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Which of the compounds below has the smallest heat of combustion?

1-tert-butyl-2,4-dimethylcyclohexane

I know that the heat of combustion is indirectly proportional to the stability of a molecule. And here both $\ce{CH3}$ and $\ce{C(CH3)3}$ are +I groups (inductive effect) but apart from that, I am stuck on how to compare these compounds.

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    $\begingroup$ I guess, you are expected to recall energy difference for equatorial and axial positions of substituent in chair conformation of cyclohexane ring. However, I'd say that IRL this effect is very small and dispersion interactions in liquid phase may trump it, but are much harder to predict in this case. $\endgroup$ – permeakra Jan 8 '16 at 13:35
  • $\begingroup$ @permeakra so how could we compare in this $\endgroup$ – user101522 Jan 8 '16 at 13:44
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    $\begingroup$ "you are expected to recall energy difference for equatorial and axial positions of substituent in chair conformation of cyclohexane ring" - that's literally the entire answer $\endgroup$ – orthocresol Jan 8 '16 at 14:07
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Which of the compounds below have the smallest heat of combustion?

The question is asking, which of these 4 compounds is the most stable. The most stable compound will have the lowest heat of combustion.

In the cyclohexane ring system, bulky substituents prefer the equatorial position rather than the axial position. This is due to steric (this can also be described in electronic terms since it is due to the repulsion between interpenetrating electron clouds) destabilization. For example, in methylcyclohexane, the methyl group can be in an axial or equatorial position. In the axial position, it is destabilized by the steric (electronic) interactions it has with the axial hydrogens on carbons 3 and 5.

enter image description here

These interactions are nicely described by cyclohexane A-Values. The A-Value measures the energy difference (in kcal/mol) between having the substituent in the axial and equatorial positions. The larger the A-Value, the larger the preference the substituent has for the equatorial position. The A-Value for a methyl group is 1.7 kcal/mol. The A-Value for a t-butyl group is so large (>4 kcal/mol) that the t-butyl group is effectively locked into the equatorial position. t-Butyl substituted cyclohexanes do not undergo chair-chair interconversion - this would place the t-butyl group in an axial position, hence they are conformationally locked into the chair with the t-butyl in an equatorial position.

It is this last piece of information that helps simplify our problem. Here are the structures of the 4 cyclohexanes redrawn in the chair conformation.

enter image description here

Each structure has the t-butyl group in the equatorial position. Compound 1 has one methyl group in an axial position; this adds 1.7 kcal/mol to the energy of the molecule. Molecule 2 has two axial methyl groups, therefore it is 3.4 kcal/mol higher in energy.

I'll leave molecules 3 and 4 to you to figure out. Once you determine their relative energies, which one of the 4 has the lowest energy relative energy?

Note: There are exceptions to the additivity of A-Values. See near the bottom of this page for a few examples.

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