Notice that references available do not give information about the dependences of
X
18
and X
38
complexes concentrations upon the time in the controlled crystallization
process. Therefore, the data in fig.11 and 12 are valuable and allow us to judge of the
rate of equilibrium establishment in calcium subsystem.
In particular, the determined c
18
and c
38
parameters are important for the
investigation of CHCS kinetics. For example, the specific time of CaHCO
3
+
complex
dissociation may be determined from (27): T
18
=1/(C
18
k
18
) ≈ 10.2min. This time is in
proper proportion to the time of achieving the Ca
2+
concentration maximum in Fig.3,
T
m
≈ 9min.
From fig. 11 and 12 we can see that dynamically determined complexes
concentrations differ significantly from the evaluation of their values by equilibrium
relations. Especially it refers to the neutral calcium carbonate complexes X
38
(CaCO
3
0
)
concentration of which was calculated by equilibrium formulae for quickly changing
processes that may be exceeded by more than 10 times. From fig. 12 it also follows
that at pH < 9.5 (range of pH change in our experiments) the contribution of X
18
into
the total carbonate sum does not exceed 10%.
Substituting the solutions of (27) and (28) into (3a) we can check the adequacy of
this expression with the experiments (initial value of the total Ca
2+
ions concentration
o
Ca
S
= 4.8 mol/dm
3
) within the range of 55 < i < 70, see fig. 13, without crystallization
(
)
38
18
o
Ca
8
X
X
S
X
+
−
=
, (29)
The value X
8
calculated by (29) is shown in fig. 13.
There is a good agreement at i > 65 and a satisfactory
one with 10% error at smaller measurements numbers.
There is a quick change of CO
2
concentrations, calcium
ions and pH at the section i < 65. The discrepancy may
be caused by measurements errors (sensors inertia) or
by the influence of the processes that were not taken into
account. However, the equations (3a) and (3b) for i > 65
are in good agreement with the experimental data and
we will use them in the further analysis. On the basis of
(3b) simulate the process of solid calcium carbonate
formation within the range of 6 < pH < 9.5 where the crystallization process is
accompanied by the simultaneous change of bicarbonates and dissolved CO
2
concentration. According to (3b) the rate of CaCO
3
formation within this pH range is
given by the expression
)
X
X
(
X
X
38
18
8
10
+
−
−
=
,
(30)
We draw your attention to the fact that by (30) the rates of change of crystallized
CaCO
3
and Ca
2+
ions are not equal by value though while modeling the crystallization
1
2
i
Figure 13. Comparison of
calculated by (29), curve 1 and
measured Ca
2+
concentrations,
curve 2 mol/dm
3
.
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