Liquid Water Content g m

FIGURE 7.2 Frequency distribution for liquid water content average values for various cloud types over Europe and Asia.

The equilibrium between gaseous and dissolved A is usually expressed by the so-called Henry's law coefficient HA

where pA is the partial pressure of A in the gas phase (atm) and [A(aq)] is the aqueous-phase concentration of A (mol L ') in equilibrium with pA. The customary units of the Henry's law coefficient HA are mol L-1 atm-1. The unit mol L_1 is usually written as M, a notation that we will use henceforth. Henry's law constant values are reported in the literature in several different unit systems that may give rise to some confusion. For example, if the gas-phase concentration is expressed in moles per liter of air, and the aqueous-phase concentration in moles per liter of water, the Henry's law constant is dimensionless (actually it is in liters of air per liters of water). Some investigators define the Henry's law constant H'A by the reverse of (7.3), pA = H'A[A]; then H'A = l/HA. We are going to use the definition of (7.3), but when making use of published Henry's law data, one should always check the definition of the Henry's law constant. By our definition, soluble gases have large Henry's law coefficients. Finally, note that the aqueous-phase concentration of A given by (7.3) does not depend on the amount of liquid water available or on the size of the droplet.

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We should emphasize at this point that Henry's law is strictly applicable only to dilute solutions. If the solution is not sufficiently dilute, the concentration of the solute, [A(aq)], in equilibrium with pA deviates from Henry's law. These deviations from ideal behavior will be examined in Chapter 10. When considering the behavior of atmospheric gases at typical concentrations in equilibrium with cloud or fog droplets or large natural bodies such as lakes, Henry's law is generally accepted as a good approximation.

Table 7.2 gives the Henry's law coefficients for some atmospheric gases in liquid water at 298 K. The values given reflect only the physical solubility of the gas, that is, only the equilibrium (7.2) regardless of the subsequent fate of A once dissolved. Several of the species given in Table 7.2, once dissolved, either undergo acid-base equilibria or react with water. We will consider the effect of these further processes shortly. A detailed compilation of Henry's law coefficients for species important in environmental chemistry can be found in Sander (1999).

TABLE 7.2 Henry's Law Coefficients of Some Atmospheric Gases

Species'3

//(Matm"1) at 298 K

o2

1.3 x ltr3

no

1.9 x 1(t3

C2H4

4.8 x 1(T3

NO2

1.0 x 10~2

o3

1.1 x 10"2

n2o

2.5 x 10~2

C02

3.4 x 10"2

H2S

0.1

DMS

0.56

HCl

1.1

so2

1.23

NO3

1.8

ch3ono2

2.0

ch3o2

6

oh

25

HNO2

49

nh3

62

ch3oh

220

ch3ooh

310

ch3c(0)00h

473

ho2

5.7 x 103

HCOOH

3.6 x 103

HCHO*

2.5

CH3COOH

8.8 x 103

h2o2

1 x 105

hno3

2.1 x 105

" The values given reflect only the physical solubility of the gas regardless of the subsequent fate of the dissolved species. These constants do not account for dissociation or other aqueous-phase transformations. ''The value is 6.3 x 103 if the diol formation is included.

" The values given reflect only the physical solubility of the gas regardless of the subsequent fate of the dissolved species. These constants do not account for dissociation or other aqueous-phase transformations. ''The value is 6.3 x 103 if the diol formation is included.

The temperature dependence of an equilibrium constant such as Henry's law coefficient is given by the van't Hoff equation (Denbigh 1981)

where AHa is the reaction enthalpy at constant temperature and pressure. AHa is a function of temperature, but over small temperature ranges it is approximately constant, and therefore by integrating (7.4) with respect to temperature,

Table 7.3 gives the values of A//a(298 K) for several species of atmospheric interest. Henry's law coefficients generally increase in value as the temperature decreases, reflecting a greater solubility of the gas at lower temperatures. For example, the Henry's law constant for 03 increases from 1.1 x 10~2 to 2.35 x l() 2Matm 1 as T decreases from 298 to 273 K, and that for S02 from 1.23 to 3.28 M atm 1 over the same temperature range.

The definition of how soluble a gas is in water is relative, as a gas may be regarded as soluble in one context but insoluble in another. For example, acetone with Ha — 25.6M atm-1 is very soluble compared to aliphatic hydrocarbons but is insoluble compared to formaldehyde with Ha = 6300 M atm-1. A useful solubility benchmark for

TABLE 7.3 Heat of Dissolution for Henry's Law Coefficients

Species

AHa (kcal mop1 ) at 298 K

C02

-4.85

nh3

-8.17

so2

-6.25

h202

- 14.5

hno2

-9.5

no2

-5.0

no

-2.9

ch3o2

-11.1

ch3oh

-9.7

pan

-11.7

hcho

- 12.8

hcooh

- 11.4

HCl

-4.0

ch3ooh

-11.1

ch3c(0)00h

- 12.2

o3

-5.04

Source: Pandis and Seinfeld (1989a).

Source: Pandis and Seinfeld (1989a).

atmospheric applications is the distribution of a species between the gas and the aqueous phases in a typical cloud; species that reside mainly in the gas phase are considered insoluble, and species that are almost exclusively in the aqueous phase are considered very soluble. Intermediate species, with significant fractions in both phases, are considered moderately soluble. Let us formulate the above statements mathematically by defining the aqueous/gas-phase distribution factor.

The distribution factor,/a, of a species A is defined as the ratio of its aqueous-phase mass concentration caq[g(L of air)-1 ] to its gas-phase mass concentration cg[g(L of air)-1],

Note that the aqueous-phase concentration is expressed per volume of air and not per volume of solution, so /a is dimensionless. The distribution factor goes to infinity for very soluble species (cg <C caq) and approaches zero as the solubility of A approaches zero (icg » caq). Assuming Henry's law equilibrium one can show that

where HA is in M atm~1, R is the ideal-gas constant equal to 0.08205 atm L mol 1 K 1 ,T is the temperature in K, and L is the cloud/fog liquid water content in gm \ The factor 10~6 is a result of the units used in (7.7).

The fractions of A that exist in the gas X£ and aqueous phases X^ are given by

A _ 10~6HaRTL _ HaRTwl aq i , 1 n-fi u »tt ~ 1 , u dt... V/ yJ

The aqueous-phase fraction of A is plotted as function of the Henry's law constant and the cloud liquid water content in Figure 7.3 for a range of expected liquid water content values. For species with Henry's law constants smaller than 400M atm-1 less than 1% of their mass is dissolved in the aqueous phase inside a cloud. Such species include 03, NO, N02, and all the atmospheric hydrocarbons. A significant fraction (more than 10%) of a species resides in the aqueous phase in the atmosphere only if its Henry's law constant exceeds 5000 M atm-1.

The above analysis suggests that species with a Henry's law coefficient lower than about 1000 M atm-1 will partition strongly toward the gas phase and are considered relatively insoluble for atmospheric applications. Species with Henry's law coefficients between 1000 and 10,000 M atm-1 are moderately soluble, and species with even higher Henry's law coefficients are considered very soluble. As can be seen from Table 7.2, remarkably few gases fall into the very soluble category. This does not imply, however, that only very soluble gases are important in atmospheric aqueous-phase chemistry.

Henry Constant For So2

FIGURE 7.3 Aqueous fraction of a species as a function of the cloud liquid water content and the species' Henry's law constant.

Henry's Law Constant H , M atm-1

FIGURE 7.3 Aqueous fraction of a species as a function of the cloud liquid water content and the species' Henry's law constant.

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