1296 WATER: PROPERTIES, STRUCTURE, AND OCCURRENCE IN NATURE
hydrogen bond tends to a cluster while the breaking of one
hydrogen bond leads to the dissociation of a cluster, thereby
resulting in clusters flickering into and out of existing with
half-lives estimated at 10^ ^10 to 10^11 second.
Though the model does not define the details of the orga-
nization of the water molecules, the clusters are thought to
be compact and highly hydrogen bonded. The existence of
a single dielectric relaxation time and a structural relaxation
time approximating the neutron residence time appear to
rule out the presence of Frank–Wen clusters in pure water
according to Davis and Jarzynski.Thermodynamics and Physical PropertiesThe isopiestic (1 bar) heat capacity of water, and the ther-
modynamic functions derived from the heat capacity, are
given in Figure 4. The heat capacity of liquid water is almost
twice that of ice at 0C or steam at 100C. Whereas the heat
capacity of ice and steam is primarily due to vibrational
energy, there is in liquid water an additional configurational
heat capacity related to the energy involved in alterations
in the structure of water. The thermodynamic constants
for the phase changes of water are given in Table 4. The
relatively low heat of fusion of water is evidence that the
hydrogen bonding in the ice structure remains intact to some
degree during fusion; the extremely high heat of vaporiza-
tion reflects the disappearance of hydrogen bonding upon
vaporization (Westall and Stumm, 1980).
P – V – T Relationships The density of water reaches a
maximum at 4C above the melting point (Figure 5). This
extraordinary maximum may be explained as the result of
two counteracting phenomena: as the temperature of liquid
water is increased, (i) the open four-coordinated structure
of water is further broken down, decreasing the volume;
(ii) the amplitude of anharmonic intermolecular vibrations
increases, increasing the volume. Below 4C the first effect
predominates.
The pressure-temperature curve for water is given in
Figure 6. The triple point, at which ice, liquid water, and
water vapor coexist at equilibrium, is a convenient reference
state: T = 0.01C, P = 6.11 mbar.TABLE 4
Thermodynamic constants for phase changes of H 2 O (Eisenberg and
Kauzmann, 1969)Fusiona Vaporizationa Sublimationb
Temperature ºK 273.15 273.15 273.16
Cp (j mol^1 ºC^1 ) 37.28 41.93 —
Cp (kJ mol^1 ) 6.01 40.66 51.06
S (J mol^1 ºC^1 ) 22.00 108.95 186.92
V (cm^3 mol^1 ) 1.621 3.01 104 —
E (kJ mol^1 ) 6.01 37.61 48.79
a At 1 atm.
b At ice I-liquid-vapor triple point.1.000.990.980.970.960.950.940.930.920.910.90–20 (^020406080100)
Temperature [°C]
1.0000
0.9999
0.9998
0.9997
0 2 4 6 8 10
ICE I
Density [g.cm
–3
]
FIGURE 5 The density (at 1 atm) of ice and liquid water
as a function of temperature. The inset shows the density in
the domain of its maximum. (Data for ice from Eisenberg
and Kauzmann, 1969; data for water from Kell, 1967).
Dielectric constant The dielectric properties of
water result from (1) electronic and atomic polarization of
molecules (formation of induced dipoles) and (2) the orienta-
tion of permanent dipoles. The high value of the dielectric
constant of water is chiefly the result of the orientation of
permanent dipoles, whereby not only the orientation of indi-
vidual molecules, but also the mutual orientation of neighbor-
ing molecules, is important. For comparison, the dielectric
constant of ice I is 91 at 0C, and that of liquid water is 88
at the same temperature. As the temperature is increased, the
degree of orientation of the molecules, and the dielectric con-
stant, decreases (Figure 7).
The preceding discussion dealt with the dielectric prop-
erties of water in a static electric field. In a high frequently
alternating electric field, the permanent dipoles can no longer
reorient with the variable electric field; then the observed
dielectric constant is due solely to the induced dipoles. For
liquid water the value of this high frequently dielectric con-
stant, , is between 4.5 and 6.0.
Viscosity The shear viscosity of water can be defined
by the equation
tmzx x
x
v
d
d
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