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 \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O},(\mathbf{c})\) a dihydroxy compound with the formula \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{2},(\mathbf{d})\) 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 as follows: (a) Butanoic acid: \(CH_3CH_2CH_2COOH\) (b) Cyclopentanone: \(C_5H_8O\) or \(\text{cyclo}(CH_2)_4CO\) (c) Dihydroxy compound: \(HOCH_2CH_2CH_2OH\) (d) γ-butyrolactone: \(\text{cyclo}(CH_2)_3CO_2\)

Step-by-step solution

(a) Acid with the formula C4H8O2

Given that the compound is an acid with the formula C4H8O2, it must have a carboxylic acid functional group. The condensed structural formula for a carboxylic acid is RCOOH, where R is an alkyl group. Since we have 4 carbons, the longest possible carbon chain would be butanoic acid. The condensed structural formula for butanoic acid is: \(CH_3CH_2CH_2COOH\).

(b) Cyclic ketone with the formula C5H8O

In a cyclic ketone, a carbonyl group (C=O) is bound to two other carbons in a ring structure. The molecular formula indicates that there are 5 carbons and 1 oxygen in the compound. Since it is a ketone, it has a general formula of RCOR', where R and R' are alkyl groups. The only possible 5-carbon cyclic ketone is cyclopentanone, which has a condensed structural formula: \(C_5H_8O\) or \(\text{cyclo}(CH_2)_4CO\).

(c) Dihydroxy compound with the formula C3H8O2

A dihydroxy compound contains two hydroxyl groups (-OH) bound to different carbon atoms. Given the molecular formula C3H8O2, there are only three carbons, so the hydroxyl groups must be bound to terminal carbons. The condensed structural formula for this compound would be: \(HOCH_2CH_2CH_2OH\).

(d) Cyclic ester with the formula C5H8O2

A cyclic ester, also known as a lactone, contains an ester functional group (RCOO) within a ring structure. Given the molecular formula C5H8O2, there are 5 carbons and 1 oxygen in the compound. The oxygen in the formula must be part of the ester functional group. The only possible cyclic ester with 5 carbons is γ-butyrolactone, which has a condensed structural formula: \(\text{cyclo}(CH_2)_3CO_2\).

Key concepts

Structural Formulas

In organic chemistry, structural formulas are a way to represent molecules, showing the arrangement of atoms within the compound. Unlike molecular formulas that only indicate the number and type of atoms, structural formulas give a visual depiction of the molecular structure. This is crucial because the structure of a molecule influences its chemical properties and reactivity.

Using condensed structural formulas simplifies writing out each molecule while still indicating the bonding arrangement.
For example:

• A linear chain is shown without detailed bonds—like the progression from one carbon to the next.
• Functional groups, such as hydroxyl (OH) or carboxyl (COOH), are shown in a compact form.

This approach is especially useful when dealing with complex organic molecules.

Carboxylic Acids

Carboxylic acids are organic compounds characterized by the presence of a carboxyl group (\[\text{COOH}\]). This functional group is highly polar and often found in naturally occurring and synthetic substances. Carboxylic acids have distinct properties due to their ability to release a hydrogen ion (\[\text{H}^+\]), making them acidic.

In condensed structural formulas:

• The carboxyl group is usually represented at the end, such as in butanoic acid: \(CH_3CH_2CH_2COOH\).
• The formula reflects the sequence of carbon atoms leading up to the acid group.

This feature explains why carboxylic acids are such important compounds in biochemistry and the food industry.

Cyclic Ketones

Cyclic ketones are a fascinating class of organic compounds featuring a carbonyl group (\[\text{C=O}\]) located within a carbon ring. This structure means the carbonyl group is not at the end but bonded to two other carbon atoms inside a ring.

A common example is cyclopentanone:

• It has a closed ring of five carbon atoms with one double-bonded oxygen.
• This structural feature gives cyclic ketones unique stability and reactivity.

Cyclic ketones are found in various natural compounds and are useful in the synthesis of biological molecules and pharmaceuticals.

Dihydroxy Compounds

Dihydroxy compounds are a type of alcohol with two hydroxyl (\(OH\)) groups. These groups can be attached to the same or different carbon atoms, altering the compound's properties significantly.

With a molecular formula like \(C_3H_8O_2\), dihydroxy compounds, such as 1,3-propanediol:

• Have two terminal hydroxyl groups, providing high solubility and often used as solvents.
• The structure enables participation in various chemical reactions, making them valuable in polymer production.

Understanding their structure is key to unlocking their potential uses in many industrial applications.

Cyclic Esters

Cyclic esters, also known as lactones, have distinctive ring structures with an ester bond (\[\text{RCOO}\]) integrated within the ring. The versatility of lactones is tied to their cyclic nature and the effects of the ester functional group.

For example, γ-butyrolactone:

• Consists of a four-carbon ring with an internal ester linkage.
• The combination of the ring and ester group gives lactones special reactivity.

Lactones are often used in flavorings and fragrances, showcasing the intersection between chemistry and everyday products.