AB A + B() d where intergartion is over • all possible wavelengths • Note that calculation of I() is difficult • I() is a function of altitude  k is a function of altitude • For a purely absorbing atmosphere, • I(,z) = Io() exp{-1/(cos ) [k() nk(z)]dz} • where, Io() is the photon flux of wavelength  at the • top of the atmosphere,  is the solar zenith angle, • the summation is over all possible absorbers k, and • the integration is from z to the top of the atmosphere

  14. CHEMICAL KINETICS • Chemical kinetics • A study of the rate at which chemical reactions take place and the detailed chemical mechanism by which they occur • Rules • Mass balance integrity of atoms is preserved in a chemical reactions  number of atoms of each each element on each side of the reaction must balance • CO + 2O2  CO2 + O3 • Charge conservation  electrons are conserved in chemical reactions  net charge of reactants are equal to net charge of products • HCO3-  CO32- + H+

  15. REACTION RATES • aA + bB  gG + hH • Stoichiometry • Relative number of moles involved  For every a moles of A that react with b moles of B, g moles of G and h moles of H are formed • Net reaction may be composed of many individual reactions set of reactions is called a reaction mechanism • Rate = (-1/a)dnA/dt = (-1/b)dnB/dt = (1/g)dnG/dt = (1/h)dnH/dt • Reaction rate expression • Experimentally, it is often found that reaction rate is proportional to number concentration of reactants • Rate = k nA nB • k, , and  are experimentally determined parameters • k is called specific reaction rate or rate constant

  16. ORDER AND MOLECULARITY OF A REACTION • aA + bB  gG + hH • (-1/a)dnA/dt = (-1/b)dnBdt = (1/g)dnG/dt = (1/h)dnH/dt = k nA nB • Molecularity of reaction • Number of molecules of reactants = a + b • Order of reaction • Sum of powers in rate expression =  +  • Elementary reaction • Reaction that cannot be split into simpler reactions and order of reaction = molecularity of reaction • Note • If reaction is elementary  rate = knAa nBb • But if rate = k nAa nBb  does not necessarily mean reaction is elementary

  17. TYPES OF ELEMENTARY REACTIONS • Unimolecular reactions • A  B + C • -dnA/dt = dnB/dt = dnC/dt = k nA • A  B + B • -dnA/dt = (1/2)dnB/dt = k nA • k is in units of s-1 • Bimolecular reactions • A + B  C + D • -dnA/dt = -dnB/dt = dnC/dt = dnD/dt = k nA nB • A + A  B + C • (-1/2)dnA/dt = dnB/dt = dnC/dt = k nA2 • k is in units of cm3 molecule-1 s-1 • Termolecular reactions • A + B + M  C + M • -dnA/dt = -dnB/dt = dnC/dt = k nA nB nM • A + A + M  B + M • (-1/2)dnA/dt = dnB/dt = k nA2 nM • k is in units of cm6 molecule-2 s-1

  18. INTEGRATED RATE LAWS no n 0 t 1/n 1/no 0 t • First-order loss • -dn/dt = k n • n = no e-kt • Second-order loss • -dn/dt = k n2 • 1/n - 1/no = kt

  19. CHEMICAL KINETICS AND EQUILIBRIUM • aA + bB  gG + hH • Rate of forward elementary reaction = kf nAa nBb • Rate of backward elementary reaction = kr nGg nHh • At equilibribrium • nA = nAe; nB = nBe; nG = nGe; nH = nHe • kf nAea nBeb = kr nGeg nHeh • kf/kr = (nGeg nHeh)/(nAea nBeb) = K (the equil. const.) • Note Net rate of forward reaction = kf nAa nBb - kr nGg nHh kf/kr is always equal to K (nGg nHh)/(nAa nBb) is equal to K (i.e. kf/kr) only at equil.

  20. COLLISION RATE OF MOLECULES • aA + bB  gG + hH • Limiting rate det. by rate at which 2 molecules collide • 2 molecules (say A and B) of radius r collide when they are within a distance 2r • Conceptually similar to molecule A of radius 2r colliding with a molecule of B of radius 0 • Rate of molecular collisions • Molecule has thermal velocity vT (function of T, mol. wt.) • Rate at which volume is swept out by molecule A of radius 2r =  (2r)2 vT • Rate of collision between one molecule of A and all B • =  (2r)2 vT nB • Rate of collision per unit volume between all A and all B • =  (2r)2 vT nB nA

  21. LIMITING RATE FOR BIMOLECULAR REACTIONS • aA + bB  gG + hH • (-1/a)dnA/dt = (-1/b)dnBdt = (1/g)dnG/dt = (1/h)dnH/dt = k nAa nBb • Rate of molecular collisions • Rate of collision per unit volume between all A and all B • =  (2r)2 vT nB nA • = limiting rate of reaction = kmax nAa nBb • Gas-kinetic rate for bimolecular reactions • kmax =  (2r)2 vT • 2r  3 x 10-10 m; vT  500 m s-1 • kmax = 1.4 x 10-10 cm3 molecule-1 s-1 • k lower due to molecular steric and energy requirements • k dependent on temperature

  22. STERIC REQUIREMENTS NO + NO3 2NO2 • Steric factor (p) accounts for geometric orientation req. • p < 1

  23. Ea E reaction pathway ENERGY REQUIREMENTS NO + NO3 2NO2 Ea (reverse rxn.) • Energy barrier to reaction that must be overcome • Usually referred to as activation energy (Ea) • E is the net internal energy change • Note Ea (forward reaction)  Ea (reverse reaction) • E (forward reaction) = -E (reverse reaction)

  24. REACTION-SPECIFIC ENERGY REQUIREMENTS

  25. MAXWELL-BOLTZMANN ENERGY DITRIBUTION FUNCTION • Explanation for temp. dependence of collision reactions

  26. THE ARRHENIUS EXPRESSION • Standard form of expressing k for bimolecular reactions • k = A e-Ea/RT • pre-exponential termexponential term • Pre-exponential term accounts for steric requirements • A = gas-kinetic rate x p • Exponential term accounts for energy requirements • exp. form due to math. form of Maxwell-Boltzman distrib. • Examples of units • k, A - cm3 molecule-1 s-1 • Ea - J mole-1 • R - J mole-1 K-1 • T - K

  27. Photochemistry

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