Question

Would you expect cis- or trans-1, 2-dimethylcyclopropane to be the more stable? Explain.

Short answer

The trans-1,2-dimethylcyclopropane is more stable than the cis isomer. This is primarily due to lower steric strain in the trans isomer, as the methyl groups are further apart, resulting in fewer steric interactions and a more stable molecule with lower energy.

Step-by-step solution

Identify the cis and trans isomers

To compare the stability of cis- and trans-1,2-dimethylcyclopropane, we first need to identify the difference between the two isomers. In the cis isomer, both methyl groups are on the same side of the cyclopropane ring. In the trans isomer, the methyl groups are on opposite sides.

Assess steric strain in the isomers

Steric strain is a contributing factor to the overall stability of a molecule. Molecules with higher steric strain generally have higher energies and are less stable. In the case of the cis isomer, the methyl groups are both on the same side of the cyclopropane and are relatively close to each other. This close proximity leads to significant van der Waals repulsion between the two groups, creating a higher steric strain. In the trans isomer, the methyl groups are further apart, resulting in fewer steric interactions and lower steric strain.

Consider other factors influencing stability

There are other factors that can also contribute to the overall stability of the molecule, such as ring strain and conformation. However, in this case, the most significant factor is the steric strain, as the ring strain is the same for both isomers and there are no specific conformations that would favor one isomer over the other.

Compare the stability of the isomers

Based on the steric strain in the cis and trans isomers, we can conclude that the trans-1,2-dimethylcyclopropane is more stable than the cis isomer. This is because the trans isomer has less steric strain due to the methyl groups being further apart, which results in a more stable molecule with lower energy.

Key concepts

Cis-trans Isomerism

Cis-trans isomerism is a form of stereoisomerism where the orientation of substituent groups in a double-bonded or a cyclic compound differ spatially, affecting the compound's properties and stability. To illustrate this concept, let's take the example from the exercise, involving 1,2-dimethylcyclopropane. The 'cis' prefix indicates that the two methyl groups are on the same side of the cyclopropane ring, hence the name 'cis-isomer'. On the other hand, the 'trans' prefix means the methyl groups are on opposite sides, forming the 'trans-isomer'.

These distinct spatial arrangements result in unique physical and chemical characteristics for each isomer. For instance, the cis-isomer typically exhibits different dipole moments, boiling points, solubility, and reactivity compared to the trans-isomer due to the different positioning of the methyl groups.

Steric Strain

Steric strain plays a pivotal role in the stability of molecules and is a type of strain caused by the repulsive forces between the electron clouds of nearby atoms or groups that are not bonded to each other. In the context of our example, with cis-1,2-dimethylcyclopropane, there's a notable steric strain as the two methyl groups vie for space on the same side of the small cyclopropane ring. This close proximity results in an increase in the electron cloud repulsions, leading to higher energy and lower stability.

Conversely, the trans isomer allows the methyl groups to be positioned on opposite sides of the ring, spreading out the electron repulsion and significantly reducing steric strain. This decreased steric strain contributes to a lower energy state, and therefore, improves the stability of the trans isomer.

Conformational Analysis

Conformational analysis involves studying the different orientations that a molecule's atoms can adopt due to rotation around single bonds. As relevant to our exercise, both the cis and trans isomers of 1,2-dimethylcyclopropane have distinct conformations stemming from their unique spatial arrangements; however, due to the rigidity of the cyclopropane ring, these conformations are limited. The molecule's stability is impacted by the conformational preferences and the degree of strain present.

In our example, while both isomers share the same ring strain due to the bond angles in the three-membered ring, the cis isomer has a conformation that increases steric strain, leading to higher potential energy and less stability. The trans isomer, with its methyl groups placed in less conflicting positions, experiences less steric hindrance. Consequently, the trans isomer's more favorable conformation gives it a lower potential energy and a greater degree of stability.