Environmental Engineering Reference
In-Depth Information
Quantitative determination of the mass transfer rates thus requires estimation
of the equilibrium partition constant between air and water phases. Note that
it appears both in the driving force and in the overall mass transfer coefficient
expressions.
Note from Figure 4.3 that there exists a discontinuity in concentrations at the inter-
face. However, fugacity changes gradually without discontinuity. Since the fugacity
in air is different from that in water, a concentration difference between the two phases
exists and the system moves toward equilibrium, where
f
i
f
i
. From the dis-
cussion in Chapter 3 on fugacity capacity, it can be shown (Mackay, 1991) that the
mass transfer flux can also be written in terms of fugacity as
f
i
=
=
K
w,f
f
i
f
i
,
N
i
=
−
where
N
i
is in mol/m
2
/s as defined earlier, and
K
w,f
is given in terms of fugacity
capacities (
Z
w
=
1
/K
aw
and
Z
a
=
1
/RT)
as
1
K
w,f
=
1
k
w
Z
w
+
1
k
a
Z
a
.
(4.6)
K
w
/K
aw
with
K
w
as in Equation 4.5. The definition of
K
aw
is given
in Chapter 3. The net flux is identified as the algebraic sum of the net volatilization
from water,
K
w,f
f
i
, and the net absorption rate from air,
K
w,f
f
i
.When these two rates
are equal the system is at equilibrium. The term
f
i
Note that
K
w,f
=
f
i
−
is appropriately called the
departure from equilibrium.
A variety of methods can be employed to obtain Henry's constants for both organic
and inorganic compounds in air-water systems. The following are the descriptions of
some of the more common methods:
4.1.1 E
STIMATION OF
H
ENRY'S
C
ONSTANT FROM
G
ROUP
C
ONTRIBUTIONS
Hine and Mookerjee (1975) suggested one method of estimating the air-water par-
tition constant by summing bond or group contributions in a molecule. Meylan and
Howard (1992) recently refined the method. The method is analogous to the one
discussed in Chapter 3 for the determination of log
K
ow
. It relies on the assumption
that the free energy of transfer of a molecule between air and water is an additive
function of the various groups or bonds present in the molecule. The correlation was
developed to obtain the reciprocal of the air-water partition constant defined in this
topic. Thus the method gives 1
/K
aw
. An extensive listing of the bond and group con-
tributions is given in Hine and Mookerjee (1975). It is best to illustrate this method
through examples.
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