The heat of combustion of cis-1,2-dimethylcyclopropane is larger than that of the trans isomer. Which isomer is more stable? Use drawings to explain this difference in stability

Verified step by step guidance

1. Identify the structural differences between cis-1,2-dimethylcyclopropane and trans-1,2-dimethylcyclopropane. The cis isomer has both methyl groups on the same side of the cyclopropane ring, while the trans isomer has them on opposite sides.
2. Understand that the heat of combustion is a measure of the energy released when a compound is burned. A higher heat of combustion indicates that the compound is less stable because it releases more energy to reach a stable state.
3. Recognize that the cis isomer has more steric strain due to the proximity of the two methyl groups on the same side of the ring, leading to increased torsional strain and angle strain in the small cyclopropane ring.
4. Compare the trans isomer, which has less steric strain because the methyl groups are on opposite sides, reducing the torsional strain and making the molecule more stable.
5. Conclude that the trans isomer is more stable than the cis isomer because it has a lower heat of combustion, indicating it is at a lower energy state due to reduced steric and torsional strain.

Key Concepts

Isomerism

Isomerism refers to the phenomenon where compounds have the same molecular formula but different structural arrangements. In organic chemistry, isomers can be classified into structural isomers, which differ in the connectivity of atoms, and stereoisomers, which have the same connectivity but differ in the spatial arrangement of atoms. The stability of isomers can vary significantly based on their structure, influencing their physical and chemical properties.

Heat of Combustion

The heat of combustion is the amount of energy released when a substance is completely burned in oxygen. It is an important measure of the stability of a compound; generally, a higher heat of combustion indicates a less stable compound, as more energy is released when it is converted to more stable products. Comparing the heats of combustion of isomers can provide insights into their relative stabilities.

Steric Strain

Steric strain arises when atoms in a molecule are forced closer together than their preferred distance, leading to increased energy and decreased stability. In cycloalkanes, such as cyclopropane derivatives, steric interactions between substituents can significantly affect stability. The cis isomer of 1,2-dimethylcyclopropane experiences more steric strain due to the proximity of the methyl groups, making the trans isomer more stable despite the higher heat of combustion of the cis isomer.