Question

Write a condensed structural formula for each of the following: (a) an acid with the formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2},\) (b) a cyclic ketone with the formula \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O},\) (c) a dihydroxy compound with the formula \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{2},\) (d) a cyclic ester with the formula \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{2}\).

Short answer

The condensed structural formulas for the given compounds are: (a) Acid: \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\) (b) Cyclic ketone: cyclopentanone, \(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{CO}\) (c) Dihydroxy compound: 1,3-propanediol, \(\mathrm{CH}_{2} \mathrm{OHCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (d) Cyclic ester: γ-butyrolactone, \(\mathrm{C}_{4}\mathrm{H}_{7}\mathrm{COO}\)

Step-by-step solution

(a) Acid Condensed Structural Formula:

For the acid with the formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\), we can recognize it as a carboxylic acid due to the presence of an \(\mathrm{O}_{2}\) group. A carboxylic acid has the general formula \(\mathrm{R-COOH}\). Thus, for the given molecular formula, the condensed structural formula for the acid is: \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\).

(b) Cyclic Ketone Condensed Structural Formula:

For the cyclic ketone with the formula \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}\), we need to form a ring structure with a carbonyl group (C=O) inside the ring. In this case, the carbonyl group will be attached to one of the carbon atoms in the ring. The condensed structural formula for the cyclic ketone is: \(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{CO}\) or more specifically, cyclopentanone.

(c) Dihydroxy Compound Condensed Structural Formula:

For the dihydroxy compound with the formula \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{2}\), there are two hydroxy groups (-OH) present, attached to the carbon atoms. A possible condensed structural formula for the dihydroxy compound is: \(\mathrm{CH}_{2} \mathrm{OHCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\), which represents 1,3-propanediol.

(d) Cyclic Ester Condensed Structural Formula:

For the cyclic ester with the formula \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{2}\), we have to form a ring structure with an ester group (\(\mathrm{COO}\)) linking two carbon atoms of the ring. A possible condensed structural formula for the cyclic ester is: \(\mathrm{C}_{4}\mathrm{H}_{7}\mathrm{COO}\) or more specifically, γ-butyrolactone.

Key concepts

Carboxylic Acids

Carboxylic acids are an important class of organic compounds that contain a carboxyl group (\(-\text{COOH}\)). This group is composed of a carbon atom double-bonded to an oxygen atom, and single-bonded to a hydroxyl group (OH). Carboxylic acids often play vital roles in biochemistry and industrial contexts due to their acidic properties.
These acids can release hydrogen ions \(\text{H}^+\) into solutions, which is why they are considered acidic. One common carboxylic acid is acetic acid, found in vinegar.
In the context of the condensed structural formula, such as \(\text{CH}_3\text{CH}_2\text{CH}_2\text{COOH}\), the formula shows how the atoms are arranged and connected. Here, the part before \(-\text{COOH}\), which is a chain of carbons and hydrogens, is termed as the alkyl group 'R'. This basic understanding helps in identifying other members in the carboxylic acid family.

Cyclic Compounds

Cyclic compounds consist of elements, typically carbon atoms, arranged in a closed ring formation. These compounds are fundamental to organic chemistry, ranging from simple structures like cyclopropane to complex aromatic compounds like benzene.
A key feature of cyclic compounds is their stability, influenced by the number of carbon atoms forming the ring. Compounds like cyclopentanone are cyclic due to their closed-loop structure.
Cyclopentanone (\(\text{C}_4\text{H}_7\text{CO}\)) is an example of a cyclic ketone, distinguished by the presence of a carbonyl group inside the ring. Analyzing cyclic compounds includes understanding their ring size and identifying any functional groups they possess, which affects their chemical properties.

Functional Groups

Functional groups are specific groups of atoms within molecules that are responsible for the characteristic chemical reactions of those molecules. In organic chemistry, these groups determine the properties and reactivity of the complex molecules they compose.
Common examples include:

• Hydroxyl group \(-\text{OH}\)
• Carboxyl group \(-\text{COOH}\)
• Keto group \(-\text{C=O}\)
• Ester group \(-\text{COO}\)

In dihydroxy compounds like 1,3-propanediol (\(\text{CH}_2\text{OHCH}_2\text{CH}_2\text{OH}\)), the presence of two hydroxyl groups makes it an alcohol, which can alter its boiling point and solubility in water.
Identifying functional groups within a molecule is crucial for predicting how the molecule will react in different chemical environments, making them an essential concept in organic chemistry.

Organic Chemistry

Organic chemistry is the branch of chemistry concerned with the structure, properties, composition, reactions, and preparation of carbon-containing compounds. This includes not only hydrocarbons but also compounds with any number of other elements, including hydrogen, nitrogen, oxygen, the halogens, phosphorus, silicon, and sulfur.
The study of organic chemistry is significant because it lays the foundation for understanding complex biological processes and the development of new materials. It includes studying the behavior of different functional groups and chemical reactions centered around carbon-containing molecules.
For instance, in cyclic esters or lactones like \(\gamma\text{-butyrolactone}\), understanding the ester linkage provides insights into how these molecules participate in chemical reactions. Organic chemistry also emphasizes the importance of structures, like those described in condensed structural formulas, to predict molecular behavior and properties in both the laboratory and real-world applications.