Transcript Slide 1

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
• 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
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
WAVE CHARACTERISTICS OF LIGHT
• 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 =  
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
SCATTERING AND ABSORPTION OF SOLAR RADIATION
Scattering by
gases and particles
Scattered
direct radiation
SUN
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)
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
PHOTOCHEMICAL PROCESSES
• Absorption of light leads to excited molecule
h
AB  AB*
• Primary photochemical processes
Ionization: AB*  AB+ + eLuminescence: 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
h
AB  A + B
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
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
PHOTOCHEMICAL RATE CONSTANT
• AB h
 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
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+
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
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
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
INTEGRATED RATE LAWS
no
• First-order loss
-dn/dt = k n
n = no e-kt
• Second-order loss
-dn/dt = k n2
1/n - 1/no = kt
n
0
t
1/no
0
t
1/n
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.
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
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
STERIC REQUIREMENTS
NO + NO3  2NO2
• Steric factor (p) accounts for geometric orientation req.
• p < 1
ENERGY REQUIREMENTS
NO + NO3  2NO2
Ea
Ea (reverse rxn.)
E
reaction pathway
• 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)
REACTION-SPECIFIC ENERGY REQUIREMENTS
MAXWELL-BOLTZMANN ENERGY DITRIBUTION FUNCTION
• Explanation for temp. dependence of collision reactions
THE 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
Photochemistry