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

Expert verified
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

01

(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: \(CH_3CH_2CH_2COOH\).
02

(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 \(\text{cyclo}(CH_2)_4CO\).
03

(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: \(HOCH_2CH_2CH_2OH\).
04

(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: \(\text{cyclo}(CH_2)_3CO_2\).

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