Name all the aldehydes and ketones that have the formula$\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}$ .

Since the molecular formula for these aldehydes and ketones is \(\mathrm{C}_5\mathrm{H}_{10}\mathrm{O}\), first we need to find the possible carbon chains that can be formed with 5 carbon atoms. There are only two possible elemental structures for a hydrocarbon chain with five carbon atoms: linear (non-branched) and branched. The linear chain has five carbon atoms connected in a line, and the branched chain has a four carbon linear chain with an additional carbon atom attached to one of the middle carbons, forming an isopropyl group. Linear chain: -C-C-C-C-C- Branched chain: -C-C(-C)-C-C-

The functional group of an aldehyde is -C(=O)H. Since aldehydes have the carbonyl group located at the end of a carbon chain, let's put the functional group at the end of the two possible hydrocarbon chains: 1. Linear chain aldehyde: \(H_3\)C-CH_2-CH_2-CH_2-CHO 2. Branched chain aldehyde: \(H_3\)C-CH-CH_2-CH(-CH_3)-CHO Note that the branched chain cannot have the aldehyde group on the carbon branched with middle carbon, as it would form an unstable molecule with pentavalent carbon.

The functional group of a ketone is -C(=O)-. Ketones have the carbonyl group within the chain, not at the ends like aldehydes. We will now place the carbonyl group in different positions within the hydrocarbon chains: 1. Linear chain ketone: (a) \(H_3\)C-CH_2-C(=O)-CH_2-CH_3 (b) \(H_3\)C-C(=O)-CH_2-CH_2-CH_3 (this structure is identical to option a, so it is not counted as a separate unique structure). 2. Branched chain ketone: (a) \(H_3\)C-CH-C(=O)-CH_2-CH_3 (2-pentanone) (b) \(H_3\)C-CH_2-C(=O)-CH(-CH_3)-CH_3 (3-methyl-2-butanone) There are no unique ketone structures produced by adding the carbonyl group to the branch in the branched chain, since placing a carbonyl group at that location would result in a molecule that is not a ketone. In total, we have identified 4 unique aldehyde and ketone structures with the molecular formula \(\mathrm{C}_5\mathrm{H}_{10}\mathrm{O}\): 1. \(H_3\)C-CH_2-CH_2-CH_2-CHO (pentanal, a linear aldehyde) 2. \(H_3\)C-CH-CH_2-CH(-CH_3)-CHO (4-methylbutanal, a branched aldehyde) 3. \(H_3\)C-CH_2-C(=O)-CH_2-CH_3 (2-pentanone, a linear ketone) 4. \(H_3\)C-CH_2-C(=O)-CH(-CH_3)-CH_3 (3-methyl-2-butanone, a branched ketone)