Question

The number of isomeric ethers corresponding to the formula \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\) is

Short answer

There are 5 isomeric ethers with the formula \(C_5H_{12}O\).

Step-by-step solution

Understanding the Problem

We need to find the number of isomeric ethers that can be formed with the molecular formula \(C_5H_{12}O \). An ether has the general formula \(R-O-R'\), where \(R\) and \(R'\) are alkyl groups. The task is to partition the carbon atoms into two groups attached to an oxygen atom.

Identifying Possible Combinations

With 5 carbon atoms, we need to divide them between the two alkyl groups \(R\) and \(R'\). Possible combinations are: \(4+1\) (4 carbons in one group, 1 in the other), \(3+2\), and \(2+3\). The sum of carbons in two groups must always add up to 5.

Generating Isomers for Each Combination

For \(4+1\): This results in one ether with a butyl group \((C_4H_9)\) and a methyl group \((CH_3)\).For \(3+2\): This allows multiple structures since both groups are flexible. Possible ethers are: - Propyl (3C) and ethyl (2C) ether: \(CH_3CH_2CH_2-O-CH_2CH_3\).- Isopropyl (3C) and ethyl (2C) ether: \((CH_3)_2CH-O-CH_2CH_3\).For \(2+3\): This mirrors the \(3+2\) case and yields:- Ethyl (2C) and propyl (3C) ether: \(CH_3CH_2-O-CH_2CH_2CH_3\).- Ethyl (2C) and isopropyl (3C) ether: \(CH_3CH_2-O-(CH_3)_2CH\).

Counting the Distinct Isomers

Now, combine unique ethers considering structural differences. The distinct ethers formed are: 1. Butyl methyl ether. 2. Propyl ethyl ether. 3. Isopropyl ethyl ether. 4. Ethyl propyl ether. 5. Ethyl isopropyl ether. We can count these out to confirm there are five distinct isomers.

Key concepts

Molecular Formula

The molecular formula tells us how many of each type of atom are present in a molecule. For the molecule in question, the molecular formula is \( \mathrm{C}_5 \mathrm{H}_{12} \mathrm{O} \). This means the molecule comprises 5 carbon atoms, 12 hydrogen atoms, and 1 oxygen atom.

Understanding a molecular formula is essential when creating or identifying different chemical compounds. Here, it informs us about the core building blocks we have to work with. When considering isomeric ethers (which share the same molecular formula but have different structures), all variations must adhere to this combination of atoms.

The general structure for ethers is \( R-O-R' \), where \( R \) and \( R' \) are carbon-containing groups. This formula allows us to consider different ways these carbon and hydrogen atoms can combine to form different structures.

Carbon Partitioning

Carbon partitioning refers to the way carbon atoms are divided into distinct groups when forming a compound. In the case of ethers with the molecular formula \( \mathrm{C}_5 \mathrm{H}_{12} \mathrm{O} \), we need to partition the carbon atoms into two alkyl groups.

Because there are 5 carbon atoms, we explore different combinations for splitting them into two groups connected by an oxygen atom. The possible partitions include:

• One group has 4 carbon atoms, and the other has 1 (denoted as 4+1).
• One group has 3 carbon atoms, and the other has 2 (denoted as 3+2).
• Mirroring case 3+2, where a 2-carbon group can join with a 3-carbon group (denoted as 2+3).

Each partitioning pattern suggests a unique way to construct ethers, influencing the possible structural isomers.

Alkyl Groups

Alkyl groups are key components when constructing ethers. They consist of carbon and hydrogen atoms and determine the molecular structure connected by an oxygen atom in the \( R-O-R' \) formula.

For the molecular formula \( \mathrm{C}_5 \mathrm{H}_{12} \mathrm{O} \), alkyl groups like methyl (\( \mathrm{CH}_3 \)), ethyl (\( \mathrm{C}_2\mathrm{H}_5 \)), propyl (\( \mathrm{C}_3\mathrm{H}_7 \)), and butyl (\( \mathrm{C}_4\mathrm{H}_9 \)) are used to generate different ethers.

• A methyl group joined with a butyl group forms butyl methyl ether.
• A propyl group coupled with an ethyl group forms propyl ethyl ether.
• Combining an isopropyl group with an ethyl group creates isopropyl ethyl ether.

These combinations allow chemists to understand how various alkyl groups can influence the structure and functionality of ethers.

Structural Isomers

Structural isomers are compounds that share the same molecular formula but have different structures. This means that while the number of each type of atom is constant, the way they connect varies. For \( \mathrm{C}_5 \mathrm{H}_{12} \mathrm{O} \), structural isomers include all valid ethers using these atoms.

The process involves arranging the 5 carbon atoms differently between the two alkyl groups, resulting in distinct ether molecules. For example:

• Butyl methyl ether is different from propyl ethyl ether not because of their components, but because of their structural arrangement.
• Different structural isomers capture the diverse ways that these atoms can situate themselves around the ether oxygen atom.
• This structural diversity leads to different physical and chemical properties, even though each isomer shares the same molecular formula.

Understanding structural isomers is crucial for learning about the chemical diversity and complexity present within simple molecular formulas like \( \mathrm{C}_5 \mathrm{H}_{12} \mathrm{O} \).