Question

Propose structures for compounds that fit the following descriptions: (a) A hydrocarbon with seven lines in its 13 C NMR spectrum (b) A six-carbon compound with only five lines in its 13 C NMR spectrum (c) A four-carbon compound with three lines in its \({ }^{13}\) C NMR spectrum

Short answer

a) Cycloheptane, b) Methylcyclopentane, c) Isobutane.

Step-by-step solution

Understanding 13C NMR Spectrum

The 13C NMR spectrum provides information about the carbon environment in organic molecules. Each distinct carbon environment corresponds to a unique line. Identical carbon environments are represented by the same line.

Analyze Part (a)

For a hydrocarbon with seven lines, each carbon must be in a unique environment, suggesting a molecule with symmetry, but no carbon being identical. Given that it is a hydrocarbon, we can propose a simple structure like cycloheptane, which has each carbon in a distinct environment.

Analyze Part (b)

A six-carbon compound with only five lines suggests at least two carbons are identical. A common structure fitting this description could be a cyclohexane with one substituent having identical opposite carbons, like methylcyclopentane.

Analyze Part (c)

A four-carbon compound with three lines implies one set of carbons is identical. A straightforward structure is 2-methylpropane (isobutane), which has two equivalent methyl groups contributing to fewer distinct lines.

Key concepts

Hydrocarbons

Hydrocarbons are organic compounds consisting entirely of hydrogen and carbon. They are the simplest form of organic compounds and can take various shapes, such as chains or rings. There are two primary types of hydrocarbons:

• Aliphatic hydrocarbons: These can be either straight or branched chains. Examples include alkanes, alkenes, and alkynes.
• Aromatic hydrocarbons: These contain one or more benzene rings, such as benzene itself or naphthalene.

In 13C NMR spectroscopy, hydrocarbons show distinct lines based on the number of unique carbon environments. For example, cycloheptane is a cyclic hydrocarbon with each carbon atom in a distinct environment, leading to seven lines in its 13C NMR spectrum. This happens because each carbon has a different position or bonding angle in the molecule.

Carbon Environments

In 13C NMR spectroscopy, carbon environments refer to the unique magnetic surroundings experienced by carbon atoms in a molecule. The number of lines in a spectrum corresponds to the number of unique carbon environments. Some important factors affecting carbon environments include:

• Position in the molecule: Carbons bonded to different groups or atoms exhibit different environments.
• Molecular symmetry: Symmetrical molecules may have carbons that are identical environments, reducing the number of distinct lines.
• Bond types: Single, double, or triple bonds can significantly influence the chemical shift observed in NMR spectroscopy.

For instance, in methylcyclopentane, identical opposite carbons contribute to fewer distinct lines than the number of total carbons, thus exhibiting symmetry.

Molecular Symmetry

Molecular symmetry plays a crucial role in determining the 13C NMR spectrum of a compound. Symmetrical molecules may have multiple carbons in identical environments, resulting in fewer observable lines. Key concepts related to symmetry in molecules include:

• Plane of symmetry: Divides the molecule into two mirror-image halves, affecting carbon environments.
• Axial symmetry: Molecules can be rotated around an axis and remain unchanged, influencing line patterns in spectra.

In the case of 2-methylpropane, its molecular structure leads to only three distinct lines for a four-carbon compound due to two equivalent methyl groups and symmetry in the carbon chain.

Organic Chemistry

Organic chemistry is the branch of chemistry that deals with the structure, properties, and reactions of organic compounds containing carbon. It covers a wide range of studies, including hydrocarbons, their transformations, and functional groups.
In studying organic chemistry, 13C NMR spectroscopy becomes an invaluable tool as it helps elucidate the structure of organic compounds by providing insight into the carbon framework of molecules. This spectroscopic technique can distinguish different carbon environments and thus helps chemists propose or confirm molecular structures.
For example, by analyzing the 13C NMR spectrum, chemists determine that isobutane, despite having four carbon atoms, shows only three lines because the molecule possesses symmetry and two identical methyl groups.