CALCULATION OF PHOTOLYSIS RATES
X  h  ...
d[ X ]
 k[ X ]
dt
k is the photolysis rate constant (also called photolysis frequency or J-value)

k   q X ( ) X ( ) I ( ) d 
0 quantum
yield
absorption
x-section
actinic flux
(omnidirectional)
photon
is not
absorbed
Probability of absorption for incoming
photons = σ/A
Absorption
crosssection 
photon
is absorbed
Molecular
cross-section
A
CALCULATION OF 3-BODY REACTION RATES
A  B  AB *
(1)
AB*  A  B
(2)
AB *  M  AB  M * (3)
M *  M  heat
(4)
Net: A  B  M  AB  M
General solution:
A and B are reactants;
AB* is the activated product;
AB is the stable product;
M is the “third body” (N2, O2 )
d [ AB] k1k3[ A][ B][ M ]

dt
k2  k3[ M ]
Low-pressure limit (Rate(2) >> Rate (3)):
High-pressure limit (Rate(2) << Rate (3)):
d [ AB] k1k3

[ A][ B][ M ]
dt
k2
d [ AB]
 k1[ A][ B]
dt
THE OZONE LAYER
1 Dobson Unit (DU) is defined to
be 0.01 mm thickness at STP
Latest satellite ozone data:
http://jwocky.gsfc.nasa.gov/
ABSORPTION OF SOLAR UV RADIATION BY OZONE
Solar UV radiation spectrum at different altitudes
THE NATURAL OZONE LAYER
Based on ozonesonde observations in the 1970s
SOLAR SPECTRUM AND ABSORPTION X-SECTIONS
O2+hv
O3+hv
ENERGY STATES OF THE O ATOM (1s22s22p4)
determined by the arrangement of the four electrons in the 2p orbitals
multiplicity
total electronic
orbital angular
momentum 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
94 kJ/,ole
: O:
..
Energy
O(1 S)
O(1D)
O(3P)
CHAPMAN MECHANISM FOR STRATOSPHERIC OZONE
(1930)
(R1)
O 2  h  O + O
(R2)
O + O 2  M  O3  M
(R3)
O3  h  O 2  O
(R4)
O3  O  2O 2
slow
O2
R1
fast
R3
R4
slow
(  320 nm)
Odd oxygen family
[Ox] = [O3] + [O]
R2
O
( < 240 nm)
O3
STEADY-STATE ANALYSIS OF CHAPMAN MECHANISM
Lifetime of O atoms:
[O]
1
O 

k2 [O][O2 ][M]+k4 [O3 ][O] k2CO2 na2
1s
…is sufficiently short to assume steady state for O:
k3
O
[O]
R 2  R3  k2 [O][O2 ][M]=k3[O3 ] 


2
[O3 ] k2CO 2 na  O3
 [Ox ]  [O3 ]
…so the budget of O3 is controlled by the budget of Ox.
Lifetime of Ox:
 Ox
[Ox ]
1


2k4 [O3 ][O] 2k4 [O]
Steady state for Ox:
τOx
1
2
3
 k1k2 
2
2R1  2R4  k1[O2 ]  k4 [O3 ][O]  [O3 ]  
 CO2 na
 k3k4 
1
PHOTOLYSIS RATE CONSTANTS: VERTICAL DEPENDENCE

X+h  ...
k   qX ( ) X ( ) I  d 
0
I ( z  dz )
optical depth d  ( O2nO2 ( z)   O3nO3 ( z))dz
I ( z)
I ( z)  I () e

   ( O 2 nO 2 ( z ')  O3nO3 ( z '))dz '
z
quantum
yield
absorption
X-section
photon
flux
CHAPMAN MECHANISM vs. OBSERVATION
shape
determined
by k1nO2
-3
Chapman mechanism reproduces shape, but is too high by factor 2-3
e missing sink!
EVOLUTION OF O2 AND O3 IN EARTH’S ATMOSPHERE
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.
RADICAL REACTION CHAINS IN THE ATMOSPHERE
Initiation:
non-radical
Propagation: radical + non-radical
Termination:
radical + radical
radical + radical + M
radical + radical
photolysis
thermolysis
oxidation by O(1D)
non-radical + radical bimolecular
redox reactions
non-radical + non-radical radical redox
reaction
non-radical + M 3-body recombination
WATER VAPOR IN STRATOSPHERE
H2O mixing ratio
Source: transport from troposphere, oxidation of methane (CH4)
Ozone loss catalyzed by hydrogen oxide
(HOx ≡ H + OH + HO2) radicals
H2O + O( D)  2OH
1
Initiation:
OH + O3  HO2  O2
Propagation:
HO2 + O3  OH + 2O2
Net:
Termination:
2O3  3O2
OH + HO2  H2O + O2
slow
H2O
OH fast HO2
slow
HOx radical family
Supersonic aircraft (Concorde) cruising at 60,000’
Questions
1, A sink for HOx radicals in the stratosphere is formation of hydrogen peroxide
(H2O2):
HO2  HO2  H 2O2  O2
H2O can then go on to either photolyze or react with OH:
H 2O2  h  2OH
H 2O2  OH  H 2O  HO2
Is this an effective termination pathway for HOx-catalyzed ozone loss?
2. Write a catalytic cycle of propagation reactions starting with the reaction
HO2  NO  OH  NO2
and based on the reactions we have seen so far. Does your cycle destroy ozone or
is it a null cycle?
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!
NITROUS OXIDE IN THE STRATOSPHERE
H2O mixing ratio
ATMOSPHERIC CYCLING OF NOx AND NOy
STRATOSPHERIC OZONE BUDGET FOR MIDLATITUDES
CONSTRAINED FROM 1980s SPACE SHUTTLE OBSERVATIONS
STRATOSPHERIC DISTRIBUTION OF CF2Cl2 (CFC-12)
ATMOSPHERIC CYCLING OF ClOx AND Cly
SOURCE GAS CONTRIBUTIONS TO
STRATOSPHERIC CHLORINE (2004)
CHLORINE PARTITIONING IN STRATOSPHERE
Decrease of Cl-containing gases following Montreal protocol
 = 45 years
 = 100 years
 = 5 years
 = 26 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
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 + M
HNO4 + 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?
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
SPATIAL EXTENT OF THE OZONE HOLE
Mean October
data
Movie of October 1979-2013 Antarctic ozone
http://ozonewatch.gsfc.nasa.gov/
Isolated concentric region around Antarctic continent is called the polar vortex.
Strong westerly winds, little meridional transport
THE OZONE HOLE IS A SPRINGTIME PHENOMENON
Movie of the 2013 ozone hole
VERTICAL STRUCTURE OF THE OZONE HOLE:
near-total depletion in lower stratosphere
Argentine Antarctic station
southern tip of S. America
High ClO in polar vortex
Sept. 1987 ER-2 aircraft measurements at 20 km altitude south of Punta Arenas
O3
ClO
O3
Sep. 16
Sep. 2, 1987
ClO
20 km
altitude
Measurements by Jim Anderson’s group (Harvard)
Edge of
Polar
vortex
SATELLITE OBSERVATIONS OF ClO
IN THE SOUTHERN HEMISPHERE STRATOSPHERE
WHY THE HIGH ClO IN ANTARCTIC VORTEX?
Release of chlorine radicals from reactions of reservoir species in
polar stratospheric clouds (PSCs)
PSC FORMATION AT COLD TEMPERATURES
PSC formation
Frost point of water
Seasonal PSCs in the Antarctic stratosphere
HOW DO PSCs START FORMING AT 195K?
HNO3-H2O PHASE DIAGRAM
Antarctic
vortex
conditions
PSCs are not water but nitric acid trihydrate (NAT) clouds
DENITRIFICATION IN THE POLAR VORTEX:
SEDIMENTATION OF PSCs
CHRONOLOGY OF ANTARCTIC OZONE HOLE
Chronology of 2013 ozone hole
http://ozonewatch.gsfc.nasa.gov/
Increasing CO2 cools the stratosphere
15 m
(220 K)
Add CO2 to stratosphere (T2 ).
At 15 m:
f T 1 4
f T 2 4
f T 2 4
T1 = 220 K
Net heating = f(T14 - 2T24 ) < 0
Greenhouse gases warm the surface but cool the stratosphere
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?
Correlation of Arctic ozone loss with temperature
Unusually cold Arctic stratosphere in spring 2011
2011 Arctic ozone hole
SKIN CANCER
EPIDEMIOLOGY
PREDICTIONS