Question

Propose structures for carboxylic acids that show the following peaks in their \({ }^{13} \mathrm{C}\) 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

(a) 2,2-dimethylbutanoic acid; (b) Benzoic acid.

Step-by-step solution

Analyze NMR Data for Compound (a)

The molecular formula is \( \mathrm{C}_7 \mathrm{H}_{12} \mathrm{O}_2 \). There are two \(2^{\circ} \) carbons at 25.5 and 25.9 ppm, another \(2^{\circ} \) at 29.0 ppm, a \(3^{\circ} \) carbon at 43.1 ppm, and a \(4^{\circ} \) carbon at 183.0 ppm. The 183.0 ppm is characteristic of a carboxyl group \((\mathrm{COOH})\), indicating a carboxylic acid.

Propose Structure for Compound (a)

Given the presence of \(2^{\circ}\) and \(3^{\circ}\) carbons and a carboxylic group, one possible structure is 2,2-dimethylbutanoic acid. This structure has a tert-butyl group (for the \(3^{\circ}\) carbon) and a parent chain terminating with the carboxyl group.

Analyze NMR Data for Compound (b)

The molecular formula is \( \mathrm{C}_8 \mathrm{H}_8 \mathrm{O}_2 \). There is a \(1^{\circ} \) carbon at 21.4 ppm, two \(3^{\circ}\) carbons at 129.0 and 129.7 ppm, and a \(4^{\circ}\) carbon at 168.2 ppm. The peaks at 128.3 and 143.1 likely represent aromatic carbons \((4^{\circ} \text{and} 3^{\circ})\). The 168.2 ppm suggests a carboxyl group as well.

Propose Structure for Compound (b)

With the presence of both a carboxyl group and aromatic carbons, benzoic acid could be a viable structure. The aromatic system accounts for most of the carbon peaks, and the carboxyl group aligns with both the DEPT assignment and ppm value for the \(4^{\circ}\) carbon.

Key concepts

Carboxylic Acids

Carboxylic acids are organic acids characterized by the presence of a carboxyl group (\(-\mathrm{COOH}\)). This group consists of a carbonyl and a hydroxyl group, usually written as \( - \mathrm{COOH} \). They are an important class of organic compounds and are widely found in nature. These acids are known for their acidity due to the ability to donate a proton (\(\mathrm{H}^+\)) from the carboxyl group, forming a carboxylate ion \(\mathrm{RCOO}^-\).
Carboxylic acids are typically weak acids, but they exhibit higher acidity compared to alcohols due to resonance stabilization of the carboxylate ion. The presence of the carbonyl groups can be easily identified using NMR spectroscopy, particularly Carbon-13 NMR (\(^{13}\mathrm{C}\) NMR), where the carboxyl group presents a distinct chemical shift.

Carbon-13 NMR

Carbon-13 NMR, or \(^{13}\mathrm{C}\) NMR, is an analytical technique used to determine the environment of carbon atoms within a molecule. Unlike proton NMR \( ( ^1\mathrm{H} \mathrm{NMR} ) \), which focuses on hydrogen, \(^{13}\mathrm{C}\) NMR provides detailed insights about the types and environments of carbon atoms. This is particularly useful for organic compounds such as carboxylic acids.
In \(^{13}\mathrm{C}\) NMR spectra, each distinctive carbon atom in a molecule produces a unique peak. Peaks are observed based on the number of carbons and their chemical environments, making it possible to deduce the structure of the molecule. \(\mathrm{C}=\mathrm{O}\) carbons in carboxylic acids typically appear at very downfield (high ppm) due to their deshielded nature.

DEPT-NMR

Distortionless Enhancement by Polarization Transfer (DEPT-NMR) is an NMR technique that separates carbon signals based on the number of hydrogen atoms attached, thereby enhancing structural analysis. It identifies the type of carbon (primary, secondary, tertiary, or quaternary) which is crucial for interpreting the molecular structure, like that of carboxylic acids.
DEPT-NMR can differentiate between various types of carbons such as:

• Primary (\(1^\circ\)) carbon: Attached to only one hydrogen.
• Secondary (\(2^\circ\)) carbon: Attached to two hydrogens.
• Tertiary (\(3^\circ\)) carbon: Attached to three hydrogens.
• Quaternary (\(4^\circ\)) carbon: Not attached to any hydrogens.

By using DEPT-NMR, one can deduce the connectivity in carboxylic acids, and pinpoint the carboxyl carbon as quaternary due to the absence of direct hydrogen attachment.

Chemical Shifts

Chemical shifts are an essential concept in NMR spectroscopy that give information about the electronic environment surrounding a nucleus, usually measured in parts per million (ppm). In \(^{13}\mathrm{C}\) NMR, the chemical shift tells about the nature of carbon atoms in the molecule.
For carboxylic acids and similar compounds, the environment around each carbon atom varies, causing different shift values. For example, carboxyl carbons often display peaks at high ppm values, typically around 160 ppm or more due to the electron-withdrawing nature of the \(\mathrm{C}=\mathrm{O}\) (carbonyl) bond.
Interpreting these shifts helps deduce the overall structure, as different functional groups and bonding situations lead to distinct chemical shifts.

Molecular Structure Elucidation

Molecular structure elucidation is the process of determining the specific arrangement of atoms within a molecule based on spectroscopic data. For compounds like carboxylic acids, this often involves analyzing \(^{13}\mathrm{C}\) NMR spectra alongside DEPT-NMR.
This task involves:

• Assigning chemical shifts to specific carbons.
• Using DEPT-NMR to determine the type of each carbon.
• Interpreting ppm values to recognize functional groups.
• Proposing structural configurations that best match the spectral data.

In the case of unknown carboxylic acids, identifying the carboxyl carbon peak, typically at a high ppm, is crucial. The combination of identified carbon types and their associated chemical shifts helps significantly in proposing the molecular structure.