# How many gauche butane interactions are present in cis-1,2-dimethylcyclohexane?

We were asked to find out the number of Gauche-Butane interactions for this compound:

I proceeded by drawing the Newman Projection for this chair conformation as follows and marked the Gauche-Butane interactions (as shown by red curves):

They told me that I was almost correct and asked me to try once again but I can't find out where I probably went wrong.

Can someone guide me out in this regard?

• #3 looks dubious. Consider that the gauche interaction stretches over four carbons: C–C–C–C. – orthocresol Jun 17 '20 at 16:09
• @orthocresol, I thought that the methyl group involved in the step 3 suffers steric repulsion from that carbon like in step 1. Isn't it so? If not, what should it be? – Sanu_012 Jun 17 '20 at 16:14
• Which 4 carbons should I choose? Should I start from the carbon in step 3 to all the way left ? – Sanu_012 Jun 17 '20 at 16:16
• Ahem, well, I don't really want to give you the answer straight up (and indeed, I don't think you need it). The equatorial methyl group is only involved in one gauche interaction, which is your #2. The other carbons are anti to it, so that's not an issue. Your #1 and #2 are quite correct. Your #3 isn't. Have a think about it. By the way, are you supposed to ignore gauche interactions that are within the ring itself? Even without the methyl groups, unsubstituted cyclohexane has some gauche interactions, which you haven't included. – orthocresol Jun 17 '20 at 16:36
• Is this from an entrance exam preparation manual/worksheet? – Micelle Jun 17 '20 at 16:59

The difference in the number of gauche interactions - namely, two - between these epimers is approximated by the difference in their heats of combustion[1] which is $$\pu{1.54 kcal/mol}$$. [1,2 cis: $$\Delta H^\circ_\mathrm{comb} = \pu{-1248.31 kcal/mol}$$; 1,2 trans: $$\Delta H^\circ_\mathrm{comb} = \pu{-1246.77 kcal/mol}$$.] A typical value for a gauche interaction is $$\pu{0.9 kcal/mol/interaction}$$.
1. Walter H. Johnson, Edward Prosen, and Frederick D. Rossini, Heats of Combustion and Isomerization of the Eight $$\ce{C8H16}$$ Alkylcyclohexanes. Research Paper RP1S12, Volume 39, July 1947. PDF via NIST