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

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)):

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

ABSORPTION OF SOLAR UV RADIATION BY OZONE

Solar UV radiation spectrum at different altitudes

THE NATURAL OZONE LAYERBased on ozonesonde observations in the 1970s

SOLAR SPECTRUM AND ABSORPTION X-SECTIONS

O2+hv O3+hv

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

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

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

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

CHAPMAN MECHANISM vs. OBSERVATION

-3

shapedeterminedby k1nO2

Chapman mechanism reproduces shape, but is too high by factor 2-3e 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

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

WATER VAPOR IN STRATOSPHERE

Source: transport from troposphere, oxidation of methane (CH4)

                             

H2O mixing ratio

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

Supersonic aircraft (Concorde) cruising at 60,000’

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

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 TOSTRATOSPHERIC CHLORINE (2004)

CHLORINE PARTITIONING IN STRATOSPHERE

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

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?

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

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

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

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)

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

Antarcticvortexconditions

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:

fT14

T1 = 220 K

fT24

fT24

Net heating = f(T14 - 2T2

4 ) < 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

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