present phase diagrams of the NaClH2O and CaCl2H2O systems under atmospheric
pressure. It is helpful to recall the phase rule when examining these phase diagrams. For
nonreacting systems, the phase rule states
F=C+2P
(55)
where F is the degrees of freedom, C is the number of components, and P is the number of
phases (McGlashan 1979). A two-phase system (i.e., iceNaCl solution) that is composed of
two components (i.e., NaCl and H2O) has (2 + 2 2) two degrees of freedom, that is, fixing
two independent variables will specify the state of the system. Three independent variables
are most natural: pressure, temperature, and composition. Since pressure is fixed by the
atmosphere, the choice of temperature or composition will specify the other independent
variable. This dependence is represented by the icesolution coexistence lines in Figures 11
and 12. Simple NaCl solutions with molalities above 5.2 that are cooled below 0C will not
coexist with ice but rather with a solid phase composed of hydrohalite [NaCl 2H2(cr)].
The icesolution hydrohalitesolution coexistence curves converge at the eutectic point,
the unique temperature-
0
composition combination
where these three phases
coexist, a triple point that is
10
specified entirely by the
Water
number of phases and the
20
lone independent variable,
Ice
pressure.
30
The phase rule can be
extended to the interpreta-
tions of the freezing behav-
40
ior of natural waters.
Salt
When natural waters are
50
frozen, solute effects must
0
200
400
600
800
1000
be considered. In particu-
Water (g)
lar, several salts precipitate Figure 13. Phase diagram for seawater. (Courtesy of Dr. G.M.
from freezing solutions as Marion, USACRREL.)
the remaining liquid water
solutions concentrate. This progression has been studied most closely in the freezing be-
havior of seawater, the properties of which may be used as an approximate model for soil
solutions in freezing and frozen ground. A phase diagram for seawater is presented in Fig-
ure 13.
PHYSICALCHEMICAL PROPERTIES OF ICE
Heat capacity
As for many solids, the heat capacity of ice as a function of temperature can be fitted to
the equation of Maier and Kelly (1932):
c
Cp,H 2O(cr,I) = a + bT +
(50)
*
T2
a = 10.6644 (1.5999) J K1 mol1
where
b = 0.1698 (0.0046) J K2 mol1
c = 198 148 (28 230) J K mol1.
The changes in molar enthalpy and entropy can thereby be calculated via the following
integrals:
(
)
1
1
Tf
b 2
Cp,H 2O(cr,I)dT = a(Tf - Trw ) +
∫
Tf - Tr2 + c
-
*
(51)
w
Trw Tf
2
Trw
18
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