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.

needs to calculate:

* 2O(l) (Trw , *p*rw ) - * 2O(l) (Trc , *p*rc )

(11)

H

H

=

298.15 K

where *T*rc

=

273.15 K

=

227.15 K

=

0.1

=

0.101325 MPa.

Equation 11 can be evaluated with

* (Trw , *p*rw ) - * (Trc , *p*rc )

B

B

= -*S*B (Trc , *p*rc )(Trw - *T*rc ) +

∫

*

*

(12)

C*,B

∫

∫

-*T*rw

d*T *+

*

B

(J K1 mol1), and VB* is the molar volume of pure B (m3 mol1).

Equation 12 is equivalent to

* (Trw , *p*rw ) - * (Trc , *p*rc ) = -*S*B (Trc , *p*rc )(Trw - *T*rc ) + *H*B (Trw , *p*rc ) - *H*B (Trc , *p*rc )

*

*

*

B

B

- *T*rw *S*B (Trw , *p*rc ) - *S*B (Trc , *p*rc ) +

∫

*

*

(13)

*

where *H*B is the molar enthalpy of pure B (J mol1).

Standard reference tables (e.g., Chase et al. 1985) provide some of the required values:

*

The equation-of-state model for water (Hill 1990) can be used to calculate some of the terms

directly:

(

)

(

)

rw

rc

rc

rc

H 2O(1)

H 2O(1)

*

*

10

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