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I was watching a video lecture today on hydrocarbons and came across this. The instructor says that, as there is a plane of symmetry, cis-1,2-dimethylcyclohexane is a meso-compound:

Alleged mirror plane in cis-1,2-dimethylcyclohexane

However, the cyclohexane ring is never planar as it adopts a chair conformation. I cannot find any plane of symmetry in chair form. Like this:

enter image description here

Is the compound meso or not?

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cis-1,2-Dimethylcyclohexane is achiral, not because there is a plane of symmetry, but because it consists of two enantiomeric conformations which interconvert rapidly via ring flipping at normal temperatures.

This is exactly the same case as amine inversion. "Chiral nitrogens" such as that in $\ce{NHMeEt}$ do not lead to chirality or optical activity because of rapid inversion of configuration at the nitrogen atom, leading to interconversion of the two enantiomeric forms 1a and 1b.

Conformers of N-methylethanamine

Likewise, the ring flip in cis-1,2-dimethylcyclohexane leads to two different conformers. I have deliberately chosen to depict the ring flip in the following fashion, to make the mirror image relationship more obvious. The green methyl group, equatorial in conformer 2a, is changed into an axial methyl group in conformer 2b. Likewise, the blue methyl group goes from axial to equatorial. The 1,2-cis relationship between the two methyl groups is retained in both conformers.

Conformers of cis-1,2-dimethylcyclohexane

Each individual conformer can be said to be chiral, but just like how the amine is considered achiral, cis-1,2-dimethylcyclohexane as a whole is considered achiral.

Is the compound meso? According to the IUPAC Gold Book, a meso-compound is defined as:

A term for the achiral member(s) of a set of diastereoisomers which also includes one or more chiral members.

1,2-Dimethylcyclohexane possesses two diastereomers, one cis and one trans form. The trans form is chiral, but the cis form is achiral, as explained above. Therefore, the cis form satisfies the above definition and is considered a meso-compound.

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  • $\begingroup$ Can we get it cold enough to freeze the enantiomers long enough to detect them? Can we see evidence of non-racemization in an optically active environment? $\endgroup$
    – Oscar Lanzi
    Jan 14, 2018 at 14:46
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    $\begingroup$ Sir, I'd like to ask one thing, suppose we have the compound 1-(chloromethyl)-3,5-dimethylcyclohexane in which all three substituents (the 2 methyl and one chloromethyl) are coming out of the plane, is this compound meso? Due to the same reason as explained in this answer (flipping of ring)? It does have two stereogenic centres (the 3,5 positions)... $\endgroup$
    – V.G
    Jan 23, 2021 at 19:50
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    $\begingroup$ @LightYagami Yes, it is the same thing. $\endgroup$
    – orthocresol
    Jan 23, 2021 at 20:36
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    $\begingroup$ @Infinite (1) It's a bit of a grey area, but the key point is that the enantiomers are not isolable at RT. "Racemic" implies that you can separate and isolate the two enantiomers. (2) It being (R,S) means that the compound is optically inactive, which completely agrees with what I wrote. This, however, does not rule out that a specific conformation may be chiral. On balance, when all conformations are considered, it will be optically inactive. Note that the same is true of, say, meso-tartaric acid, for which one can easily construct a chiral conformation. $\endgroup$
    – orthocresol
    Jan 26, 2022 at 9:58
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    $\begingroup$ @Infinite Note, further, that if you are describing one particular species or conformation, then it is better to use the term "chiral" or "achiral". On the other hand, "optically active" or "optically inactive" should only be used to refer to a bulk sample of such a compound, because optical activity is something you can only measure on a bulk sample. You can't go into the lab and determine how a single molecule rotates plane-polarised light. You can, however, use symmetry arguments etc. to show that the molecule is or isn't superimposable on its mirror image: hence chiral or achiral. $\endgroup$
    – orthocresol
    Jan 26, 2022 at 10:02
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I'd like to add a few points definition wise from the IUPAC goldbook.
(Because recently the original website seems to be broken I am using links via the internet archive.)

meso
A prefix to indicate the presence of a symmetry element of the second kind (see chirality) in a chemical species which is usually one of a set of diastereoisomers that also includes a chiral member.

However, there is a more general definition, too:

meso-compound
A term for the achiral member(s) of a set of diastereoisomers which also includes one or more chiral members.

The first part clearly does not apply to the cis-isomer, (1R,2S)-1,2-dimethylcyclohexane, the second does because of the definition of chirality.

chirality
The geometric property of a rigid object (or spatial arrangement of points or atoms) of being non-superposable on its mirror image; such an object has no symmetry elements of the second kind (a mirror plane, σ = S1, a centre of inversion, i = S2, a rotation-reflection axis, S2n). If the object is superposable on its mirror image the object is described as being achiral.

I think the key point of this definition is in this case, that the object needs to be rigid, which (1R,2S)-1,2-dimethylcyclohexane is not at room temperature. If you cool down the solution, inhibiting the ring flip, you would probably be able to find both configurations; that is a racemic mixture of them.

Since (1R,2R)-1,2-dimethylcyclohexane and (1S,2S)-1,2-dimethylcyclohexane, the trans-conformers, are both chiral (and enantiomers), the remaining member of the set (1R,2S)-1,2-dimethylcyclohexane can be considered a meso-compound, since it is achiral.

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