Table 1. FREZCHEM2 model input for freez-
Verification of the model
ing seawater from 0C down to 40C with a
To verify the program, phase diagrams from
2C decrement.
Spencer et al. (1990) and point computations from
Marion and Grant (1994) were recalculated. The
SMW
model reproduces these computations with good
seawater
Title of the task
accuracy. Table 4 shows the temperatures at the
appearance of solids during seawater freezing,
0.48695
Sodium (mol/kg)
0.01063
Potassium (mol/kg)
taken from Spencer et al. (1990) with an added
0.00953
Calcium (mol/kg)
column obtained by the FREZCHEM2 model
0.05516
Magnesium (mol/kg)
using their thermodynamic data.
0.56818
Chloride (mol/kg)
It is interesting to note that, according to the
0.02939
Sulfate (mol/kg)
free energies of chemical reactions in the model, a
0.0
Carbonate (mol/kg)
0.0
Hydrogen (mol/kg)
solid reaction
273.15
initial temperature
1
freezing (2 for evaporation)
NaCl 2H2O(cr) → NaCl(cr) + 2H2O(cr,I)
233.15
final temperature (final amount of water for
evaporation)
takes place at temperatures lower then 57.15C.
2.0
temperature decrement (water decrement for
evaporation)
To verify this independently, the heat capacity
equations for these phases at low temperatures
pendent components (presently Na+, K+, Ca+2,
are needed.
Mg+2, Cl , SO42 , and CO32 are included) per 1
kg of water. Thus, an initial amount of water in the
LITERATURE CITED
system is equal to 1 kg or 55.51 moles. If the molal
quantity of an independent component is equal
Fujino, K., E.L. Lewis, and R.G. Perkin (1974) The
to zero, all substances in the file DATABASE that
freezing points of seawater at pressures up to 100
contain it will be ignored. The program calculates
bars. Journal of Geophysical Research, 79: 1792
a charge balance and, if it is different from zero,
1797.
proposes to add some amount of any cation or
Harvie, C.E., J.P. Greenberg, and J.H. Weare (1987)
anion depending on the value and the sign of the
A chemical equilibrium algorithm for highly non-
charge balance, after which the program starts its
ideal multiphase system: Free energy minimiza-
work. FREZCHEM2 is able to calculate both 1) a
tion. Geochimica et Cosmochimica Acta, 51: 1321.
cooling/heating scenario (in this case one enters
Karpov, I.K., A.V. Kiselev, and F.A. Letnikov (1976)
initial and final temperatures and temperature
Computer modeling of natural mineral formation. (In
decrement/increment) and 2) an evaporation/
Russian.) Moscow: Nedra.
dilution scenario at constant temperature (in this
Khodakovsky, I.L. (1992) DiaNIK--Thermody-
case it needs a temperature, a water amount
namic databases of minerals and calculations of
decrement/increment, and a final mass of water).
equilibrium compositions of natural systems. In
The model is also able to calculate the process of
Abstracts of the 12th IUPAC Conference on Chemical
Thermodynamics, Snowbird, Utah, U.S.A., p. 157
is present in Table 1 for seawater freezing from
158.
0 to 40C for a 2C temperature decrement. The
Korn, G.A., and T.M. Korn (1963) Mathematical
explanations are written in italics.
Handbook for Scientists and Engineers. New York:
Output from the program is to the RESULT file.
McGraw-Hill Book Company.
As examples of output, results of computation of
Marion, G.M., and S.A. Grant (1994) FREZCHEM:
seawater freezing at 228.15 K (45C) and at
A chemical thermodynamic model for aqueous
218.15 K (55C) are given in Table 2. Output of
solutions at subzero temperatures. USA Cold Re-
evaporation of seawater at 273.15 K (0C) down
gions Research and Engineering Laboratory, Spe-
to 50 g of water is given in Table 3.
cial Report 94-18.
Distribution of the independent components
Mironenko, M.V. (1983) Physical-chemical mod-
among solids and solution phases is given in the
eling of uranium ore formation in the uranium
BALANCE table at the bottom of the output table.
deposite [in Russian]. Ph.D. dissertation (unpub-
The last column of this table has been printed to
lished), Vernadsky Institute of Geochemistry and
show the equivalence of input and computed bal-
Analytical Chemistry, Moscow.
ances.
Mironenko, M.V., and A.N. Salaskin (1991) PTX-
6
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