Stereochemistry: Determining Molecular Chirality
Exercise Solutions

a. 3-Methylhexane: 

This molecule is chiral because the mirror images are not superposable.  The case is very much like 2-chlorobutane, except the molecule has a propyl group instead of a chlorine atom.  Each molecule has a single stereocenter.  Examination of other molecules with single stereocenters should rapidly convince you that molecules with a single stereocenter are always chiral.

b. Benzene: 

Benzene is achiral because it has many internal mirror planes.  Perhaps the most obvious of these is the molecular plane that contains all twelve atoms.

c. Cyclohexane: 

Cyclohexane can exist in many different conformations (chair, boat, etc.).  In cases of conformationally fluxional molecules, if there is one conformation that is achiral, then the molecule as a whole is achiral.  The chair conformation has a mirror plane through the middle of the ring, containing C1 and C4, so this conformation is achiral.  Because the chair conformation is achiral, we consider cyclohexane to be an achiral molecule.

This molecule contains no mirror planes, and mirror image molecular models are not superposable.  Therefore this molecule is chiral.

This molecule has two stereocenters, so at first guess, it might appear to be chiral.  However, it has an internal mirror plane:

This is a meso compound, and is achiral, as are all meso compounds.  Note that for a compound to be meso, the pairs of stereocenters must have the same groups attached to them.

At first glance, this compound appears to be chiral because it contains no apparent internal mirror plane.  As with the cyclohexane case, we need to examine all conformations to see if any are achiral.  A good way to do this in a molecule with multiple stereocenters is to hold one stereocenter still (the left hand one in this case), and rotate around the single bonds to try and make the stereocenters align.  Such a rotation in this molecule reveals an internal mirror plane:

This molecule is therefore a conformational isomer of the molecule in (e), and is thus achiral.

At first glance, we might suspect this to be a meso compound because the two stereocenters have the same attachments.  However, rotation around the bond that attaches the stereocenters reveals that they are not reflected by an internal mirror plane:

Careful examination will reveal that this molecule has no conformations with an internal mirror plane and so it is chiral.

In the quest for an internal mirror plane, rotation around the bond connecting the two stereocenters reveals the molecule to be meso and therefore achiral:

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