Question

How many absorptions would you expect to observe in the \({ }^{13}\) C NMR spectra of the following compounds? (a) 1,1 -Dimethylcyclohexane (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OCH}_{3}\) (c) tert-Butylcyclohexane (d) 3-Methylpent-1-yne (e) cis-1,2-Dimethylcyclohexane (f) Cyclohexanone

Short answer

(a) 3, (b) 3, (c) 4, (d) 5, (e) 6, (f) 3.

Step-by-step solution

Understanding 13C NMR Spectroscopy

In a {13} C NMR spectrum, each unique carbon environment gives rise to a separate peak (signal). To determine the number of absorptions or peaks, count the number of unique carbon environments in the molecule.

Analyzing Compound 1: 1,1-Dimethylcyclohexane

1,1-Dimethylcyclohexane has three types of carbon environments: (1) the 1,1-dimethyl group carbons, which are equivalent, (2) the carbons in the cyclohexane ring that are attached to the methyl groups, and (3) the remaining carbons in the cyclohexane ring. There are a total of three unique carbon environments.

Analyzing Compound 2: CH3CH2OCH3

For CH3CH2OCH3 (ethyl methyl ether), there are three unique types of carbon environments: (1) the methyl carbon attached to the oxygen, (2) the methylene group carbon, and (3) the terminal methyl group carbon. This results in three absorptions.

Analyzing Compound 3: tert-Butylcyclohexane

tert-Butylcyclohexane has four unique carbon environments: (1) the three equivalent carbons in the tert-butyl group, (2) the quaternary carbon that the tert-butyl group is attached to, (3) the cyclohexane carbon bonded to the quaternary carbon, and (4) the remaining carbons in the cyclohexane ring. A total of four absorptions.

Analyzing Compound 4: 3-Methylpent-1-yne

3-Methylpent-1-yne has five unique carbon environments: (1) the terminal methyl group, (2) the methylene group, (3) the alkyne carbon adjacent to the methylene group, (4) the central carbon in the alkyne, and (5) the methyl group attached to this alkyne carbon. Thus, there are five absorptions.

Analyzing Compound 5: cis-1,2-Dimethylcyclohexane

cis-1,2-Dimethylcyclohexane has six unique carbon environments: (1) each methyl group is in a unique environment due to the cis-relationship, (2) the carbon atoms bonded to the methyl groups, and (3) the other four carbons of the cyclohexane ring. A total of six absorptions.

Analyzing Compound 6: Cyclohexanone

Cyclohexanone has three unique carbon environments: (1) the carbonyl carbon, (2) the two carbons adjacent to the carbonyl carbon, which are equivalent, and (3) the remaining four ring carbons, which are also equivalent. Therefore, there are three absorptions.

Key concepts

Carbon Environments

A carbon environment in \(^{13}\text{C} \) NMR spectroscopy refers to the unique chemical settings in which carbon atoms reside within a molecule. Carbon atoms in a molecule are considered to be in the same environment if they are structurally and chemically equivalent, meaning they are bonded in the same way to similar atoms or groups.Distinct carbon environments are detected as separate peaks in a \(^{13}\text{C} \) NMR spectrum. This is because each unique environment results in a different resonance frequency of the carbon nuclei. For example, if two carbons are bonded to different groups or are in distinct molecular positions, they will appear as different peaks.When analyzing molecules, it's crucial to recognize these environments:

• *Identical groups*: Carbons bonded in a similar pattern to identical groups, like methyl groups attached to a ring, may be equivalent.
• *Symmetry*: Molecular symmetry can make distinguishable carbons equivalent, reducing the number of unique carbon environments.

A thorough understanding of carbon environments aids in predicting the number of absorptions seen in the \(^{13}\text{C} \) NMR spectrum for a given molecule.

Chemical Shift

Chemical shift is a core concept in \(^{13}\text{C} \) NMR that refers to the variations in the resonant frequency of the carbon atoms caused by their chemical environment. Chemical shifts are measured in parts per million (ppm) and represent the differences in resonance frequency compared to a standard reference.Factors affecting chemical shift include:

• *Electronegativity*: Atoms or groups with high electronegativity, like oxygen or nitrogen, electron-withdrawing elements, shift nearby carbon signals downfield (towards higher ppm).
• *Pi-bonding*: Carbon atoms in alkenes, aryl groups, or near carbonyl groups resonate at higher ppm values due to deshielding effects by the pi-electron cloud.
• *Hybridization*: The hybridization state of a carbon atom affects its chemical shift; for instance, sp³ carbons generally resonate at lower ppm than sp² or sp carbons.

These elements make chemical shifts an insightful tool for identifying the types and surroundings of carbons in a molecule. Understanding these shifts helps in deducing the structure of the organic compounds effectively.

Nuclear Magnetic Resonance

Nuclear Magnetic Resonance (NMR) is a powerful analytical technique used to determine the structure of organic compounds by identifying the spatial arrangement of atoms. The \(^{13}\text{C} \) NMR, specifically, focuses on the carbon-13 isotope, which is less abundant but crucial for structural analysis when examining complex molecules. NMR processes rely on the magnetic properties of certain nuclei, including \(^{13}\text{C} \), ^1^H, and others.These nuclei behave like tiny magnets due to their spin, and when placed in a magnetic field, they resonate at a specific frequency related to their immediate environment.

• *Field Strength*: The strength of the magnetic field applied in \(^{13}\text{C} \) NMR directly influences the resolution and sensitivity of the spectra obtained.
• *Signal Processing*: Advanced techniques such as Fourier Transform are employed to convert raw NMR data into spectra, which can be interpreted.
• *Sensitivity*: Due to the low natural abundance of \(^{13}\text{C} \) (about 1.1%), \(^{13}\text{C} \) NMR is less sensitive compared to proton NMR and requires longer scan times or more concentrated samples.

NMR, by revealing detailed information about molecular structure, aids chemists in understanding organic compounds' composition and the arrangement of atoms within these compounds.