Question

Propose structures for carboxylic acids that show the following peaks in their \({ }^{13}\) C NMR spectra. Assume that the kinds of carbons \(\left(1^{\circ}, 2^{\circ}, 3^{\circ},\right.\) or \(4^{\circ}\) ) have been assigned by DEPT-NMR. (a) \(\mathrm{C}_{7} \mathrm{H}_{12} \mathrm{O}_{2}: 25.5 \delta\left(2^{\circ}\right), 25.9 \delta\left(2^{\circ}\right), 29.0 \delta\left(2^{\circ}\right), 43.1 \delta\left(3^{\circ}\right), 183.0 \delta\left(4^{\circ}\right)\) (b) \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{2}: 21.4 \delta\left(1^{\circ}\right), 128.3 \delta\left(4^{\circ}\right), 129.0 \delta\left(3^{\circ}\right), 129.7 \delta\left(3^{\circ}\right), 143.1 \delta\) \(\left(4^{\circ}\right), 168.2 \delta\left(4^{\circ}\right)\)

Short answer

Compound (a): 3,3-dimethylbutanoic acid. Compound (b): Phenylacetic acid.

Step-by-step solution

Analyzing the Molecular Formula and NMR Peaks for Compound (a)

The molecular formula of compound (a) is \( \text{C}_7 \text{H}_{12} \text{O}_2 \), indicating one carboxylic acid group (\( \text{-COOH}\)) because of the \( \text{O}_2 \). The \( ^{13}\text{C} \) NMR chemical shifts are: 25.5, 25.9, 29.0, 43.1, and 183.0 \( \delta \). The 183.0 \( \delta \) peak is likely the carboxyl carbon (\( 4^{\circ} \) carbon), usually found between 170-185 \( \delta \) in acids.

Assigning Carbon Types Based on DEPT-NMR for Compound (a)

The chemical shifts provided correspond to the types of carbons identified by DEPT-NMR: two \( 2^{\circ} \) carbons at 25.5 \( \delta \) and 25.9 \( \delta \), one \( 2^{\circ} \) carbon at 29.0 \( \delta \), one \( 3^{\circ} \) carbon at 43.1 \( \delta \), and one \( 4^{\circ} \) carboxyl carbon at 183.0 \( \delta \). These suggest a structure featuring a tertiary carbon adjacent to the carboxyl group.

Proposing a Structure for Compound (a)

The presence of a \( 3^{\circ} \) carbon suggests a branching point, likely at the position next to the carboxyl carbon. Given the molecular formula \( \text{C}_7 \text{H}_{12} \text{O}_2 \), a proposed structure is 3,3-dimethylbutanoic acid, with the tertiary carbon connected to two methyl groups, resulting in the peaks and specific carbon environments observed.

Analyzing the Molecular Formula and NMR Peaks for Compound (b)

The molecular formula of compound (b) is \( \text{C}_8 \text{H}_8 \text{O}_2 \). The \( ^{13}\text{C} \) NMR peaks are 21.4, 128.3, 129.0, 129.7, 143.1, and 168.2 \( \delta \). The 168.2 \( \delta \) peak is typical for a carboxyl carbon (\( 4^{\circ} \)), indicating the presence of a carboxylic acid group.

Assigning Carbon Types Based on DEPT-NMR for Compound (b)

Given the DEPT assignments: one \( 1^{\circ} \) carbon at 21.4 \( \delta \), two \( 3^{\circ} \) carbons at 129.0 \( \delta \) and 129.7 \( \delta \), and two \( 4^{\circ} \) carbons at 128.3 \( \delta \) and 143.1 \( \delta \), the compound likely includes an aromatic ring.

Proposing a Structure for Compound (b)

The NMR data suggests the possibility of a benzene ring with a side chain. A plausible structure is phenylacetic acid, where the aromatic carbons match the chemical shifts observed, and the alkyl side chain accounts for the \( 1^{\circ} \) carbon observed at 21.4 \( \delta \).

Key concepts

DEPT-NMR Analysis

Understanding DEPT-NMR (Distortionless Enhancement by Polarization Transfer) is essential in analyzing the carbon environments in molecules. This technique helps differentiate types of carbons:

• CH (primary carbons)
• CH₂ (secondary carbons)
• CH₃ (tertiary carbons)
• Carbons without hydrogen bonds (quaternary carbons)

For instance, in the analysis of compound (a), DEPT-NMR identified peaks at 25.5, 25.9, and 29.0 δ as secondary carbons. The 43.1 δ was identified as a tertiary carbon, and the 183.0 δ as a quaternary carbon, typical of a carboxyl carbon. This method provides clarity on the molecular backbone, making it easier to propose possible structures by distinguishing carbon types.

Chemical Shift Interpretation

Chemical shift interpretation in NMR is a cornerstone for elucidating molecular structures. Chemical shifts are influenced by electron environments around nuclei. In carboxylic acids, chemical shifts offer clues about the carbon types and functional groups.
The large shift around 183.0 δ in compound (a) indicates a carboxyl carbon, typically found in the 170-185 δ range. Compound (b) exhibits shifts such as 21.4 δ for a primary carbon, which aligns with alkyl groups. Understanding these shifts allows chemists to deduce the presence of specific functional groups and devise likely structures.

Molecular Structure Determination

Determining molecular structures involves piecing together carbon types and chemical shifts. In compound (a), recognizing the tertiary carbon at 43.1 δ alongside the carboxyl carbon at 183.0 δ led to the proposal of 3,3-dimethylbutanoic acid. Similarly, the combination of aromatic shifts and a primary carbon in compound (b) suggested phenylacetic acid as a probable structure.
Such deductions rely on integrating DEPT-NMR data with known chemical shift ranges, offering a systematic way to understand complex molecules. This process underscores the revelation of carbon frameworks and functional groups within a molecule.

Organic Chemistry Education

Organic chemistry education prepares students to navigate and utilize techniques like NMR spectroscopy for molecular analysis. It's crucial to grasp core concepts such as interpreting DEPT-NMR data and chemical shifts. These skills form a foundation for unraveling complex organic structures.
Using real-world examples, like determining carboxylic acid structures from NMR data, enhances learning. It bridges theoretical knowledge with practical application, empowering students to decode intricate molecular puzzles. Mastering these techniques in educational settings not only aids academic success but is pivotal for scientific research and development.