Question

Draw structures of the nine isomers of \(\mathrm{C}_{7} \mathrm{H}_{16}\).

Short answer

There are nine isomers of \(\text{C}_7\text{H}_{16}\).

Step-by-step solution

Understanding the Problem

We are asked to draw all possible isomers of the molecular formula \( ext{C}_7 ext{H}_{16}\). Isomers are compounds that have the same molecular formula but different arrangements of atoms, leading to different structures.

Drawing the Linear Isomer

Start by drawing the straight-chain alkane (also known as normal alkane) which is heptane for \( ext{C}_7 ext{H}_{16}\). The structure is: \[ \text{CH}_3 - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]

Identifying and Drawing Branched Isomers

Next, we create branched structures to form the different isomers possible for heptane.

Drawing one 6-carbon chain with one methyl group (2-Methylhexane)

Replace one hydrogen with a methyl group \(\text{CH}_3\) on the second carbon in a 6-carbon chain. This structure is 2-Methylhexane: \[ \text{CH}_3 - \text{CH} (\text{CH}_3) - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]

Drawing 3-Methylhexane

Position the methyl group on the third carbon of a 6-carbon chain to form 3-Methylhexane: \[ \text{CH}_3 - \text{CH}_2 - \text{CH} (\text{CH}_3) - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]

Drawing 4-Methylhexane

Attach the methyl group to the fourth carbon on the 6-carbon chain to get 4-Methylhexane: \[ \text{CH}_3 - \text{CH}_2 - \text{CH}_2 - \text{CH} (\text{CH}_3) - \text{CH}_2 - \text{CH}_3 \]

Creating 5-Carbon Chains with Dimethyl Substituents (2,2-Dimethylpentane)

Place two methyl groups on the second carbon of a 5-carbon chain: \[ \text{CH}_3 - \text{CH}(\text{CH}_3)_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]

Forming 2,3-Dimethylpentane

Place one methyl group on the second carbon and another on the third carbon of a 5-carbon chain to form 2,3-Dimethylpentane: \[ \text{CH}_3 - \text{CH} (\text{CH}_3) - \text{CH} (\text{CH}_3) - \text{CH}_2 - \text{CH}_3 \]

Building 2,4-Dimethylpentane

Attach one methyl group on the second carbon and another on the fourth carbon of a 5-carbon chain to form 2,4-Dimethylpentane: \[ \text{CH}_3 - \text{CH} (\text{CH}_3) - \text{CH}_2 - \text{CH} (\text{CH}_3) - \text{CH}_3 \]

Forming 3,3-Dimethylpentane

Add two methyl groups on the third carbon of a 5-carbon chain to form 3,3-Dimethylpentane: \[ \text{CH}_3 - \text{CH}_2 - \text{C}(\text{CH}_3)_2 - \text{CH}_2 - \text{CH}_3 \]

Constructing 3-Ethylpentane

Place an ethyl group on the third carbon of a 5-carbon chain to form 3-Ethylpentane: \[ \text{CH}_3 - \text{CH}_2 - \text{CH}(\text{CH}_2\text{CH}_3) - \text{CH}_2 - \text{CH}_3 \]

Confirming All Isomers

We have listed 9 structures: Heptane, 2-Methylhexane, 3-Methylhexane, 4-Methylhexane, 2,2-Dimethylpentane, 2,3-Dimethylpentane, 2,4-Dimethylpentane, 3,3-Dimethylpentane, and 3-Ethylpentane. These cover all possible configurations for \(\text{C}_7\text{H}_{16}\).

Key concepts

Alkanes

Alkanes are a family of hydrocarbons that consist solely of carbon and hydrogen atoms, all connected by single bonds. These compounds are known for being saturated hydrocarbons, meaning they have no double or triple bonds, allowing every carbon atom in the molecule to bond fully with hydrogen atoms.
The simplest alkane, methane, consists of one carbon atom bonded to four hydrogen atoms:

• General Formula: The general molecular formula for alkanes is \( ext{C}_n ext{H}_{2n+2}\), where \(n\) represents the number of carbon atoms.
• Characteristics: Alkanes are combustible and often used as fuels, with methane, ethane, and propane being common examples.
• Structure: Alkanes can vary from a simple linear structure, known as a straight-chain, to more complex branched structures.

Recognizing the structural diversity in alkanes is important when studying isomers, as these variations form different compounds with the same molecular formula.

Molecular Formula

The molecular formula of a compound communicates the exact number of atoms of each element present in a molecule. In the case of alkanes, such as heptane, the molecular formula \(\text{C}_7\text{H}_{16}\) provides specific information regarding its composition.
This formula means that the molecule contains:

• Seven carbon atoms \(\text{C}\)
• Sixteen hydrogen atoms \(\text{H}\)

The molecular formula is pivotal in identifying how many different structures, or isomers, can exist for a specific alkane. Although different isomers share the same molecular formula, they can have significantly different chemical and physical properties depending on the arrangement of atoms.

Carbon Chain Structure

Carbon chain structure determines the shape and characteristics of an alkane. Carbon atoms have the unique ability to form strong covalent bonds with other carbon atoms, creating long chains that define the backbone of organic molecules.
In alkanes, these chains can be either:

• Straight Chains: Alkanes with a continuous linear arrangement of carbon atoms, like in heptane, result in a straightforward structure with its own distinct properties.
• Branched Chains: When the carbon atoms form branches, the structure becomes more complex. This branching leads to multiple isomers, as seen with the different configurations of \(\text{C}_7\text{H}_{16}\).

Understanding these variations is essential for distinguishing between different isomers. The physical structure of the molecule affects how it interacts with other molecules, influencing properties such as boiling points and reactivity.