Chemistry Reference
In-Depth Information
trans
(b)
(a)
cis
(c)
(d)
Figure 2.
Four possible arrangements of H-bonds within a 16-water-molecule orthorhombic
unit cell of ice Ih. Here, cis and trans bonds are defined as whether protons lie on the same or opposite
side of the H-bond, respectively, as indicated for structure (a). The H-bond isomers are summarized
mathematically by directed graphs in which directional bonds point from H-bond donor to H-bond
acceptor, as illustrated for the isomer (b).
in the lattice of ice Ih, the phase of ice formed when water freezes under ambient
pressures. The contribution to the entropy would be
R
ln
0
.
806 cal K
−
1
mol
−
1
.
Pauling's estimate would prove to be remarkably accurate compared with more
powerful solutions of the counting problem [3, 4]. Earlier in 1932, based on the
measurements of others, Giauque and Ashley [5] had calculated the residual en-
tropy of ice Ih near 0
K
to be in the range of 0.87-0.96 cal K
−
1
mol
−
1
, and at-
tributed the entropy at 0
K
to “the persistence of rotation of water in ice below
10
◦
K”. In 1936, Giauque and Stout [6] measured the heat capacity of ice. Com-
bining their results with known thermodynamic properties of the liquid and vapor
and a spectroscopic estimate of the absolute entropy of water vapor, they estimated
the residual entropy of ice to be 0
.
82 cal K
−
1
mol
−
1
, which is
R
ln
3
2
=
3
2
within their
experimental error of 0
.
05 cal K
−
1
mol
−
1
. The experiment confirmed that the H-
bonds in ice are in a nearly random arrangement, (i.e., the H-bonds are disordered).
Thus, somewhere between the freezing temperature of water and 0 K, ice falls out
of equilibrium.
While the origin of the residual entropy of ice seemed settled, it was recognized
that an ordered phase of ice Ih could exist if a suitable experimental means was
available to allow equilibration [7]. Little progress was made concerning a possible
