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

Reaction Kinetics

SOLAR IRRADIANCE SPECTRA 1  m = 1000 nm = 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 (<  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 O 2 and O 3 in the stratosphere Tropospheric photochemistry Absorption of UV~ nm

Light = Ensemble of waves of different wavelengths Speed of light (c) = x 10 8 m s -1 Wavelength ( ) Distance between successive crests or troughs Frequency ( ) Number of crests or troughs that pass a point per second c = WAVE CHARACTERISTICS OF LIGHT

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

SUN EARTH Direct solar radiation Scattering by gases and particles Scattered direct radiation Scattered reflected radiation Reflected solar 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 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 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 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 YIELD

AB  A + B By definition, for an elementary reaction Rate of reaction = -dn AB /dt = dn A /dt = dn B /dt = kn AB 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 ( ) n AB where, I( ) = photon flux of wavelength  AB ( ) = absorption cross-section of AB at wavelength n AB = number density of AB RATE OF PHOTOCHEMICAL PROCESSES h

AB  A + B Rate of reaction = -dn AB /dt = dn A /dt = dn B /dt = kn AB =  I( )  AB ( ) n AB  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) = I o ( ) exp{-1/(cos  )  [  k ( ) n k (z)]dz} where, I o ( ) 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 CONSTANT h

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 + 2O 2  CO 2 + O 3 Charge conservation  electrons are conserved in chemical reactions  net charge of reactants are equal to net charge of products HCO 3 -  CO 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)dn A /dt = (-1/b)dn B /dt = (1/g)dn G /dt = (1/h)dn H /dt Reaction rate expression Experimentally, it is often found that reaction rate is proportional to number concentration of reactants Rate = k n A  n B  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)dn A /dt = (-1/b)dn B dt = (1/g)dn G /dt = (1/h)dn H /dt = k n A  n B  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 = kn A a n B b But if rate = k n A a n B b  does not necessarily mean reaction is elementary

TYPES OF ELEMENTARY REACTIONS Unimolecular reactions A  B + C -dn A /dt = dn B /dt = dn C /dt = k n A A  B + B -dn A /dt = (1/2)dn B /dt = k n A k is in units of s -1 Bimolecular reactions A + B  C + D -dn A /dt = -dn B /dt = dn C /dt = dn D /dt = k n A n B A + A  B + C (-1/2)dn A /dt = dn B /dt = dn C /dt = k n A 2 k is in units of cm 3 molecule -1 s -1 Termolecular reactions A + B + M  C + M -dn A /dt = -dn B /dt = dn C /dt = k n A n B n M A + A + M  B + M (-1/2)dn A /dt = dn B /dt = k n A 2 n M k is in units of cm 6 molecule -2 s -1

1/n t0 1/n o n t nono 0 INTEGRATED RATE LAWS First-order loss -dn/dt = k n n = n o e -kt Second-order loss -dn/dt = k n 2 1/n - 1/n o = kt

CHEMICAL KINETICS AND EQUILIBRIUM aA + bB  gG + hH Rate of forward elementary reaction = k f n A a n B b Rate of backward elementary reaction = k r n G g n H h At equilibribrium n A = n Ae ; n B = n Be ; n G = n Ge ; n H = n He k f n Ae a n Be b = k r n Ge g n He h k f /k r = (n Ge g n He h )/(n Ae a n Be b ) = K (the equil. const.) Note Net rate of forward reaction = k f n A a n B b - k r n G g n H h k f /k r is always equal to K (n G g n H h )/(n A a n B b ) is equal to K (i.e. k f /k r ) 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 v T (function of T, mol. wt.) Rate at which volume is swept out by molecule A of radius 2r =  (2r) 2 v T Rate of collision between one molecule of A and all B =  (2r) 2 v T n B Rate of collision per unit volume between all A and all B =  (2r) 2 v T n B n A

LIMITING RATE FOR BIMOLECULAR REACTIONS aA + bB  gG + hH (-1/a)dn A /dt = (-1/b)dn B dt = (1/g)dn G /dt = (1/h)dn H /dt = k n A a n B b Rate of molecular collisions Rate of collision per unit volume between all A and all B =  (2r) 2 v T n B n A = limiting rate of reaction = k max n A a n B b Gas-kinetic rate for bimolecular reactions k max =  (2r) 2 v T 2r  3 x m; v T  500 m s -1 k max = 1.4 x cm 3 molecule -1 s -1 k lower due to molecular steric and energy requirements k dependent on temperature

STERIC REQUIREMENTS Steric factor (p) accounts for geometric orientation req. p < 1 NO + NO 3  2NO 2

ENERGY REQUIREMENTS Energy barrier to reaction that must be overcome Usually referred to as activation energy (E a )  E is the net internal energy change Note E a (forward reaction)  E a (reverse reaction)  E (forward reaction) = -  E (reverse reaction) NO + NO 3  2NO 2 reaction pathway EaEa EE E a (reverse rxn.)

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 -E a /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 - cm 3 molecule -1 s -1 E a - J mole -1 R - J mole -1 K -1 T - K

Photochemistry