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

Reaction KineticsReaction Kinetics

SOLAR IRRADIANCE SPECTRASOLAR IRRADIANCE SPECTRA

1 m = 1000 nm = 10-6 m

• Note: 1 W = 1 J s-1

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

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

• 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

• 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

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

• 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

• 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

• 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

• 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

• 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

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+

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

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

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

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

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.

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

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

STERIC REQUIREMENTSSTERIC REQUIREMENTS

• Steric factor (p) accounts for geometric orientation req.

• p < 1

NO + NO3 2NO2

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.)

REACTION-SPECIFIC ENERGY REQUIREMENTSREACTION-SPECIFIC ENERGY REQUIREMENTS

MAXWELL-BOLTZMANN ENERGY DITRIBUTION FUNCTIONMAXWELL-BOLTZMANN ENERGY DITRIBUTION FUNCTION

• Explanation for temp. dependence of collision reactions

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

PhotochemistryPhotochemistry