Chemistry Reference
In-Depth Information
o
ρ
1
∞
βϕ
ρ
p
d
ρ
ρ
∫
(
)
2
1
ln
=
A
−
1
(9.37)
Kr
o
0
From this relation, a formulation can be made in terms of the infinite dilution properties
of hydration for water as the solvent, such as the difference of Gibbs energies between
the fluid at the designated reference pressure,
p
0
, and the infinitely dilute solute at
p
,
ln
ϕ
∞
p
(
)
=
2
∞
∆
h
GTp
,
T
(9.38)
2
0
p
This yields Henry's constants via
HTp
(,) xp
=
−
∆
h
G
∞
(,)
Tp RT
(9.39)
21
2
Standard thermodynamic manipulations yield the infinite dilution enthalpy, entropy,
and isobaric heat capacity of hydration (Plyasunov, O'Connell, and Wood 2000;
Sedlbauer, O'Connell, and Wood 2000). For example,
2
∞
dGT
dT
∆
∞
2
h
2
2
∆
CT
=−
(9.40)
h
p
,2
The issues are how to utilize known solution information at low temperatures and
pressures that do depend on
T
and how to express the properties at conditions below the
critical temperature where there is temperature dependence of
A
Kr
. This approach need
not be limited to aqueous systems, but those are the only ones which have been treated.
The first approach (Plyasunov, O'Connell, and Wood 2000) was to augment the
high-density function of Equation 9.25 with temperature-dependent correlations of
cross (
B
12
) and pure solvent (
B
11
) second virial coefficients to include the low-density
behavior for the integral of Equation 9.37. An analytically integrable form was adopted:
(
)
(
)
(
)
+
+
{
}
0
A
=−
1
αα
1
−
C
2
ρ
BT BT
()
−
()exp
k
ρ
Kr
1
1
11
12
11
1
(9.41)
α
(
)
−
2
5
+
ρ
+
α
exp
k
ρ
1
3
2
T
where values of
B
11
and
B
12
are obtained from the square-well potential model,
k
1
and
k
2
are universal constants, and α
1
, α
2
, and
α
3
are solute-dependent parameters. The
full final relations of Equation 9.37 through Equation 9.40 are given by Plyasunov
et al. (2000). These have been used to obtain infinite dilution thermodynamic
properties of many organic substances in water (Plyasunov et al. 2001; Plyasunov,
