Question

Write structural formulas for all of the possible cistrans isomers of the following compounds: a. \(1,2,3\) -trimethylcyclopropane b. 1,3 -dichlorocyclopentane c. \(1,1,3\) -trimethylcyclohexane d. (3-methylcyclobuty1)-3-methylcyclobutane

Short answer

The structural formulas of the possible cis-trans isomers for the given compounds are as follows: a. \(1,2,3\)-trimethylcyclopropane has no cis-trans isomers due to its small ring size. b. 1,3-dichlorocyclopentane has two isomers: - cis-1,3-dichlorocyclopentane:  - trans-1,3-dichlorocyclopentane:  c. 1,1,3-trimethylcyclohexane has two isomers: - cis-1,1,3-trimethylcyclohexane:  - trans-1,1,3-trimethylcyclohexane:  d. (3-methylcyclobutyl)-3-methylcyclobutane has two isomers: - cis-(3-methylcyclobutyl)-3-methylcyclobutane:  - trans-(3-methylcyclobutyl)-3-methylcyclobutane: 

Step-by-step solution

1a. Trimethylcyclopropane isomers

Since it is a cyclopropane molecule, there are no possible cis-trans isomers due to the small carbon ring size which leads to no geometric isomerism. Therefore, \(1,2,3\)-trimethylcyclopropane forms only one structure that is given below: 

1b. 1,3-dichlorocyclopentane isomers

In the case of 1,3-dichlorocyclopentane, two possible cis-trans isomers can be formed: (1) cis-1,3-dichlorocyclopentane: In this isomer, both chlorine atoms are located on the same side of the carbon ring. (2) trans-1,3-dichlorocyclopentane: In this isomer, chlorine atoms are located on opposite sides of the carbon ring. These isomers can be represented as follows: cis-1,3-dichlorocyclopentane:  trans-1,3-dichlorocyclopentane: 

1c. 1,1,3-trimethylcyclohexane isomers

Due to the presence of two methyl groups on carbon 1 and one on carbon 3, we obtain three possible cis-trans isomers for 1,1,3-trimethylcyclohexane: (1) cis-1,1,3-trimethylcyclohexane: In this isomer, carbon 3 methyl group is on the same side as the other two methyl groups. (2) trans-1,1,3-trimethylcyclohexane: In this isomer, the carbon 3 methyl group is on the opposite side of the other two methyl groups. The three isomers can be represented as follows: cis-1,1,3-trimethylcyclohexane:  trans-1,1,3-trimethylcyclohexane: 

1d. (3-methylcyclobutyl)-3-methylcyclobutane isomers

For this compound, we will have two possible cis-trans isomers: (1) cis configuration: Both methyl groups are located on the same side of their respective carbon rings. (2) trans configuration: The methyl groups are located on the opposite sides of their respective carbon rings. These isomers can be represented as follows: cis-(3-methylcyclobutyl)-3-methylcyclobutane:  trans-(3-methylcyclobutyl)-3-methylcyclobutane: 

Key concepts

Cyclopropane

Cyclopropane is a fascinating molecule because of its small ring structure consisting of three carbon atoms. This unique structure forms a triangle with bond angles of approximately 60 degrees, which is much less than the ideal tetrahedral angle of 109.5 degrees.
Due to this highly strained ring, cyclopropane does not exhibit cis-trans isomerism. In larger rings, geometric isomerism occurs because the ring is rigid enough to allow different spatial arrangements of substituents. However, the tension in cyclopropane prevents it from having these isomeric forms.
For example, in the compound 1,2,3-trimethylcyclopropane, the possible positions for substituents do not allow variations like cis and trans. This means only one structural formula is feasible for this compound. Understanding why cyclopropane can't have geometric isomers underlines the importance of ring size in isomerism.

Structural Formulas

Structural formulas are a vital tool in chemistry, providing a visual representation of a molecule’s composition and architecture. This type of formula shows how atoms in a molecule are bonded to each other, thus giving insight into both electronic and spatial arrangements.
By representing chemicals this way, scientists and students can predict properties like reactivity and allow for the study of isomers. For instance, when dealing with cyclic compounds such as 1,3-dichlorocyclopentane, the structural formula helps to visualize both the cis and trans isomers.
In the cis isomer, the chlorine atoms are positioned on the same side of the ring, whereas in the trans isomer, they reside on opposite sides. Structural formulas make such geometric distinctions clear, enabling easier comprehension of the molecular attributes.

Geometric Isomerism

Geometric isomerism, also known as cis-trans isomerism, is a type of stereochemistry that deals with the spatial arrangement of atoms in a molecule. It's especially relevant in molecules with restricted rotation, such as those with double bonds or ring structures.
For example, in cyclopentane derivatives, restricted rotation around the carbon ring allows for geometric isomers to exist when substituents are present. In 1,3-dichlorocyclopentane, as discussed in our steps, the chlorine atoms can either be on the same side (cis) or opposite sides (trans) of the ring.
This form of isomerism impacts many of the compound's physical and chemical properties, such as boiling and melting points, polarity, and reactivity. Recognizing these differences is crucial for understanding the behavior of molecules in various environments.

Cyclopentane

Cyclopentane is a five-membered carbon ring that is less strained than cyclopropane, allowing for more flexibility in terms of substituent placement and the existence of geometric isomers.
The relatively larger ring size compared to cyclopropane means that cis-trans isomerism can occur because the ring is not as terminally restricted. For instance, when 1,3-dichlorocyclopentane is in question, the flexibility allows for the formation of both cis and trans isomers.

• The cis isomer places both substituent groups on the same side of the ring.
• The trans isomer puts them on opposite sides.

This ability to form geometric isomers is significant in studying their chemical properties, which are often quite diverse due to their spatial arrangement.