Applications of Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 144

4.2.4 D RY D EPOSITION F LUX OF G ASES FROM THE A TMOSPHERE
Gaseous molecules can exchange with the aqueous phase via dissolution and/or
volatilization. This dissolution is driven by the concentration gradient between the
gas and water phases. At the beginning of this chapter (Section 4.1), the concept of a
two-film theory of mass transfer across the air-water interface was introduced. The
flux of solute i (mass transferred per unit area per unit time) across the interface is
given by

C i a
K aw −

C i w , J Dry ( G ) = K w · (4.48)

where the overall mass transfer coefficient K w is given by

1
K w =

1
k w +

1
k a K aw

. (4.49)

The equilibrium air-water partition constant appears in both the concentration driving
force and mass transfer coefficient terms. The overall mass transfer coefficient is
composed of two terms: an aqueous-phase coefficient k w and an air-phase coefficient
k a . The reciprocal of the transfer coefficient, k w , is the resistance to mass transfer in
the aqueous film, whereas the reciprocal of k a K aw is the mass transfer resistance in
the gaseous film. If 1 /k w 1 /k a K aw , the solute transfer is said to be aqueous phase

controlled and K w ≈ k w . On the other hand, if 1 /k w 1 /k a K aw , then the solute

transfer is said to be gas phase controlled and K w ≈ k a K aw . A number of gaseous

compounds of interest (e.g., oxygen, CFCs, methane, and carbon monoxide) are said
to be liquid phase controlled. So also are many of theVOCs (e.g., chloroform, carbon
tetrachloride, perchloroethylene, and 1,2-dichloroethane). Some highly chlorinated
compounds (e.g., diledrin, pentachlorophenol, and lindane) are predominantly gas
phase controlled. A general rule of thumb is that compounds with K aw ≥

0.2 are
liquid (aqueous) phase controlled, whereas those with K aw ≤ 2 × 10 − 4 are gas phase
controlled.Table4.9liststhevaluesofliquid-andgas-phasemasstransfercoefficients
for some compounds of environmental significance. For water crossing the interface
fromthebulkphaseintoair,thereexistsnoresistanceintheliquidphaseandhenceitis
completely gas phase controlled.A mean value of k a for water was estimated as 8.3 ×

10 − 3 m/s (Liss and Slater, 1974). For all other gas-phase-controlled chemicals, one
can obtain k a values by multiplying the above value for water with the ratio of the gas-
phase diffusivity of water and the specific gas. Generally, the mass transfer coefficient
is a function of the wind velocity over the water body (atmospheric turbulence). In
the case of those species that dissociate in aqueous solution, associate with or react
withotherspecies(suchascolloids,ions,andothermacromolecules),amorecomplex
dependence of the transfer rate on the aqueous chemistry has been observed. For these
compounds only the truly dissolved, unassociated fraction in water will equilibrate
withthevaporinair.Therefore,theeffectsofthevariousparametersontheequilibrium
partitioning (Henry's law) for compounds that we studied in Section 4.1.1 are of direct
relevance in this context.