Question

There are three different substances that contain a carbon-carbon double bond and have the formula \(\mathrm{C}_{4} \mathrm{H}_{8}\). Draw them, and tell how they differ.

Short answer

The compounds are but-1-ene, but-2-ene, and 2-methylpropene; they differ in the position of the double bond and carbon chain branching.

Step-by-step solution

Understanding the formula

The molecular formula given is \(\mathrm{C}_4 \mathrm{H}_8\). This means we need to draw compounds containing four carbon atoms and eight hydrogen atoms. Since these compounds contain a carbon-carbon double bond, they should be alkenes and follow the general formula for alkenes \(\mathrm{C}_n \mathrm{H}_{2n}\). Thus, \(\mathrm{C}_4 \mathrm{H}_8\) is an alkene.

Drawing Structure 1: But-1-ene

Draw the structure with the double bond between the first and second carbon of a carbon chain: \(\mathrm{CH}_2=\mathrm{CHCH}_2\mathrm{CH}_3\). This is called but-1-ene, where the double bond is at the end of the carbon chain.

Drawing Structure 2: But-2-ene

Draw the structure with the double bond between the second and third carbon of a carbon chain: \(\mathrm{CH}_3\mathrm{CH}=\mathrm{CHCH}_3\). This is called but-2-ene, where the double bond is interior in the carbon chain, allowing for additional geometric isomerism (cis and trans forms).

Drawing Structure 3: 2-Methylpropene

Draw the structure with a three-carbon chain and a methyl group attached to the second carbon with a double bond: \((\mathrm{CH}_3)_2\mathrm{C}=\mathrm{CH}_2\). This compound is called 2-methylpropene, where the branching occurs at the second carbon.

Comparing the structures

But-1-ene, but-2-ene, and 2-methylpropene all have the molecular formula \(\mathrm{C}_4 \mathrm{H}_8\) but differ in the position of the double bond and branching of the carbon chain. But-2-ene has geometric isomers (cis/trans) due to the double bond location, while 2-methylpropene has a different carbon chain branching.

Key concepts

Molecular Formula

When looking at the molecular formula \(\mathrm{C}_4 \mathrm{H}_8\), we are dealing with alkenes. Alkenes are hydrocarbons that contain at least one carbon to carbon double bond. The molecular formula is a concise way to express the number and type of atoms present in a molecule.
For alkenes, the general formula is \(\mathrm{C}_n\mathrm{H}_{2n}\). In our case, with \(\mathrm{C}_4 \mathrm{H}_8\), it means our compound contains four carbon atoms and eight hydrogen atoms.
This simple ratio also suggests that the compound is unsaturated, allowing for a carbon-carbon double bond to exist.

Chemical Structure

The chemical structure of alkenes is crucial to understand, as it determines the compound's physical and chemical properties. For \(\mathrm{C}_4 \mathrm{H}_8\), there are three main isomers to consider, based on the position of the double bond and the arrangement of the carbon atoms.

• But-1-ene: Here, the double bond is positioned between the first and second carbon atoms: \(\mathrm{CH}_2=\mathrm{CHCH}_2\mathrm{CH}_3\). This linear arrangement makes it a straightforward alkene structure.
• But-2-ene: In this case, the double bond is found between the second and third carbon atoms: \(\mathrm{CH}_3\mathrm{CH}=\mathrm{CHCH}_3\). This structure is internal with respect to the carbon chain.
• 2-Methylpropene: This structure features a branched arrangement, with a methyl group attached to the second carbon. The structure looks like this: \(\left(\mathrm{CH}_3\right)_2\mathrm{C}=\mathrm{CH}_2\).

Geometric Isomerism

Geometric isomerism is a form of stereoisomerism resulting from the different spatial arrangements of atoms. The C=C double bond in alkenes restricts rotation, leading to different geometric forms.
In the alkene \(\mathrm{C}_4\mathrm{H}_8\), the compound but-2-ene exhibits geometric isomerism. This results from the arrangement of substituents around the double bond:

• Cis-But-2-ene: Both the larger groups (methyl groups, in this case) are on the same side of the double bond, leading to a more restricted shape.
• Trans-But-2-ene: Here, the methyl groups are on opposite sides of the double bond, which tends to be more linear and thus can result in different properties, like boiling point changes.

This type of isomerism can significantly impact the chemical behavior and physical characteristics of the alkene.

Carbon Chain Branching

Carbon chain branching is a fundamental concept in organic chemistry, affecting both the physical and chemical properties of the molecule. It occurs when carbon atoms attempt to connect to more than two other carbons.
In the case of \(\mathrm{C}_4 \mathrm{H}_8\), the compound 2-methylpropene showcases branching. The structure consists of a primarily three-carbon chain with a methyl group branching from the second carbon atom.
Branching affects the boiling and melting points of compounds and their reactivity. For example, branching can lead to a lower boiling point due to the decrease in surface area, reducing the van der Waals forces between molecules. This is critical in understanding the behavior of isomers in various chemical reactions.