Fundamentals of air Pollution – Atmospheric Photochemistry - Part A
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Fundamentals of air Fundamentals of air Pollution – Atmospheric Pollution – Atmospheric Photochemistry - Part APhotochemistry - Part A
Yaacov MamaneYaacov Mamane
Visiting ScientistVisiting ScientistNCR, RomeNCR, Rome
Dec 2006 - May 2007Dec 2006 - May 2007CNR, Monterotondo, ItalyCNR, Monterotondo, Italy
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Reaction KineticsReaction Kinetics
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SOLAR IRRADIANCE SPECTRASOLAR IRRADIANCE SPECTRA
1 m = 1000 nm = 10-6 m
• Note: 1 W = 1 J s-1
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ENERGY TRANSITIONSENERGY 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
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UV ABSORPTION AND PHOTOCHEMISTRYUV 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
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• Light = Ensemble of waves of different wavelengths Speed of light (c) = 2.998 x 108 m s-1
-1.5
-1
-0.5
0
0.5
1
1.5
• Wavelength () Distance between successive crests or troughs• Frequency () Number of crests or troughs that pass a point per second• c =
WAVE CHARACTERISTICS OF LIGHTWAVE CHARACTERISTICS OF LIGHT
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• 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
PARTICLE CHARACTERISTICS OF LIGHTPARTICLE CHARACTERISTICS OF LIGHT
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SUN
EARTH
Direct solar radiation
Scattering by gases and particles
Scattered direct radiation
Scattered reflected radiation
Reflectedsolar radiation
ATMOSPHERIC SLAB
• Actinic flux (I) Number of photons entering slab per unit area per unit time from any direction (photons cm-2 s-1)
SCATTERING AND ABSORPTION OF SOLAR RADIATIONSCATTERING AND ABSORPTION OF SOLAR RADIATION
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• 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
PRINCIPLES OF PHOTOCHEMISTRYPRINCIPLES OF PHOTOCHEMISTRY
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• 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
PHOTOCHEMICAL PROCESSESPHOTOCHEMICAL PROCESSES
h
h
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• 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
QUANTUM YIELDQUANTUM YIELD
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• 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
RATE OF PHOTOCHEMICAL PROCESSESRATE OF PHOTOCHEMICAL PROCESSES
h
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• 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
PHOTOCHEMICAL RATE CONSTANTPHOTOCHEMICAL RATE CONSTANT
h
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CHEMICAL KINETICSCHEMICAL KINETICS
• Chemical kineticsA study of the rate at which chemical reactions take place and the detailed chemical mechanism by which they occur
• RulesMass 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- CO3
2- + H+
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REACTION RATESREACTION 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 formedNet 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 expressionExperimentally, it is often found that reaction rate is proportional to number concentration of reactants
Rate = k nA nB
k, , and are experimentally determined parametersk is called specific reaction rate or rate constant
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ORDER AND MOLECULARITY OF A REACTIONORDER 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 reactionNumber of molecules of reactants = a + b
• Order of reactionSum of powers in rate expression = +
• Elementary reactionReaction that cannot be split into simpler reactions and order of reaction = molecularity of reaction
• Note
If reaction is elementary rate = knAa nB
b
But if rate = k nAa nB
b does not necessarily mean
reaction is elementary
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TYPES OF ELEMENTARY REACTIONSTYPES OF ELEMENTARY REACTIONS
• Unimolecular reactionsA 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 reactionsA + 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 nA
2
k is in units of cm3 molecule-1 s-1
• Termolecular reactionsA + 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 nA
2 nM
k is in units of cm6 molecule-2 s-1
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1/n
t0
1/no
n
t
no
0
INTEGRATED RATE LAWSINTEGRATED RATE LAWS
• First-order loss-dn/dt = k nn = no e-kt
• Second-order loss-dn/dt = k n2
1/n - 1/no = kt
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CHEMICAL KINETICS AND EQUILIBRIUMCHEMICAL KINETICS AND EQUILIBRIUM
aA + bB gG + hH Rate of forward elementary reaction = kf nA
a nBb
Rate of backward elementary reaction = kr nGg
nHh
• At equilibribriumnA = nAe; nB = nBe; nG = nGe; nH = nHe
kf nAea nBe
b = kr nGeg nHe
h
kf/kr = (nGeg nHe
h)/(nAea nBe
b) = K (the equil. const.)
• Note
Net rate of forward reaction = kf nAa nB
b - kr nGg nH
h
kf/kr is always equal to K
(nGg nH
h)/(nAa nB
b) is equal to K (i.e. kf/kr) only at
equil.
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COLLISION RATE OF MOLECULESCOLLISION RATE OF MOLECULES
aA + bB gG + hH
• Limiting rate det. by rate at which 2 molecules collide2 molecules (say A and B) of radius r collide when they are within a distance 2rConceptually similar to molecule A of radius 2r colliding with a molecule of B of radius 0
• Rate of molecular collisionsMolecule 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
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LIMITING RATE FOR BIMOLECULAR REACTIONSLIMITING RATE FOR BIMOLECULAR REACTIONS
aA + bB gG + hH(-1/a)dnA/dt = (-1/b)dnBdt = (1/g)dnG/dt = (1/h)dnH/dt = k nA
a nBb
• Rate of molecular collisionsRate of collision per unit volume between all A and all B = (2r)2 vT nB nA
= limiting rate of reaction = kmax nAa nB
b
• Gas-kinetic rate for bimolecular reactionskmax = (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
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STERIC REQUIREMENTSSTERIC REQUIREMENTS
• Steric factor (p) accounts for geometric orientation req.
• p < 1
NO + NO3 2NO2
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ENERGY REQUIREMENTSENERGY REQUIREMENTS
• Energy barrier to reaction that must be overcomeUsually 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)
NO + NO3 2NO2
reaction pathway
Ea
E
Ea (reverse rxn.)
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REACTION-SPECIFIC ENERGY REQUIREMENTSREACTION-SPECIFIC ENERGY REQUIREMENTS
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MAXWELL-BOLTZMANN ENERGY DITRIBUTION FUNCTIONMAXWELL-BOLTZMANN ENERGY DITRIBUTION FUNCTION
• Explanation for temp. dependence of collision reactions
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THE ARRHENIUS EXPRESSIONTHE ARRHENIUS EXPRESSION
• Standard form of expressing k for bimolecular reactions
k = A e-Ea/RT
pre-exponential term exponential 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
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PhotochemistryPhotochemistry
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