Stereochemistry and projections

What the exam asks

Expect to be handed a structure or a description and asked to count stereoisomers, assign R or S, classify a pair as enantiomers or diastereomers, or predict an optical rotation. The commonest items are: count stereocentres and apply two to the power of n, spot the meso compound that makes the count wrong, and decide what a mixture does to plane-polarised light. The trap that catches most candidates is treating stereocentres as proof of chirality. They are not: a meso compound has them and is achiral, and the giveaway is a molecule whose two ends are substituted identically, because that symmetry is what lets the mirror plane exist. Before answering any chirality question, look for the plane. The second trap is assuming an optically inactive sample must contain no chiral molecules. Zero rotation has two quite different causes, an achiral compound such as a meso one, or a racemic mixture of two chiral enantiomers, and a question that gives you a rotation of zero has usually built itself on that ambiguity.

Stereochemistry is what is left when connectivity has been settled. Two molecules with the same atoms joined in the same order can still be different compounds, because the arrangement in space differs, and the exam is interested in exactly one question about that: is the molecule superimposable on its mirror image, or is it not?

That question has a name, chirality, and a practical test. Look for an internal mirror plane. A molecule that can be sliced into two halves that reflect each other is superimposable on its mirror image and is achiral, whatever else is true of it. A molecule with no such plane is chiral, and it has a partner it can never be rotated into. The usual cause of chirality is a carbon carrying four different groups, but the cause is not the definition, which is why counting those carbons is a starting point and never the finish.

Most errors here are counting errors dressed as chemistry. The count of stereoisomers is at most two to the power of the number of stereocentres, and the phrase that matters is at most. Internal symmetry can make two of the supposed isomers turn out to be the same molecule, and the compound that results, achiral despite containing stereocentres, is called meso. It is the single most examined idea in the topic, because it punishes anyone who counted stereocentres and stopped thinking.

Optical activity is the physical consequence. A chiral compound rotates plane-polarised light; its mirror image rotates it by the same angle the other way; and anything achiral, or any exactly balanced mixture of the two, rotates it not at all.

What to hold

• A molecule is chiral if it is not superimposable on its mirror image, and the working test at this level is whether it has an internal mirror plane: if it has one, it is achiral.
• A stereocentre is usually a carbon bonded to four different groups, and swapping any two of those groups converts that centre into its opposite configuration.
• A molecule with exactly one stereocentre is always chiral. Beyond one, the count of stereocentres no longer settles the question by itself.
• A compound with n stereocentres has at most two to the power of n stereoisomers, and the actual number is lower whenever internal symmetry makes two of them identical.
• A meso compound contains stereocentres but has an internal mirror plane, so it is achiral, superimposable on its mirror image, and optically inactive despite its stereocentres.
• Meso is why the two to the power of n count is an upper bound: two stereocentres carrying identical sets of substituents give three stereoisomers, not four, because the supposed pair of mirror images turns out to be one compound.
• R and S are assigned by ranking the four groups by Cahn-Ingold-Prelog priority, pointing the lowest priority away from you, and reading one to two to three: clockwise is R, anticlockwise is S.
• Priority is decided by atomic number at the first point of difference, working outward from the stereocentre atom by atom, and a double bond counts as two bonds to that atom.
• If the lowest priority group points towards you rather than away, determine the rotation as you see it and then reverse the answer.
• Enantiomers are non-superimposable mirror images, which means every stereocentre is inverted. Invert only some of them and you have a diastereomer instead.
• Enantiomers have identical melting point, boiling point and solubility in ordinary conditions, and differ only in the direction they rotate plane-polarised light and in how they react with other chiral things.
• Diastereomers are different compounds with different physical properties, so they can be separated by ordinary means such as distillation or crystallisation, while enantiomers cannot.
• Cis and trans isomers of an alkene or a ring are diastereomers: stereoisomers that are not mirror images of each other.
• A racemic mixture is equal amounts of two enantiomers and rotates plane-polarised light by zero, because the two contributions cancel exactly.
• The R/S label and the direction of optical rotation are unrelated: R/S comes from a rule applied on paper, rotation is measured in an instrument, and neither predicts the other.
• In a Fischer projection, horizontal bonds point towards the viewer and vertical bonds point away, which is why the projection cannot be lifted off the page and flipped over without changing what it means.