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What is the stereochemical relationship between ortho, meta, and para-dimethyl benzene, given that interconversion between the three structures requires you to break and form new bonds?

I know that ortho relates to the 1,2 position, the meta position relates to the 1,3 position and the para position relates to the 1,4 position.

However, what does it mean by 'stereochemical relationship'? Does it just mean that if the methyl is placed at the different carbon numbers, they're different molecules?

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    $\begingroup$ There is no sterochemistry in any of the dimethylbenzenes. Benzene is a planar molecule, which rules out both chirality and geometrical isomerism. $\endgroup$ – Pritt Balagopal Mar 30 '18 at 11:47
  • $\begingroup$ They are constitutional (structural) isomers; there is no "stereochemical relationship" because they are not stereoisomers. [(E) and (Z)-butene are stereoisomers. The two are constitutional isomers of 1-butene.] $\endgroup$ – user55119 Mar 30 '18 at 21:42
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These compounds do not have a stereochemical relationship. Stereoisomers have the same connectivity of atoms (constitution) with different arrangement in space. The (1,2), (1,3), and (1,4) in the names of these compounds indicate that this is not the case. These are not stereoisomers of any kind.

dtructures of ortho-, meta-, and para- 1,2-dimethylbenzene

Not that the qualifying text about having to break bonds to interconvert is unhelpful and irrelevant. All isomers require bond-breaking to interconvert.

So, what then are the relationships between these three compounds? Let's look at a decision flowchart for relationship between structures: isomer relationship flowchart

Do they have the same formula?

Yes.

Do they have the same connectivity?

No. Thus, they are constitutional isomers. Constitutional isomerism is not a type of stereoisomerism. The two main types of stereoisomerism are enatiomerism and diastereomerism.

It would be worth contacting your instructor and asking for clarification, noting that these are not examples of any kind of stereoisomerism. It could be an honest mistake in the wording of the question. As someone in the teaching profession, my experience is that most instructors are happy when a student understands the content at a level high enough to catch mistakes.

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