Abstract
The stratospheric ozone layer results from the photolysis of molecular oxygen by ultraviolet (UV) solar radiation in the high atmosphere. This large atmospheric layer is stable and, therefore, affects the general atmospheric circulation by decreasing significantly the vertical motions of air parcels. In addition, ozone protects the Earth from harmful UV radiation. Therefore, its destruction by anthropogenic activities may lead to public health impacts. This chapter presents first some fundamentals of atmospheric chemical kinetics (i.e., the speed at which chemical reactions occur in the atmosphere), which are needed to understand the processes leading to the presence of the ozone layer. These notions are also needed to understand the formation of gaseous and particulate pollutants, which is presented in the following chapters. Next, the processes that govern the ozone layer are described in terms of its natural formation and its destruction by man-made substances. Finally, the public policies introduced to address the protection of the stratospheric ozone layer are summarized.
The stratospheric ozone layer results from the photolysis of molecular oxygen by ultraviolet (UV) solar radiation in the high atmosphere. This large atmospheric layer is stable and, therefore, affects the general atmospheric circulation by decreasing significantly the vertical motions of air parcels. In addition, ozone protects the Earth from harmful UV radiation. Therefore, its destruction by anthropogenic activities may lead to public health impacts. This chapter presents first some fundamentals of atmospheric chemical kinetics (i.e., the speed at which chemical reactions occur in the atmosphere), which are needed to understand the processes leading to the presence of the ozone layer. These notions are also needed to understand the formation of gaseous and particulate pollutants, which is presented in the following chapters. Next, the processes that govern the ozone layer are described in terms of its natural formation and its destruction by man-made substances. Finally, the public policies introduced to address the protection of the stratospheric ozone layer are summarized.
7.1 Fundamentals of Chemical Kinetics
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:
– Moles per unit volume of air
– Molecules per unit volume of air
– Molar fraction (also called mixing ratio)
– 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:
(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 Cmolec be the molecular concentration expressed in molec cm−3. The molar fraction expressed in ppm, Cppm, is calculated as follows (V is expressed here in m3):
(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 Cmass be the mass concentration of a chemical species (expressed here in μg m−3). It is calculated from the molecular concentration, Cmolec (expressed here in molec cm−3), as follows:
(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:
(7.4) where the factor 103 corresponds to conversions of molar fraction to ppb and of mass from μg to g.
Example: Conversion in ppm of 4 μg m−3 of sulfuric acid, H2SO4
Conditions are 1 atm and 25 °C. The molar masses of H, S, and O are 1, 32, and 16 g mole−1, respectively.
The molar mass of sulfuric acid is:
Thus, Cppm = 4 × 8.2 × 10−5 × 298 / 98Cppm=4×8.2×10−5×298 / 98
7.1.2 Chemical Species and Chemical Reactions
The following types of chemical species are present in the atmosphere:
– 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.
– 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.
– 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.
– 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).
– 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, Ep, 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:
(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), Eb,O2, is 500 kJ mole−1, i.e., 5 × 105 / N J molec−1, where N is Avogadro’s number.
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?
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:
where σJ(λ) is the absorption cross-section of the molecule, which represents its capacity to absorb the radiation (in cm2 per molecule), IJ(λ) is the actinic flux, which represents the amount of radiation received from all directions (in photons per cm2 per s), and ɸJ(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, θz, depends on latitude, date, and hour. It is calculated with the following formula (Jacobson, 2005):
where ɸ is the latitude, δs is the Sun’s declination angle (which depends on the date), and θh is the angle of the local hour. The declination angle is given by the following formula:
where εob is the inclination (or obliquity) of the ecliptic and λec 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:
(7.9) where DJ is the Julian day, in a chronology starting on January 1of year −4,713 BC, at noon on the Greenwich meridian. DJ = 2,457,388.5 for January 1, 2017.
The angle of the local hour is given by the following formula:
(7.10) where ts is time in seconds starting at noon. Therefore, θh = 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(θz) = 0.9.
It is straightforward to calculate that at the tropics (latitude = 23.44 °) on June 21 (solstice) at noon: θz = 0 (the Sun is at the zenith). At the equator (latitude = 0 °) on March 20 (equinox) at noon: θz = 0. (Actually, θz ≈ 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.
– 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.
– 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.
– 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, Ea, 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, Et (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:
(7.11) where kB is the Boltzmann constant (1.38 × 10−23 J K−1). Thus, Et = 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:
(R7.1) 
(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:
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):
(7.12) where k1, k2, and k3 are the reaction rate constants. Therefore, the kinetics of the chemical reaction (also called the reaction rate), rr (molec cm−3 s−1) leading to the formation of B and C is as follows:
(7.13) Thus, the rate constant expressed under its unimolecular form is as follows:
(R7.4) 
(7.14)