Geoscience Reference
In-Depth Information
where h is the Planck constant, K
6¼
is the equilibrium constant of the activated
complex, C
A
and C
B
are the concentrations of the components A and B, and
ν
A
and
ν
6¼
is the activity coefficient of
ν
B
are the activity coefficients of the nutrients, and
the active complex.
In nonspecific solvation when the medium is not homogeneous, i.e., the sol-
vent
solute interaction is not homogeneous and continuous, such an interaction
plays a significant role for ionic compounds only
[20,21]
. The classical electrostatic
model links the rate of reaction constant
ξ
(in a given known dielectric value
ε
),
with the rate constant (in the medium with
ε
5
N
),
Eq. (4.18)
:
!
2
6¼
r
3
6¼
r
B
2
μ
e
2
Z
A
r
A
1
Z
B
r
B
2
ð
Z
B
Þ
ε
kT
μ
B
Z
A
1
ln
ξ
5
ln
ξ
0
1
ð
4
:
19
Þ
1
3
4
2
ε
kT
r
6¼
where r is the radius of the particle,
is the dipole moment of the particles, Z is
the charge number, k is the Boltzmann constant, T is the temperature, and e is the
electron charge.
This equation shows that the log of the rate constant depends linearly upon the
reverse (negative) values of the dielectric constants.
Let us consider briefly the role of water as a solvent in the hydrothermal growth
of crystals. Water is the major component of hydrothermal solutions, always with a
varied chemical composition in the laboratory and in nature.
All the solutions used in hydrothermal experiments vary from one another in
their properties, ability to dissolve and crystallize, and in the nature of the linking
between water and electrolyte. Moreover, the properties of each solution depend
upon physicochemical aspects and the structure of the pure water. The formation of
associates and complexes in the aqueous solutions of electrolytes is possible
because of the presence of structural water, i.e., consisting of water molecules with
directional hydrogen bonding. Above the critical point, the density of water varies
greatly with a little change in temperature and pressure. Because of the drastic
change in density, all the fluid properties change greatly around the critical point,
including the dielectric constant that is a controlling factor of reaction rate, equilib-
rium, and solubility of metal oxides. Therefore, it is necessary to understand the
basic principles, which insist upon the understanding of the properties of water,
including density, dielectric constant, and ion product, varying greatly around the
critical point of water and result in a specific reaction atmosphere
[22]
. The experi-
mental PVT-behavior of water has been reviewed and summarized by several
workers
[23
μ
26]
.
Figure 4.6
shows the PVT relation of water
[22]
. The reaction
rate, equilibrium, phase behavior, solubility of metal oxides, and distribution of sol-
uble chemical species change greatly at the critical point range. Various models
have been proposed to describe the variation of reaction rate or equilibrium over a
range of supercritical state
[27,28]
. Due to the variation in the properties of water,
phase behavior changes greatly around the critical point. Since supercritical water
is a high density steam, light gases like oxygen or hydrogen form a homogeneous
phase with supercritical water.
Figure 4.7
shows the critical loci for binary systems
