, and each C-H
bond distance is 1.09
angstroms (Å), or 4.29 {times} 10{sup -9} inches; 1Å
= 1 {times} 10{sup -10} metres. The three-dimensional shape
of a molecule is best demonstrated with a
molecular model, of which
the so-called
ball-and-stick model is
the most common. The earliest ball-and-stick models were made
of wood and were assembled by connecting balls, representing
atoms, with dowels, representing bonds. These, as well as the
later plastic versions, have been largely replaced by
computer-graphics renderings
of ball-and-stick models such as the one shown for methane in
Figure 38A. Three-dimensional
geometries are often portrayed using wedges and dashes, respectively,
to depict bonds directed toward or away from the viewer (
Figure 38B).
A tetrahedral geometry allows for the maximum separation of
the electron pairs in the four C-H bonds of methane. Higher
alkanes have bonds that are tetrahedrally disposed on each carbon
except that the resulting C-C-C and H-C-H angles are slightly
larger and smaller, respectively, than the ideal value of 109.5
characteristic of a perfectly symmetrical tetrahedron. Carbon-carbon
bond distances in alkanes are normally close to 1.53 angstroms.
An important aspect of the three-dimensional shape of alkanes
and other organic molecules is their
conformations, the nonidentical
arrangements of atoms that are generated by the rotation that
is possible about single bonds. Of the infinite number of conformations
possible for
ethane--which are related
by tiny increments of rotation of one CH
group with respect to the other--the
eclipsed conformation
(Figure 39) is the least
stable and the
staggered conformation
(Figure 40) the most stable.
The eclipsed conformation is said to suffer torsional strain
because of repulsive forces between electron pairs in the C-H
bonds of adjacent carbons. These repulsive forces are minimized
in the staggered conformation since all C-H bonds are as far
from one another as possible. Although rotation about the C-C
bond of ethane is exceedingly rapid (millions of times per second
at room temperature), at any instant most of the molecules exist
in the staggered conformation.
For butane, two different staggered conformations, called anti and gauche (shown below), are possible. Methyl is a larger substituent than hydrogen, and the greater separation between methyl groups in the anti conformation makes it slightly more stable than the gauche.
The three-dimensional structures of higher alkanes are governed by the tetrahedral disposition of the four bonds to each carbon atom, the preference for staggered conformations, and the greater stability of anti C-C-C-C arrangements over gauche.
