SCOPE 21 -The Major Biogeochemical Cycles and Their Interactions 

ABSTRACT

The cycles of C, N and S interact in the atmosphere within the condensed phases of aerosol particles and clouds. Much of this interaction occurs in the aqueous phase due to the hygroscopic nature of compounds like NH₄, HSO₄ and the water solubility of trace gases, such as SO₂ and NH₃. In order to explore the nature of these interactions, the equilibria of the system H₂O(1), SO₂, NH₃, H₂SO₄ and CO₂ are examined. Subsequently, oxidation of S(IV) to S(VI) within the aqueous phase is considered as a function of NH₃, H₂O(1), and the source strength of S(IV).

• Almost all S(IV) is in the gas phase when clouds are acidified below pH5.5, while most ammonia is present as aqueous NH₄⁺. Gas phase ammonia concentrations are probably often in the range of 0.5 to 5.0 pptv.
• The amount of S(IV) available for oxidation in the water phase is a strong function of pH, with more S(IV) available at higher pH, and is increased by adding NH₃.
• CO₂ is unimportant to the pH of atmospheric water in most cases.
• S(IV) slowly oxidizes to S(VI) in aerosols and clouds, but can produce significant amounts of SO₄^2- after a number of passages through clouds.
• The products of oxidation of S(IV) in cloud water decrease the reaction rate such that the production of SO₄^2- is a nonlinear function of time and of source strength of SO₂^.
• The overall effect of increased SO₂ emissions could be a slowing of its oxidation allowing geographical regions under the influence of acid precipitation to increase in area.

4.1 INTRODUCTION

The heterogeneous interactions of C, N, and S cycles within the atmosphere depend on the existence of aerosols and water clouds. * These particles provide sites for rapid reaction of key molecules that otherwise react slowly (or not at all) in the gas phase. Such reactions in or on particles are expected to be particularly important in situations where photochemistry is not effective (Shaw and Rodhe, 1981). In addition, many of the reaction products of gaseous N and S compounds are themselves liquids or solids of low vapour pressure under normal conditions and are found as aerosol particles. The water solubility of these reactions products allows their incorporation into cloud droplets and removal from the atmosphere by precipitation. The nature of the interactions of C, N, and S cycles thus will depend on the physical and chemical characteristics of both aerosols and clouds. In addition, these interactions cause shifts in chemical equilibria that in turn cause nonlinear responses of atmospheric concentrations and fluxes to changes in the source strength of materials injected into the air.

Atmospheric aerosols are chemically heterogeneous and are composed of large numbers of compounds. While it has been customary and useful to treat these simply as physically mixed systems (Junge, 1963), more recent results demonstrate clearly that both the chemical composition and chemical interactions of the tropospheric aerosol are strong and regular functions of particle size (Stevens et al., 1978). Most of the available data are from low altitudes in industrialized continental regions, but similar results are found in marine areas (Duce, Chapter 16, this volume).

*Aerosols are defined as suspensions in a gas of particles of liquid or solid material that are stable to either gravitational sedimentation or Brownian coagulation over some period of time. In the case of atmospheric aerosols, the relevant time scale is a fraction of an hour or longer. Thus, ordinary water clouds are aerosols; however, it is customary to designate water clouds separately as having a relative humidity over 100%. Fog may be defined as cloud in contact with the ground.

The mass or volume distributions of aerosols are consistent with the composition-size dependence and show that the particles have distinctly different chemical composition and morphology above and below 1 µm (Figures 4.1 and 4.2). The mass mode below 1 µm is often called the accumulation mode, because mass accumulates there due to condensation and coagulation. These same processes tend to mix internally the accumulation mode particles (i.e. each particle has some of each constituent). In contrast, the lack of condensation and coagulation of coarse mode particles, along with their mechanical origins, tends to leave these aerosols as an external mixture (i.e., individual particles may have different compositions). In addition, the coarse and accumulation modes are externally mixed with each other, and do not interact chemically to any known extent. Because of their chemical composition the sub-µm aerosols usually contain some liquid water in an aqueous phase.

Figure 4.1 The volume distributions of aerosols plotted as dV/d (log D_p) (linear) versus diameter (D_p) on a log scale. (Whitby and Sverdrup, 1980). Reproduced by permission of John Wiley & Sons, Inc.

The accumulation mode aerosols are to a large degree the result of interactions of C, N and S cycles, both within a condensed phase and via preceding gas-phase production reactions. From Crutzen's review of homogeneous reactions (Chapter 3, this volume), gas phase production of H₂SO₄ (reactions R3335) results either in nucleation with H₂O of new particles of hydrated H₂SO₄ or in the condensation of H₂SO₄ and H₂O on the surfaces of pre-existing particles. Both of these possibilities are important. The former is a necessity for the creation of new particles in the absence of direct injection of particles into the atmosphere (e.g. from combustion). The latter results in a build-up of the mass of sulphate compounds in the size class between 0.1 and 1 µm. Chemical reaction of NH₃ with H₂SO₄ results in an aerosol of composition ranging from NH₄HSO₄ to neutralized (NH₄)₂SO₄. The reaction of NO₂ with OH produces HNO₃, some of which may attach to or be dissolved in pre-existing aerosol particles. HNO₃ can be neutralized by NH₃ forming NH₄NO₃ in the condensed phase of accumulation mode aerosols. Sulphate and nitrate combined with ammonium usually are the dominant inorganic species formed in the accumulation mode by direct gas-particle conversion. In addition, a wide variety of organic materials are often found in this same size range, although their total mass is usually considerably less than the mass of sulphates and nitrates, The gas-phase interactions discussed by Crutzen (Chapter 3, this volume) thus have direct implications for the formation and composition of submicrometer aerosols.

Figure 4.2 A conceptual representation of the volume or mass distributions of aerosols as related to source, transformation and sink processes. Fine particulate matter also contains some primary emissions such as C (0) (elemental carbon) and Pb. Ordinate is as in Figure 4.1 (Shaw and Stevens, 1980), Reproduced by permission of New York Academy of Sciences

Besides such gas phase interactions, C, N, and S compounds interact within the condensed, aqueous phase of aerosols and clouds, with chemical reactions resulting in an increased mass of dissolved substances. In particular, the oxidation of SO₂ in the liquid phase of clouds results in increased amounts of dissolved SO₄²-. Since most clouds evaporate and do not result in precipitation, the dissolved material is released back to the atmosphere in the accumulation mode of the aerosol. There are several known reaction mechanisms of SO₂ and its dissociation products in the aqueous phase. Among the more likely are oxidation by O₃ and H₂O₂ (Penkett et al., 1979) although oxidation by O₂ may be of some importance. No single mechanism can be identified yet as the most important one.

The lifetimes in air of the two mass modes are also distinctly different, largely due to the different mechanisms of removal, Particles greater than several µm tend to be removed by sedimentation and usually have lifetimes of much less than a day, Particles below 1 µm diameter have very small sedimentation velocities (<10^-2 cm s^-1) and are removed from the air mainly by incorporation into cloud droplets and precipitation, As a result, their lifetime is dictated by the period between precipitation events, and typically is a few days to perhaps a few weeks in mid-latitudes. As a result of little, if any, extensive interaction of the gas phase with the coarse mode, there is little interaction of C, N and S cycles with particles much above ca, 1 µm in size. Although we will emphasize sub-µm particles, we note the importance to precipitation chemistry of below-cloud scavenging by rain of basic soil dust. We also leave open the question of coarse-particle interaction with NO_x and HNO₃.

Clouds of liquid water have droplets from ca 5 to 50 µm diameter, typically yielding liquid water contents of perhaps 0.10.5 g m^-3; some vigorously precipitating clouds may have water contents in excess of 0.5 g m^-3. Fogs have somewhat lower liquid water contents, typically below 0.1 g m^-3, as well as somewhat smaller droplets. The water in clouds and fogs contains soluble salts from the remains of condensation nuclei, water soluble gases (e.g. CO₂, SO₂, NH₃, etc.) as well as suspended but insoluble materials (e.g. mineral grains and soot). The lifetime of an individual cloud droplet is often a fraction of an hour though several hours may be possible in fog. Since only a small fraction of clouds result in precipitation, aerosol particles take part in the condensationevaporation cycle many times before precipitation can remove them. In the physical process of cloud nucleation, the chemical property of water solubility of the nuclei is a dominant factor. Due to the solubility of the key compounds (ammonium sulphates and nitrates) the products of interaction of N and S cycles in the atmosphere are probably the dominant cloud condensation nuclei. To illustrate the ways in which the cycles of C, N, and S influence each other within aerosols and clouds, we will select a limited family of interactions as useful examples. After choosing the system, NH₃CO₂SO₂-H₂SO₄H₂O(1), we will examine the characteristics of the equilibria that control the interactions of the dissolved species. We can then investigate chemical reactions that occur within this system in the presence of O₂, O₃, and H₂O₂. This allows consideration of the response of sulphate production in aerosols and clouds to changes in the source strengths of SO₂ and NH₃. The results allow an understanding of the nonlinearity of sulphate production in response to varying SO₂ strengths.

4.2 GENERAL NATURE OF INTERACTIONS IN AEROSOLS AND CLOUDS

That the atmospheric cycles of C, N, and S interact within both aerosols and clouds is indicated by several observations:

• Submicrometer aerosols usually contain NH₄⁺, SO₄^2-, C(O) (graphitic carbon as soot) and organic carbon (see Table 4.1).
• Sulphur dioxide is known to oxidize to form H₂SO₄. In turn, H₂SO₄ has a low vapour pressure and condenses as particles, NH₃ is known to be emitted from the ground and reacts with H₂SO₄ particles to form the salts (NH₄)₂SO₄, NH₄HSO₄, etc.
• Clouds and fog form on soluble nuclei of condensation such as sulphates, and cloud and fog water usually contain dissolved ammonium and sulphate ions (see Table 4.2).
• Precipitation usually contains measurable amounts of SO₄^2-, NH₄⁺, NO₃^-, C(O) and HCO₃^- and may be an important source of these compounds to terrestrial ecosystems (see Table 4.3).
• NH₃, SO₂, HNO₃ and NO₂ are water soluble, are present in air and to some degree dissolve in cloud and fog water as well as in hydrated aerosol particles (see Table 4.4).

1. Chemical reaction (e.g. 2NH₃ + H₂SO₄ (NH₄)₂SO₄)
2. Gas exchange and equilibria with hydrated, wet particles or droplets (e.g. SO₂ + H₂O(1) H₂SO₃ H⁺ + HSO₃^-, etc.)
3. Condensation of low vapour pressure material to yield either new particles or to add to the mass of pre-existing ones (e.g. condensation of H₂SO₄ that was produced photochemically)
4. Adsorption of materials into the surfaces or pre-existing particles (e.g. on the surface of carbon particles where specific areas of 100 m² g^-1 are possible)
5. Surface reactions (e.g. OH + organic film products)
6. Capture of a basic particle (e.g. CaCO₃) by a cloud or rain drop with subsequent reaction.

Table 4.1 Typical composition of atmospheric aerosols, concentrations in µg m^-3 

a) Industrial Region*
Specie or element		Concentration
Diameter less than 2.5 µm
	SO42-	1.070.0
	Al	0.0080.05
	As	0.04
	Br	0.013.0
	C (graphitic)	010.0
	Cd	0.020.4
	Cl	0.0055.0
	Cr	00.002
	Cu	0.0020.14
	Fe	0.021.0
	K	0.010.2
	Mg	0.0060.15
	Mn	0.0020.03
	NH4+	0.55.0
	Ni	0.0020.1
	NO3-	3.060.0
	Pb	0.56.0
	Si	0.060.6
	Ti	0.030.06
	V	0.0040.007
	Zn	0.003-0.06
Diameter greater than 2.5 µm
	Al	0.3 2.0 or more (from soil)
	Si	1.0 10.0 or more (from soil)
	P	0.030.1
	S	0.20.5
	Cl	0.2 5.0 or more (from oceans)
	Ca	0.4 1.0 or more (from soil)
	Fe	0.3 1.0 or more (from soil)
*Adapted from Charlson et al. (1978) and Stevens et al., (1978).
b) Background Aerosol†
		Concentrations (µg m-3)
Specie		Continental boundary layer	Marine boundary layer	Free troposphere
SO42-  (excess)‡		< 0.20.4	0.33.0	< 0.1 0.6
NH4+		0.040.1	< 0.01 0.2	< 0.02
†from Huebert and Lazrus (1980).
‡SO41- (excess) is the amount of SO42- remaining after the amount from sea-salt is subtracted
based on either Na+ or Cl data.

Table 4.2 Example cloud water composition, µeq litre^-1

Table 4.3 Inorganic composition of rain and snow water, Forshult Station, Sweden 19751979 (incl)*

Table 4.4 Gas Phase SO₂, NH₃, CO₂* 

Background
SO2	Northern Hemisphere
	Boundary Layer		89 ± 69 ppt
	Free Troposphere		122 ± 85
	Southern Hemisphere
	Boundary Layer		57 ± 18
	Free Troposphere		90 ± 21
NH3	Very uncertain
	1001000 ppt (ocean surface equilibrium)
	1-100 ppt (equilibrium with acidic, wet sulphate aerosols)
CO2	340 ppm

Industrial Region, Boundary Layer (estimates)
Away from	SO2	0.13 ppb
sources	NH3	10-31 ppb
	CO2	340400 ppm
Close to	SO2	up to 1 or a few ppm
sources	NH3	10-31 ppb or more (uncertain)
	CO2	3401000 ppm or more
*Adapted from Maroulis et al. (1980) and Lau and Charlson (1977).,

Collectively, these interactions play significant roles in controlling the molecular form of the aerosol particles as well as the ionic species present in rain and snow water.

The sub-µm sulphate aerosol often exhibits the chemical features of a single compound. For example, some particle samples show deliquescence and X-ray diffraction of pure (NH₄)₂SO₄ (Charlson et al., 1978) or the volatility of H₂SO₄ at ca. 125°C (Coburn et al., 1980) Since there are no known direct sources of fine-particle (NH₄)₂SO₄, its existence also demonstrates the simplest interactions of the S and N cycles in the atmosphere. This also indicates the sub-µm aerosol particles containing deliquescent salts (e.g. NH₄NO₃, NH₄HSO₄, (NH₄)₂SO₄) or hygroscopic liquid (e.g. H₂SO₄) understandably also contain liquid water. At 80% R.H., taking Raoult's law as a means of approximating the composition, such particles would be 80 mole percent water and 20 mole percent dissolved species. Hence at R.H. < 90 or 95%, the aqueous phase of such particles is sufficiently concentrated that non-ideal behaviour will occur.

The calculations presented in this paper are for water solutions that behave ideally. Extension to non-ideal solutions is not included, but the general tendency will be for the concentration of dissolved gaseous species to decrease (salting-out effect) and for ionic forms to increase since their activity coefficients will be substantially less than unity.

Figure 4.3 Matrix of potential interactions of C, N and S in air defined by oxidation state. Elemental sulphur is omitted because it is not known to occur in air. The shaded corner (SO₄²-, SO₂, CO₂, NH₃, and RNH₂) will be treated in section 4.4

4.3 POSSIBLE INTERACTIONS

In order to explore objectively the range of interactions, we consider the various C, N and S compounds that exist in tropospheric air. Figure 4.3 depicts a three-dimensional matrix of the oxidation states and species that are involved. Because COS reacts on time scales of years (Johnson, 1981) and because H₂S and RSH (mercaptans) are expected to react fairly rapidly to SO₂, oxidation states IV and VI of sulphur are of primary interest. Neither N₂ nor N₂O react on or in particles, nor does CO.

Thus, we can focus on interactions of S(IV) and S(VI) with organic C, CO₂, NH₃, NO, NO₂, HNO₂, HNO₃ and H₂O(1). These are represented qualitatively in Figures 4.4 and 4.5 for S(IV) and S(VI) respectively. Here we assume that NO oxidizes to NO₂ before any interactions with C or S in particles, and we further assume that NO₂ produces HNO₃ and HNO₂ upon incorporation in hydrated particles. For convenience we list all organic compounds as C(IV).

The most common interactions are acid equilibria, gasliquid exchanges and the influence of NH₃ or amines as bases neutralizing weak or strong acids. A potential source of gas phase HNO₃ is its volatilization that may be caused if sufficient H₂SO₄ is added to a particle, e. g. by photochemical production. Since S(IV) and S(VI) coexist in the same particles, acidbase equilibria are clearly sensitive to the proportions of the weak and strong acids that are present. Because the rate of oxidation of S(IV) to S(VI) depends on which dissolved species are present, it is necessary to consider the equilibria that are involved.

Figure 4.4 Interactions of S(IV) with C and N in wet particles. Note: (1) Acid equilibria occur in all nine cases. (2) Catalytic oxidation of S(IV) by C(O) may occur independently of the presence of any N species

Figure 4.5 Interactions of S(VI) with C and N in wet particles. Note: (1) Volatilization of HNO₃ probably occurs under acidic conditions independent of the presence of some C species (Tang, 1980). (2) Neutralization of H₂SO₄ by NH₃ is probably independent of C

In order to approach a complete list of factors controlling the equilibrium, we might include the components used by Liljestrand and Morgan (1981): SO₂, NO, NO₂, HNO₂, HNO₃ NH₃, HCl, H₂SO₄, CO₂, kaolinite, Al(OH)₃ and H₂O(1). However, it is instructive at this stage to limit this discussion to the simpler system SO₂, CO₂, NH₃, H₂SO₄ and H₂O(1) (Figure 4.3, shaded corner). This may be justified for understanding the chemistry of these components alone, and may be further justified to the extent that there are atmospheric situations in which the other components are present in concentrations that are low enough to be neglected.

4.4 THE SYSTEM SO₂, CO₂, NH₃, H₂SO₄, AND H₂O (LIQUID) 

Chemical equilibrium of gaseous SO₂, CO₂ and NH₃ with wet particles of less than 5 µm diameter occurs in less than a few seconds (Freiberg and Schwartz, 1981). Thus, multiple equilibrium expressions can be used to approximate the overall composition that results from the weak acid/weak base interactions that occur along with the existence of strong acids such as H₂SO₄ (Liljestrand and Morgan, 1981). This step is a necessary prelude to examining the oxidation of S(IV) in solution, a discussion of which follows in section 4.5. The equilibrium concentrations can be calculated numerically; however, they also may be presented graphically, a form which reveals more clearly the interrelations of the many constituents.

Table 4.5 lists the relevant expressions and constants that were used to construct the log concentration versus pH diagrams (Sillén, 1967) in Figures 4.64.8 and further used for the oxidation computations in section 4.5. In addition, Table 4.6 gives the partitioning of SO_2, and NH₃ between liquid and gas phases in clouds and fog.

Figures 4.6 4.8 are the simplest representation of a master variable diagram (Sillén, 1967) in which the concentration of each species is given as a function of a master variable, in this case, pH. The nine equilibrium expressions of Table 4.5 first can be put into logarithmic form, resulting in nine linear equations. The three Henry's law expressions (Equations (2), (5), and (7)) yield aqueous concentrations of SO₂ • H₂O, NH₃•H₂O and CO₂•H₂O that are independent of pH and are governed by the gas phase equilibrium pressure of each gaseous species. These result in values represented by three lines parallel to the pH axis.

The remaining six equations can be solved to yield linear expressions for the concentration of each dissociated species as a function of pH, giving six more lines. A seventh line is log[H⁺] = pH, and [SO₄^2-] is included as a pH-independent quantity. The equilibrium condition is depicted by the pH at which the sum of the positive ions is equal to the sum of the negative ions. At this pH, the equilibrium concentrations of the other species are also graphically depicted. We caution that these plots do not include equations of mass balance and hence apply only at the equilibrium condition. Each plot expresses one solution to the equations for a particular set of data and therefore must not be interpreted literally as dynamic diagrams in which processes can be studied.

The three example conditions depicted in Figures 4.64.8 were selected to represent a range of concentrations of SO₂, NH₃, [SO₄^2-] and liquid H₂O as might be found in actual cases; CO₂ is constant at 340 ppmv. The equilibrium conditions in Figure 4.6 are intended to represent an industrial region and have been selected as the initial condition for some of the oxidation calculations of section 4.5. The initial (SO₄^2-₎ level of 3 ppbv and SO₄^2- of 5 µg m^-3 represents a polluted industrial location that is well removed from the immediate influence of sources. The bulk of the (NH₄⁺) was initially contained in nuclei of condensation ((NH₄)₂SO₄) and the liquid water content reached in this activated cloud is 0.5 g m^-3. The resulting equilibrium partial pressure of NH₃ is only 7 pptv, due to the acidity of the solution.

Table 4.5 Values of constants used

	Equilibrium	Equilibrium constant		Value at 5°C	Reference
(1)	H2O H+ + OH	Kw = [H+][OH]		1.82 x 10-15 mol2 litre-2	Yui (1940)
					Robinson and Stokes (1959)
(2)	SO2(g) + H2O SO2 . H2O	KHS =	PCO2 [SO2 . H2O]	0.379 atm litre  mol-1	Johnstone and Leppla (1934)  Lowell et al. (1970)
(3)	SO2 . H2O H+ + HSO3	K1S=	[H+][HSO3] [SO2 . H2O]	0.0206 mol litre-1	Lowell et al. (1970)  Yui (1940)
(4)	HSO3H+ + SO32	K2S =	[H+][SO32 ]     [HSO3]	8.88 x 10-8 mol  litre-1	Lowell et al. (1970)  Yui (1940)
(5)	NH3(g) + H2O NH3 . H2O	KHN =	PNH3 [NH3 . H2O]	7.11 x 10-3 atm litre mole-1	Morgan and Maass (1931)  Freiberg (1974)
(6)	NH3 + H2O NH4+ + OH	Kb =	[NH4][OH] [NH3 . H2O]	1.5 x 10-5 mol  litre-1	Yui (1940) Freiberg (1974)
(7)	CO2(g) + H2OCO2 . H2O	KHC =	PCO2 [CO2 . H2O]	16.6 atm litre mol-1	Robinson and Stokes (1959) Morgan and Maass (1931)
(8)	CO2 . H2O H+ + HCO3	K1C	[H+][CO3] [CO2 . H2O]	2.94 x 10-7 mol litre-1	Yui (1940) Robinson and Stokes (1959)
(9)	HCO3 H+ + CO32-	K2C =	[H+][CO32]     [HCO3]	2.74 x 10-11 mol  litre-1	Yui (1940) Robinson and Stokes (1959)

Figure 4.6 Industrial region. The equilibrium pH of the system is determined at the point of charge balance (O). At that pH, the concentrations of other species are also given for the equilibrium conditions. We caution that these plots do not include equations of mass conservation and thus strictly apply only at the equilibrium pH. Assumptions:

	aerosol (SO24)	= 5.0 µg m-3
	liquid water	= 0.5 g m-3
	aerosol (NH4+)	= 1.7 µg m-3
	PSO2	= 3 ppbv; 7.86 µg m-3
	Calculated: PNH3	= 7.1 x 10-12 atm = 5 x 10-3 µg m-3
	pH	= 4.6

For comparison to the hypothetical case of Figure 4.6, we can consider the composition of rain-water from an actual site downwind of an industrial region. Here we assume that rain-water has a composition similar to and governed by the composition of the clouds from which it fell. Figure 4.7 is based on 5 years of precipitation chemistry data from Forshult, Sweden (Table 4.3) with the assumption of an SO₂ concentration of 1 ppbv. This case might be termed a cloud in well-aged industrial or continental air.

Figure 4.7 Forshult (Sweden) precipitation 19751979. Assumptions: 

 Finally, Figure 4.8 represents a clean background case, either in the boundary layer or free troposphere. The total SO₂ concentrations, i.e. SO₂ (gas) plus SO₂ (dissolved), are representative of remote locations in the northern hemisphere (Maroulis et al., 1980). Recent data for sulphate aerosol in remote locations indicate sulphate concentrations of 0.1 to 1 µg per standard cubic meter with molar ratios of (NH₄⁺) to SO₄^2- between 1 and 2. The [NH₄⁺]/[H⁺] of 2 was picked arbitrarily for this example.

1. Almost all the S(IV) is present as SO₂ gas, for realistic liquid water contents and pH < 5.5. In contrast, almost all the ammonia is in solution as NH₄⁺.
2. At any realistic pH (3.5 or higher) SO₂^.H₂O is less than one-tenth of the other dissolved forms of S(IV), largely due to the high value of K_1S. As a result, the total amount of dissolved S(IV) is always a strong function of pH. This implies that the production rate of SO₄² in a cloud decreases as hydrogen ion in the cloud water increases, regardless of oxidation mechanism. (This presumes reaction rates for HSO₃ or SO₃² comparable to or greater than for SO₂^.H₂O).
3. Carbon dioxide is important for the pH of atmospheric liquid water only in cases of low (SO₂)_. and low (SO₄²) as in Figure 4.8. Even then it is not dominant.
4. The charge balance of cloud water may be significantly effected at times by HSO₃, even in the presence of realistic amounts of (SO₄^2-) (Hales and Dana, 1979).
5. pH below ca. 5 also requires the presence of strong acids, except in the instance of high concentrations of SO₂, such as near sources.

Figure 4.8 Background cloud. Assumptions: Liquid water content = 0.5 g m^-3

	T  = 5C
	[NH4+]/[H+] =2
Mass concentration (SO42) = 0.1 to 1.0 µg m-3
	PNH3 = 1.6 X 10-12 atm (10-3 µg m-3)
	PSO2= 0.1 ppbv (0.26 µg m-3)
	At (SO42) = 0.1 µg m-3 pH = 5.6 NH4+ (aq) = 0.05 µg m-3
	S (IV) (aq) = 0.06 µg m-3
	At (SO42) = 1 µg m-3 pH = 4.95 NH4+ (aq) = 0.2 µg m-3
	S(IV) (aq) = 0.013 µg m-3
	Note: [SO32] and [CO32] are omitted for simplicity

Given this set of equilibrium conditions, it is now possible to consider chemical reactions that occur within the liquid phase. In doing so, we want to emphasize the ways in which ammonia and pH influence the reaction rates. A major goal in doing this is to study the overall response of the amounts of reaction products (e.g. (SO₄^2-) to changes in the inputs of reactants (SO₂).

Table 4.6 Partitioning* of SO₂ and NH₃ between liquid and gas phases as functions of liquid water content, L, and [H⁺]

x=

L[x]RT     Px

†SO2	LK1SRT   [H+]KHS	for pH <6
‡NH3=	LKb[H+]RT   KHNKw

4.5 OXIDATION OF S(IV) TO S(VI) IN WET PARTICLES 

One of the outstanding practical problems of atmospheric chemistry is to be able to understand and to predict the response of chemical processes in the atmosphere to increases or decreases of input materials. In the case of the system in section 4.4, we would like to know what happens to the composition of cloud and rain-water when SO_2. sources are increased (e.g. due to industrial development) or decreased (e.g. when controls are instigated). Not only must we consider the changes in equilibria, we also must include the effects of chemical reaction.

We have already seen in Chapter 3 (Crutzen, this volume) the possibility of delays in the oxidation of SO₂. These may be due to effective competition by NO₂ for OH radicals in the gas phase (reaction R10) or by decreases in H₂O₂ and subsequent decrease in oxidation of SO₂ in cloud-water caused by competition for HO₂ radicals by NO (reaction R5 followed by R36). Such interactions of NO_x with the oxidation of SO₂ would cause some SO₂ to be transported farther before being oxidized and deposited in rain-water, possibly leading to increases in the area of regions influenced by acid precipitation. Besides such gas phase interactions, shifts of equilibria in the liquid phase can lead to similar effects.

It is well established that S(IV) is easily oxidized in aqueous solutions. Models of the oxidation of SO₂ in clouds have been developed that include oxidation by O₂ (Scott and Hobbs, 1967; Easter and Hobbs, 1974; Hegg and Hobbs, 1979). Other models simply treat the oxidation rate as an input parameter, typically in the range of a few to several percent per hour (see e.g. Scott, 1981). Considerable effort has been expended on studies of various liquid-phase reaction mechanisms, including oxidation by O₂, O₃, and H₂O₂ and catalysis by metal ions as well as the role of mass transport of gases within clouds (Freiberg and Schwartz, 1981). Table 4.7 lists the reaction mechanisms we include in our calculations.

As noted numerous times in the literature, the oxidation rates show dependences on pH and on NH₃. The sense of this dependence is that the rate of conversion of S(IV) to S(VI) decreases as the aqueous phase becomes acidic. Thus a reaction product, H₂SO₄, tends to decrease the rate of reaction indicated earlier for the case of the effect of gas phase reactions of NO_x, acidification of cloud water by the production of H₂SO₄ should also delay the oxidation of SO₂. To explore the role of this pH dependence, we will calculate the rate of production of SO₄^2- in a cloud as a function of the SO₄^2- source strength. Although they are clearly important, we neglect entirely any gas phase reactions. The purpose of this section is not to study liquid-phase oxidation mechanisms, but rather to use the mechanisms that have been proposed to address the question of the relationship of SO₄^2- production rates in cloud-water to SO₄^2- source strengths. We are particularly interested in determining the response of SO₄^2- production to SO₄^2- source strengths, the nature of the responses (e.g., linear versus nonlinear) and to what degree this depends on NH₃. We herein include a brief description of our model and qualitative results; the model will be presented in detail elsewhere (Taylor et al., in preparation).

The presence of ambient ammonia or other basic gases or particles increases the liquid-phase oxidation rate (Junge and Ryan, 1958; Scott and Hobbs, 1967) by neutralizing the pH as acid sulphates are formed. The concentration of ammonia in the gas phase has such a large effect on the rate and total amount of oxidation (Easter and Hobbs, 1974; Adamowicz, 1979; Overton et al., 1979) that ammonia concentrations and source rates must be studied along with SO₄^2- concentrations and source rates in any attempt to understand the effect of varying these parameters on SO₄^2- production.

Table 4.7 Oxidation mechanisms

There is no general acceptance as to the ambient air concentration of NH₃ (Lau and Charlson, 1977; Hales and Drewes, 1979), and there are also major questions as to source strengths of NH₃. Söderlund and Svensson (1976) could only account for approximately one-quarter of the NH₃ sources that are needed to balance the global NH₃ cycle. We therefore include a source of ammonia as a variable parameter in our model and make no attempt to analyse or justify the relationship between NH₃ and SO₂ emission rates.

Our calculations were done using a simple box model of uniform wet haze at 5°C. The box is a closed system except for sources of SO₂ and NH₃ which are assumed to be instantaneously and uniformly mixed. The box has dimensions 1 km x 1 km x 1 km and there are no advection or sink terms. The liquid water content of the haze is determined by the choices of initial sulphate aerosol concentration, size and sulphate composition of the condensation nuclei (CN), the fraction of total sulphate used as CN, and the supersaturation. To simplify the calculation only one form of sulphate ((NH₄)₂SO₄) and one composition and size of CN are used, resulting in only one size droplets. All droplets have the same concentration of SO₄^2- and associated cations. Also for simplicity all SO₄^2- in the initial calculations is assumed to be in the CN.

The droplet equilibrium size is determined by the standard Köhler curve equation. We chose to use the equilibrium size before activation and to keep the droplet the same size throughout the oxidation process (this is an approximation that is true only if the increase in mass of the droplet remains small). The chemical composition of the CN is impure (NH₄)₂SO₄; however, its effect on the equilibrium droplet size is approximated as if it were pure (NH₄)₂SO₄. The impurities are assumed to be chemically inert. The parameters remaining that must be defined are the supersaturation and the mass of the CN, and they in turn determine the resulting liquid water content, L, and the initial concentration of NH₄⁺ and SO₄^2- in the liquid water.

Our values of 3.0 µm for the droplet radii and 0.01 g m^-3 for the liquid water content seem reasonable when compared to measurements made by Garland et al. (1973). In choosing one size droplet to comprise the entire liquid water content of the system, 3.0 µm gives a reasonable number of droplets and liquid water content for a high humidity haze. The liquid water content measured by Garland et al. (1973) was 0.05 g m^-3 40 minutes after the onset of the fog, so 0.01 g m^-3 would seem reasonable for earlier in a developing fog or haze. Clearly, our assumption that the droplets do not grow must be considered only a first approximation, taken to avoid the complexity of the cloud droplet growth equations. We also consider higher liquid water content later in order to assess the sensitivity of the model to this parameter.

The pressures of gas that initially come into contact with the above droplets are 3 ppb SO₂, 330 ppm CO₂ and a variable amount of ammonia (0.110 ppb). For any given condition the total amount of NH₃ and NH₄⁺ is constant. The resulting equilibrium concentrations are found by simultaneously solving the equations for P_SO2,P_NH3 and [H⁺] from Table 4.5, and taking into account that total nitrogen will include the [NH₄⁺] from the CN as well as from NH₃(g).

Oxidation rate calculations were carried out using the mechanisms listed in Table 4.7 and starting with the above initial conditions (time = 0). The oxidation proceeded for 30 minutes, a typical lifetime for a cloud droplet, after which the composition changes were assessed. The oxidation of S(IV) to S(VI) is assumed to be the rate determining step and considered to be irreversible.

The concentration of ozone was held constant at 50 ppb during the oxidation. The concentration of hydrogen peroxide was 0.3 ppb, all of which dissolved in the water to give a concentration of 1.3 x 10^-3 mole litre^-1. H₂O₂ was depleted during oxidation and was solved simultaneously with the other differential equations.

d[H2O2 ] dt

= kH2O2[H2O2][S(IV)]

where  [H2O2] =

PH2O2     LRT

The amount of sulphate produced per cubic meter of fog or cloud by these oxidation mechanisms was evaluated for nine different SO₂ source rates (Q_SO2). Initial levels of NH₃ (0.1, 1.0 and 10 ppb) and a source strength of 4.5 10^-4 kg km^-2 min^-1 were used for three separate cases. An ammonia source strength of 4.5 10^-5 kg km^-2 min^-1 and a source strength of NH₃ proportional to that of SO₂ provide two more cases. These first five cases had liquid water contents of 0.01 g m^-3, while the sixth case had 0.5 g m^-3.

Figure 4.9 shows the influence of the initial amounts of NH₃, with increasing amounts of sulphate produced with increasing initial NH₃. As expected, the amount of sulphate produced is a nonlinear function of Q_SO2. Figure 4.10 compares the cases of fixed Q_NH3 with one where NH₃ sources are proportional to sources of SO₂. This might be the case, for instance, where NH₃ is used as a fertilizer in the same region where SO₂ is produced. Here, the amount of SO₄^2- produced is a nonlinear function of Q_SO2 in the opposite sensethat is positive as opposed to negative feedback occurs. Figure 4.11 compares production rates of SO₄^2- for liquid water contents of 0.01 and 0.5 g m^-3 with the initial values and source strength of NH₃ as used previously (Case 1). Here, more SO₄^2- is produced at the higher liquid water content while the nonlinear behaviour is preserved. 

Figure 4.9 Amount of sulphate produced (µg m-3) in model fog of 0.01 g m-3 liquid water in 30 minutes versus source strength of SO2 (QSO2) kg km-2 min-1. Other parameters:
Case 1:	PNH3 (t=0) = 0.1 ppb
	QNH3 = 4.5 10-4 kg km-2 min-1
	PSO2 (t=0) = 3 ppb
Case 2:	PNH3 (t=0) = 1.0 ppb
	QNH3 = 4.5 10-4 kg km-2 min-1
Case 3:	PNH3 (t=0) = 10 ppb
	QNH3 = 4.5 10-4 kg km-2 min-1

4.6 CONCLUSIONS: FLUX RELATIONSHIPS

The major goals of this approach are to quantify the relationships between fluxes and reaction rates and to explore departures from linearity. However, before this can be done, it is clearly necessary to identify key pathways and to establish the sensitivities of the cycles to key variables. The use of simple, diagnostic models make it possible to ascertain at least some of the controlling factors. However, we caution that this kind of model is only diagnostic and not well suited for predictive applications. Perhaps the most important outcome at this stage is that the results from the model will guide further modelling exercises and will suggest the important variables that need to be measured. Among the conclusions at this stage are:

Figure 4.11 The same as Figure 4.9, except:
Case 6:	L (liquid water content) = 0.5g m-3
	PNH3 (t=0) = 0.1 ppb
	QNH3 =  4.5 10-4 kg km-2 min-1

1. As expected, Q_NH3 is important to the pH of atmospheric water and to the rate of conversion of S(IV) to S(VI). The high liquid-phase solubility at pH < 5 predicates low (ppt) gas-phase concentrations in many instances. While actual environmental values for P_NH3 and Q_NH3 are needed to improve the model, the low concentrations of NH₃ make determining these parameters difficult.
2. Increased Q_SO2 causes increased production of SO₄^2- in wet aerosols, an effect that is enhanced by increasing Q_NH3. Decreased pH of atmospheric water causes a decrease in the rate of oxidation of S(IV) so that the induced production rate of SO₄^2- is a nonlinear function of Q_SO2. This could conceivably cause SO₂ to be transported farther prior to oxidation or dry deposition and an increase in the geographical area influenced by acid deposition.
3. S(IV) in wet aerosols and clouds is apparently an effective sink for low levels of H₂O₂. Future models might consider the relationship of Q_SO2 and Q_H2O2 in an air parcel. Since 0.3 ppb of H₂O₂ is small compared to the initial 3 ppb SO₂, it is quickly consumed. While 0.3 ppb is on the low side of usual atmospheric concentrations (Kok, 1980) it is reasonable value for areas not influenced by much photochemistry.

These results are consistent with the observations of Altshuller (1976, 1980) that reductions in local SO₂ emissions in the Eastern and Midwestern U.S.A. between 1963 and 1972 caused only modest reductions in sulphate aerosol concentration. Data collected in 1974 in Europe (LRTAP) similarly showed a possible nonlinear relationship of sulphate in rain-water as a function of total sulphur (SO₂ and SO₄^2-) (OECD, 1977). In their cloud model, Easter and Hobbs (1974) found, using several oxidation mechanisms, that sulphate production decreased as initial SO₂ rose above 10 ppb. This is also consistent with the lack of a clear-cut trend of decreasing pH in rain in recent years in Scandinavia (Granat, 1978).

Since oxidation of sulphur dioxide is considered to be the major source of sulphate aerosols (Gartrell and Friedlander,1975; Yuen et al., 1979) as well as the major source of acid precipitation and since reaction in aerosol and cloud particles seems to be possible or probable (Hegg and Hobbs, 1978, 1979) it is worthwhile to develop a more complete and quantitative understanding of these interactions. We fully can expect these interactions to be nonlinear due to both homogeneous gas-phase reactions and heterogeneous cloud and aerosol reactions. The expected nonlinearity in both cases is a slowing-down or delay of the oxidation of SO₂ as SO₂ and NO sources increase. However, the degree of nonlinearity is not known at this time, resulting in uncertainties in the effectiveness of various control strategies.

ACKNOWLEDGEMENTS 

Financial support was provided by the International Meteorological Institute in Stockholm and also by the National Science Foundation, under Grant ATM 7808163. Special thanks are due to Professor Bert Bolin for suggesting the topic, and Professors Henning Rodhe, Peter Liss, Robert Duce, Dr. Rolf Söderlund and Dr. Robert Cook for helpful discussions.

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