Propose structures for carboxylic acids that show the following peaks in their ¹³C NMR spectra. Assume that the kinds of carbons (1°, 2°, 3°, or 4°) have been assigned by DEPT-NMR.

$$\begin{gathered} \mathbf{a}\mathbf{)}\mathbf{}{\mathbf{C}}_{\mathbf{7}}{\mathbf{H}}_{\mathbf{12}}{\mathbf{O}}_{\mathbf{2}}\mathbf{,}\mathbf{}\mathbf{25}\mathbf{.}\mathbf{5}\mathbf{\delta }\left(20\right)\mathbf{,}\mathbf{25}\mathbf{.}\mathbf{9}\mathbf{\delta }\left(20\right)\mathbf{,}\mathbf{29}\mathbf{\delta }\left(20\right)\mathbf{,}\mathbf{43}\mathbf{.}\mathbf{1}\mathbf{\delta }\left(30\right)\mathbf{,}\mathbf{183}\mathbf{\delta }\left(40\right) \\ \mathbf{b}\mathbf{)}\mathbf{}{\mathbf{C}}_{\mathbf{8}}{\mathbf{H}}_{\mathbf{8}}{\mathbf{O}}_{\mathbf{2}}\mathbf{,}\mathbf{}\mathbf{21}\mathbf{.}\mathbf{4}\mathbf{\delta }\left(1^o\right)\mathbf{,}\mathbf{128}\mathbf{.}\mathbf{3}\mathbf{\delta }\left(4^o\right)\mathbf{,}\mathbf{129}\mathbf{\delta }\left(3^o\right)\mathbf{,}\mathbf{129}\mathbf{.}\mathbf{7}\mathbf{\delta }\left(3^o\right)\mathbf{,}\mathbf{143}\mathbf{.}\mathbf{1}\mathbf{\delta }\left(4^o\right)\mathbf{,}\mathbf{168}\mathbf{.}\mathbf{2}\mathbf{\delta }\left(4^o\right) \end{gathered}$$

The molecular formula is C₇H₁₂O₂. On ignoring oxygen from the parent compound will become C₇H₁₆. The molecular has 4 hydrogen which is less than the parent and thus two unsaturation units. The one is the ring and the other must be the carboxyl carbonyl group. The compound has 7 carbon atoms and has five signals. The compound has the structure of symmetry. The carboxyl carbon at 183 δ and signals at 25.55 δ, 25.9 δ and 29 δ. The tertiary carbon at which attached to the carboxyl group at 43.1 δ. Thus, the compound is cyclohexane carboxylic acid.

The structure for the compound can be drawn as,

The molecular formula for the compound is C₈H₈O₂. On ignoring the oxygen from the parent compound will become C₈H₁₈. The molecule has 10 hydrogens less than the parent and has 5 unsaturation units. The one compound is carboxyl carbonyl and the other is phenyl rings. The compound has 8 carbon atoms and six signals. There are 3 quaternary carbons and the aromatic ring at 128.3 δ, and 143.1 δ which indicates the p-substituted benzene presence in the ring. The signal at 129 δ and 129.7 δ to the carbons and attachment in the carboxyl group. The compound is p-methyl benzoic acid.

The structure can be drawn as,