Chemistry · General chemistry II · Concept

Enantiomers, diastereomers and meso compounds

Stereoisomers share their connections and differ in arrangement. Mirror-image pairs are enantiomers, and stereoisomers that are not mirror images are diastereomers. A molecule with $n$ stereocenters has at most $2^{n}$ stereoisomers, fewer when symmetry makes some identical: a meso compound has stereocenters but is its own mirror image. Enantiomers share most physical properties but rotate polarized light in opposite directions by equal amounts, and an equal mixture of the two, a racemic mixture, does not rotate it. The excess of one enantiomer over the other follows from the measured rotation.

A concrete case

Mixing two enantiomers

Pure (S)-butan-2-ol has a specific rotation of about $+ 13.5$ , measured as the liquid at $20 ° C$ . Its enantiomer, (R)-butan-2-ol, has about $- 13.5$ . Every other ordinary property of the two liquids is the same.

Pour them together in equal amounts and the rotation is $0$ . Each molecule of one form cancels the rotation of one molecule of the other. Mix $75$ parts of (S) with $25$ parts of (R) instead. The $25$ parts of (R) cancel $25$ parts of (S), and the $50$ parts of (S) left over rotate the light. The mixture shows half the rotation of pure (S), about $+ 6.75$ .

That excess of one enantiomer over the other, $50$ percentage points here, is what a polarimeter measures. This lesson sorts stereoisomers into kinds and then reads the composition of a mixture from its rotation.

(0.75 - 0.25) (13.5) = 6.75

The rule

Two kinds of stereoisomer

Stereoisomers have the same atoms bonded in the same order but arranged differently in space. If two of them are mirror images, they are enantiomers. If they are not, they are diastereomers.

cis-But-2-ene and trans-but-2-ene are diastereomers, since neither is the mirror image of the other. Only a chiral molecule has an enantiomer.

Counting up to $2^{n}$

Each stereocenter, and each double bond that can be E or Z, can be arranged in two ways. With $n$ of them there are at most $2^{n}$ stereoisomers.

2,3-Dibromobutane has two stereocenters, so at most four: (2R,3R), (2S,3S), (2R,3S) and (2S,3R). Only three exist, because the last two are the same compound.

N_{max} = 2^{n}

Meso compounds

A meso compound has stereocenters but is achiral. An internal mirror plane makes one half the reflection of the other, so the molecule is identical to its mirror image. This can happen only when two centers carry the same set of groups. Their labels are opposite, as in (2R,3S), and writing (2S,3R) instead names the same compound.

meso-Tartaric acid is the standard example. A meso compound is one compound, not a pair, and it does not rotate polarized light.

Specific rotation and enantiomeric excess

Plane-polarized light turns as it passes through a sample of one enantiomer. The observed angle $α$ grows with the path length $l$ and the concentration $c$ , so chemists report the specific rotation $[α] = α \div (l \times c)$ . The path length is in decimeters and the concentration in grams per milliliter. The wavelength, temperature and solvent are stated beside the value. Clockwise rotation is $(+)$ and counterclockwise is $(-)$ .

An equal mixture of two enantiomers is a racemic mixture, written $(\pm)$ , and shows no rotation. In any other mixture, the enantiomeric excess is the percentage of the major enantiomer minus that of the minor one. It equals the sample’s specific rotation divided by the pure enantiomer’s, times $100 %$ . The major enantiomer makes up half of $100 %$ plus the excess.

[α] = \frac{α}{l c}

Why it works

Why mirror images match and diastereomers do not

Reflect a molecule in a mirror and every distance between two atoms stays the same. The bonds, the angles and the energy of the molecule are unchanged. That is why enantiomers share melting point, boiling point, density and solubility in ordinary solvents.

They differ only toward something that is itself chiral. Polarized light is twisted in one sense, and a receptor in the body has a handed pocket. A right hand fits a right glove, and its mirror image does not.

Diastereomers are not mirror images, so the distances inside them differ. In meso-2,3-dibromobutane the two bromine atoms can sit at a different distance from each other than in the (2R,3R) form. Different distances give different energies, so diastereomers differ in ordinary physical properties.

The rotation of a mixture follows from the cancelling. Each molecule of the minor enantiomer cancels one of the major, so only the excess rotates the light.

The method

Sorting stereoisomers in five steps

1. Count the stereocenters and the double bonds that can be E or Z. Call the total $n$ .

2. List the $2^{n}$ combinations of letters, such as (2R,3R), (2R,3S), (2S,3R) and (2S,3S).

3. Pair each combination with its mirror image by inverting every letter.

4. Look for a combination that is its own mirror image. That happens when two centers carry the same set of groups and opposite letters. Each such combination is one meso compound, not a pair.

5. Relate what is left. Mirror-image pairs are enantiomers, and any two stereoisomers that are not mirror images are diastereomers.

Where it breaks

$2^{n}$ is a ceiling, not a count. It is reached only when no combination is meso. 3-Bromobutan-2-ol has two centers with different groups, so it has all four stereoisomers, while 2,3-dibromobutane has three.

Zero rotation does not prove a sample is achiral. A meso compound and a racemic mixture both show $0$ , for different reasons. A racemic mixture is two compounds, and a meso compound is one. They differ in melting point, because the meso compound is a diastereomer of each enantiomer.

The sign of rotation is measured, never predicted from R and S. A specific rotation also changes with the solvent, the temperature and the wavelength, so an enantiomeric excess compares two values measured the same way. Chalk does not model optical rotation.

Enantiomers cannot be separated by distillation or ordinary crystallization, since they share those properties. Diastereomers can.

Check your answer

Recount the stereoisomers. Your total must be $2^{n}$ minus one for each pair that collapsed into a meso compound. For 2,3-dibromobutane, $4 - 1 = 3$ .

Test each pair you called enantiomers. Inverting every letter of one must give the other. If only some letters change, the two are diastereomers.

Check a mixture both ways. The two percentages must add to $100 %$ , and their difference must equal the enantiomeric excess, as $80.0 % - 20.0 % = 60.0 %$ .

Chalk compares two drawings. Draw both structures, choose Analyze → Compare and pick the second, and Chalk names the relationship, such as “Enantiomers” or “Diastereomers”. Rotation arithmetic goes in a Math box, one row per step, with each value on its own row. Write the excess as a calculation, such as $(24.0 \div 40.0) \times 100 %$ $= 60.0 %$ , without the letters ee in front. Chalk does not yet read ee as a name, and it marks such a row ✗ even when the arithmetic is right.

Separating enantiomers

Enantiomers share boiling point and solubility, so ordinary methods cannot separate a racemic mixture. Chemists turn the two enantiomers into diastereomers for a while instead. A racemic acid reacts with one pure enantiomer of a chiral amine, the resolving agent, to make two salts.

The two salts share the amine’s center and differ at the acid’s, so they are diastereomers with different solubilities. One crystallizes first. Each salt is then split to give back the amine and one pure enantiomer of the acid. A chiral chromatography column works the same way, through short-lived diastereomeric contacts that make one enantiomer move more slowly.

The molecules of living things are almost all single enantiomers. Proteins are built from L-amino acids and nucleic acids from D-sugars, which is why a drug’s two enantiomers can act so differently in the body.

Common mistakes

Expecting $2^{n}$ stereoisomers every time. Tartaric acid has two centers but three stereoisomers, because its (2R,3S) and (2S,3R) forms are one meso compound.
Treating a meso compound as a racemic mixture. A meso compound is one achiral compound, while a racemic mixture is an equal mix of two chiral ones.
Concluding a sample is achiral because its rotation is zero. It may be a racemic mixture of two chiral enantiomers, which also shows no rotation.
Calling cis and trans isomers enantiomers. They are diastereomers, because neither is the mirror image of the other.
Assuming diastereomers behave alike. They differ in melting point and solubility, because they are not mirror images and their inner distances differ.
Taking the enantiomeric excess as the share of the major enantiomer. An excess of $60.0 %$ means $80.0 %$ and $20.0 %$ , because the excess is the difference between the two.

Key terms

Enantiomer: One of a pair of molecules that are mirror images and cannot be superimposed on each other.
Diastereomers: Stereoisomers that are not mirror images of each other. Unlike enantiomers, they differ in ordinary physical properties such as melting point and solubility.
Meso compound: A compound with stereocenters that is identical to its mirror image because of an internal mirror plane. It is achiral and does not rotate polarized light.
Racemic mixture: An equal mixture of two enantiomers. It is optically inactive because their rotations cancel.
Optical activity: The ability of a substance to rotate the plane of polarized light. One enantiomer rotates it, its mirror image rotates it by the same angle the other way, and an equal mixture of the two does not rotate it.
Specific rotation: The observed rotation $α$ of polarized light, in degrees, divided by the path length $l$ in decimeters and the concentration $c$ in $g / mL$ : $[α] = α \div (l \times c)$ . It is reported with the wavelength, temperature and solvent.
Stereoisomers: Isomers with the same atom connectivity but different three-dimensional arrangements, including geometric isomers and enantiomers.

Work through an example

${CH}_{3} {CHBrCHBrCH}_{3}$ has two stereocenters. How many different stereoisomers does it have, and how are they related?

Compare the stereoisomers of 2,3-dibromobutane →

Find enantiomeric excess from optical rotation →

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Study the 7 key terms Draw (2R,3R)-2,3-dibromobutane Draw (2S,3S)-2,3-dibromobutane Draw meso-2,3-dibromobutane Open worked example on a board Stereochemistry rules in Chemistry Reference

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