Unfortunately, equation (5) does not indicate which part of calcium ions is
transformed into ion complexes and into solid state. Besides, it does not give
information regarding the nature (mechanism) of crystallization.
Analysis of dynamic models on the basis of equation (3). Equation (3) is taken
as the basic one. The validity of model equations resulting from (3) may be only
confirmed by comparison of calculated by them and measured values. To obtain
concrete conclusions from (3) it is necessary to investigate time behavior of X
18
and
X
38
concentrations that are formed and dissociated by the schemes.
8
1
18
X
X
X
+
,
(25)
8
3
38
X
X
X
+
,
(26)
These reactions are described by kinetic equations of binary type
(
)
18
18
8
1
18
18
X
k
X
X
c
X
−
=
,
(27)
(
)
38
38
8
3
38
38
X
k
X
X
c
X
−
=
,
(28)
c
18
and c
38
– kinetic constants responsible for complexes generation and c
18
·k
18
,
c
38
·k
38
– describe their dissociation. Under the conditions of the experiments c
18
and
c
38
had such values:
(
2
38
2
18
10
4.44
c
;
10
2.96
c
−
−
=
=
) dм
3
/(mol·s).
X
1
and X
8
concentrations were measured and to integrate (27) and (28) is not
difficult. Unknown c
18
and c
38
were found by means of comparison of dynamically
determined X
18
and X
38
with their equilibrium values that correspond to the final phase
of crystallization. Results of calculations of X
18
and X
38
dependences upon the time
during the experiments are shown in fig. 11 and 12.
Figure 11. Concentration dependence,
mol/dm
3
of CaHCO
3
+
complexes upon the
number of measurement i. Curve 1 -
equilibrium value; curve 2 – calcu-lated by
(27), ∆i = 27s.
еХ
18і
, Х
18і
і
1
2
і
е
еХ
38і
, Х
38і
2
1
Figure 12. Concentration dependence
mol/dm
3
of CaCO
3
0
complexes upon the
number of measurement i: curve 1 –
equilibrium value, curve 2 – calculated by
(28), ∆i = 27s.
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