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220 Physical Organic Chemistry

mixture, designated by a prefix(±)-. The process of sepa- both). These are diastereomers. The former is called cis
rating the individual enantiomers from a racemic mixture and the latter is trans.IfR 1 = R 2 , both of these are chiral,
is called resolution. The conversion of an optically active so each can exist as a pair of enantiomers. The configura-
material into its racemic mixture is called racemization. tion at each stereocenter can be designated as (R)or(S).
Diastereomers are stereoisomers that are not mirror If R 1 = R 2 , only 51 is chiral, since 50 has a vertical plane
images of each other. Cis/trans isomers like 39 are di- of symmetry between the two CHR carbons and is meso.
astereomers. Another form of diastereomerism occurs
with molecules that have two or more stereocenters.
For example, a second stereoisomer of (R,S)-1,2-
dibromo-1,2-dichloroethane (47)is(R,R)-1,2-dibromo-
1,2-dichloroethane (48) and a third is (S,S)-1,2-dibromo-

1,2-dichloroethane (48 ). These last two are enantiomers Cyclohexane can eliminate both angle strain and tor-
sional strain by distorting from coplanarity to the chair
of each other, but neither is the enantiomer of 47. Each
conformation (52). This has the feature of axial and equa-
must then be a diastereomer of 47. Even though diastere-
torial hydrogens in two distinctly different environments,
omers have identical connectivity and therefore all the
as depicted in 52 and 52 , respectively. Rotation about

same bonds, they are genuinely different from each other,
the single bonds converts 52 into a different chair confor-
with different melting points, boiling points, solubilities,
mation, 53, whereby each hydrogen that was axial (e.g.,
spectral characteristics, stability, and reactivity.
the boldface H at the rear of 52) becomes equatorial (bold-
This characteristic of diastereomers makes possible the
face in 53) and each hydrogen that was equatorial becomes
resolution of a racemic mixture into its enantiomers. The
axial. This process, called ring inversion, occurs quickly
process also takes advantage of the fact that chiral natural
(within microseconds at 25 C).
◦
substances exist as single enantiomers. If the racemic mix-
ture of (+) and (−) enantiomers can react with a natural
substance that is (for definiteness) the (R) stereoisomer,
the products are (+, R) and (−, R). These are diastere-
omers, with different solubilities, so they can be separated
by treatment with a suitable solvent. Then the (+) enan-
tiomer can be recovered from the (+, R) product and the
(−) enantiomer from the (−, R).
E. Cyclic Compounds
Cyclic compounds can show various combinations of
A monosubstituted cyclohexane thus exists as a rapidly
these stereochemical features, including conformations,
equilibrating mixture of two conformers (54, 55, most
stereocenters, chirality, enantiomerism, diastereomerism,
hydrogens omitted). The conformer with a bulky R sub-
and another form of cis/trans stereoisomerism. The con-
stitutent in the axial position (55) is destabilized by steric
formational behavior of cycloalkanes, C n H n , depends on
repulsion with the two axial hydrogens nearby.
the ring size. For n = 3, 4, or 5 the small ring constrains
the CCC angle to <109.5 , leading to an instability called
◦
angle strain that arises from increased repulsion between
electron pairs and poorer overlap. Also, there is torsional
strain along each C C bond, which is eclipsed in the pla-
nar conformation (e.g., 49). For n = 4 or 5 small distor- A disubstituted cyclohexane can be either cis or trans.
tions from planarity reduce the torsional strain but at the If the substitution pattern is 1,4 (56, 57), these are diastere-
expense of an increase of angle strain. omers. Both are achiral, as guaranteed by a vertical plane
of symmetry through carbons 1 and 4. Each can undergo
ring inversion, so each is a mixture of two conformers,
only one of which is shown. If the substitution pattern
is 1,2 or 1,3 and if R 1 = R 2 , the cis and trans molecules
are both chiral. If R 1 = R 2 , the cis-1,3-disubstituted cyclo-
A disubstituted cycloalkane can have both of the sub- hexane is achiral, but the trans-1,2, the trans-1,3, and the
stituents on the same face of the ring, as in 50, or they cis-1,2 (58) are all chiral. However, an unusual feature of
can be on opposite faces, as in 51 (hydrogens omitted in this last is that ring inversion rapidly converts it to another