In a symmetric molecule such as carbon disulfide, figure o/1,
the dipole moment vanishes by symmetry. For if we rotate the
molecule by 180 degrees about any one of the three coordinate
axes defined in the caption of the figure, the molecule is un-
changed, which means that its dipole moment is unchanged. A
zero vector is the only vector that can stay the same under all
these rotations.
o/Example 6. The positivexaxis
is to the right,y is up, andzis
out of the page. Dark gray atoms
are carbon, and the small light
gray ones are hydrogen. Some
other elements are labeled when
their identity would otherwise not
be clear.If we wish, we can think of this vanishing of the dipole moment as
arising from a cancellation of two dipole vectors, one for each of
the molecular bonds. Each chemical element has a certain affin-
ity for electrons, which is represented by the column in which it
lies on the periodic table, and is ultimately determined by quan-
tum physics (section 13.4.7, p. 938). Sulfur “likes” electrons just
slightly more than carbon, so that the electron cloud shifts out-
ward somewhat from the center. This gives rise to two dipole
vectors, each of which points inward, toward the positive charge.
(Chemists use an opposite convention for the direction.) These
two vectors add up to zero.
Similar symmetry arguments show that sulfur hexafluoride, o/2,
and benzene o/3, have vanishing dipole moments.
The formaldehyde molecule, o/4, does not have enough symme-
try to guarantee that its dipole moment must vanish, but it does
have enough to dictate that the dipole vector must lie along the
x axis. To determine the sign ofDx, we must use the fact that
oxygen has a much higher electron affinity than carbon, so this
creates a strong contribution to the dipole moment in the nega-
tivexdirection. Carbon in turn has a higher electron affinity than
hydrogen, so there is also a dipole moment associated with each
CH bond, pointing toward the hydrogen and therefore contribut-
ing a further negativeDx. Theycomponents cancel. A similar
analysis for chloroform, o/5, shows that the dipole moment points
in the positivezdirection.
From these arguments we can tell, for example, that carbon disul-
fide will be soluble in benzene, but chloroform will not.
Section 10.1 Fields of force 587