QUESTIONSQUESTIONS

 1. What is the most abundant greenhouse gas in the Earth’s atmosphere?  2. What is the radiative equilibrium temperature of the Earth’s surface at the poles in winter? What prevents this temperature from ever being achieved?

3. How would you observe savanna and forest fires from space? (Clue:fires are hot).

4. Clouds are the wild card in predictions of future climate change. They reflect solar radiation, thereby cooling the Earth; but they also absorb in the IR, thereby warming the Earth.  Whether a cloud has a net warming or cooling effect depends mainly on its altitude. Why?

CLIMATE FEEDBACK FROM HIGH vs. LOW CLOUDSCLIMATE FEEDBACK FROM HIGH vs. LOW CLOUDS

convection

To

Tcloud≈ To

Clouds reflect solar radiation (A > 0) cooling;…but also absorb IR radiation (f > 0) warming

WHAT IS THE NET EFFECT?

To4

Tcloud4≈ To

4

LOW CLOUD: COOLING

Tcloud4 < To

4

To4

HIGH CLOUD: WARMING

PRINCIPLES OF PHOTOCHEMISTRYPRINCIPLES OF PHOTOCHEMISTRY

SUN AND EARTH E/M SPECTRASUN AND EARTH E/M SPECTRAAs we saw last class…Emission = f(T) [Stefan-Boltzmann Law]

NOTE: Sun Planck function actually much larger (higher T), normalized here

RADIATION IN THE ATMOSPHERERADIATION IN THE ATMOSPHEREIncoming radiation: solar (blackbody emission at 5800K). Radiation drives atmospheric chemistry by dissociating molecules into fragments that are often highly reactive.

Photon energy per mole:

Radiation of interest for tropospheric chemistry is from visible (~700 nm) to near-UV (~290 nm). The corresponding energies are sufficient to break chemical bonds such as:

weak O2-O bond in ozone (~ 100 kJ/mol)moderately strong C-H bond in formaldehyde(~368 kJ/mol)

23

23

5

6.02 10

6.02 10

1.2 10/

h

hc

kJ mol

nm

Shorter wavelengths are attenuated as they travel through the atmosphere (by molecular

O2 and N2 and ozone)

MAJOR PHOTODISSOCIATING SPECIESMAJOR PHOTODISSOCIATING SPECIES

NO2 + hv NO + O < 420 nm

O3 + hv O(3P) + O2 315 < < 1200 nm O(1D) + O2 < 315 nm

HNO2 + hv NO + OH < 400 nm

H2O2 + hv 2OH

NO3 + hv NO + O2 NO3 “stores” NOx at night NO2 + O

HCHO + hv HCO + H CO + H2 dominant path for > 320 nm

A photon (hv) is a reactant.

Reminder: λ> 290 nm only in the troposphere!

EXAMPLE: PHOTODISSOCIATION OF OXYGENEXAMPLE: PHOTODISSOCIATION OF OXYGEN

Estimate the wavelength of light at which photodissociation of O2 into2 ground-state oxygen atoms:

O2 + hv O + O

The enthalpy for this reaction is H=498.4 kJ/mol (endothermic)

51.2 10

240

nm

nm

So O2 cannot photodissociate at wavelengths longer than about 240 nm

GASES:GHGs are absorbing in the IR(as seen for example for CO2)Gases can scatter in the UV/visible Rayleigh scattering

LIGHT: REFLECTING, SCATTERING AND ABSORBINGLIGHT: REFLECTING, SCATTERING AND ABSORBING

AEROSOLS:Absorption depends on composition (eg. black carbon)Scattering explained by Mie Theory reduction in visibility

BEER-LAMBERT LAW AND OPTICAL DEPTHBEER-LAMBERT LAW AND OPTICAL DEPTHBeer-Lambert Law: Attenuation of radiation

This holds if number density

does not vary significantly over dx

I = radiation flux=cross section [cm2/molecules]n = number densityl = path length (x2-x1) = optical depth [dimensionless] = solar zenith angle (SZA)

2

1

( , ) ( , )

1 0

2

1

1

0

( ) ( )

( ) ( , ) ( , )

( ) ( )

( )

x

x

n x x dx

x

x

I I e

n x x dx

n l

ITransmissivity T

I

zTOATop of Atmosphere

l=zTOA/cos()

If account for angle of light transmitted to Earth’s surface(at angle):

0

1( ) ( , ) ( , )

cos( )

TOAz

n z z dz

n, σ

ACTINIC FLUXACTINIC FLUX

ACTINIC RADIATION: the integrated radiation (photon flux) from all directions to a sphere (sum of direct, scattered, reflected light)

ACTINIC FLUX (J):Number of photons absorbed by species X:

( ) ( ) ( )[ ]aF J X

()=absorption cross section[cm2/molecules]

J()=actinic flux [photons/cm2/s]

Fa()=number of photons abs by X [photons/cm3/s]

[X] is in units of number density

Actinic flux will be modified by SZA (thus time, season, latitude), as well as by scattering and absorption by gases and particles. The absorption is mostly from stratospheric O3 (the ozone column).

Must also consider not only direct solar, but also scattered/reflected radiation need surface albedo estimates

Computational codes developed to calculate actinic flux for different constituent profiles, angles, locations

COMPUTING RATES OF PHOTOLYSISCOMPUTING RATES OF PHOTOLYSIS

Molecule is excited into an electronically excited state by absorption of a photon:A + hv A*

The excited molecule may release the absorbed energy by any of:1. Dissociation A* B1 + B22. Direct Reaction A* + B C1 + C23. Fluorescence A* A + hv4. Collisional deactivation A* + M A + M5. Ionization A* A+ + e-

The relative efficiency of each of these is described by the quantum yield (i): number of excited molecules of A* undergoing a process (i) to the total number of photons absorbed. By Stark-Einstein Law, I = 1

You may come across the “overall quantum yield of a stable product A” (A) which is defined as the number of molecules of A formed over the number of photons absorbed. A > 1 for a chain reaction

COMPUTING RATES OF PHOTOLYSIS (CONT’D)COMPUTING RATES OF PHOTOLYSIS (CONT’D)

290

( ) ( ) ( )[ ]

[ ]

i

nm

Rate J X

j X

The total rate of photolysis of X: Rate [molecules/cm3/s]j = photolysis rate constant [s-1]

Note, the use of j distinguishes the photolysis rate constant from other rate constants (k).

Example: Two photochemical processes for formaldehyde to produce (H+HCO) or(H2+CO) thus, ()= H+HCHO + H2+CO To compute the rate of disappearance of HCHO according to 1st rxn use only H+HCHO

DISCOVERY OF PHOTOCHEMICAL REACTIONS IN DISCOVERY OF PHOTOCHEMICAL REACTIONS IN THE ATMOSPHERETHE ATMOSPHERE

Some observations which remained unexplained until ~1960:

1. NO is oxidized to NO2 in photochemical smog the known thermal oxidation rxn is too slow: 2NO + O2 2NO2

2. Organics are rapidly oxidized during smog formationKnown before 1970, for example for propylene were rxns:

a. C3H6 + O3 productsb. C3H6 + O products

with rates too slow compared to propylene loss rates

Leighton (1961) speculated that free radicals might be formed from organics and involved in oxidation:

R alkyl (formed from any hydrocarbon group, eg. CH4, C2H8)RO2 alkyl peroxyRO alkoxyOH hydoxylHO2 hydroperoxyH hydrogen free radical

Time (min)

Pro

py

len

e L

os

s R

ate

Observed

Reaction a

Reaction b

DISCOVERY OF PHOTOCHEMICAL REACTIONS IN DISCOVERY OF PHOTOCHEMICAL REACTIONS IN THE ATMOSPHERE (cont’d)THE ATMOSPHERE (cont’d)

In mid 1960’s reactions of CO or hydrocarbons with OH were found to be rapid.

Chain reactions were proposed in 60’s which regenerate OH, convert NONO2 and involve HC species:

CO + OH H + CO2 (1)H + O2 + M HO2 + M (2)HO2 + NO OH + NO2 (3)

Note the chemical effects:oxidation of CO (CO CO2)conversion of NO NO2 (as observed to occur in atmosphere)reactions are fast (as observed in atm)free radicals are used up, but also created in each step

This sequence (1-3) is important in the clean troposphere. In the polluted air, organic species play a role similar to that of CO.

GENERATION OF OHGENERATION OF OHOH radical drives the daytime chemistry of both polluted and clean atmosphere

What is the source of OH (and other radicals)?

Major source:O3 + hv ( 320 nm) O(1D) + O2

O(1D) + H2O 2OH

Other sources:HONO + hv (< 400 nm) OH + NOnitrous acid (photodissociation)

H2O2 + hv (< 370 nm) 2OHhydrogen peroxide

HO2 + NO OH +NO2 (sources and sinks of HO2 effectively sources and sinks of OH HOx)

What is steady state [O3]?SS for O: R2=R1 [O] depends on [NO2]

SS for NO2: R1=R3SS for NO: R3=R1SS for O3: R3=R2 sub R1 for R2 from above:

BASIC PHOTOCHEMICAL CYCLE OF NOBASIC PHOTOCHEMICAL CYCLE OF NO22, NO AND O, NO AND O33

NOx is released in combustion processes, also saw that there are natural sources, such as lightning. The following is a “fast” photochemical cycle with no net consumption or production of species:

NO2 + hv NO + O (1)O + O2 + M O3 + M (2)O3 + NO NO2 + O2 (3)

2

2

1[ ][ ]

2[ ][ ]

j NOO

k O M

23

1[ ][ ]

3[ ]SS

j NOO

k NO

NONO2

hv

O3

O3

This is the photostationary state relation. The steady state concentration of ozone is controlled by the ratio of NO2 to NO here.However, 3 rxn cycle is incomplete for predicting ozone concentrations don’t forget carbon compounds!

FREE RADICAL KINETICS EXAMPLE: ETHANE PYROLYSISFREE RADICAL KINETICS EXAMPLE: ETHANE PYROLYSIS

Step 1: inititation (generates free radicals)C2H6 + M 2 CH3 + M (1) (thermal initiation step)

1. Products we expect are generated in (3), (4), (5) and (7)2. “Side products are generated in (2), (8), (9), (10)3. If there were no termination reaction, (1) would only need to occur once to start the “chain”4. The “chain length” is the average number of times the chain sequence is repeated before a

chain-propagating radical is terminated5. Rate is NOT equal to k[C2H6]! Need reaction mechanism to describe the kinetics, even if net

result is described by (*)

C2H6 C2H4 + H2 (*)

C2H6

C2H4

H2

Step 2: chain propagation (free radical free radical)CH3 + C2H6 CH4 + C2H5 (2)C2H5 + M C2H4 + H + M (3)H + C2H6 H2 + C2H5 (4)

Step 3: termination: two free radicals combine to form a stable molecule2H H2 (5)H + C2H5 C2H6 (6)H + C2H5 C2H4 + H2 (7)H + CH3 CH4 (8)CH3 + C2H5 C3H8 (9)2C2H5 C4H10 (10)

FREE RADICAL KINETICS EXAMPLE: ETHANE PYROLYSISFREE RADICAL KINETICS EXAMPLE: ETHANE PYROLYSISC2H6 + M 2 CH3 + M (1)

CH3 + C2H6 CH4 + C2H5 (2)C2H5 + M C2H4 + H + M (3)H + C2H6 H2 + C2H5 (4)

2H H2 (5)H + C2H5 C2H6 (6)H + C2H5 C2H4 + H2 (7)H + CH3 CH4 (8)CH3 + C2H5 C3H8 (9)2C2H5 C4H10 (10)

To determine overall rate: Each step is an “elementary” reaction so can be written:

R1 = k1[C2H6][M]d[C2H6]/dt = -R1 + ….

OPTIONS:1.Write mass conversation eqns for all species and solve ODEs numerically to get [C2H6](t)2.Use simplifying assumptions to get analytical expression for d[C2H6]/dt

Assumption: SS applies to free radicals:for H: R3 = R4 (consider only propogation reactions for now)

analysis shows k3[M] << k4[C2H6] so can arguethat for termination (10) is most important

for CH3: R2 = 2R1for C2H5: R3 + 2R10 = R2 + R4 sub in above, find R10=R1

Plug results into rate equation for ethane to get:

rxn order = 1/2

2 5 2 6

[ ] 3[ ]

[ ] 4[ ]

H k M

C H k C H

1/21/22 6

2 6 2 6

[ ] 1[ ]3 1[ ][ ] 3[ ] [ ]

10

d C H k Mk M C H k M C H

dt k

If assume long chain lengths, can ignore initiation (R1)