2.2 Physicochemical Model 75
MgCl
2
/100 g of H
2
O). All reported diagrams of this system the author of the present
monograph is aware of (Solubility 1954; Solubility 1979; Processing … 1985;
Buksha and Shestakov 1997) were plotted by simple connecting the eutonic points
obtained at 20 and 50°C with straight lines that correspond to a monotonic shift
from the “invert” eutonic line to the “direct” one with increase of Mg concentration
in the solution.
Also, convexity of E
20
0
–E
20
i
isotherm is directed toward the ordinate, and that of
the E
55
0
–E
55
i
line is directed toward the abscissa (Fig. 2.8a). Isotherms of 30, 40, and
45°C occupy intermediate positions. Extrapolating the converging E
20
0
–E
20
i
and
E
55
0
–E
55
i
isotherms reveals their inversion in point A corresponding to about 22 wt%
of MgCl
2
content (≈30 g of MgCl
2
/100 g of H
2
O). The convergence of isothermal
lines also appears in the diagram plotted according to Pitzer’s method, but in
this case the convergence is insignificant in comparison with our data and the
plotted lines cannot be inverted (Fig. 2.8c: the diagram was plotted by Dr. L.M.
Cheremnykh, Research Institute of Mineral-Salt Production).
The convergence of isothermal lines and their inversion are accompanied by
directional shift of eutonic lines in respect to the directions of the axes. This is
schematically shown in Fig. 2.9. As MgCl
2
concentration increases, orientation of
the eutonic line in temperature range of 20–40°C changes from “inverted,” converg-
ing with abscissa with increase of temperature (Fig. 2.9a, ∼0–5 wt% of MgCl
2
),
to “straight” (Fig. 2.9b, ∼5–22 wt% of MgCl
2
), and then again to “inverted,”
converging, as the temperature rises, with the ordinate axis (Fig. 2.9c; >22 wt% of
MgCl
2
). Subsequent extrapolation assumes a possible transition to the “reversed”
eutonics (Fig. 2.9d). At the same time, in the 40–55°C interval, orientation of
the eutonic line changes in accordance with another scheme: “direct” – “inverted
toward the abscissa” – “reversed.” The new terms mentioned above need explana-
tion. “Eutonics inverted toward the abscissa axis” corresponds to a positive
temperature gradient of KCl solubility and a negative temperature gradient of NaCl
solubility, i.e., as the temperature rises, the equilibrium concentration of KCl
increases, while that of NaCl diminishes. “Direct eutonics” corresponds to positive
solubility temperature gradients for the both substances. “Eutonics inverted toward
the ordinate axis” corresponds to a negative temperature gradient of KCl solubi-
lity and a positive temperature gradient of NaCl solubility. Finally, the “reversed
eutonics” corresponds to negative temperature solubility gradients for the both
substances, i.e., as the temperature rises, the equilibrium concentrations of both
components decrease.
Noteworthy is the fact that at high concentrations of MgCl
2
(above ≈20 wt% of
MgCl
2
, or ≈30 g of MgCl
2
/100 g of H
2
O), both isothermal and isoconcentration
eutonic lines almost merge in the neighborhood of point A (Fig. 2.8a). In particular,
it is typical for the left-wing region of E
20
30
isotherm. It means that in this region
the equilibrium and kinetic properties of the system become irresponsive toward the
minor changes of MgCl
2
content and the solution temperature.
The curved isothermal and isoconcentration eutonic lines plotted above disagree
with the reported data (Figs. 2.8b, c). However, taking into consideration their
compliance with kinetic data (see below) and with our control measurements of