calculation of photolysis rates k is the photolysis rate constant (also called photolysis frequency...
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CALCULATION OF PHOTOLYSIS RATES
[ ]... [ ]
d XX h k X
dt
k is the photolysis rate constant (also called photolysis frequency or J-value)
0
( ) ( ) ( )X Xk q I d
quantumyield absorption
x-section
actinic flux (omnidirectional)
photonis absorbed
Molecularcross-section A
Absorptioncross-section s
photonis notabsorbed
Probability of absorption for incomingphotons = σ/A
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CALCULATION OF 3-BODY REACTION RATES
* (1)
* (2)
* * (3)
* heat (4
)
Net:
A B AB
AB A
A B
B
AB M AB M
M
M B
M
A M
Low-pressure limit (Rate(2) >> Rate (3)):
A and B are reactants;AB* is the activated product;AB is the stable product;M is the “third body” (N2, O2 )
1 3
2 3
[ ][ ][ ][ ]
[ ]
k k A B Md AB
dt k k M
General solution:
1
[ ][ ][ ]
d ABk A B
dt
1 3
2
[ ][ ][ ][ ]
k kd ABA B M
dt k
High-pressure limit (Rate(2) << Rate (3)):
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1 Dobson Unit (DU) is defined to be 0.01 mm thickness at STP
Latest satellite ozone data:http://jwocky.gsfc.nasa.gov/
THE OZONE LAYER
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ABSORPTION OF SOLAR UV RADIATION BY OZONE
Solar UV radiation spectrum at different altitudes
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THE NATURAL OZONE LAYERBased on ozonesonde observations in the 1970s
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SOLAR SPECTRUM AND ABSORPTION X-SECTIONS
O2+hv O3+hv
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ENERGY STATES OF THE O ATOM (1s22s22p4)
multiplicity total electronicorbital angularmomentum number
Multiplicity = 2S+1, where S is the spin. The spin of an electron is (+/‐) 1/2.
Hund’s Rule: lowest-lying energy state is the one of maximum multiplicity
EnergyO(1 S)O(1D)O(3P)
determined by the arrangement of the four electrons in the 2p orbitals
O
.
.
: :
.
.
94 kJ/,ole
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CHAPMAN MECHANISM FOR STRATOSPHERIC OZONE (1930)
2
2 3
3 2
3 2
(R1) O O + O ( < 240 nm)
(R2) O + O M O M
(R3) O O O ( 320 nm)
(R4) O O 2O
h
h
O O3O2
slow
slow
fast
Odd oxygen family [Ox] = [O3] + [O]
R2
R3
R4
R1
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STEADY-STATE ANALYSIS OF CHAPMAN MECHANISMLifetime of O atoms:
O 22 2 4 3 2 O2
[O] 11 s
[O][O ][M]+ [O ][O] ak k k C n
…is sufficiently short to assume steady state for O:
3 O2 2 3 3 2
3 2 2 3
x 3
[O]2 3 [O][O ][M]= [O ] 1
[O ]
[O ] [O ]O a O
kR R k k
k C n
…so the budget of O3 is controlled by the budget of Ox.
Lifetime of Ox:
xOx
4 3 4
[O ] 1
2 [O ][O] 2 [O]k k
Steady state for Ox:1
321 2 2
3 O23
1 2 44
3 [O2 1 2 4 [O ] [O O] ]][ aR R kk k
C nk k
k
τOx
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PHOTOLYSIS RATE CONSTANTS: VERTICAL DEPENDENCE
0X+ ... ( ) ( )X Xh k q I d
quantumyield
absorptionX-section
photonflux
2 2 3 3optical depth ( ( ) ( ))O O O Od n z n z dz
( )I z dz
( )I z
2 2 3 3
( ) ( ) e
( ( ') ( ')) 'O O O Oz
I z I
n z n z dz
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CHAPMAN MECHANISM vs. OBSERVATION
-3
shapedeterminedby k1nO2
Chapman mechanism reproduces shape, but is too high by factor 2-3e missing sink!
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EVOLUTION OF O2 AND O3 IN EARTH’S ATMOSPHERE
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Questions
1. Show that the loss of ozone in the Chapman mechanism depends quadratically on the ozone concentration, i.e., L(O3) ~ [O3]
2
2. The production of ozone by photolysis of O2, P(O3) = k1[O2],
appears to depend linearly on the O2 concentration but the
dependence is in fact much weaker than linear. Explain why.
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RADICAL REACTION CHAINS IN THE ATMOSPHERE
non-radical radical + radicalInitiation:photolysisthermolysisoxidation by O(1D)
radical + non-radical non-radical + radicalPropagation: bimolecularredox reactions
non-radical + non-radicalTermination: radical redox reaction
radical + radical
non-radical + M radical + radical + M 3-body recombination
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WATER VAPOR IN STRATOSPHERE
Source: transport from troposphere, oxidation of methane (CH4)
H2O mixing ratio
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Initiation:1
2H O + O( ) 2OHD
Propagation: 3 2 2
2 3
3
2
2
OH + O HO O
HO +
Net:
O OH +
2O
2O
3O
Termination:2 2 2OH + HO H O + O
OH HO2H2Oslow
slow
fast HOx radical family
Ozone loss catalyzed by hydrogen oxide (HOx ≡ H + OH + HO2) radicals
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Supersonic aircraft (Concorde) cruising at 60,000’
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Questions
1, A sink for HOx radicals in the stratosphere is formation of hydrogen peroxide (H2O2):
H2O can then go on to either photolyze or react with OH:
Is this an effective termination pathway for HOx-catalyzed ozone loss?
2. Write a catalytic cycle of propagation reactions starting with the reaction
and based on the reactions we have seen so far. Does your cycle destroy ozone or is it a null cycle?
2 2 2 2 2HO HO H O O
2 2
2 2 2 2
2H O h OH
H O OH H O HO
2 2HO NO OH NO
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WHAT IS A RATE-LIMITING STEP?
• From IUPAC: “A rate-controlling (rate-determining or rate-limiting) step in a reaction occurring by a composite reaction sequence is an elementary reaction the rate constant for which exerts a strong effect — stronger than that of any other rate constant — on the overall rate.”
It is not necessarily the slowest reaction in the sequence!
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NITROUS OXIDE IN THE STRATOSPHERE
H2O mixing ratio
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ATMOSPHERIC CYCLING OF NOx AND NOy
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STRATOSPHERIC OZONE BUDGET FOR MIDLATITUDES CONSTRAINED FROM 1980s SPACE SHUTTLE OBSERVATIONS
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STRATOSPHERIC DISTRIBUTION OF CF2Cl2 (CFC-12)
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ATMOSPHERIC CYCLING OF ClOx AND Cly
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SOURCE GAS CONTRIBUTIONS TOSTRATOSPHERIC CHLORINE (2004)
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CHLORINE PARTITIONING IN STRATOSPHERE
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Decrease of Cl-containing gases following Montreal protocol
= 45 years
= 100 years
= 26 years = 5 years
• Original Montreal protocol (1987): cap production rates at 1980s levels• London (1990), Copenhagen (1992) amendments: phase-out in developed world• Beijing (1999): worldwide ban on production
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Questions
1. It has been argued that a fleet of supersonic aircraft releasing NOx in the lower stratosphere would decrease chlorine-catalyzed ozone loss. Why? [Hint: think of the chlorine reservoirs]
2. Peroxynitric acid (HNO4) is produced and removed in the stratosphere by
HO2 + NO2 + M → HNO4 + MHNO4 + OH → H2O + NO2 + O2
What is the effect on stratospheric ozone? Think of the effects on both the NOx and HOx budgets.
3. Photochemical model calculations for the stratosphere including only the Chapman mechanism overestimate observed ozone levels by a factor of 3. However, in a budget calculation constrained by ozone observations we find that the O3 + O reaction accounts for only 10% of the Ox sink. Can you reconcile these two results?
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OZONE TREND AT HALLEY BAY, ANTARCTICA (OCTOBER)
Farman et al. paper published in Nature
1 Dobson Unit (DU) = 0.01 mm O3 STP = 2.69x1016 molecules cm-2
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SPATIAL EXTENT OF THE OZONE HOLE
Isolated concentric region around Antarctic continent is called the polar vortex.Strong westerly winds, little meridional transport
Mean Octoberdata
http://ozonewatch.gsfc.nasa.gov/
Movie of October 1979-2013 Antarctic ozone
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THE OZONE HOLE IS A SPRINGTIME PHENOMENON
Movie of the 2013 ozone hole
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VERTICAL STRUCTURE OF THE OZONE HOLE:near-total depletion in lower stratosphere
Argentine Antarctic station southern tip of S. America
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Sep. 2, 1987
Sep. 16
20 km altitude
High ClO in polar vortexSept. 1987 ER-2 aircraft measurements at 20 km altitude south of Punta Arenas
ClO
ClO
O3
O3
Edge ofPolar vortex
Measurements by Jim Anderson’s group (Harvard)
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SATELLITE OBSERVATIONS OF ClO IN THE SOUTHERN HEMISPHERE STRATOSPHERE
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WHY THE HIGH ClO IN ANTARCTIC VORTEX?Release of chlorine radicals from reactions of reservoir species in
polar stratospheric clouds (PSCs)
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PSC FORMATION AT COLD TEMPERATURES
PSC formation
Frost point of water
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Seasonal PSCs in the Antarctic stratosphere
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HOW DO PSCs START FORMING AT 195K?HNO3-H2O PHASE DIAGRAM
Antarcticvortexconditions
PSCs are not water but nitric acid trihydrate (NAT) clouds
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DENITRIFICATION IN THE POLAR VORTEX:SEDIMENTATION OF PSCs
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CHRONOLOGY OF ANTARCTIC OZONE HOLE
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Chronology of 2013 ozone hole
http://ozonewatch.gsfc.nasa.gov/
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Increasing CO2 cools the stratosphere
15 m(220 K)
Add CO2 to stratosphere (T2 ). At 15 m:
fT14
T1 = 220 K
fT24
fT24
Net heating = f(T14 - 2T2
4 ) < 0
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Greenhouse gases warm the surface but cool the stratosphere
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Questions
1. What ratio of HCl to ClNO3 concentrations in Antarctic fall will lead to the largest ozone depletion the following spring?
2. Satellite observations of ClO in the Antarctic stratosphere in the middle of winter show a "collar" of maximum values around 60 degrees S. Why isn't ClO highest over the South Pole, where temperatures are lowest?
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Correlation of Arctic ozone loss with temperature
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Unusually cold Arctic stratosphere in spring 2011
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2011 Arctic ozone hole
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SKIN CANCER EPIDEMIOLOGY PREDICTIONS