Environmental Engineering Reference
In-Depth Information
The solubility of gases in liquids is obtained from Henry's law.
Let us now consider a sparingly soluble liquid (say a hydrocarbon H) in contact
with water. The solubility of the liquid hydrocarbon in water may be considered to
be an equilibrium between a pure phase (H) and an aqueous phase (W).Applying the
criterion of equal fugacity at equilibrium,
f
i
=
f
i
,
(3.56)
w
i
x
i
f
l
0
H
i
x
i
f
l
0
γ
= γ
,
i
i
where
f
l
i
is the pure component reference fugacity of
i
at system temperature. For
pureHwehave
x
i
H
i
1. Noting that
x
i
x
i
, the saturation solubility in
=
1 and
γ
=
=
water, we can write
1
γ
i
x
i
=
.
(3.57)
The above equation states that the activity coefficient of a saturated solution of a
sparingly soluble
compound in water is the reciprocal of its saturation mole fraction
solubility in water.
For the compound
i
which is only sparingly soluble in water, we also have the
following Henry's law expression:
1
x
i
·
K
H
= γ
i
P
i
=
P
i
.
(3.58)
For solutes that are solids, the basic condition of equal fugacity still holds at
equilibrium. If solid (s) is a pure species in contact with water (w),
f
s
0
i
w
i
x
i
f
l
0
= γ
(3.59)
i
where
f
s
0
i
is the fugacity of pure solid
i
and
f
l
i
is the fugacity of pure liquid
i
. This
is the hypothetical sub-cooled liquid state for compounds that are solids at room
temperature (see the discussion on phase diagrams). Thus the saturation solubility of
i
in water is given by
f
s
0
i
f
l
0
i
1
γ
i
1
γ
i
exp
1
T
−
.
−
Δ
H
m
R
1
T
m
x
i
=
=
(3.60)
The ratio of fugacity coefficients was obtained from Prausnitz et al. (1999). In the
above equation,
H
m
is the molar enthalpy of fusion or melting (J/mol) and
T
m
is the
melting point of the solid (K). Since according to Trouton's rule
Δ
Δ
S
m
= Δ
H
m
/T
m
,
and for most organic compounds
Δ
S
m
/R
∼
13.6 entropy units, we have
1
γ
i
exp
6.8
1
.
T
T
m
x
i
=
−
(3.61)
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