Chemical properties
Thermodynamic properties
To calculate the chemical thermodynamic properties of aqueous solutions below 0C, the
relevant properties of the solvent must be calculated. The conventional reference tempera-
ture and pressure (298.15 K and 0.1 MPa) are inappropriate because of Speedy's (1987) em-
pirical model upper limit of applicability of 273.15 K and were determined under a pressure
of 1 atm. Initially then, the chemical potential of water at 273.15 K and 0.101325 MPa must
be calculated.
Chemical potential of water at 273.15 K. To state the chemical potential of water at 0C, one
needs to calculate:
* 2O(l) (Trw , prw ) - * 2O(l) (Trc , prc )
(11)
H
H
=
298.15 K
where Trc
Trw
=
273.15 K
Ts
=
227.15 K
prc
=
0.1
prw
=
0.101325 MPa.
Equation 11 can be evaluated with
* (Trw , prw ) - * (Trc , prc )
B
B
Trw
= -SB (Trc , prc )(Trw - Trc ) +
∫
*
*
(12)
Cp,BdT
Trc
C*,B
prw
Trw
VB* (Trw , p)dp
p
∫
∫
-Trw
dT +
T
Trc
prc
*
B
(J K1 mol1), and VB* is the molar volume of pure B (m3 mol1).
Equation 12 is equivalent to
* (Trw , prw ) - * (Trc , prc ) = -SB (Trc , prc )(Trw - Trc ) + HB (Trw , prc ) - HB (Trc , prc )
*
*
*
B
B
prw
- Trw SB (Trw , prc ) - SB (Trc , prc ) +
∫
*
*
VB* (Trw , p)dp
(13)
p rc
*
where HB is the molar enthalpy of pure B (J mol1).
Standard reference tables (e.g., Chase et al. 1985) provide some of the required values:
SH 2O(l) (Trc , prc ) = 69.950 J K 1 mol 1.
*
The equation-of-state model for water (Hill 1990) can be used to calculate some of the terms
directly:
(
)
(
)
T , p - S*
T , p = -6.616 04 J K 1 mol 1
S
rw
rc
rc
rc
H 2O(1)
H 2O(1)
HH 2O(1) (Trw , prc ) - HH 2O(1) (Trc , prc ) = -1.88 547 kJ mol -1
*
VH 2O(1) (Trw , prc ) = 0.018 018 09 dm 3 mol -1
*
10
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