[21385]

I have some trouble understanding the connection between 1,3-diaxial steric strain and gauche interaction of butane. This is from the McMurry Organic textbook. Basically, it says that the gauche strain in butane is similar to any 4-carbon fragment of a trans-1,2-dimethylcyclohexane, because they have both 4-carbon fragments. I understand this but in one of its practice questions, it asks you to find the gauche strain of CH3 and CH2CH3 in cis-1-ethyl-2-methylcyclohexane. It calculates the gauche strain as 3.8 kJ/mol, which is the same value as butane's gauche strain between CH3 and CH2CH3. The gauche strain of CH3 and CH2CH3 in cis-1-ethyl-2-methylcyclohexane is a 5-carbon fragment while a butane's gauche strain is 4-carbon fragment. I would expect the CH3 and CH2CH3 gauche strain to be larger because of the increased size. Can anyone help me?

Thanks a lot.

[movies]

It will be slightly larger than the Me-Me gauche interaction, but extending a straight alkyl chain like that (i.e., from Me to Et to n-Pr, etc.) has a very small effect on the strain because the floppy part of the sidechain can situate itself pointing away from the gauche interaction.  If you were to look at a Me-Me gauche interaction, most of the conflict comes from 2 of the 3 H atoms on the Me group (the third H points the other way), so substituting the third H with an Me is a small change in the actual interaction.

If the groups were locked into close proximity, there would be a large effect, as your intuition suggested.  You can see this in what is called a "syn-pentane" interaction.  The syn-pentane interaction is responisible for the strain in one of the chair flip conformations of cis-1,3-dimethylcyclohexane.  In a cyclohexane system, these interactions are usually called 1,3-diaxial interactions, the syn-pentane terminology usually refers to an acyclic system.

[21385]

Thanks, I really appreciate your answer to my question. But I am still a bit unsure about this. So, if it is cyclic structure like the structure I mentioned, can I assume that every Me to Ethyl in an 1,2 conformation has the same gauche strain energy as a Me to Me gauche strain? But if it is a Me to Propyl in a 1,2 conformation, then it is different, right? Also, if the cyclo structure is a less flexible structure such as cyclopropane, the Me to Ethyl gauche strain would be much greater, right?

[movies]

Well, not quite.  Me-Me and Me-Et gauche strain will be slightly different, and Me-Pr will be slightly higher still.  The point is that the change is relatively small because of the conformational flexibility of a straight alkyl chain.

As for smaller ring sizes, that gets much more complicated because you are changing bond angles a lot.  I would only use gauche strain to describe acyclic strain or strain in 6-membered rings.  There is still strain in these smaller ring systems, but it's a lot different so I wouldn't use the same terminology.