Question

Write structural formulas for all the \(\mathrm{C}_{5} \mathrm{H}_{10}\) alkenes, and identify the relationship (constitutional isomer or stereoisomer) of each one to the others. Are any chiral?

Short answer

The alkenes are constitutional isomers and none are chiral.

Step-by-step solution

Understand the Molecular Formula

The formula \( \mathrm{C}_{5} \mathrm{H}_{10} \) suggests the presence of an alkene with a carbon-carbon double bond. This is because a saturated hydrocarbon with 5 carbons should have the formula \( \mathrm{C}_{5} \mathrm{H}_{12} \), and the given formula has two fewer hydrogens, indicating a double bond.

Identify Possible Carbon Skeletons

For \( \mathrm{C}_{5} \mathrm{H}_{10} \), the possible carbon skeletons are: a straight chain of 5 carbons, a branched chain with 4 carbons (with a methyl group branching off), and possibly a structure with a three-carbon chain and two methyl groups.

Draw Structural Formulas

1. Pent-1-ene: A straight carbon chain with the double bond between the first and second carbons (\( \mathrm{CH}_{2}=\mathrm{CHCH}_{2}\mathrm{CH}_{2}\mathrm{CH}_{3} \)).2. Pent-2-ene: A straight carbon chain with the double bond between the second and third carbons (\( \mathrm{CH}_{3}\mathrm{CH}=\mathrm{CH}\mathrm{CH}_{2}\mathrm{CH}_{3} \)).3. 2-Methylbut-1-ene: A branched chain with a double bond at the end (\( \mathrm{(CH}_{3})_{2}\mathrm{C=CHCH}_{3} \)).4. 2-Methylbut-2-ene: A branched chain with a double bond in the middle (\( \mathrm{CH}_{3}\mathrm{C(CH}_{3})=\mathrm{CH}_{2} \)).5. Cyclopentane structure can also be considered for 5 carbons (not considered here as per instruction).

Identify Isomers and Their Relationships

Pent-1-ene and Pent-2-ene are straight-chain isomers. 2-Methylbut-1-ene and 2-Methylbut-2-ene are branched-chain isomers. All these are constitutional isomers because they differ in the connectivity of the carbon atoms

Determine Chirality

Check each structure for asymmetry. None of the structures have a chiral center because there isn’t a carbon with four different substituents in the described structures.

Key concepts

Constitutional Isomer

Constitutional isomers, also known as structural isomers, are molecules that have the same molecular formula but different connectivities between their atoms. This means that even though they have the same number of carbon and hydrogen atoms, those atoms are bonded in different ways.
Key points to remember about constitutional isomers:

• They can vastly differ in physical and chemical properties.
• Their distinct structures can lead to different functional groups appearing in the isomers.
• In alkenes, as with \(\mathrm{C}_{5}\mathrm{H}_{10}\), constitutional isomers can arise through variations in position of the double bond or branching of the alkyl chain.

For example, in the case of \(\mathrm{C}_{5}\mathrm{H}_{10}\), Pent-1-ene and Pent-2-ene are constitutional isomers because the double bonds are located at different positions along the carbon chain. Similarly, 2-Methylbut-1-ene and 2-Methylbut-2-ene differ due to the branching of the carbon skeleton.

Stereoisomer

Stereoisomers are molecules with the same structural formula and sequence of bonded atoms, but they differ in the three-dimensional orientation of their atoms. This means that while the atoms connect in the same order, their spatial arrangement sets them apart.
Stereoisomers can be tricky because they often look very similar at a glance. Here are some characteristics and forms of stereoisomers:

• Cis-Trans Isomerism: Occurs in alkenes when two substituents are either on the same side (cis) or on opposite sides (trans) of a double bond.
• Enantiomers: Also a form of stereoisomerism but specifically in chiral centers, leading to molecules that are mirror images of each other.

Though we discussed \(\mathrm{C}_{5}\mathrm{H}_{10}\) structures like Pent-1-ene having no stereoisomers due to linear chain symmetry, Pent-2-ene could exhibit cis-trans isomerism because it possesses a central double bond with substituents potentially arranged differently in space.

Chiral Center

A chiral center is a carbon atom that is bonded to four different substituents, making the molecule nonsuperimposable on its mirror image. This concept is a cornerstone in the study of stereochemistry, as chirality can significantly influence the behavior and interaction of molecules in biological systems.
Some important aspects of chiral centers:

• Chirality leads to a pair of enantiomers, which are mirror images that cannot overlap.
• Chiral centers are crucial in pharmaceuticals, flavor chemistry, and more, since enantiomers may have very different effects.
• Presence of a lone chiral center often makes a compound optically active, rotating plane-polarized light.

In the context of \(\mathrm{C}_{5}\mathrm{H}_{10}\) alkenes examined, none exhibit a chiral center. The structures analyzed (like Pent-2-ene) do not meet the criteria as they lack a carbon atom connected to four different groups.

Carbon Skeletons

In organic chemistry, the carbon skeleton refers to the backbone of carbon atoms in a molecule. This structure determines the primary framework from which other functional groups branch off.

• Straight Chain: All carbon atoms are connected in a single sequence. The alkenes like Pent-1-ene and Pent-2-ene have a straight chain skeleton.
• Branched Chain: Some carbons branch off from the main chain. In \(\mathrm{C}_{5}\mathrm{H}_{10}\), 2-Methylbut-1-ene and 2-Methylbut-2-ene are examples where alkyl groups branch off the main carbon chain.
• The arrangement of carbon skeletons affects the physical properties and reactivities of compounds due to differences in shape and surface area.

Understanding carbon skeletons helps chemists predict how a molecule might react or intermingle with others. It’s this diversity in skeletons that contributes to the wide variety of organic compounds, despite limited core elements like carbon and hydrogen.