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).

Short answer

(a) The empirical formula for a cyclic ether containing four carbon atoms in the ring is \(C_4H_8O\). The structural formula is: ``` O / \ C C | | H2 H2 \ / C | H2 | C | H2 ``` (b) A straight-chain compound that is a structural isomer of the cyclic ether is 1-butanol or butan-1-ol, with the structural formula: ``` H H H | | | C-C-C-C | | | O H H H H ```

Step-by-step solution

1. Empirical Formula and Structural Formula for a Cyclic Ether with Four Carbon Atoms in the Ring

Cyclic ethers are organic molecules that contain an oxygen atom in a ring consisting of carbon atoms. Since we have four carbon atoms in the ring, the simplest cyclic ether would have a single oxygen atom in the ring with four carbon atoms. To determine the empirical formula, we need to find the ratio of carbon, hydrogen, and oxygen atoms. There are 4 carbon atoms, each bonded to 2 hydrogen atoms, so there are 8 hydrogen atoms. There is 1 oxygen atom in the ring. So, the empirical formula is: \(C_4H_8O\) Now, let's draw the structural formula for this cyclic ether: ``` O / \ C C | | H2 H2 \ / C | H2 | C | H2 ```

2. Structural Formula for a Straight-Chain Compound that is a Structural Isomer of the Cyclic Ether

A structural isomer has the same molecular formula but different arrangement of atoms. With an empirical formula of \(C_4H_8O\), let's find a straight-chain compound that can be drawn as a structural isomer: ``` H H H | | | C-C-C-C | | | O H H H H ``` This straight-chain compound is called 1-butanol or butan-1-ol. It is isomer of the cyclic ether from part (a) as both have the same molecular formula \(C_4H_8O\), but feature different structural arrangements of atoms.

Key concepts

Structural Isomers

Structural isomers are different compounds that share the same molecular formula but have different structural arrangements of atoms. In simpler terms, you can think of them as siblings with the same "genetic makeup" (molecular formula) but different appearances. For example, both 1-butanol and the cyclic ether described in the exercise share the formula \(C_4H_8O\), yet their structures diverge significantly. The cyclic ether forms a ring structure where an oxygen atom is integrated into the chain of carbon atoms. Conversely, 1-butanol's structure runs in a straight chain with four carbon atoms connected consecutively, and the single oxygen atom appears as a hydroxyl group (-OH) on one end. Understanding structural isomers is important in organic chemistry because their different structures often result in unique physical and chemical properties. While they might have the same number and types of atoms, isomers do not behave the same way in chemical reactions or have the same boiling or melting points. By exploring structural isomers, we gain valuable insights into the versatility and complexity of organic compounds.

Empirical Formula

An empirical formula is the simplest whole-number ratio of atoms of each element in a compound. It gives us a basic understanding of what the compound comprises without providing detailed insights into the structural layout. In the context of the exercise, the empirical formula \(C_4H_8O\) for the cyclic ether illustrates that for every four carbon atoms, there are eight hydrogen atoms and one oxygen atom. Writing an empirical formula involves:

• Counting the total number of each type of atom in the compound.
• Expressing these counts as the smallest possible ratio.

In our case, every carbon in the cyclic ether is bonded in a way that maintains this 4:8:1 ratio, reflective of the compound's simplest form. While the empirical formula doesn't reveal the compound's exact structure, it provides a handy, concise way to convey the basic makeup of any organic molecule. In organic chemistry, empirical formulas are a crucial starting point for determining molecular formulas and understanding the compound's stoichiometry.

Organic Molecules

Organic molecules are the cornerstone of organic chemistry, defined as compounds primarily composed of carbon atoms bonded with hydrogen, oxygen, and a few other elements such as nitrogen or sulfur. These molecules comprise a vast and diverse category of substances, including all forms of life and many synthetic products. The common denominator among organic molecules is their carbon framework; carbon's ability to form four covalent bonds leads to complex structures like chains, rings, and branches. Among these, cyclic ethers are a specific type of organic compound featuring an oxygen atom bonded within a carbon ring structure. When studying organic molecules:

• Understand the role of carbon and its four bonds in forming diverse molecular structures.
• Recognize how different functional groups, like ethers, alcohols, or acids influence properties and reactivity.
• Acknowledge how these molecules can rearrange to create structural isomers with varying properties even though they contain the same constituents.

This structural variability is what makes organic chemistry immensely rich and detailed, allowing the synthesis of countless unique compounds and the exploration of their applications in fields from medicine to materials science.