Melting Point and Molecular Symmetry
Melting Point and Molecular Symmetry
Melting Point and Molecular Symmetry
the range of validity of the rule and the underlying thermodynamics on which it is based.
The relationship between melting point and molecular
symmetry has been known since the two-part paper published
by Thomas Carnelley in 1882 (1, 2). Carnelley reviewed
approximately 15,000 melting points and stated the rule in
the following form:
That of two or more isomeric compounds, those whose
atoms are the more symmetrically and the more compactly
arranged melt higher than those in which the atomic
arrangement is asymmetrical or in the form of long chains.
724
Isomer
Name
pentane
mp/K
143.5
Name
mp/K
Name
methylbutane
113.3
2,2-dimethylpropane 256.6
mp/K
C8 H1 8
octane
216.4
3-methylheptane
152.7
hexamethylethane
373.9
C6 H1 2
methylcyclopentane
130.7
2,3-dimethyl-2-butene
198.6
cyclohexane
279.8
C7 H1 4
methylcyclohexane
146.6
1-heptene
153.5
cycloheptane
265.2
C2 H4 Cl2
1,1- dichloroethane
176.2
1,2-dichloroethane
237.7
C3 H7 OH
1- propanol
147.1
2-propanol
183.7
C4 H9 OH
1- butanol
183.3
2-methyl-1-propanol
165
2-methyl-2-propanol
298.5
C6 H4 Cl2
o - dichlorobenzene
256.5
m - dichlorobenzene
248.4
p- dichlorobenzene
325.9
225.4
p- xylene
286.4
C 8 H1 0
o - xylene
248.0
m - xylene
C 8 H1 6
ethylcyclohexane
161.9
1,1-dimethylcyclohexane 239.9
cyclooctane
288.0
C8 H8
cyclooctatetraene
268.5
cubane
405
C1 4 H1 0
phenanthrene
372.4
anthracene
488
In the Classroom
It is very striking that cage molecules have higher melting points than would be expected on the basis of molar mass,
and some data are contained in Table 3. Many cage molecules,
such as adamantane and cubane, are of high symmetry.
The Thermodynamics of Melting
Melting, or fusion, is the phase transition in which the
crystalline phase changes to the liquid phase. At a fixed
pressure, the melting point of a crystal of a pure substance is
the temperature at which the crystalline and liquid phases
are in thermodynamic equilibrium. The heat required to melt
the crystal is absorbed at a constant (or nearly constant)
temperature and is called the latent heat of melting, or latent
heat of fusion. Since melting takes place at a fixed pressure,
the latent heat of fusion is equal to the enthalpy change of
fusion.
When a crystal melts, there is an increase in both the
enthalpy and the entropy of the substance. The enthalpy
change of fusion is a measure of the amount of energy required
to convert the crystal to a liquid. The entropy change of fusion
is a measure of the increase of randomness or disorder when
the molecules are released from the constraints of the crystal
into the relative freedom of the liquid. The enthalpy change
and the entropy change are conveniently measured on a per
mole basis, and the molar entropy change of fusion can be
expressed as a multiple of the gas constant R.
Because the crystalline phase is converted reversibly to the
liquid phase at the melting point, the molar entropy change of
fusion Sfus is equal to the molar enthalpy change of fusion
Hfus divided by the melting point temperature Tfus (17 ):
S fus =
Table 2. Melting Points of
Benzene and Related Molecules
Formula
Name
mp/K
C 6 H6
benzene
278.7
C6 H5 CH3 toluene
178.2
C6 H5 F
fluorobenzene
231
C6 H5 Cl
chlorobenzene
228.0
C6 H5 Br
bromobenzene
242.6
C6 H5 I
iodobenzene
241.9
C6 H5 OH phenol
314.1
C6 F6
hexafluorobenzene
278.5
C6 F5 H
pentafluorobenzene
225.9
C5 H5 N
pyridine
231.6
C4 H4 N2
1,4-diazine
328.2
C3 H3 N3
1,3,5-triazine
358.2
Name
C10H16
adamantane
mp/K
543
buckminsterfullerene
high
C8H8
cubane
405
C10H16O camphor
452
H fus
T fus
(1)
T fus =
H fus
S fus
(2)
G
T
= S
(3)
725
In the Classroom
liquid
Tfus
Gibbs energy G
Gibbs energy G
Tfus
Temperature T
Tfus
Tfus
Temperature T
Figure 1. The molar Gibbs energy of a pure substance in its crystalline and liquid states as a function of temperature, starting at absolute
zero. The melting point is the temperature Tfus at which the curve
for the crystal crosses the curve for the liquid. To illustrate the effect
of the molar enthalpy of the crystal on the melting point, two curves
are shown for the crystalline phase, corresponding to different
hypothetical values of the molar enthalpy but with equal values of
the molar entropy at all temperatures. The crystal with lower molar
enthalpy is more stable than the other crystal; it has a larger
molar enthalpy change of fusion, and a higher melting point.
Figure 2. The molar Gibbs energy of a pure substance in its crystalline and liquid states as a function of temperature, starting at
absolute zero. To illustrate the effect of the molar entropy of the
crystal on the melting point, two curves are shown for the crystalline
phase, corresponding to different hypothetical values of the molar
entropy but with equal values of the molar enthalpy at absolute zero.
The crystal with the higher molar entropy is more disordered than
the other crystal; it has a smaller molar entropy change of fusion
and a higher melting point.
726
In the Classroom
727
In the Classroom
hig
po
C
A
low m
po
elting
int
20
18
ing
lt
me
para
16
dichlorobenzenes
14
ortho
12
meta
10
xylenes
8
6
4
2
0
0
Entropy of melting/R
pentane
8
When considering trends in melting points, it is instructive to consider separately the enthalpy change and the entropy
change of fusion, in place of the melting point itself. One
way to do this is to plot the enthalpy change and the entropy
change of fusion for each substance on a graph. If the entropy
change is plotted horizontally, as abscissa, and the enthalpy
change is plotted vertically, as ordinate, then the melting point
is equal to the slope of the line from the origin to the point
representing the data. The higher the melting point, the
steeper the slope of the line. In such a graph, compounds
with equal melting points lie on a single line passing through
the origin. This diagram will be referred to as an enthalpy/
entropy diagram.
Figure 3 shows an enthalpy/entropy diagram for three
hypothetical compounds, which are indicated by the letters
A, B, and C. Compounds B and C melt at the same temperature and compound A melts at a lower temperature. The
graph illustrates how enthalpy and entropy effects can independently affect the melting point. Compound B melts at a
higher temperature than compound A because the enthalpy
change of fusion is higher, although the entropy changes for
the two compounds are equal. Compound C melts at a higher
temperature than compound A because the entropy change of
fusion is lower. Other compounds that have the same melting
points as compounds B and C may have different combinations
of enthalpy change and entropy change, as long as the ratio
Hfus/S fus is the same.
B
int
7
6
methylbutane
5
4
2,2-dimethylpropane
3
2
1
0
0
Entropy of melting/R
In the Classroom
8
methylcyclopentane
methylcyclohexane
6
5
4
3
cyclohexane
2
cycloheptane
cyclopentane
0
0
Entropy of melting/R
400
Temperature / K
300
boiling point
melting point
200
100
CH4
NH3
H 2O
HF
Ne
ammonia
water
hydrogen fluoride
4
methane
neon
0
0
Entropy of melting/R
729
In the Classroom
12
Alcohols
1-pentanol
1-butanol
10
2-methyl-2-propanol
6
2-propanol
1-propanol
ethanol
methanol
0
0
Entropy of melting/R
500
Temperature / K
400
boiling point
300
200
melting point
100
0
1
10
11
12
40
35
12
30
15
10
5
0
0
10
12
14
16
18
Entropy of melting/R
In the Classroom
the regular stepwise increase in the melting point with increasing chain length.
Figure 11 shows the enthalpy/entropy diagram for the
straight chain alkanes up to n = 12. The high values of the
entropy change of fusion for the longer chain lengths is clear.
Straight-chain alkanes in the crystalline state may be rotationally disordered about their long axes. The striking alternation
in the entropy change of fusion beginning at n = 9 is due to
the formation of an orientationally disordered phase for odd
values of n = 9, 11, 13, , but not for even values (26 ).
This decreases the entropy change of fusion for the odd alkanes
relative to both the adjacent even alkanes. It is notable that
the graph of melting point in Figure 10 gives no hint of this
phenomenon for odd values of n beginning at n = 9.
For alkanes higher than n = 8, the difference between
the values of S fus /R for Cn and Cn+2 alkanes is approximately
2 ln 3 = 2.19, corresponding to the threefold nature of the
rotation about each of two CC single bonds (9, 13).
Methane and ethane have very low values of the entropy
change of fusion owing to rotational disorder in the crystalline
state, and the relatively high melting points of methane and
ethane are due to this disorder. This is the basis for the answer
to the original question from which this whole discussion
arose. Ethane has an orderdisorder phase transition only
0.5 K below the melting point (19), which caused some
confusion in the earlier literature.
The melting points of branched-chain alkanes do not
seem to vary systematically with the degree of branching except
where the branching leads either to an increase in symmetry or
to a globular molecular shape that facilitates rotational disorder
in the crystal (10). This is illustrated in Table 1 by the isomers
of octane.
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