The solvent and solute mole fractions could be calculated by:

1

(23)

(24)

2

where MH2O is the molar mass of water (0.018 015 28 kg mol1).

We fitted by regression the freezing-point depression data calculated by the For-

(25)

where *K*f is an approximate cryoscopic constant for the H2ONaCl system, which

we found to be 4.12207 K kg mol1. This compares with the expected cryoscopic

constant for a single electrolyte completely disassociated in water of 3.72 K kg

mol1 (Atkins 1990).

The quantity Sm,H2O ≡ *S*m [H2O(cr, I)] at a temperature and pressure of interest

∗s

∗

can be calculated by adding the entropy changes due to cooling and freezing to the

entropy of water at a reference point (i.e., *T*r = 273.15 K and *p*r = 0.1 MPa). This

quantity is calculated by evaluating

[

]

[

]

*

*

(26)

[

]

+ ∆T r 273.15 Sm H2O(l), *p*r

=

∗

(27)

+ ∆lcr,I Sm (H2O, *T *= 273.15, *p*r )

∗

(28)

[

]

+ ∆T =273.15 Sm H2O(cr, I), *p*r .

∗

(29)

The starting point of the calculation (eq 26) is the molar entropy of pure water at

a reference temperature (*T*r = 273.15 K) and pressure (*p*r = 0.1 MPa), for which the

*

1985).

Haida et al. (1974) reported the entropy change due to the constant-pressure

cooling of water from 298.15 K to its freezing point, ∆T =273.15Sm [H2O(l), *p*r ] = 6.615

∗

0.01 (eq 27). This quantity can also be calculated with the equation-of-state model

for water (Hill 1990):

*

*

(30)

We used the latter value in our calculations.

*

is calculated by

∆lcr,I Hm (H2O, *T *= 273.15, *p*r )

*

(H2O, *T *= 273.15, *p*r ) =

∆lcr,ISm

*

.

(31)

273.15

Haida et al. (1974) reported a molar enthalpy of melting of 6006.8 J mol1. Giauque

and Stout (1936) earlier reported a value of 6007.0 3.8 J mol1.

13