Source: Dr Uyeda, Purdue University, Lectures 10–11 | Textbook Ch. 3 (7th/8th Ed.)
Difficulty: Intermediate | Prerequisites: Part 1 of these notes (R/S assignment, CIP priority rules)
Tags: multiple stereocenters, enantiomers, diastereomers, meso compound, internal mirror plane, Fischer projection, stereoisomer relationships, cis trans cyclic, CHEM 25500, organic chemistry, Purdue
Most biologically relevant molecules have more than one stereocenter. Once you move beyond a single chiral carbon, the number of possible stereoisomers grows and new relationships between molecules appear: enantiomers, diastereomers, and the occasionally surprising meso compound that has stereocenters yet is still achiral. Fischer projections give you a compact way to draw and compare these structures, particularly for sugars. This section builds directly on the R/S fundamentals from Part 1.
A molecule with n stereocenters can have up to 2^n stereoisomers. Enantiomers are non-superimposable mirror images (every stereocenter flipped). Diastereomers are stereoisomers that are not mirror images (some but not all stereocenters flipped). Meso compounds contain stereocenters but have an internal plane of symmetry, making them achiral overall. Fischer projections are a shorthand for drawing stereocenters, with vertical lines going back and horizontal lines coming forward.
Enantiomers
A pair of stereoisomers that are non-superimposable mirror images of each other. Every stereocenter in one molecule has the opposite R/S configuration in the other. Think of them as a left glove and a right glove.
Diastereomers
Stereoisomers that are not mirror images of each other. At least one stereocenter has the same configuration while at least one is different. In simple terms, they are "mismatched" rather than perfectly opposite.
Meso compound
A molecule that contains stereocenters but is achiral because it possesses an internal plane of symmetry. The stereocenter configurations cancel each other out. Think of it as a molecule whose left half is the mirror image of its right half.
Racemic mixture (racemate)
A 50:50 mixture of two enantiomers. Because the optical rotations cancel, a racemic mixture shows zero net rotation of plane-polarised light.
Fischer projection
A 2D shorthand for representing stereocenters. Vertical lines represent bonds going back into the page; horizontal lines represent bonds coming out towards the viewer. Commonly used for drawing sugars and amino acids.
Cis (same side)
In cyclic molecules, describes two substituents on the same face of the ring.
Trans (opposite side)
In cyclic molecules, describes two substituents on opposite faces of the ring.
The maximum number of stereoisomers for a molecule with n stereocenters is 2^n. Two stereocenters give up to four stereoisomers; three give up to eight.
The actual number may be fewer than the maximum when a meso compound is present.
Enantiomers: every stereocenter is inverted. (R,R) ↔ (S,S) or (R,S) ↔ (S,R).
Diastereomers: not all stereocenters are inverted. (R,R) and (R,S) are diastereomers.
Enantiomers have identical physical properties (melting point, boiling point, solubility) in an achiral environment.
Diastereomers have different physical and chemical properties, full stop. They are different compounds.
A meso compound has two or more stereocenters, but the molecule as a whole is achiral.
The giveaway: an internal plane of symmetry that makes one half of the molecule the mirror image of the other.
When you draw the mirror image of a meso compound and assign R/S to each stereocenter, the mirror image is superimposable on the original (they are the same molecule, not enantiomers).
Example from the lecture: a molecule with configurations (R,S) where the two stereocenters carry identical sets of substituents. The R and S cancel, giving an internal mirror plane.
Draw all possible combinations of R/S at the two centres: (R,R), (S,S), (R,S), (S,R).
Identify the enantiomeric pairs: (R,R) and (S,S) are enantiomers; (R,S) and (S,R) are enantiomers.
Check whether any pair is actually the same compound (meso). If (R,S) is superimposable on (S,R) via rotation, it is meso, and you have three unique stereoisomers instead of four.
Identify the remaining diastereomeric relationships. The (R,R) molecule is a diastereomer of the (R,S)/meso molecule.
Convention: the carbon chain runs vertically, with the most oxidised carbon at the top (for sugars, the aldehyde or carboxylic acid end).
Vertical lines = bonds going away from you (into the page).
Horizontal lines = bonds coming towards you (out of the page).
To find the enantiomer in a Fischer projection, swap the two horizontal substituents at every stereocenter (or, equivalently, reflect the projection left to right).
You may rotate a Fischer projection 180° in the plane of the page and it still represents the same molecule. Rotating 90° gives the enantiomer (this is a common trap).
In ring systems, cis and trans labels describe the relative positions of substituents.
Cis: substituents on the same face of the ring.
Trans: substituents on opposite faces.
A disubstituted cyclohexane with two different substituents (e.g. 1-fluoro-4-chlorocyclohexane) can have cis and trans forms that are diastereomers of each other.
Within the cis or trans family, a pair of enantiomers may exist.
Example from the lecture: 1-fluoro-2-chlorocyclohexane gives four unique stereoisomers (two cis enantiomers and two trans enantiomers). In contrast, 1-fluoro-4-chlorocyclohexane (same substituent pattern but related by a plane of symmetry) gives only two unique stereoisomers (cis is achiral/meso, trans is achiral/meso), because each isomer has an internal mirror plane.
When the two substituents on the ring are the same (e.g. 1,2-dimethylcyclohexane), the trans isomer may be chiral (two enantiomers) while the cis isomer is meso.
Maximum stereoisomers = 2^n (where n = number of stereocenters)
Enantiomers: all stereocenters inverted (R ↔ S at every position)
Diastereomers: some but not all stereocenters inverted
Meso: stereocenters present, but internal mirror plane makes the molecule achiral overall
The difference between enantiomers and diastereomers is critical in pharmacology. Diastereomers, because they have different physical properties, can be separated using ordinary techniques like chromatography or crystallisation. Enantiomers, with their identical physical properties, require chiral resolution methods, such as chiral columns or enzymatic reactions, making single-enantiomer drug production more expensive and technically demanding.
Students often assume that any molecule with stereocenters must be chiral. Meso compounds are the classic counterexample: stereocenters present, molecule still achiral.
Rotating a Fischer projection 90° does not give the same molecule. It gives the enantiomer. Only 180° rotation keeps the configuration intact.
Cis and trans are relative descriptors (same side vs. opposite side of a ring). They are separate from R/S, which is an absolute assignment at each individual stereocenter. A trans compound can be either (R,R) or (S,S), depending on the substituents.
Students sometimes confuse "identical" with "meso." Two molecules that are superimposable are identical. A single molecule that has an internal mirror plane is meso. These are different concepts that can overlap in the same problem.
⚠️ Drawing all stereoisomers of a two-stereocenter molecule and identifying the relationships between each pair is a very common exam question. Practise the systematic (R,R), (S,S), (R,S), (S,R) approach.
⚠️ Expect at least one question requiring you to spot a meso compound. The internal plane of symmetry is the fastest way.
⚠️ Fischer projection manipulation (especially the 90° vs. 180° rotation trap) appears frequently on exams.
⚠️ For cyclic molecules, you may be asked to draw all stereoisomers and state how many are unique. Remember to check for meso cases.
True or false: A molecule with two stereocenters always has exactly four stereoisomers.
Fill in the blank: Enantiomers have ________ physical properties in an achiral environment.
True or false: A meso compound has no stereocenters.
Fill in the blank: In a Fischer projection, horizontal lines represent bonds coming ________ the viewer.
True or false: Diastereomers have identical boiling points.
Answers: 1. False (a meso compound reduces the count). 2. Identical. 3. False (it has stereocenters but is still achiral due to an internal mirror plane). 4. Towards. 5. False (diastereomers have different physical properties).
Q: A molecule has the configuration (R,R). What is the configuration of its enantiomer?
A: (S,S). Every stereocenter is inverted in an enantiomer.
Q: You draw all four stereoisomers of a compound with two stereocenters and find that the (R,S) form is superimposable on the (S,R) form. What does this tell you?
A: That molecule is a meso compound. The (R,S) and (S,R) drawings represent the same achiral molecule, so there are only three unique stereoisomers instead of four.
Q: What is the relationship between (R,R)-2,3-butanediol and (R,S)-2,3-butanediol?
A: They are diastereomers. Only one of the two stereocenters has a different configuration.
Q: In a Fischer projection of a sugar, you swap the horizontal groups at every stereocenter. What have you drawn?
A: The enantiomer of the original sugar.
Q: Are cis-1,2-dimethylcyclohexane and trans-1,2-dimethylcyclohexane enantiomers or diastereomers?
A: Diastereomers. They are stereoisomers that are not mirror images of each other.
The enantiomer/diastereomer distinction comes back in substitution reactions (Ch. 6–7), where the stereochemical outcome of SN1 vs. SN2 depends on whether you get inversion, retention, or racemisation. Fischer projections are essential for carbohydrate chemistry later in the course (and in biochemistry). Meso compounds reappear in symmetry arguments throughout physical organic chemistry.
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