Question

The \(^{13} \mathrm{C}\) NMR spectrum of acetic acid (14.15) has signals at \(\delta 20.6\) and 178.1 ppm. Assign the spectrum.

Short answer

\(\delta 20.6\) ppm is the \(\text{CH}_3\) carbon; \(\delta 178.1\) ppm is the \(\text{COOH}\) carbon.

Step-by-step solution

Understanding the Exercise

We need to assign the carbon signals in the \(^{13} \mathrm{C}\) NMR spectrum of acetic acid to the appropriate carbon atoms in the molecule. Acetic acid has two types of carbon atoms: a methyl group (\(\text{CH}_3\)) and a carboxylic acid group (\(\text{COOH}\)).

Identify Typical Chemical Shifts

In \(^{13} \mathrm{C}\) NMR spectroscopy, the carbon of a methyl group (\(\text{CH}_3\)) typically has a chemical shift around \(10-30\) ppm, while the carbon in a carboxylic acid group (\(\text{COOH}\)) usually resonates at \(160-185\) ppm due to its more electronegative environment.

Assign the Methyl Carbon

The signal at \(\delta 20.6\) ppm fits within the range typically assigned to a methyl carbon (\(\text{CH}_3\)). Therefore, the peak at \(\delta 20.6\) ppm corresponds to the methyl carbon of acetic acid.

Assign the Carboxylic Acid Carbon

The signal at \(\delta 178.1\) ppm is within the range expected for a carboxylic acid carbon (\(\text{COOH}\)). Thus, the peak at \(\delta 178.1\) ppm corresponds to the carboxylic acid carbon.

Key concepts

Chemical Shifts in \(^{13}\text{C}\) NMR Spectroscopy

In \(^{13}\text{C}\) NMR spectroscopy, chemical shifts are vital in identifying the environment around carbon atoms. A chemical shift is a resonant frequency of a nucleus relative to a standard in a magnetic field. This shift occurs due to surrounding electronic environments. These are reflected in parts per million (ppm) on the NMR spectrum.

In essence, each type of carbon within a molecule can give a distinct signal. Such signals depend heavily on surrounding atoms and functional groups present. More electronegative atoms, like oxygen in a carboxylic acid, deshield adjacent carbons. This increases their ppm value. Conversely, less electronegative environments, like a methyl group, result in lower ppm values. Understanding these shifts helps assign peaks to specific carbons within a molecule.

The Methyl Group in NMR Spectroscopy

A methyl group consists of one carbon atom bonded to three hydrogen atoms (\(\text{CH}_3\)). In \(^{13}\text{C}\) NMR, this group is key for its distinctive chemical shifts. These shifts typically occur between \(10-30\) ppm. This range occurs because the three hydrogens have a lower electron-withdrawing effect. Thus, the carbon is relatively shielded.

For acetic acid, with a methyl group attached, you will observe a signal around \(\delta 20.6\) ppm. This fits neatly within the typical range for methyl carbons. Identifying such a shift in the NMR spectrum can indicate the presence of methyl groups within a sample.

Understanding Carboxylic Acids in NMR

Carboxylic acids contain a \(\text{COOH}\) functional group, known for impacting NMR readings significantly. The carbon in a carboxylic acid is bonded to an OH group and doubly bonded to an oxygen atom. These oxygen atoms are highly electronegative, profoundly affecting chemical shifts.

In \(^{13}\text{C}\) NMR, you can expect to see a carboxylic acid carbon signal around \(160-185\) ppm. This range is due to the deshielding effect from the electronegative elements. For acetic acid, the carboxylic carbon falls within this range at \(\delta 178.1\) ppm. Recognizing such a signal is crucial in determining the presence of carboxylic acids in a mixture.

The Role of Acetic Acid in NMR Analysis

Acetic acid, with a chemical formula \(\text{CH}_3\text{COOH}\), is a simple example of how NMR spectroscopy distinguishes different carbon environments. It has two distinct kinds of carbon atoms: one in the methyl group and another in the carboxylic group.

Analyzing its \(^{13}\text{C}\) NMR spectrum, signals appear at \(\delta 20.6\) ppm and \(\delta 178.1\) ppm. The first is assigned to its methyl carbon. The latter correlates to its carboxylic carbon. By understanding and assigning these peaks, chemists can accurately identify the chemical structure of acetic acid and its presence in mixtures. NMR thus serves as an indispensable tool in characterizing organic compounds.