Draw condensed structural formulas for all compounds with the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}\) that contain (a) A carbonyl group (there are two aldehydes and one ketone). (b) A carbon-carbon double bond and a hydroxyl group (there are eight).

A carbonyl group is a functional group that contains a carbon double-bonded to oxygen: \(\mathrm{C}=\mathrm{O}\). Aldehydes and ketones are carbonyl-containing compounds. In aldehydes, the carbonyl group is bonded to a hydrogen atom or a carbon atom. Ketones have the carbonyl group bonded to two carbon atoms.

To find the aldehydes and ketone, let's arrange the four carbon atoms in various configurations and place the carbonyl groups accordingly, while keeping track of the number of hydrogen atoms. Aldehyde 1: \(\mathrm{CH}_3\mathrm{CH}_2\mathrm{CH}_2\mathrm{CHO}\) (Butanal) Aldehyde 2: \(\mathrm{CH}_3\mathrm{CH}\mathrm{(CH_3)}\mathrm{CHO}\) (2-methylpropanal) Ketone 1: \(\mathrm{CH}_3\mathrm{CH}_2\mathrm{CO}\mathrm{CH}_3\) (Butanone)

In this task, we need to find compounds containing both a carbon-carbon double bond and a hydroxyl group. Compounds containing a carbon-carbon double bond are alkenes, and those with a hydroxyl group are alcohols. Thus, we are looking for compounds containing both the functional groups - an alkene and an alcohol.

We will now arrange the carbons and find the combinations of double bonds and hydroxyl groups. Due to the requirement of 8 hydrogens, the double bond should be always adjacent to the hydroxyl group. 1. \(\mathrm{CH_2}\mathrm{OHCH}\mathrm{CH_2}\mathrm{CH_3}\) (3-Buten-1-ol) 2. \(\mathrm{CH_2}\mathrm{OH}\mathrm{C}({\mathrm H_3})\mathrm{CH}\mathrm{CH_3}\) (2-Methyl-3-buten-1-ol) 3. \(\mathrm{CH_3}\mathrm{CH}\mathrm{OH}\mathrm{CH}\mathrm{CH_2}\) (2-Buten-1-ol) 4. \(\mathrm{CH_3}\mathrm{CHOH}\mathrm{C}\mathrm{H}\mathrm{CH_2}\mathrm{CH_3}\) (2-Buten-2-ol) 5. \(\mathrm{CH_3}\mathrm{CH}\mathrm{OH}\mathrm{C}\mathrm{H}\mathrm{CH_3}\) (2-Methyl-1-propen-1-ol) 6. \(\mathrm{CH_3}\mathrm{CHOH}\mathrm{C}\mathrm{H}\mathrm{C}\mathrm{H_3}\) (2-Methyl-1-propen-2-ol) 7. \(\mathrm{CH_3}\mathrm{CHOH}\mathrm{CH}\mathrm{CH}\mathrm{CH_3}\) (3-Buten-2-ol) 8. \(\mathrm{CH_3}\mathrm{CH}\mathrm{CH}\mathrm{CHOH}\mathrm{CH_3}\) (1-Buten-3-ol) These are the condensed structural formulas for the compounds with the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}\) containing a carbonyl group, a carbon-carbon double bond, and a hydroxyl group.