McKay, Donald. "Front matter" Multimedia Environmental Models ...

and the series retains a similar ratio of air and water resistances. Paradoxically,
reducing vapor pressure as one ascends such a series does not reduce evaporation
rate from solution, since it is K AW that controls the rate of evaporation, not vapor
pressure.
It is noteworthy that oxygen and most low-molecular-weight hydrocarbons lie
in the water phase resistant region, whereas most oxygenated organics lie in the air
phase resistant region. The H for water can be deduced from its vapor pressure of
2000 Pa at 20°C and its concentration in the water phase of 55,000 mol/m 3 to be
0.04 Pa m 3 /mol. If a solute has a lower H than this, it may concentrate in water as
a result of faster water evaporation but, of course, humidity in the air alters the water
evaporation rate. Water evaporation is entirely air phase resistant, because the water
need not, of course, diffuse through the water phase to reach the interface. It is
already there.
Certain inferences can be made concerning the volatilization rate of one solute
from another, provided that (1) their H values are comparable, i.e., the same resistance
or distribution of resistances applies, and (2) corrections are applied for
differences in molecular diffusivity. For example, rates of oxygen transfer can be
estimated using noble gases or propane as tracers, because all are gas phase controlled.
Particularly elegant is the use of stable isotopes and enantiomers as tracers,
since the partition coefficients and diffusivities are nearly identical.
7.7.2 Derivation Using Fugacity
We can use D values instead of mass transfer coefficients and diffusivities. These
two-resistance equations can be reformulated in fugacity terms to yield an algebraic
result equivalent to the concentration version. The derivation is less painful when
fugacity is used. If the water and air fugacities are f W and f A and the interfacial
fugacity is f I, then replacing C by Zf in the steady-state Fick’s law equation yields
and
where
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N = k WA(C W – C WI) = k WAZ W(f W – f I) = D W(f W – f I) mol/h
N = k AA(C AI – C A) = k AAZ A(f I – f A) = D A(f I – f A) mol/h
D W = k WAZ W
and D A = k AAZ A
This is illustrated in Figure 7.6.
Now, the interfacial fugacity f I is not known or measureable, thus it is convenient
to eliminate it by adding the equations in rearranged form, namely,
f W – f I = N/D W