Atmospheric chemistry
Lecture 2:
Photochemistry & kinetics
Dr. David Glowacki
University of Bristol,UK
david.r.glowacki@bristol.ac.uk
Quick review of yesterday
• We discussed atmospheric structure
• Temperature & pressure gradients, as well as Coriolis
forces are related to atmospheric transport
Today…
• We’ll gain some insight into the relationship between
atmospheric structure and atmospheric chemistry
• Atmospheric chemistry depends on sunlight,
temperature, and pressure; Today we’ll learn about
• Photochemistry
• Chemical kinetics
The Atmosphere is a low
temperature chemical reactor
Important Chemistry:
UV
Stratosphere
O3 layer
Tropopause
-70oC
14 km
visible
UV absorption by O3
Troposphere
Regional and global
biogenic emissions
(CH4)
Urban Anthropogenic emissions
Surface O3
IR absorption by
Greenhouse gases
(H2O, CH4, CO2)
Surface emissions
resulting in O3 and
aerosol formation,
and acid rain
Atmospheric
Chemistry starts with sunlight
v = c/l
O 3  O +O 2
• Breaking chemical bonds
requires energy
• Sunlight has energy
• If sufficient energy is deposited
in the bond, then it will break
• O3 has a bond energy of ~105
kJ mol-1
visible
E = hv
Red
Orange
Yellow
Green
Blue
Violet
Near UV
Far UV
l
700
620
580
530
470
420
400-200
200-50
Energy/kJ mol-1
170
190
210
230
250
280
300-600
600-2400
Photoexcitation gives excited molecules, A*
• Photoexcitation may result in a number of processes:
Initial photoexcitation
Dissociation
Fluorescence
Collisional relaxation
Ionization
A + hv  A *
A*  B + C
A*  A + hv
A * + M  A + M*
A*  A + e
+
-
• Photochemistry depends on temperature, pressure, and the
wavelength of the absorbed light

Photoexcitation kinetics
• The rate of formation of A* is written:
d[A*]
 jA [A]
dt
where jA is the photochemical rate constant
 processes is determined
• Competition between subsequent
by the quantum yield, ϕ, for each process where: i 1

1
A * 

 B +C
2
A * 

A + hv
3
A * + M 

A + M*
4
A * 

A+ + e-
i
Dissociation yield =Φ1
Fluorescence yield=Φ2
Collisional relaxation yield =Φ3
Ionization =Φ4
Understanding the photolysis rate
Quantum yield: efficiency
at which absorbed photons
result in the molecular
process of interest
absorption cross section:
number of photons
absorbed by a molecule at
a particular wavelength
jA 

A
Spectral actinic flux: density
of photons in the atmosphere
at a particular wavelength
(l,T) A ( l,T)I( l)dl
  A ( li ,T) A (li ,T) I( li )li
i
need to integrate over
the entire wavelength
range
Understanding photolysis rates
Atmospheric actinic flux
O3 absorption cross section
• Photochemical processes depend on:
• temperature (absorption cross sections & quantum yields)
• Pressure (collisional relaxation)
• Altitude (actinic flux)
Atmospheric absorption of light
• Gases absorb light
• The absorption of light depends
on the concentration of the gas,
N, its absorption cross section,
σ, & the path length, l,through
the gas
• May be described by the BeerLambert law
I
T   exp(l N)
I0
,N
l

I(l )


l

Atmospheric absorption of light
•
The Beer Lambert law:
• Explains the altititude dependence of actinic flux
• Is often used to measure atmospheric trace gas concentrations
DOAS (differential optical
absorption spectrometry)
FTIR spectrometry
Chemical Kinetics
Kinetics depends on the potential energy
surface (PES)
• What molecules do is determined by
their potential energy landscapes –
energy as a function of coordinates
• Stable molecules are minima on a PES
• Potential energy surfaces (PES) are
multidimensional, but we usually think
about their motion projected in one
dimension
• T dependence of reaction
rate coefficients well
described by the Arrhenius
equation:
 E 
k(T)  Aexp a 
 RT 
First order Unimolecular kinetics
A B
k(T )
d[A]
 k[A]
dt
d[A]
 kdt
[A]
d[A]
 [A]    kdt
ln[A]0  ln[A]t  kt
[A]t  [A]0 exp(kt)
Mechanisms with more than one chemical
reactions: exact solutions
• Coupled chemical reactions, often result in mechanisms
k
of the sort:
A
B
• For this system we can
write three rate equations,
one for each species:

1
k2
B
C
In matrix form:
[A]
d[A]
 k1[A]
dn
 
 Mn where n = [B]
dt
dt

[C]

d[B]
 k1[A]  k 2[B]
-k1 0 0
dt


and M = k1 k 2 0
d[C]

k 2 [B]

k2 0
0

dt

Chemical Mechanisms with Coupled Chemical
Reactions: Coupled differential Equations
• Analytic solutions exist for this eigenvalue problem to
solve for concentration vs. time
• If the initial concentration of every species but [A] is zero,
Concentration vs time when k /k =0.5
the solutions are
2
1
B changes a lot;
Not low or constant
[A]  [A]0 ek1 t
[B]  [A]0
k1
(ek1 t  ek2 t )
k2  k1
k1ek2 t  k2ek1 t
[C]  [A]0 (1
)
k2  k1
B doesn’t change much
Low and ~constant
Concentration vs time when k2/k1=10
Chemical Mechanisms with Coupled Chemical
Reactions: Steady State Approximation
• Consider again the following mechanism:
A
B
k1
k2
B
C
d[A]
 k1[A]
dt
d[B]
 k1[A]  k 2[B]
dt
d[C]

k 2 [B]
dt
• Steady state approximation: assume the

rate of change of intermediate B is zero
Approximate Steady state solution
d[B]
 k1[A]  k 2 [B]  0
dt

k
[B]  1 [A]
k2
k
[B]  1 [A]0 ek1 t
k2
Equivalent when k2 >> k1
making [B] low & ~constant

[B]  [A]0
Exact solution
k1
(ek1 t  ek2 t )
k2  k1
Chemical Lifetimes
• Often we are interested in the average lifetime of a
molecule before it reacts away
• Lifetime has units of time
• The interplay between chemical lifetimes and
atmospheric mixing processes determines much of
atmospheric chemistry
lifetime of intermediate 

A
B
k1
k2
B
C
[intermediate ]
sum of intermediate loss processes
[B]
1
B 

k2 [B] k 2
Collision Theory
• Molecules are constantly moving
KE 
4kB T

• Molecular gases are constantly
colliding with each other with a T
& 
P dependent collision frequency
Threshold
energy
• Each collision has a particular
amount of energy associated with
it
• This energy may lead to chemical
reaction
Bimolecular Kinetics
• Atmospheric chemistry involves both unimolecular and
bimolecular processes
• Bimolecular kinetics depend on pressure, [M]
• A reasonable model for a bimolecular reaction is
Visualizing bimolecular pressure dependence:
O + O2 + M  O3 + M
M
O
OO
M = O2 or N2
O3
O + O2 reaction coordinate
Bimolecular Kinetics: The Low & High
pressure Limits
• The total bimolecular process:
We want to know the rate
of AB formation
Write rate equations for AB*
Assume AB* is in steady state
Solve for AB* and plug into
the first equation

d[AB]
 k5 [AB*][M]
dt
d[AB*]
 k3 [A][B]  k4 [AB*] k5 [AB*][M]
dt
k3 [A][B]  k5 [AB*][M]  k4 [AB*]
d[AB] k3 k5 [A][B][M]

dt
k4  k5[M]
Bimolecular Kinetics: The Low & High
pressure Limits
d[AB] k3 k 5 [A][B][M]

dt
k4  k5[M]
• Low Pressure Limit
– [M] is very small

– k4 >> k5[M]
– k5[M] goes to zero
– Overall reaction rate
depends linearly on [M]
d[AB] k3 k 5 [A][B]

[M]
dt
k4
• High Pressure Limit
– [M] is very large
– k4 << k5[M]
– k4 goes to zero
– Overall reaction rate is
independent of [M]
– Instantaneous
stabilization
d[AB]
 k3[A][B]
dt
T & P dependent kinetic effects
• Laboratory measurements of rate coefficients give rise to T
& P dependences which are well described by the kinetic
master equation
Quick Summary
• Atmospheric chemistry dominated by photolysis
• Molecular motion on a potential energy surface (PES)
determines reactivity
• In the atmosphere, simple reactions combine to form
kinetic networks (i.e., coupled sets of important
reactions)
• The steady state approximation is a useful simplification
for short lifetimes
• Chemical reactions depend on both pressure &
temperature, and are determined through a combination
of experimental & theoretical approaches