7.1.1 Atmospheric Concentration Units

The ideal gas law was shown in Chapter 4 to apply to the atmosphere. Therefore, at an atmospheric pressure P = 1 atm, i.e., at sea level, and a temperature T = 298 K (i.e., 25 °C), the air contains 40.9 moles m⁻³. Atmospheric concentrations may be expressed in various units, and the following ones are generally used in atmospheric chemistry:

1. 
   

   – Moles per unit volume of air

   
   
2. 
   

   – Molecules per unit volume of air

   
   
3. 
   

   – Molar fraction (also called mixing ratio)

   
   
4. 
   

   – Mass per unit volume of air

The conversion of moles per unit volume of air into molecules per unit volume of air is done using the Avogadro number, N, which is the number of molecules per mole (N = 6.02 × 10²³ molecules mole⁻¹).

There are 40.9 moles of air per m³ at 1 atm and 25 °C, therefore:

n/V= 40.9 moles m−3×6.02×1023molecules mole−1 = 2.46×1025molecules m−3= 2.46×1019molecules cm−3 (7.1)

Molecular concentrations are usually given in molecules per cm³ (i.e., molec cm⁻³).

The molar fraction (also referred to as mixing ratio) is the ratio of the number of moles (or molecules) of a chemical species and of the number of moles (or molecules) of air (i.e., nitrogen + oxygen + argon + other minor constituents). Therefore, the molar fraction of pure air is 1. For a gaseous pollutant, it is of course much less than 1. Accordingly, the molar fraction is usually expressed as ppm (parts per million), ppb (parts per billion), or ppt (parts per trillion). If there is a molecule of a chemical species per million molecules of air, its molar fraction is 1 ppm. If there is a molecule of a chemical species per billion molecules of air, its molar fraction is 1 ppb. The molar fraction of pure air is by definition 10⁶ ppm, i.e., 10⁹ ppb, or 10¹² ppt.

The conversion of the molar (or molecular) concentration of a species into a molar fraction (or vice versa) is done using the ideal gas law. Therefore, this conversion depends on pressure and temperature. For example, let C_molec be the molecular concentration expressed in molec cm⁻³. The molar fraction expressed in ppm, C_ppm, is calculated as follows (V is expressed here in m³):

Cppm=1012 CmolecNnV=1012 Cmolec R TN P(7.2)

where R = 8.206 × 10⁻⁵ atm m³ mole⁻¹ K⁻¹. If a chemical species is uniformly mixed within the atmosphere, its molar fraction is constant. On the other hand, its molar or molecular concentration decreases with altitude, since pressure decreases with altitude (temperature also decreases with altitude in the troposphere, but the absolute temperature gradient is less than the pressure gradient).

The mass concentration is derived from the molar concentration (or from the molecular concentration) using the molar mass of the chemical species, MM. Let C_mass be the mass concentration of a chemical species (expressed here in μg m⁻³). It is calculated from the molecular concentration, C_molec (expressed here in molec cm⁻³), as follows:

Cmass=1012 Cmolec MMN(7.3)

where the factor 10¹² corresponds to conversions from g to μg and from cm³ to m³.

The conversion of the mass concentration into molar fraction (or vice versa) is done using the ideal gas law and, therefore, depends on pressure and temperature. For example, to obtain the molar fraction in ppb from a mass concentration in μg m⁻³:

Cppb=103 CmassMM  nV=103 Cmass R TMM P(7.4)

where the factor 10³ corresponds to conversions of molar fraction to ppb and of mass from μg to g.

7.1.2 Chemical Species and Chemical Reactions

The following types of chemical species are present in the atmosphere:

1. 
   

   – Molecules such as molecular nitrogen (N₂) and molecular oxygen (O₂). Molecules do not have any free electrons and are chemically stable. Their chemical reactions with other species involve breaking a bond between two atoms, which requires energy.

   
   
2. 
   

   – Radicals such as the hydroxyl radical (OH), the hydroperoxyl radical (HO₂, also called perhydroxyl radical; the prefix “per” indicates saturation, here in terms of oxygen), and the nitrate radical (NO₃). Radicals have one or more free electrons. Therefore, they are very chemically reactive, because they aim to stabilize their electron cloud by adding one or more electrons. The presence of a free electron may be represented by a dot next to the chemical formula, for example HO₂^•; this notation is not used here for the sake of simplicity, except in some figures of chemical mechanisms presented in Chapter 8.

   
   
3. 
   

   – Atoms, which may be chemically stable or to the contrary very reactive. Some atoms such as elementary mercury (Hg°) do not have any free electron and they are, therefore, stable. Others such as the oxygen atom (O) have a free electron and are very reactive.

   
   
4. 
   

   – Excited chemical species such as the excited oxygen atom O(¹D), which has more energy than the standard oxygen atom O(³P). The excited state results from the absorption of energy (from solar radiation via a photolytic reaction, for example); the excited species then seeks to lose that extra energy through a collision with other species (typically molecules present in high concentrations such as nitrogen, oxygen or water).

   
   
5. 
   

   – In the aqueous phase, ions such as H⁺, OH⁻, and NO₃⁻. In an aqueous solution, the positive and negative electrical charges must balance each other to give a neutral solution: this is called electroneutrality (see Chapter 10).

Reactions may be categorized as photochemical and chemical reactions. Photochemical reactions (also called photolytic reactions) correspond to the absorption by a molecule of energy from solar radiation. Chemical reactions concern one (rarely, this is called thermal decomposition), two (in most cases), or three chemical species.

7.1.3 Photochemical Reactions

Solar radiation energy is carried by photons (see Chapter 5). A photon carries an energy quantity, E_p, equal to hν, where h is the Planck constant (6.626 × 10⁻³⁴ m² kg s⁻¹) and ν is the frequency of the radiation (s⁻¹). For a given wavelength, the frequency is equal to the speed of light divided by the wavelength:

ν=cλ(7.5)

Therefore, a photon of wavelength λ = 400 nm (violet light), i.e., 4 × 10⁻⁷ m, has a frequency equal to 7.5 × 10¹⁴ s⁻¹ and the energy per photon at that wavelength is about 5 × 10⁻¹⁹ m² kg s⁻², i.e., 5 × 10⁻¹⁹ J.

The dissociation energy of a bond of the oxygen molecule (O-O), E_b,O2, is 500 kJ mole⁻¹, i.e., 5 × 10⁵ / N J molec⁻¹, where N is Avogadro’s number.

Eb,O2= 500 kJ mole−1=(5×105/ 6.02×1023) J molec−1      = 8.3×10−19J molec−1

Therefore, a photon corresponding to the wavelength of violet light does not have enough energy to break the bond of molecular oxygen. Visible light ranges from 400 nm (violet) to 700 nm (red). Since the energy of photons decreases when the wavelength increases, red light has less energy than violet light. Therefore, oxygen is not photolyzed by visible light.

Example: Below which wavelength can a molecule of oxygen be photolyzed?

Eb,O2=8.3×10−19J molec−1<h cλ8.3×10−19<6.6×10−34×3×108λ

Thus: λ < 2.4 × 10⁻⁷m = 240 nmλ<2.4×10−7m = 240 nm

However, a photon with enough energy may not necessarily break a chemical bond. The rate constant of a photolytic reaction depends on several characteristics of the molecule that absorbs the radiation at a given wavelength, λ. Thus, a photochemical rate constant (also called photolysis rate constant or photolysis rate coefficient), J, is equal to the product of three terms:

J = σ_J(λ)I_J(λ)ϕ_J(λ)

J=σJ(λ) IJ(λ) ϕJ(λ)(7.6)

where σ_J(λ) is the absorption cross-section of the molecule, which represents its capacity to absorb the radiation (in cm² per molecule), I_J(λ) is the actinic flux, which represents the amount of radiation received from all directions (in photons per cm² per s), and ɸ_J(λ) is the quantum yield, which represents the probability that the molecule will be photolyzed when a photon is absorbed by the molecule (molecule per photon).

The actinic flux is maximum when the Sun is at its zenith and it is zero at night. Therefore, there are no photochemical reactions at night. This results from the fact that infrared radiation emitted by the Earth does not have enough energy, since it corresponds to large wavelengths, >700 nm, i.e., to low energy.

The zenith angle of the Sun, θ_z, depends on latitude, date, and hour. It is calculated with the following formula (Jacobson, 2005):

cos(θ_z) = sin(ϕ) sin(δ_s) + cos(ϕ) cos(δ_s) cos(θ_h)

cos(θz)=sin(ϕ) sin(δs)+cos(ϕ) cos(δs) cos(θh)(7.7)

where ɸ is the latitude, δ_s is the Sun’s declination angle (which depends on the date), and θ_h is the angle of the local hour. The declination angle is given by the following formula:

δ_s = arc sin(sin(ε_ob) sin(λ_ec))

δs=arcsin(sin(εob) sin(λec))(7.8)

where ε_ob is the inclination (or obliquity) of the ecliptic and λ_ec is the ecliptic longitude of the Sun. The ecliptic is the mean plane of the orbit of the Earth around the Sun; it passes through both tropics and the equator. The inclination of the ecliptic is the angle between this plane and the equatorial plane; it is about 23.44 °, however, it decreases slightly every year by about 0.468,” i.e., 1.3 × 10⁻⁴ °. The ecliptic longitude of the Sun may be calculated as follows:

λec=Lec+1.915°sin(gec)+0.020°sin(2gec)Lec=280.460°+0.9856474°NJgec=357.528°+0.9856003°NJNJ=DJ−2451545(7.9)

where D_J is the Julian day, in a chronology starting on January 1of year −4,713 BC, at noon on the Greenwich meridian. D_J = 2,457,388.5 for January 1, 2017.

The angle of the local hour is given by the following formula:

θh=2 π ts86400(7.10)

where t_s is time in seconds starting at noon. Therefore, θ_h = 0 at noon when the zenith angle is minimum during the day. For example, at noon on June 21, 2016 in Paris (48 ° 51 ’ 12 ’’ N), the correction on solar radiation is cos(θ_z) = 0.9.

It is straightforward to calculate that at the tropics (latitude = 23.44 °) on June 21 (solstice) at noon: θ_z = 0 (the Sun is at the zenith). At the equator (latitude = 0 °) on March 20 (equinox) at noon: θ_z = 0. (Actually, θ_z ≈ 0, because the solstice and the equinox do not occur exactly at noon.)

The quantum yield is zero if the energy of the photon is less than the dissociation energy of the bond (it is an approximation because the formation of an excited molecule may occur after absorption of the photon, with subsequent reaction of the excited species with another species resulting in bond dissociation; the energy of the excited molecule must then be taken into account; this is the case, for example, for the photolysis of nitrogen dioxide, NO₂). For some molecules, the quantum yield may be equal or close to 1 at some wavelengths.

Since chemical species with free electrons are more reactive than molecular species and stable atoms, photolysis (which generates radicals and atoms with free electrons, as well as excited species) leads to an atmosphere that is more chemically reactive. Therefore, the formation of secondary pollutants, which are produced via chemical reactions in the atmosphere, is more important when photolysis occurs, i.e., during the day. At night, the atmosphere is not very chemically reactive, because photochemical reactions do not take place.

Data (absorption cross-sections and quantum yields) for the main atmospheric photochemical reactions are available in the evaluations of the Jet Propulsion Laboratory (Burkholder et al., 2015).

7.1.4 Chemical Reactions

General Considerations

Atmospheric gas-phase chemical reactions may be grouped in three main categories.

1. 
   

   – Unimolecular reactions lead to the dissociation of a molecule via absorption of thermal energy. In the atmosphere, the amount of thermal energy that may be absorbed by a molecule is much smaller than the energy available from solar radiation. Nevertheless, some molecules may undergo thermal dissociation. An important thermal dissociation reaction in air pollution is the dissociation of peroxyacetyl nitrate (PAN), which may dissociate into nitrogen dioxide (NO₂) and a peroxyacetyl radical (CH₃COO₂). PAN is formed from those two species and is, therefore, considered to be a reservoir species, since PAN can form NO₂ back by dissociation when the ambient temperature increases.

   
   
2. 
   

   – Bimolecular reactions are the most common. Two chemical species undergo a collision. Note that such a bimolecular reaction does not necessarily involve two molecules, but may also correspond to a reaction between a molecule and a radical, a molecule and an atom, two radicals or a radical and an atom. With some probability, this collision may lead to the dissociation of some chemical bonds and the formation of new chemical species. The species that collide and react are called the reactants. The species that are produced by a chemical reaction are called the products. A reaction may lead to one or more products.

   
   
3. 
   

   – Trimolecular (or termolecular) reactions, require the presence of a third molecule for the reaction to take place. In the atmosphere, this third molecule is N₂ or O₂; it is represented by M. As for bimolecular reactions, a trimolecular reaction may involve a radical or an atom as one of the three chemical species involved.

For a reaction to occur, a chemical bond must be broken and, therefore, a quantity of energy greater than the bond dissociation energy must be added. One defines for each reaction an activation energy, E_a, which is the energy required for the reaction to occur. Once the reaction occurs, the products have different chemical bonds than the reactants. The difference between the energies of the products and reactants may be calculated from the energies of their chemical bonds (for a molecule with only two atoms, the bond energy is equal to the bond dissociation energy; for molecules with more than two atoms, the energy of a chemical bond is an average value, which differs from the dissociation energy of that bond). If the total energy of the products is greater than that of the reactants, the reaction is endothermic (the net budget requires adding thermal energy); if the total energy of the products is less than that of the reactants, the reaction is exothermic (the net budget leads to a release of thermal energy). For example, combustion is exothermic.

The mean thermal energy of a gas, E_t (J mole⁻¹), is usually too low compared to the activation energy of a chemical reaction. It is related to the kinetic energy of its molecules and is given by the following equation:

Et=32N kB T(7.11)

where k_B is the Boltzmann constant (1.38 × 10⁻²³ J K⁻¹). Thus, E_t = 3.7 kJ mole⁻¹ at T = 25 °C. However, the kinetic theory of gases implies that the velocities of the atoms and molecules (and, therefore, their kinetic energy) are not uniform, but follow a distribution, which is called the Maxwell–Boltzmann distribution. Thus, some molecules or atoms may have velocities sufficiently high to exceed the activation energy of the chemical reaction so that the reaction may occur.

The kinetics of most reactions increases with temperature, because (1) the random motion of molecules, atoms, and radicals in the gas increases with temperature (and, therefore, the number of collisions increases) and (2) the velocity distribution of molecules, atoms, and radicals changes in such a way that the probability of high velocities increases.

The kinetics of a chemical reaction is limited by the diffusion of molecules, atoms, and radicals in the gas, since two chemical species must collide for the reaction to occur. The kinetic theory of gases implies that there is a maximum value of the kinetics of bimolecular reactions that corresponds to the case where each collision results in a reaction between the two chemical species; this maximum value of the rate constant is about 4.3 × 10⁻¹⁰ molec⁻¹ cm³ s⁻¹.

Chemical Kinetics of Unimolecular Thermal Dissociation Reactions

There are few unimolecular thermal dissociation reactions. A unimolecular reaction is usually a reaction consisting of two elementary reactions. The first reaction is bimolecular and leads to an excited state of the molecule of interest. The second reaction corresponds to the decomposition of the excited molecule:

A + M ↔k2k1 A*+M(R7.1)

A*→k3 B+C(R7.2)

where M represents the air molecules, either molecular oxygen (O₂) or molecular nitrogen (N₂). The excited molecule may either dissociate into two distinct chemical species due to its extra energy or return to its initial state. Therefore, there are actually three elementary reactions, which correspond to what is perceived as a unimolecular dissociation:

A → B + C

A→ B+C (R7.3)

The kinetics of this type of reaction has been studied by Lindemann, Hinshelwood, and Troe. Two extreme regimes may be considered: one at low pressure (low concentration of M) and the other at high pressure (high concentration of M).

Assuming that the excited molecule A* is at steady-state, due to its unstable excited energy state (brackets, [ ], indicate concentrations):

[A*]=k1[A][M]k2[M]+k3(7.12)

where k₁, k₂, and k₃ are the reaction rate constants. Therefore, the kinetics of the chemical reaction (also called the reaction rate), r_r (molec cm⁻³ s⁻¹) leading to the formation of B and C is as follows:

rr=k3[A*]=k3k1[A][M]k2[M]+k3(7.13)

Thus, the rate constant expressed under its unimolecular form is as follows:

A→(+M) B+C(R7.4)

k=k3k1[M] k2[M]+k3;  rr=k[A] (7.14)

The rate constant may be expressed in terms of two constants representing the extreme cases at low pressure (low concentration of M) and high pressure (high concentration of M):

k=1 k2 k1 k3+1k1 [M] =11k∞+1k0[M]; k0=k1; k∞=k1k2k3(7.15)

In the original formulation, k₀ = k₁ [M] (Troe, 1983); however, the formulation used in Equation 7.15 is now used, so that k₀ depends only on temperature and does not depend on pressure (Finlayson-Pitts and Pitts, 2000; Jacobson, 2005). At low pressure, the concentration of air molecules is low and the probability of dissociation is greater than that of deexcitation by collision with M. Therefore, k₂ [M] ≪ k₃, and k ≈ k₁ [M]. Then, the rate constant k is proportional to pressure, i.e., [M]. At high pressure, there is saturation of air molecules; the limiting step of the kinetics is the dissociation of the excited molecule A* and the rate constant is simply proportional to k₃ and the equilibrium constant k₁/k₂. The rate constant may be written in terms of these two rate constants, k₀ and k_∞, which may be estimated experimentally at low and high pressures. This is called the Lindemann-Hinshelwood expression (after the names of the English scientists who introduced and developed the concept of these elementary steps involving an excited molecule). A correction was proposed by Troe (1983) for the intermediate pressure regime:

k=k∞ k0[M]k∞+k0 [M]  Fc[1+(logk0[M]k∞)2]−1(7.16)

where k₀ and k_∞ are the rate constants for the low and high pressure cases, respectively, and the Troe correction uses the factor F_c (sometimes called the falloff factor), which is estimated theoretically and tends toward 1 when the pressure tends toward 0 or infinity. The rate constants k₀ and k_∞ are expressed in cm³ molec⁻¹ s⁻¹ and s⁻¹, respectively, and [M] is expressed in molec cm⁻³. The constants k₀ and k_∞ depend on temperature, as described in the section on bimolecular reactions. When [M] tends toward 0, k tends toward k₀ [M] and when [M] tends toward infinity, k tends toward k_∞ and does not depend on [M]. For atmospheric reactions, the Troe correction factor, F_c, ranges between 0.3 and 0.9 depending on the reaction.

Chemical Kinetics of Bimolecular Reactions

Chemical kinetics consists of quantifying the rate at which a chemical reaction occurs. It is governed by the law of mass action. Let us consider the following generic bimolecular reaction:

αA + βB → γC + δD

α A + β B → γ C + δ D(R7.5)

The coefficients α, β, γ, and δ are the stoichiometric coefficients. They are typically equal to 1, although in some cases some may be equal to 2.

The reaction rate is as follows:

r_r = k[A]^α [B]^β

rr=k [A]α [B]β(7.17)

where k is the rate constant and the brackets indicate concentrations.

The changes in chemical concentrations with respect to time are defined as follows:

rr=−1αd[A] dt=−1βd[B] dt=+1γd[C] dt=+1δd[D] dt(7.18)

The negative signs correspond to the consumption of a reactant, and the positive signs correspond to the formation of a product. This equation conserves the total mass of reactants and products.

The rate constant depends on temperature and is defined in its most general form as follows:

k=AT TBT exp(−EaR T)(7.19)

where A_T is a pre-exponential factor, B_T is the exponent of the temperature term, E_a is the activation energy of the reaction (J mole⁻¹), R is the ideal gas law constant (8.314 J mole⁻¹ K⁻¹), and T is temperature (K).

The most commonly used expression is the Arrhenius expression, which is a simplified version where the pre-exponential term does not depend on temperature:

k=AT exp(−EaR T)(7.20)

However, when the activation energy is very small, e.g., on the order of 1 kJ mole⁻¹, the exponential term tends toward 1 and the temperature dependence is then governed by the pre-exponential term T^BT.

Chemical Kinetics of Trimolecular Reactions

In the case of a trimolecular reaction in the atmosphere, the third molecule is a molecule of air, i.e., an oxygen molecule (O₂) or a nitrogen molecule (N₂). Therefore, this type of reaction depends on the atmospheric pressure. The trimolecular reaction process is not an elementary reaction, because the probability that three molecules collide simultaneously is very low. It represents a series of reactions with the formation of an intermediate excited species (i.e., a species with excess energy), which returns to a stable energy level either by dissociation into the original reactants, or by colliding with a third molecule (O₂ or N₂). Thus:

A +B ↔k2k1AB*→k3 (+M)C(R7.6)

An approach similar to that used for unimolecular reactions is used to express the rate constant as a function of its extreme values under low- and high-pressure regimes. Assuming steady state for the excited molecule AB*, due to its highly unstable nature:

[AB*]=k1[A][B]k2+k3[M](7.21)

The kinetics of the formation of C is given by the following expression:

rr=k3[AB*][M]=k3k1[A][B]k2+k3[M][M](7.22)

Therefore, a rate constant corresponding to the formulation of the trimolecular reaction expressed as a bimolecular reaction may be written as follows:

A +B→(+M) C(R7.7)

k=k3k1 [M]k2+k3[M]; rr=k[A][B](7.23)

The rate constant may be written as a function of two constants representing the extreme cases, i.e., at low and high pressure:

k=11k1k2k3[M]+1k1=11k0[M]+1k∞; k0=k1k2k3; k∞=k1(7.24)

At low pressure, the concentration of the air molecules is limiting the formation of C and, therefore, the rate constant is proportional to pressure, i.e., [M], as well as to the equilibrium constant between the two reactants and the excited molecule, k₁/k₂. Thus, the reaction appears as being a trimolecular reaction. At high pressure, there is saturation of air molecules. The limiting step is the formation of the excited molecule AB* and the rate constant is simply k₁ (i.e., the kinetics of the dissociation of the excited molecule into the original reactants becomes negligible) and the reaction appears to be bimolecular. The rate constant can be written as a function of these two rate constants, k₀ and k_∞, which depend only on temperature. These two constants may be estimated experimentally under low- and high-pressure conditions, respectively. The expression of the rate constants, taking into account the Troe correction is as follows:

k=k∞ k0[M]k∞+k0[M]  Fc[1+(logk0[M]k∞)2]−1(7.25)

where k₀ and k_∞ are the rate constants for the cases at low and high pressures, respectively, and [M] is the total concentration of N₂ and O₂ (i.e., corresponding to the atmospheric pressure). Therefore, k₀ is expressed in cm⁶ molec⁻² s⁻¹, k_∞ is expressed in cm³ molec⁻¹ s⁻¹, and [M] is expressed in molec cm⁻³. When [M] tends toward 0, k tends toward k₀ [M] and when [M] tends toward infinity, k tends toward k_∞ and no longer depends on [M]. For atmospheric reactions, the Troe factor, F_c, ranges between 0.3 and 0.9 depending on the reaction.

The constants k₀ and k_∞ depend on temperature, as described previously in the section on bimolecular reactions. However, the temperature dependence of k₁ and k₃ is low and the temperature dependence of k₂ dominates (at high temperature, the vibrational energy of AB* is greater, which favors the backward reaction to form A and B). Therefore, the overall rate constant, k, tends to decrease as temperature increases.

Kinetic data for inorganic atmospheric reactions are available in the evaluations of the Jet Propulsion Laboratory (Burkholder et al., 2015). For organic reactions, kinetic data are available in the references provided in Chapter 8.

7.1.5 Principle of Microreversibility and Chemical Equilibrium

All elementary reactions are reversible. This is called the principle of microreversibility. An elementary reaction is a single-step reaction. However, it is possible to write “reactions” that lump several steps, i.e., several elementary reactions occurring sequentially, in order to simplify the representation of chemical reactions. The microreversibility principle is based on the fact that the reaction process can be reversed in time so that the elementary reaction may occur in the reverse (backward) direction (the products become the reactants and the reactants become the products). In most cases, the kinetics of the reverse reaction is much slower than that of the forward reaction; therefore, only the forward reaction is of interest. In some case, both kinetics are commensurate. Then, there is chemical equilibrium:

A +B→kfC+D(R7.8)

A +B←krC+D(R7.9)

At equilibrium, the rates of the forward and reverse reactions are equal:

The equilibrium relationship is defined as follows:

Keq=[C][D][A][B]=kfkr (7.27)

where K_eq is the equilibrium constant. It depends on temperature, since the rate constants k_f and k_r depend on temperature. If the forward reaction dominates, the equilibrium is displaced toward the chemical species C and D, i.e., the products of that reaction. If the reverse reaction dominates, the equilibrium is displaced toward the chemical species A and B, i.e., the reactants of the forward reaction.

7.2.1 Chapman Cycle

As mentioned in Section 7.1.3, solar radiation at wavelengths less than 240 nm has enough energy to dissociate oxygen molecules and to lead to the formation of oxygen atoms:

O2+hν → 2 Oλ<242 nm(R7.10)

These oxygen atoms may react with oxygen molecules to form ozone. This reaction requires an air molecule:

Ozone may be photolyzed:

O3 + hν → O(1D)+O2240<λ<320 nm(R7.12a)

O(¹D) is an excited oxygen atom, which may lose its excess energy by reaction with air molecules (N₂ or O₂), which are represented by M (the oxygen atom at its lowest energy level is O(³P), which is represented here by O for the sake of simplicity):

In addition, ozone may react with oxygen atoms to form molecular oxygen:

This set of reactions is called the Chapman cycle, after the British mathematician and physicist Sydney Chapman, who first proposed it in 1930 to explain the high ozone concentrations observed in the stratosphere.

In this reaction cycle, reactions R7.12a and R7.12b may be combined into a single reaction by assuming that O(¹D) reacts only with air molecules:

O3+hν → O+O2240<λ<320 nm(R7.12)

Then, the Chapman cycle includes four reactions. Here, the rate constants k₁, k₂, k₃, and k₄ are used for reactions R7.10, R7.11, R7.12, and R7.13, respectively. Reactions R7.10 and R7.13 are slow, whereas reactions R7.11 and R7.12 are fast. Therefore, the ozone concentration in the stratosphere may be calculated by considering that the Chapman cycle consists of two sets of two reactions each. First, two reactions with slow kinetics (with a characteristic time on the order of one day to several years depending on altitude and latitude):

O2+hν → 2 Oλ<242 nm(R7.10)

Second, two reactions with fast kinetics (with a characteristic time on the order of a minute):

O3+hν → O+O2240<λ<320 nm(R7.12)

Since these two reactions are fast, steady-state may be assumed and at equilibrium their rates are equal:

Then, the concentration of oxygen atoms may be calculated from the ozone concentration:

[O]=[O3] k3k2 [O2] [M] (7.29)

Equilibrium between the two reactions with slow kinetics may also be assumed for large time scales:

Substituting [O] by its expression as a function of [O₃]:

k1 [O2]=2 k4 [O3]2k3k2 [O2] [M](7.31)

Thus, [O₃] may be expressed as a function of [O₂] and [M]:

[O3]=[O2]( k1 k2 [M]2 k4 k3  )1/2(7.32)

Example: What is the ozone concentration at an altitude of 25 km?

At an altitude of 25 km, atmospheric conditions are assumed to be: P = 0.025 atm and T = 221 K, i.e., −52 °C.

The rate constants are as follows:

k1=1.2×10–11 s−1at 25 km altitudek2=6×10–34×(300/T)2.3molec−2cm6 s−1k3=6×10–4 s−1at 25 km altitudek4=8×10–12exp(−2060/T) molec−1 cm3 s−1

At T = 221 K, k₂ = 1.21 × 10⁻³³ molec⁻² cm⁶ s⁻¹ and k₄ = 7.16 × 10⁻¹⁶ molec⁻¹ cm³ s⁻¹. Also, [M] = 8.3 × 10¹⁷ molec cm⁻³. Then, the ozone concentration is calculated as follows:

[O3] =1.18 × 10–4[O2][O2] =0.21 [M]=1.74 × 1017molec cm−3

Thus: [O₃] = 2.05 × 10¹³ molec cm⁻³

Actually, the ozone concentrations calculated with the Chapman cycle overestimate the measured concentrations. The observed concentrations may be simulated better by taking into account the reaction of the excited oxygen atom with water vapor:

O(¹D) + H₂O → 2 OH

O(1D)+H2O → 2 OH(R7.14)

where OH is the hydroxyl radical. This radical is very reactive and leads to other reactions:

O₃ + OH → O₂ + HO₂

O3+OH→ O2+HO2 (R7.15)

O₃ + HO₂ → 2 O₂ + OH

O3+HO2 → 2 O2+OH(R7.16)

OH + HO₂ → H₂O + O₂

OH+HO2 → H2O+O2(R7.17)

where HO₂ is the hydroperoxyl radical. As long as the OH and HO₂ radicals have not reacted with each other, they convert ozone into molecular oxygen, which explains the overestimation of ozone when these reactions are not taken into account.

7.2.2 Ultraviolet Radiation

The presence of oxygen and ozone in the stratosphere leads to an absorption of ultraviolet (UV) radiation. Therefore, in the troposphere, this radiative flux is significantly attenuated. UV radiation may be classified according to wavelengths as follows, starting from the visible light: UV A (400 to 315 nm), B (315 to 280 nm), and C (280 to 153 nm). This classification corresponds to the health hazards of UV radiation interactions with human skin. UV A radiation penetrates deeply and leads to suntan. However, it also leads to skin aging and may be harmful because it may trigger skin diseases such as cancers (carcinoma and melanoma). UV B radiation does not penetrate as deeply. It leads to sunburns and is harmful to the eyes, because it is not stopped by the eye lens. It leads to skin aging and skin cancer. UV C radiation has the most energy and may penetrate deeply; however, it is entirely stopped in the stratosphere. The ozone layer protects from UV radiation, in particular, from UV B radiation. Therefore, its destruction may lead to a greater flux of UV radiation reaching the Earth’s surface, which may lead to a public health problem due to an increase in skin cancer cases.

7.2.3 Depletion of the Stratospheric Ozone Layer

The first theory concerning the potential depletion of the stratospheric ozone layer was proposed in the early 1970s. Harold Johnston, a chemistry professor at the University of California at Berkeley, suggested that nitrogen oxide emissions (NO_x) from supersonic aircraft (such as the Franco-British Concorde airplane) could react in the stratosphere and lead to a cycle of reactions that would deplete ozone concentrations (Johnston, 1971). Nitrogen oxide emissions consist mostly of nitric oxide (NO). The following reactions occur:

Thus, NO is converted into NO₂, which is then converted back to NO. This reaction cycle may continue for a while, leading to the following net reaction budget:

This cycle ends when, for example, NO₂ reacts with OH to form nitric acid (HNO₃). Overall, there is a reduction of O₃ concentrations, which is similar to that obtained in Section 7.2.1 via the cycle involving the OH and HO₂ radicals of reactions R7.15 and R7.16. (NO₂ also gets photolyzed, but the corresponding cycle leads to no net change in the O₃ and O₂ budget; see Chapter 8.) Reactions with NO and NO₂ could have been an issue if NO emissions in the stratosphere had become important. However, stratospheric commercial aircraft flights have been limited and their impact on the stratospheric ozone has, therefore, been negligible.

Then, in the 1970s, another category of chemical species, the chlorofluorocarbons (CFC, also called “freons,” which was their commercial name given by the American company Dupont de Nemours), was identified as potentially leading to a depletion of the stratospheric ozone layer. CFC were used, for example, as refrigerants and in some aerosol spray products. The most common CFC were CFCl₃ and CF₂Cl₂, also called CFC 11 and CFC 12 according to the nomenclature of Dupont de Nemours (this CFC nomenclature uses the abc numbering system, where a is the number of carbon atoms – 1 (omitted if zero), b is the number of hydrogen atoms + 1, and c is the number of fluorine atoms). These substances are chemically very stable and, therefore, they have a long tropospheric lifetime. Chemistry professor Sherwood Rowland and his postdoctoral student Mario Molina of the University of California at Irvine suggested that, because of their chemical stability, these chemical species would be transported up to the stratosphere, where they would be photolyzed at wavelengths that are not available in the troposphere, because of the UV radiation filtering effect of O₂ and O₃ (Molina and Rowland, 1974). The photolysis of chlorofluorocarbons leads to the production of chlorine atoms, because the carbon-chlorine bonds are much weaker than the carbon-fluorine bonds. They proposed the following chemical mechanism for the stratosphere:

Initiation

Propagation

The net budget is a conversion of ozone and oxygen atoms (which are equivalent to ozone since there is a quasi-steady state, see reactions R7.11 and R7.12 in Section 7.2.1) into molecular oxygen. Therefore, there is partial depletion of the stratospheric ozone layer. This cycle ends when the chlorine radicals are stabilized:

Termination

Paul Crutzen, a Dutch meteorologist, then at the National Center for Atmospheric Research (NCAR) in Boulder, Colorado, who had been investigating stratospheric chemistry, confirmed the impact of the CFC industry on the stratospheric ozone layer (Crutzen et al., 1978). In the 1980s, measurements confirmed that the CFC were depleting the ozone layer and the chemistry Nobel Prize was awarded in 1995 to Paul Crutzen, Sherwood Rowland, and Mario Molina (only three people may share a Nobel Prize; therefore, Harold Johnston was not officially recognized for his theory concerning the potential impact of NO_x from supersonic commercial flights on the ozone layer, which inspired the theory of the impact of CFC).

The depletion of the ozone layer is greater at the South Pole, because of processes involving heterogeneous reactions on ice crystals in polar stratospheric clouds (PSC) (e.g., Solomon, 1988). The South Pole is characterized by an important vortex, which isolates this cold region during winter (the isolation is less important at the North Pole, because the presence of a greater land mass in the northern hemisphere leads to more dynamic perturbations of the atmosphere). The following heterogeneous reactions occur during the polar winter night (the “psc” subscript indicates molecules present in ice crystals of polar stratospheric clouds):

These heterogeneous reactions are faster when the temperature is very low (Burkholder et al., 2015), i.e., when the polar air masses are isolated from other (warmer) air masses. When spring arrives, solar radiation leads to the photolysis of the molecular chlorine molecules that have accumulated during the cold and dark winter:

Then, the destruction cycle of the ozone layer is triggered with the cycle presented previously in this section. It leads to the so-called ozone “hole” at the South Pole.

Chlorofluorocarbons that contain a hydrogen atom (HCFC) are chemically reactive in the troposphere, because hydroxyl radicals, OH, react with the hydrogen atom to form water vapor, thereby leading to the formation of a carbonaceous radical (see Chapter 8 for a description of the chemistry of organic compounds with OH). Chemical-transport simulations showed that these HCFC did not reach the stratosphere in significant amounts and, therefore, had little impact on the stratospheric ozone layer (e.g., Seigneur et al., 1977). Therefore, such commercial products were used in substitution of CFC 11 and 12. However, these compounds are greenhouse gases (see Chapter 14) and their commercial use is now being reduced (see Figure 7.2).

Figure 7.2. Timeline of atmospheric emissions and concentrations of selected chlorofluorocarbons (CFC), hydrochlorofluorocarbons (HCFC), and chlorocarbons. Top figure: global annual emissions (Gg y⁻¹); bottom figure: atmospheric concentrations (ppt).

Source of the data: WMO (2014); AFEAS (1998) (for emissions prior to 1980). Emissions after 1980 were obtained by inverse modeling from ambient concentration measurements.

Bromine-containing compounds (for example, halons) also play a role in the depletion of the stratospheric ozone layer, because bromine plays a role equivalent to that of chlorine. Compounds containing carbon and one or more halogen atoms (i.e., chlorine, bromine, and/or fluorine) are called halocarbons (including, therefore, freons and halons).

The potential of a halocarbon to deplete the stratospheric ozone layer may be characterized with an indicator called the ozone depletion potential (ODP). It depends in great part on the atmospheric lifetime of the halocarbon. ODP are calculated with respect to CFCl₃ (which has by definition an ODP equal to 1). ODP may be determined with a numerical model or via a combination of observations and modeling. The second approach is called a semi-empirical method; it is currently the most commonly used method. Both approaches lead to comparable results. Table 7.1 summarizes the ODP of the halocarbons evaluated in a recent report by the World Meteorological Organization (WMO, 2014). Halons (chemical species containing bromine) have ODP, which are greater than those of CFCl₃, because of the large chemical reactivity of bromine. HCFC have ODP, which are smaller than those of CFC, because of their tropospheric chemical reactivity.

The reduction of halocarbon emissions has been addressed in several international protocols. The first one was the Montreal protocol in 1987 (originally signed by 24 countries and the European Economic Community). It was later amended, in particular in 1990 (London), 1992 (Copenhagen), 1997 (Montreal), and 1999 (Beijing). As of 2015, all 197 countries of the United Nations had ratified the protocol and its amendments. Measurements that are now performed continuously (for example, via satellite measurements of the atmospheric ozone column) show that the stratospheric ozone “hole,” which deepened during the 20th century, now starts to recover. Therefore, the halocarbon emission controls start to show benefits (see Figure 7.2). However, the long lifetimes of CFC and of some other halocarbons imply that the recovery of the stratospheric ozone layer to its original state (i.e., pre-CFC) will happen slowly.