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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

]][[][][ BAkBdtdA

dtd

=−=−

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,

RTEaAek /−=

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.

]*][[][5 MABk

dtABd

= (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] (9.3)

][]][[

*][54

3

MkkBAk

AB+

=

][]][][[][

54

53

MkkMBAkk

dtABd

+= (9.5)

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][]][][[][

54

53

MkkMBAkk

dtABd

+=

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,

]][][[][

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53 MBAkkk

dtABd

= .

ko = k3k5/k4 is referred as the low-pressure limit rate constant.

• High-pressure limit case: R independent of [M].

[M] is sufficiently large. k5[M] >> k4,

]][[][3 BAk

dtABd

= .

k3 is referred as the high-pressure limit rate constant k∞.

General form of the rate of a three-body reaction

][1

]][][[][

Mkk

MBAkdtABd

o

o

∞

+=

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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

Orange

Yellow

Green

Blue

Violet

700

620

580

530

470

420

170

190

210

230

250

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

Ionization X* → X+ + e

The general form of photolysis reactions:

X + hv → Y + Z (R11).

The rate of reaction is:

][][][][ XkZdtdY

dtdX

dtd

===− , (9.11)

k: photolysis rate constant for reaction R11, unit: s-1.

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Determination of k:

Iqk xxσ= . (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:

λλσλλ

λ λλ dIqk i

nm x∫ ==

290)()( . (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.

)(')()(290

λλσλλ

λ

Iqki

nm∑

=

=

)(λσ and )(λq : the values averaged over a wavelength interval ∆λ

centered at λ, ( )(λσ : 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 )(λσ and k:

)(λσ

• The absorption cross sections are determined at various gas phase

concentrations in 1 atm of ultra-pure air using a conventional UV-

visible 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 Photochemical process comment ozone O3 + hν O1D + O2 λ < 320 nm

O3 + hν O3P + O2 λ ≥ 320 nm Not siginifant in tropospheric chemistry

Nitrogen dioxide NO2 + hν O3P + NO λ < 397.8 nm A key step in ozone formation chemistry

Nitrous acid HONO + hν OH + NO λ < 400 nm A major source for OH radicals

Organic nitrite RONO + hν RO + NO λ < 430 nm Nitric acid HNO3 + hν OH + NO2

200nm <λ < 320nm

Organic nitrate RCH2NO2 + hν RCH2O + NO2 200nm <λ < 330nm

Peroxyacetyl nitrate (PAN)

CH3C(O)OONO2 CH3C(O)OO + NO2 200nm <λ < 300nm

Negligible compared to its thermal decomposition

Nitrate radical NO3 + hν NO + O2, λ ≥ 580 nm NO2 + O3P 470nm <λ < 580nm

Nitrosyl chloride ClNO + hν Cl + NO λ < 540 nm Important in marine urban environments

Hydrogen peroxide

H2O2 + hν 2 OH λ ≤ 360 nm A source for OH radicals

formaldehyde HCHO + hν H + HCO λ < 370 nm H2 + CO λ < 370 nm

acetaldehyde CH3CHO + hν CH3 + HCO λ < 330 nm CH4 + CO λ < 300 nm

acetone CH3COCH3 + hν CH3 + CH3CO λ < 330 nm

dicarbonyls e.g. (CHO)2 + hν 2 CO + H2 HCHO + CO λ < 470 nm

Photolysis predominates over reaction with OH or O3

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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 radical + radical

Radical propagation

Radical + nonradical Radical + nonradical

Radical termination

Radical + radical nonradical + nonradical

Radical + radical + M 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:

tB

A

t BB

kk

AA

][][

ln][][

ln 00 =

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

tAA

][][

ln 0 versus tB

B][][

ln 0

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

MClONOMNOClO +↔++ 22 (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.