Atmospheric chemistry
Lecture 2. Chemical Kinetics
1. Thermal and Photolysis Reactions
Two basic types of atmospheric reactions:
i) thermal reactions in which the collision of molecules or the interval
vibrations of molecules causes a reaction. These reactions are
a) decomposition reactions
b) combination reactions
c) disproportion reactions
ii) photochemical reactions in which the absorption of a photon
provides energy for reaction. A number of processes can occur after
photon absorption.
a) collisonal deactivation reaction
b) photodissociation reaction
c) intramolecular rearrangement reactions:
d) photoisomerization reactions
e) direct reaction: the excited species directly react with another
molecule
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2. Thermal Reaction Rates
2.1. Bimolecular reactions
Consider the following bimolecular reaction
A+B→C+D
The reaction rate is expressed as
−
d
d
[ A] = − [ B ] = k[ A][ B ]
dt
dt
In this expression the concentrations are expressed as number densities
so that the product [A][B] is proportional to the frequency of collisions.
The temperature dependence for the reaction rate constant k,
k = Ae − Ea / RT
where
A is the A-factor or the pre-exponential factor,
Ea is the activation energy or the threshold energy for reaction,
R is the gas constant,
T is the gas temperature.
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A is related to
molecular cross-section × mean relative collision velocity × steric factor
• The maximum possible value of the rate constant of a bimolecular
reaction is achieved if every molecular collision between A and B
results in reaction. This is called the gas-kinetic collision rate.
• The corresponding value of the second order rate constant k at 298
k for molecules of interests in atmospheric chemistry is in the
range of 10 –10 cm3 molecule s-1.
• Most reactions have rate constants less than this.
o (1) The activation energy Ea must be overcome for the reaction to
proceed.
o (2) Molecules that are geometrically complex may have to be aligned
properly at the point of collision for reaction to take place and perfect
alignment is not achieved in every collision.
Examples of bimolecular reactions:
O3 + NO → NO2 + O2, k = 2.0×10-12 exp(-1400/T)
OH + HCHO → HO2 + CO + H2O, k = 8.8×10-12 exp(25/T)
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2.2 Three-body reactions
A + B + M → AB + M
• A three-body reaction involves reaction of two species A and B to
form one single product AB.
• This reaction requires a third body M to stabilize the excited
product AB* by collision.
• The third body M is any inert molecule that can remove the excess
energy from AB* and eventually dissipate it as heat. (N2, O2 in the
atmosphere)
Example 1:
O + O + M → O2 + M
The elementary steps of a third body reaction are:
A + B → AB* (R3)
AB* → A + B (R4)
AB* + M →AB + M* (R5)
M* → M + heat (R6)
Example 2:
OH + NO2 + M → HNO3 + M
Example 3:
O + O2 + M → O3 + M
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The rate of a three-body reaction is defined as the formation rate of AB.
d [ AB]
= k 5 [ AB*][M ]
dt
(9.3)
In the atmosphere, [M] is simply the number density of air.
pseudo-steady-state approximation (PSSA)
• When an intermediate (e.g., AB*) has a very short lifetime and
reacts as soon as it is produced, the rate of generation of AB* is
equal to the rate of disappearance.
• PSSA is a fundamental way to deal with such reactive
intermediates when deriving the overall rate of a chemical reaction
mechanism.
PSSA gives
k3[A][B] = k4 [AB*] + k5[AB*][M]
[ AB*] =
k 3 [ A][ B ]
k 4 + k5 [M ]
d [ AB ] k 3 k 5 [ A][ B ][ M ]
=
dt
k 4 + k5 [M ]
5
(9.5)
(9.3)
d [ AB ] k 3 k 5 [ A][ B ][ M ]
=
dt
k 4 + k5 [M ]
The formation rate of AB depends on the concentration of M, i.e.,
pressure-dependent.
• Low-pressure limit case: R α [M]
k5[M] << k4, Æ
d [ AB ] k 3 k 5
=
[ A][ B ][ M ] .
dt
k4
ko = k3k5/k4 is referred as the low-pressure limit rate constant.
• High-pressure limit case: R independent of [M].
[M] is sufficiently large. Æ k5[M] >> k4, Æ
d [ AB]
= k 3 [ A][ B] .
dt
k3 is referred as the high-pressure limit rate constant k∞.
General form of the rate of a three-body reaction
d [ AB ] k o [ A][ B ][ M ]
=
k
dt
1 + o [M ]
k∞
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3. Photolysis reactions
Sunlight drives the chemistry of the atmosphere.
These reactions that involve the breaking of a chemical bond by an
incident photon are called photolysis reactions.
Table 1. Comparison of photon energies with chemical bond
energies
Name
Typical wavelength
(nm)
Typical range
of energies
(kJ/mol)
Visible
Red
700
170
Orange
620
190
Yellow
580
210
Green
530
230
Blue
470
250
Violet
420
280
Near ultraviolet
400-200
300-600
Vacuum ultraviolet
200-50
600-2400
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Figure 1. Some of the photolysis reactions that occur at various altitudes in
the atmosphere.
(Source: Atkins, Physical Chemistry, pp820.)
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The primary step of a photolysis reaction is:
X + hv → X*
X*: an electronically excited state of molecule X.
X* subsequently undergo either physical or chemical processes:
Physcial processes:
Fluorescence
X* → X + hv
Collisional deactivation
X* + M → X + M
Chemical processes:
Dissociation
X* → Y + Z
Isomerization
X* → X’
Direct reaction X* + Y → Z1 + Z2
Intramolecular rearrangement
X* → Y
X* → X+ + e
Ionization
The general form of photolysis reactions:
X + hv → Y + Z
(R11).
The rate of reaction is:
−
d
d
d
[ X ] = [Y ] = [ Z ] = k[ X ] , (9.11)
dt
dt
dt
k: photolysis rate constant for reaction R11, unit: s-1.
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Determination of k:
k = q xσ x I
. (9.12)
qx: quantum yield (molecules photon-1), varying from 0 to 1.
σx: absorption cross-section in units of cm2 molecule-1.
I: number of photos crossing a unit horizontal area per unit time from
any direction (unit: photons cm-2 s-1).
3.1 Actinic flux
The actinic flux at the earth’s surface is affected by the extent of light
absorption and scattering in the atmosphere, the zenith angle, the extent
of surface reflection, and the presence of clouds.
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Estimation of the actinic flux: use a radiative transfer model.
Figure 3. Calculated actinic flux
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Table 2. Calculated Actinic flux as a function of wavelength and
zenith angle
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3.2. Calculation of photolysis rates
The three parameters, qx, σx, and I, vary with wavelength. It is necessary
to integrate over the wavelength spectrum to obtain the total rate of
photolysis:
k=∫
λi
λ = 290 nm
q x (λ )σ λ (λ ) I λ dλ . (9.13)
λi: the longest wavelength at which the light absorption occurs.
(The shortest wavelength for photochemistry in the troposphere is 290 nm).
In practice, the sum of product q(λ) σ(λ) I(λ) over discrete wavelength
intervals ∆λ is used.
k=
λi
q (λ )σ (λ )I ' (λ )
∑
λ
= 290 nm
σ (λ ) and q(λ ) :
the values averaged over a wavelength interval ∆λ
centered at λ, ( σ (λ ) : cm2 molecule-1)
I'(λ): actinic flux in photons cm-2s-1 summed over the wavelength
interval ∆λ centered at λ.
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Experimental methods for
σ (λ )
and k:
σ (λ )
• The absorption cross sections are determined at various gas phase
concentrations in 1 atm of ultra-pure air using a conventional UVvisible spectrophotometer.
• An alternate, experimentally more convenient method, is to
measure the absorption spectrum of the compound dissolved in an
inert organic solvent.
k
• following the simultaneous rates of disappearance of the species of
interest and of a reference organic in an irradiated NO-organic-air
mixture.
o limitation: the minimum value of k which can be accurately measured
is about 1 x 10-5 s-1). This is a relatively rapid rate, thus while nitrite,
α-dicarbonyls, and nitrosamine photolysis rates could be measured,
that of simple aldehydes and ketones could not.
• use experimentally determined absorption cross sections σ(λ), q(λ)
available in the literature, in combination with actinic flux
estimates I(λ), to calculate k.
o Limitation: Many q(λ) values available in the literature were obtained
at reduced pressures in absence of air, which subjects the calculated k
to significant errors.
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3.3 Important atmospheric species that undergo photolysis
Species
ozone
Photochemical process
O3 + hν Æ O1D + O2 λ < 320 nm
O3 + hν Æ O3P + O2 λ ≥ 320 nm
Nitrogen dioxide NO2 + hν Æ O3P + NO λ < 397.8 nm
Nitrous acid
HONO + hν Æ OH + NO λ < 400 nm
Organic nitrite
Nitric acid
RONO + hν Æ RO + NO λ < 430 nm
HNO3 + hν Æ OH + NO2
200nm <λ < 320nm
RCH2NO2 + hν Æ RCH2O + NO2
200nm <λ < 330nm
CH3C(O)OONO2 ÆCH3C(O)OO + NO2
200nm <λ < 300nm
Organic nitrate
Peroxyacetyl
nitrate (PAN)
comment
Not siginifant in
tropospheric
chemistry
A key step in ozone
formation chemistry
A major source for
OH radicals
Negligible compared
to its thermal
decomposition
NO3 + hν Æ NO + O2, λ ≥ 580 nm
Æ NO2 + O3P 470nm <λ < 580nm
Nitrosyl chloride ClNO + hν Æ Cl + NO λ < 540 nm
Important in marine
urban environments
A source for OH
Hydrogen
H2O2 + hν Æ 2 OH λ ≤ 360 nm
radicals
peroxide
formaldehyde
HCHO + hν Æ H + HCO λ < 370 nm
Æ H2 + CO λ < 370 nm
acetaldehyde
CH3CHO + hν Æ CH3 + HCO λ < 330 nm
Æ CH4 + CO λ < 300 nm
acetone
CH3COCH3 + hν Æ CH3 + CH3CO
λ < 330 nm
dicarbonyls
Photolysis
e.g. (CHO)2 + hν Æ 2 CO + H2
predominates over
Æ HCHO + CO
reaction with OH or
λ < 470 nm
O3
Nitrate radical
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4. Radical-assisted reactions
Radicals: chemical species with an unpaired electron in the valence
shell.
Examples: ●OH, HO2●, ●CH3, ●OCH3, Cl
How about NO, O ?
Radical Initiation, propagation, and termination
Radical Initiation
Noradical + hv Æ radical + radical
Radical propagation
Radical + nonradical Æ Radical + nonradical
Radical termination
Radical + radical Æ nonradical + nonradical
Radical + radical + M Æ nonradical + M
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Exercises:
(1) The most important oxidizing species for tropospheric compounds is usually the hydroxyl
(OH) radical. A standard way of determining the OH rate constant of a compound is to measure
its decay in a reactor in the presence of OH relative to the decay of a second compound, the OH
rate constant of which is known. Consider two compounds A and B, A being the one for which
the OH rate constant is to be determined and B the reference compound for which its OH rate
constant is known. Show that the concentrations of A and B in such a reactor obey the following
relation:
ln
[ A]0 k A [ B ]0
ln
=
[ A]t k B [ B ]t
where [A]0 and [B]0 are the initial concentrations, [A]t and [B]t are the concentrations at time t,
and kA and kB are the OH rate constants. Thus, plotting
ln
[ A]0
[ B]0
versus ln
[ A]t
[ B ]t
yields a straight line with slope kA/kB. Knowing kB allows one to calculate kA from the slope.
(2) The low and high pressure limiting rate constants for the reaction of ClO with NO2 to form
chlorine nitrate at 298 K are given by ko = 1.8 x 10-31 cm6 molecule-2 s-1 and k∞ = 1.5 x 10-11 cm3
molecule-1 s-1. The chemical reaction is
ClO + NO2 + M ↔ ClONO2 + M (Forward reaction rate k1 and backward reaction rate k-1).
The thermal decomposition reaction rate was measured to be
k-1 = 10 -6.16 exp(-90.7 kJ mol-1/RT) in units of cm3 molecule-1 s-1.
Calculate (a) the effective bimolecular rate constant k1 at 298 K and 1 atm, and (b) the rate
constant k-1 for the thermal decomposition at 298 K and 1 atm.
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