Question

Which would you predict to have the larger (more negative) heat of combustion, cis- 1,4 -dimethylcyclohexane or trans-1,4-dimethylcyclohexane?

Short answer

Answer: The cis-1,4-dimethylcyclohexane isomer has a larger (more negative) heat of combustion.

Step-by-step solution

Understand the isomers of 1,4-dimethylcyclohexane

First, we need to understand the two isomers we are comparing: cis-1,4-dimethylcyclohexane and trans-1,4-dimethylcyclohexane. In the cis isomer, both methyl groups are on the same side of the cyclohexane ring, whereas in the trans isomer, they are on opposite sides.

Understand the concept of heat of combustion

The heat of combustion is the amount of heat released when a compound is burned in the presence of oxygen. More stable compounds generally have a less negative heat of combustion because they are already at a lower energy state and release less energy when they are burned.

Compare the stability of the two isomers

When comparing the stability of the two isomers, we need to consider the conformation of the cyclohexane ring and the interactions between the methyl groups. In a chair conformation of the cyclohexane ring, axial and equatorial positions are available for the substituents. The more stable conformation is the one with the least steric hindrance and the least unfavorable interactions between the substituents and the ring. For cis-1,4-dimethylcyclohexane, both methyl groups are oriented on the same side of the ring, leading to unfavorable steric interactions when they are in the axial positions. Therefore, the most stable conformation will have both methyl groups in the equatorial positions. On the other hand, for trans-1,4-dimethylcyclohexane, one methyl group will be in an axial position, and the other will be in an equatorial position in the most stable chair conformation. This arrangement has less steric hindrance than the cis isomer.

Predict the heat of combustion based on the stability

Since the trans isomer has fewer steric interactions and is more stable, it will release less energy when it is burned. Therefore, the heat of combustion for the trans isomer is less than that of the cis isomer. In other words, the cis isomer has a larger (more negative) heat of combustion.

Conclusion

Based on our analysis, we predict that the cis-1,4-dimethylcyclohexane will have a larger (more negative) heat of combustion compared to the trans-1,4-dimethylcyclohexane.