Problem 46 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Give the empirical formula and structural formula for a cyclic ether containing four carbon atoms in the ring. (b) Write the structural formula for a straight-chain compound that is a structural isomer of your answer to part (a).

Step-by-Step Solution

Answer

(a) The cyclic ether has the empirical formula \(C_4H_8O\). The structural formula is: ``` H H H H | | | | C-C-O-C-C | | | | H H H H ``` (b) A straight-chain isomer of the cyclic ether has the following structural formula: ``` H H H | | | H C-C-C-O-C | | | H H H H ```

Step 1: (a) Find the empirical formula and structural formula for the cyclic ether

The cyclic ether will have four carbon atoms in the ring and an oxygen atom to complete the ring (as ethers have an oxygen atom between two carbon atoms). The empirical formula for this cyclic ether can be found by counting the number of elements in the molecule and then simplifying the ratio. We have: - Four carbon atoms (C) - One oxygen atom (O) - Eight hydrogen atoms (H) attached to the four carbon atoms in the ring (since each carbon atom in a cyclic ether has two hydrogen atoms) This gives the empirical formula of \(C_4H_8O\). For the structural formula of the cyclic ether, 1. Start with 4 carbon atoms arranged in a ring. 2. Connect an oxygen atom to complete the ring. 3. Attach two hydrogen atoms to each carbon atom. The structural formula can be drawn as: ``` H H H H | | | | C-C-O-C-C | | | | H H H H ```

Step 2: (b) Find the structural formula for a straight-chain isomer of the cyclic ether

An isomer of the cyclic ether will have the same empirical formula, but a different structural arrangement of its atoms. To create a straight-chain isomer, we can break the four-carbon cyclic ether and convert it into a straight chain with an oxygen atom in between two carbon groups. Here's how to create the structural formula for a straight-chain isomer: 1. Start with 3 carbon atoms in a straight chain, the first and second carbon atoms connected to each other. 2. Connect an oxygen atom to the second carbon atom. 3. Connect a fourth carbon atom to the oxygen atom. 4. Attach the hydrogen atoms to the carbon atoms according to the valency (two hydrogen atoms for the first and last carbon and one hydrogen atom for the middle carbon). The structural formula can be drawn as: ``` H H H | | | H C-C-C-O-C | | | H H H H ``` So, this is the structural formula of a straight-chain compound that is a structural isomer of the cyclic ether.

Key Concepts

Structural Isomers

Structural isomers are fascinating because they have the same molecular formula but differ in the arrangement of their atoms. This difference in structure can lead to significantly different physical and chemical properties. In the context of organic chemistry, structural isomers can vary in terms of the connectivity of atoms, forming distinct compounds. For instance:

• The exercise involves a cyclic ether and its corresponding straight-chain isomer. Both have the empirical formula \(C_4H_8O\) but differ structurally.
• The cyclic ether is formed by arranging the four carbon atoms in a ring with one oxygen atom completing the cycle.
• Contrast this with the straight-chain isomer, which has the same number of carbon, hydrogen, and oxygen atoms but arranged in a linear form.

This concept illustrates the diversity of organic compounds and is crucial for understanding the complexity and variety found in organic chemistry.

Empirical Formula

The empirical formula is a simple but powerful tool in chemistry. It represents the simplest whole-number ratio of elements in a compound. It doesn't directly show the structure but simplifies the representation, making it easier to communicate the composition of a compound.

• For the cyclic ether in our exercise, the empirical formula is \(C_4H_8O\).
• This reveals that for every oxygen atom, there are four carbon and eight hydrogen atoms present.
• The empirical formula helps convey basic information without detailing the complex structure, which is useful in many areas of chemistry.

In both the cyclic ether and its straight-chain isomer, the empirical formula remains unchanged, illustrating how different compounds can share a basic composition but differ structurally and in properties.

Organic Chemistry

Organic chemistry, the study of carbon-based compounds, delves into the vast world of molecules that compose living organisms and synthetic materials. Ethers, a class of organic compounds, are particularly interesting due to their ability to form structural isomers.

• In organic chemistry, an ether comprises an oxygen atom connected to two alkyl or aryl groups.
• The cyclic ether mentioned in the exercise can be visualized as a ring structure, highlighting the versatility of organic compounds in forming diverse molecular configurations.
• The study of these compounds is essential as it aids in understanding materials like pharmaceuticals, plastics, and textiles.

Moreover, learning about structural isomers in organic chemistry enhances comprehension of how molecules can exhibit different characteristics despite having an identical molecular formula, thus broadening the appreciation of organic diversity.