Using a planar pentagon representation for the cyclopentane ring, draw structural formulas for the cis and trans isomers of the following. (a) 1,2-Dimethylcyclopentane (b) 1,3-Dimethylcyclopentane

Cis and trans isomers are geometric isomers, meaning they have different spatial arrangements of substituent groups around a double bond or a ring. In the case of cycloalkanes, cis isomers have the substituent groups on the same side of the ring, while trans isomers have the substituent groups on opposite sides of the ring.

(a) For 1,2-dimethylcyclopentane, we have two methyl groups attached to adjacent carbons on the cyclopentane ring. To determine cis and trans isomers, we can draw cyclopentane as a planar pentagon and identify the positions of methyl groups in the different isomers. 1. Cis isomer: Draw a planar pentagon, representing the cyclopentane ring, with two methyl groups attached to adjacent carbons on the same side of the ring. 2. Trans isomer: Draw a planar pentagon, representing the cyclopentane ring, with two methyl groups attached to adjacent carbons on opposite sides of the ring.

(b) For 1,3-dimethylcyclopentane, we have two methyl groups attached to carbons with one carbon in between on the cyclopentane ring. To determine cis and trans isomers, we can draw cyclopentane as a planar pentagon and identify the positions of methyl groups in the different isomers. 1. Cis isomer: Draw a planar pentagon, representing the cyclopentane ring, with two methyl groups attached to carbons with one carbon in between them on the same side of the ring. 2. Trans isomer: Draw a planar pentagon, representing the cyclopentane ring, with two methyl groups attached to carbons with one carbon in between them on opposite sides of the ring. By following these steps, you will have drawn the structural formulas for the cis and trans isomers of 1,2-dimethylcyclopentane and 1,3-dimethylcyclopentane using a planar pentagon representation for the cyclopentane ring.