20
1 A Historical Review of the Structures of Water and Ice
Table 1.1 The mobilities μ/(×10 −8 m 2 /s/V ) of different ionic species in water and their ionic
radii r c /(pm), as obtained by the molar conductivity measurements at infinite dilution and X-ray
crystallography [11]
Cations
Anions
μ
r c
μ
r c
H +
36.2
0
OH −
20.6
133
Li +
4.01
90
F −
5.74
119
Na +
5.19
116
Cl −
7.92
167
K +
7.62
152
Br −
8.09
182
Rb +
8.06
166
I −
7.96
206
Cs +
8.00
181
–
–
–
ions is low enough to neglect their mutual interactions. Neither statement has been
proved experimentally. Inasmuch as this model of electrolytes is widely used by the
scientific community, there are still several open questions which need to be clarified.
Why do different solutions have different molar conductivities at infinite dilution (as
it is assumed that they should all be pure water)? Why do ions of the same charge
attract different number of water molecules to form a solvation shell? Why do some
ions, such as, e.g., Cs
+ , have so-called negative hydration [11]? These questions
cannot be answered using the Arrhenius theory of electrolytic dissociation and ion
hydration.
1.3.2 The Autoionization of Water
The key element of electric current conduction by water is autoionization. Selfdissociation of water occurs when a water molecule, H 2 O, donates the nucleus of
one of its hydrogen atoms (i.e., a proton) to another water molecule, according to
the formula:
H 2 O + H 2 O↔H 3 O
+
+ OH
−
.
(1.10)
When this reaction goes in one direction, the donor molecule becomes a hydroxide
ion, OH
− , and the acceptor molecule becomes a hydronium ion, H 3 O
+ . Note that the
hydrogen nucleus, H
+ , does not exist as an independent particle and forms hydronium
ion with the nearest water molecule acceptor. That is why proton exchange occurs
through a lower barrier than those required for the simple detachment of a proton
from an isolated water molecule.
Figure 1.16 shows two basic intermediates of protonic transport in water. The
four-coordinated (solvated) hydronium ion, or H 9 O
+
4 (see Fig. 1.16a), is known as an
Eigen cation. The intermediate state of the proton, between two molecules, or H 5 O
+
2
1 A Historical Review of the Structures of Water and Ice
Table 1.1 The mobilities μ/(×10 −8 m 2 /s/V ) of different ionic species in water and their ionic
radii r c /(pm), as obtained by the molar conductivity measurements at infinite dilution and X-ray
crystallography [11]
Cations
Anions
μ
r c
μ
r c
H +
36.2
0
OH −
20.6
133
Li +
4.01
90
F −
5.74
119
Na +
5.19
116
Cl −
7.92
167
K +
7.62
152
Br −
8.09
182
Rb +
8.06
166
I −
7.96
206
Cs +
8.00
181
–
–
–
ions is low enough to neglect their mutual interactions. Neither statement has been
proved experimentally. Inasmuch as this model of electrolytes is widely used by the
scientific community, there are still several open questions which need to be clarified.
Why do different solutions have different molar conductivities at infinite dilution (as
it is assumed that they should all be pure water)? Why do ions of the same charge
attract different number of water molecules to form a solvation shell? Why do some
ions, such as, e.g., Cs
+ , have so-called negative hydration [11]? These questions
cannot be answered using the Arrhenius theory of electrolytic dissociation and ion
hydration.
1.3.2 The Autoionization of Water
The key element of electric current conduction by water is autoionization. Selfdissociation of water occurs when a water molecule, H 2 O, donates the nucleus of
one of its hydrogen atoms (i.e., a proton) to another water molecule, according to
the formula:
H 2 O + H 2 O↔H 3 O
+
+ OH
−
.
(1.10)
When this reaction goes in one direction, the donor molecule becomes a hydroxide
ion, OH
− , and the acceptor molecule becomes a hydronium ion, H 3 O
+ . Note that the
hydrogen nucleus, H
+ , does not exist as an independent particle and forms hydronium
ion with the nearest water molecule acceptor. That is why proton exchange occurs
through a lower barrier than those required for the simple detachment of a proton
from an isolated water molecule.
Figure 1.16 shows two basic intermediates of protonic transport in water. The
four-coordinated (solvated) hydronium ion, or H 9 O
+
4 (see Fig. 1.16a), is known as an
Eigen cation. The intermediate state of the proton, between two molecules, or H 5 O
+
2