Question

(a) Draw the condensed structural formulas for the cis and trans isomers of 3-methyl-3-hexene. (b) Can cyclohexene exhibit cis-trans isomerism? Explain. (c) Does 2 -hexyne have geometric isomers? Explain.

Short answer

(a) Cis: \(CH_2=C(\text{H})CH(\text{CH}_3)-CH_2-CH_2-CH_3\), Trans: \(CH_2=C(\text{CH}_3)CH(\text{H})-CH_2-CH_2-CH_3\) (b) No, cis-trans isomerism is impossible in cyclohexene as each carbon of the double bond has the same two groups attached. (c) No, 2-hexyne cannot have geometric isomers due to the restricted rotation around its alkyne triple bond.

Step-by-step solution

(a) Drawing cis and trans isomers of 3-methyl-3-hexene

First, let's start with drawing the parent chain of 6 carbons for hexene. The alkene (double bond) should be between carbons 3 and 4, and the methyl group should be attached to carbon 3. The cis and trans isomers can be drawn as follows: For the cis isomer: 1. Draw the parent chain with the double bond between carbons 3 (C3) and 4 (C4): \(CH_2=CH-CH_2-CH_2-CH_2-CH_3\) 2. Attach the methyl group to C3, placing it on the same side as the hydrogen on C4: \(CH_2=C(\text{H})CH(\text{CH}_3)-CH_2-CH_2-CH_3\) For the trans isomer: 1. Draw the parent chain with the double bond between carbons 3 (C3) and 4 (C4): \(CH_2=CH-CH_2-CH_2-CH_2-CH_3\) 2. Attach the methyl group to C3, placing it on the opposite side as the hydrogen on C4: \(CH_2=C(\text{CH}_3)CH(\text{H})-CH_2-CH_2-CH_3\)

(b) Cis-trans isomerism in cyclohexene

To determine if cyclohexene can exhibit cis-trans isomerism, we need to check if there are two different groups on each carbon of the double bond. In cyclohexene, the double bond is between two carbons in a six-membered ring. Cyclohexene's structure is: \[CH_2=CH-CH_2-CH_2-CH_2-CH_2 \] Each carbon of the double bond is connected to one hydrogen and one carbon from the ring. Since each of these carbons has the same two groups attached to it (hydrogen and the rest of the ring), cis-trans isomerism is impossible in cyclohexene.

(c) Geometric isomers of 2-hexyne

To determine if 2-hexyne has geometric isomers, we need to check the nature of the bond in its structure. The structure of 2-hexyne is: \[CH_3-C\equiv CH-CH_2-CH_2-CH_3 \] The bond between the second and third carbons (C2 and C3) is a triple bond (alkyne), which doesn't allow any rotation around the bond. Hence, 2-hexyne cannot have cis-trans (geometric) isomers since its structure is restricted by the triple bond.

Key concepts

Geometric Isomers

Geometric isomers are a type of stereoisomer that differ in the spatial arrangement of groups around a double bond. This phenomenon is commonly observed in alkenes, which have double bonds that prevent rotation and make different spatial arrangements possible.
One of the most common forms of geometric isomerism is cis-trans isomerism:

• Cis isomer: The same groups are on the same side of the double bond.
• Trans isomer: The same groups are on opposite sides of the double bond.

In the example of 3-methyl-3-hexene, the presence of a double bond between carbon 3 and 4 enables the formation of cis and trans isomers based on the placement of the methyl group relative to other hydrogen atoms in the molecule. Understanding these concepts helps in predicting properties like boiling points and solubilities, which may differ between isomers due to molecular polarity and shape differences.

Alkenes and Alkynes

Alkenes and alkynes are hydrocarbons characterized by the presence of carbon-carbon double and triple bonds, respectively. These bonds play crucial roles in determining the structural and chemical properties of the molecules.
**Alkenes** have at least one double bond between carbon atoms. This bond is rigid and does not allow rotation, leading to the possibility of geometric isomerism when different groups are attached to the carbons of the double bond. This is the case for 3-methyl-3-hexene, which can show cis-trans isomerism.
**Alkynes**, on the other hand, contain carbon-carbon triple bonds. These bonds are even more rigid than double bonds, so no rotation is possible, effectively eliminating the possibility of geometric isomers. This is why 2-hexyne cannot have geometric isomers, as its triple bond restricts any such spatial differences in arrangement.

Structural Formulas

A structural formula represents how atoms are arranged in a molecule, showing which atoms are bonded to each other and the type of bonds that exist. These formulas are vital for understanding isomerism as they provide the necessary detail about the molecular structure.
There are different types of structural formulas, ranging from simple line formulas to more detailed representations like Lewis structures and 3D models.
In the case of geometric isomers:

• A condensed structural formula provides a compact representation which easily highlights the position of functional groups, such as the methyl group in 3-methyl-3-hexene.
• Detailed 3D models, although not depicted in textbooks often, show how the spatial arrangement around double and triple bonds lead to different isomers.

By learning to draw and interpret these structures, students can better anticipate the physical and chemical properties of compounds, enhancing understanding in organic chemistry.