Abstract
This chapter describes the processes that lead to the formation of atmospheric pollutants in clouds and fogs via aqueous chemical transformations. Although the volume occupied by water droplets in the air is small, important chemical reactions occur in clouds. These reactions modify the atmospheric chemical composition and may lead to an increase of particulate mass when clouds and fogs evaporate or to acid rain when clouds precipitate. First, some general considerations on clouds and fogs are presented. Then, aqueous chemistry is addressed. Chemical equilibria and reactions have been described in other textbooks (e.g., Stumm and Morgan, 1995), and the focus here is on the processes pertaining to air pollution. This chapter treats in particular the transformations leading to the formation of sulfuric acid and nitric acid, two constituents of acid rain (if the cloud precipitates), as well as precursors of fine inorganic particles (if the cloud evaporates). The aqueous chemistry of organic compounds concerns mostly the formation of secondary organic aerosols (SOA) and is treated in Chapter 9. Finally, emission control strategies to reduce acid rain are discussed.
This chapter describes the processes that lead to the formation of atmospheric pollutants in clouds and fogs via aqueous chemical transformations. Although the volume occupied by water droplets in the air is small, important chemical reactions occur in clouds. These reactions modify the atmospheric chemical composition and may lead to an increase of particulate mass when clouds and fogs evaporate or to acid rain when clouds precipitate. First, some general considerations on clouds and fogs are presented. Then, aqueous chemistry is addressed. Chemical equilibria and reactions have been described in other textbooks (e.g., Stumm and Morgan, 1995), and the focus here is on the processes pertaining to air pollution. This chapter treats in particular the transformations leading to the formation of sulfuric acid and nitric acid, two constituents of acid rain (if the cloud precipitates), as well as precursors of fine inorganic particles (if the cloud evaporates). The aqueous chemistry of organic compounds concerns mostly the formation of secondary organic aerosols (SOA) and is treated in Chapter 9. Finally, emission control strategies to reduce acid rain are discussed. Atmospheric deposition processes are treated in Chapter 11, and the impacts of acid rain on ecosystems are summarized in Chapter 13. Public policy programs developed to reduce acid rain in the United States are discussed in Chapter 15.
10.1 General Considerations on Clouds and Fogs
Clouds and fogs are formed in the atmosphere when the water vapor concentration exceeds its saturation vapor pressure (which depends on temperature, see Chapter 4). Water vapor condenses on hygroscopic particles, which grow and form cloud and fog droplets.
For clouds, the exceedance of the water saturation vapor pressure occurs when the air parcel rises and becomes colder, which leads to a lower saturation vapor pressure (see Chapter 4). A weak vertical velocity of the air parcel leads to stratus clouds, whereas a strong vertical velocity (i.e., convection) leads to cumulus clouds. The term nimbus is used to characterize precipitating clouds: nimbostratus and cumulonimbus.
Fog is a cloud that is in contact with the surface of the Earth. There are radiation and advection fogs. A radiation fog is formed when the temperature of the atmosphere decreases due to radiative transfer. For example, surface cooling at night because of infrared radiative transfer leads to a decrease in the temperature of the lower layers of the atmosphere, which are in contact with the surface. An advection fog is formed when an air mass is transported over a colder surface. This occurs, for example, in coastal areas where the ocean is particularly cold (for example, in San Francisco, California); the moist air mass encounters the cold ocean surface, which leads to water vapor condensation.
Cloud precipitation (rain, snow or ice) occurs when the fall velocity of the water droplet (or that of the ice crystal or snow flake) is greater than the vertical air parcel velocity. This fall velocity depends on gravity and the frictional force (see Chapter 11). Since the vertical velocity of an air parcel leading to a stratus cloud is less than that of an air parcel leading to a cumulus cloud, raindrops of a cumulonimbus are larger than those of a nimbostratus.
The liquid water content varies depending on the type of cloud or fog. Stratus clouds have liquid water contents on the order of 0.1 g of water per m3 of air; cumulus clouds contain more liquid water with water contents up to 1 g m−3. A precipitating cloud has a liquid water content greater than the equivalent non-precipitating cloud (for example, nimbostratus versus stratus), since rain drops are larger than non-precipitating cloud droplets. The liquid water content of a fog is generally low (for example, on the order of 10 mg m−3) and the precipitation of fog droplets is small compared to that of a cloud.
A cloud contains mostly air: for a stratus cloud with a liquid water content of 0.1 g m−3, the mass of water present in one m3 of air is about 0.01 % of the mass of the air (1 m3 of air weights about 1.2 kg at 20 °C at sea level, less at higher altitudes). The volume occupied by the cloud droplets is only 0.00001 % of the volume of the air parcel (given that at a pressure of 1 atm, the density of water is about 1,000 times that of the air).
Cloud droplets are larger than atmospheric particles, but sufficiently small that their fall velocity remains less than that of the ascending air. For example, a cloud droplet may have a diameter on the order of 40 μm. A fog droplet may have a diameter on the order of 10 μm and, therefore, it has a very small sedimentation velocity. Raindrops are larger with diameters ranging up to a few mm.
More comprehensive descriptions of clouds and fogs are available in meteorology textbooks (e.g., Ahrens, 2012).
10.2 Aqueous-phase Chemistry
Several processes must be taken into account in aqueous-phase chemistry:
– Mass transfer of chemical species between the gas phase and the liquid phase
– Chemical reactions and equilibria at the interface between the gas phase and the liquid phase
– Chemical reactions and equilibria in the liquid phase
– Non-ideality of concentrated aqueous solutions
– Electroneutrality of the aqueous solution
10.2.1 Mass Transfer of Chemical Species between the Gas Phase and the Liquid Phase
The mass transfer of a chemical species in the gas phase toward the liquid phase can be seen as a sequence of three steps:
– The mass transfer of the gas-phase molecule toward the droplet surface by molecular diffusion
– The thermodynamic equilibrium between the gas-phase and aqueous-phase concentrations at the droplet surface
– The mass transfer of the dissolved molecule in the aqueous phase from the droplet surface toward the inner droplet by molecular diffusion
These processes occur in the reverse direction in the case of a chemical species that volatilizes from the aqueous phase.
In most models of cloud chemistry, the system is assumed to be at equilibrium and the two mass transfer steps are neglected. Nevertheless, it is important to take them into account for the absorption of pollutants by falling raindrops (precipitation scavenging) as well as for heterogeneous reactions, which occur at the droplet surface.
10.2.2 Henry’s Law
Thermodynamic equilibrium at the surface of a droplet is governed by Henry’s law. Henry’s law applies to dilute aqueous solutions. It relates the concentration of a chemical species in the gas phase (characterized by its partial pressure, Pi) to its activity in the aqueous phase as follows:
where Ci is the concentration in the droplet in M (moles per liter), γi is the activity coefficient of the chemical species in the aqueous phase, and Hi is the Henry’s law constant, which depends on temperature. Partial pressure is generally expressed in atm and the Henry’s law constant is, therefore, expressed in M atm−1.
If the solution is very dilute, the solution can be assumed to be ideal and the activity coefficients become 1 (i.e., the chemical species concentrations are equal to their activities). As a matter of fact, the initial formulation of Henry’s law used the species concentration, rather than its activity. This assumption is generally appropriate for clouds that have a large liquid water content. However, it may not be applicable to fogs, because they may contain high aqueous-phase concentrations of pollutants, particularly during their formation and evaporation.
The Henry’s law constants of selected atmospheric chemical species are provided in Table 10.1.
Table 10.1. Henry’s law constant, enthalpy of dissolution, effective Henry’s law constant (at pH = 5.6), and fraction present in the aqueous phase (for a liquid water content of 1 g m−3) at 25 °C for selected chemical species.
| Chemical species | Henry’s law constant (M atm−1) | Enthalpy of dissolution (kcal mole−1) | Effective Henry’s law constanta (M atm−1) | Fraction in the aqueous phase |
|---|---|---|---|---|
| NO | 1.9 × 10−3 | −2.9 | 1.9 × 10−3 | 0.000005 % |
| NO2 | 1.2 × 10−2 | −5.0 | 1.2 × 10−2 | 0.00002 % |
| O3 | 1.1 × 10−2 | −5.04 | 1.1 × 10−2 | 0.00002 % |
| CO2 | 3.4 × 10−2 | −4.85 | 4 × 10−2 | 0.0001 % |
| SO2 | 1.23 | −6.25 | 6.5 × 103 | 14 % |
| NH3 | 62 | −8.17 | 2.6 × 105 | 87 % |
| HCHOb | 6.3 × 103 | −12.8 | 6.3 × 103 | 13 % |
| H2O2 | 7.45 × 104 | −14.5 | 7.45 × 104 | 65 % |
| HNO3 | 2.1 × 105 | − | 1.3 × 1012 | 100 % |
(a) For non-ionic species, the effective Henry’s law constant is equal to the Henry’s law constant.
(b) The Henry’s law constant takes into account the hydrolysis of formaldehyde in solution, which leads to the formation of a diol (methylene glycol).
10.2.3 Ionic Dissociations
In the aqueous phase, some chemical species dissociate into cations (with a positive charge) and anions (with a negative charge). This ionic dissociation leads to a displacement of the gas/droplet equilibrium if one considers the total aqueous-phase concentration of the chemical species, i.e., the sum of the concentrations of the non-dissociated species and corresponding ions. For example, for a diacid, such as sulfuric acid, H2SO4, or sulfur dioxide (which hydrolyzes into H2SO3):
(R10.1) 
(R10.2) 
(R10.3) Assuming here an ideal solution, the concentration of the non-dissociated species is obtained according to Henry’s law:
where H is the Henry’s law constant in M atm−1, the aqueous-phase concentration of H2A is expressed in moles per liter, i.e., M, and the gas-phase concentration of H2A is expressed in atmosphere (atm).
The dissociation equilibria lead to the formation of HA− and A2- and their concentrations are related to that of H2A as follows:
(10.3) 
The ensemble of the concentrations of H2A in solution, including the ionic species HA− and A2-, [H2A(aq)]t, can be defined as follows:
Thus:
(10.6) For example, in the case of sulfur dioxide, H2SO3, A is SO3, which leads to:
(R10.4) 
(R10.5) 
(R10.6) where the notation (l) indicates liquid water. The values of the Henry’s law constant and dissociation equilibrium constants are given at 25 °C. These constants depend on temperature, according to the van’t Hoff relationship, as follows:
(10.7) where ΔHA is the enthalpy of dissolution and ΔHR is the enthalpy of reaction. The enthalpy of dissolution is negative for most major atmospheric chemical species (ΔHA = – 6.25 kcal mole−1 at 25 °C for SO2). Therefore, if T < Tref, the Henry’s law constant will be greater than its reference value (generally given at 25 °C). In other words, a lower temperature favors dissolution. The enthalpy of reaction can be positive (for example, for the dissolved species of CO2, H2CO3) or negative (for example, for the dissolved species of SO2, H2SO3). If it is positive, a lower temperature will favor the non-dissociated species (for example, H2CO3, rather than HCO3− or CO32−). If it is negative, a lower temperature will favor the ionic species (for example, SO32− and HSO3−, rather than H2SO3).
The ensemble of species corresponding to SO2(aq) is generally noted as S(IV), because sulfur is in oxidation state IV. The ensemble of species corresponding to sulfuric acid is noted S(VI), because sulfur is in oxidation state VI. For S(IV):
(10.8) 
(10.9) Therefore, the equilibrium between gas-phase and aqueous-phase SO2 is expressed as follows:
(10.10) The relative fractions of the three species of sulfur dioxide in solution can be calculated as a function of pH as follows.
Equation 10.9 provides the fraction of H2SO3(aq):
(10.11) The HSO3− and SO32− fractions are obtained from the ionic equilibrium relationships:
(10.12) 
(10.13) These fractions are illustrated as a function of pH in Figure 10.1. When the solution is acidic, the non-ionic S(IV) fraction dominates. On the other hand, when the solution is basic, the ionic equilibria are displaced toward the formation of H+ ions and the sulfite ion, SO32−, dominates. At pH values typical of clouds (i.e., between about 4 and 5.6), the bisulfite ion, HSO3−, dominates.
Figure 10.1. Dissolution of SO2 in droplets. Effective Henry’s law constant (top figure) and aqueous-phase chemical composition (bottom figure) of sulfur in oxidation state IV, S(IV), as a function of pH at 5 °C.
10.2.4 Effective Henry’s Law Constant
An effective Henry’s law constant, Heff, includes all forms of a chemical species in solution. For example, for a species with two ionic dissociations:
(10.14) This effective Henry’s law constant is proportional to the standard Henry’s law constant, but it takes into account the dissociation of the molecular species into ionic species (via the dissociation constants, K1 and K2) and it depends on the pH of the solution (via [H+]). The effective Henry’s law constant is greater than the standard Henry’s law constant, which reflects the fact that the dissociation of a molecular species in solution increases its overall solubility. This effective Henry’s law constant is illustrated as a function of pH for sulfur dioxide in Figure 10.1. As indicated by Equation 10.14, it increases with pH, because a basic solution favors the dissolution of an acid.
For a monoacid HA, such as nitric acid, HNO3:
(10.15) For a base, such as ammonia, NH3 and NH4OH:
(10.16) This latter equation includes the dissociation of water into protons (H+) and hydroxide ions (OH−):
At 25 °C, the equilibrium constant for water dissociation is as follows:
(10.17) The density of water at 25 °C and 1 atm is 0.997 g cm−3, i.e., 997 g liter−1; the molar mass of water is 18 g mole−1, thus:
(10.18) Therefore:
(10.19)