Question

Propose structures for compounds with the following formulas that show only one peak in their \({ }^{1} \mathrm{H}\) NMR spectra: (a) \(\mathrm{C}_{5} \mathrm{H}_{12}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{10}\) (c) \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\)

Short answer

(a) Neopentane, (b) Cyclopentane, (c) tert-Butyl formate.

Step-by-step solution

Analyze the Molecular Formula (a)

Given the molecular formula \( \mathrm{C}_{5} \mathrm{H}_{12} \), we need a compound with only one \( ^1 \mathrm{H} \) NMR peak. This indicates that all hydrogens in the molecule are in equivalent environments, suggesting a highly symmetrical structure. The structure meeting these criteria is neopentane \( (\mathrm{C} \text{-}(\mathrm{CH}_3)_4) \), which is symmetrical and exhibits only one type of hydrogen environment.

Analyze the Molecular Formula (b)

For \( \mathrm{C}_{5} \mathrm{H}_{10} \), with the stipulation of one \( ^1 \mathrm{H} \) NMR peak, we need a highly symmetrical cycloalkane. The only symmetric cyclic structure forming a single peak is cyclopentane (\( \mathrm{C}_5 \mathrm{H}_{10} \)), due to all of its hydrogen atoms being in identical environments on the cyclic ring.

Analyze the Molecular Formula (c)

Given \( \mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2} \), a molecule resulting in only one \( ^1 \mathrm{H} \) NMR peak implies symmetry with equivalent hydrogen atoms. A likely candidate with this formula is tert-butyl formate, where the tert-butyl group \( [(\mathrm{CH}_3)_3\mathrm{C} \text{-}] \) ensures all methyl protons are equivalent.

Key concepts

Molecular Symmetry

In the realm of chemistry and particularly in NMR spectroscopy, molecular symmetry plays a pivotal role. Compounds exhibiting high symmetry often display simplified spectra. This occurs because symmetry leads to equivalent environments for atomic nuclei like hydrogen.

When a molecule is highly symmetrical, its hydrogen atoms occupy identical or equivalent positions. This causes them all to absorb energy at the same resonance frequency in NMR. As a result, you observe a single peak in the spectrum. In our exercise, neopentane becomes a perfect example. It is symmetrical, with all hydrogen atoms in equivalent positions due to its tetrahedral carbon center, leading to uniform chemical environments.

Consider symmetry as a simplification tool in NMR spectroscopy. It helps predict the number of signals a compound will produce. Structures with fewer unique environments for hydrogen will generally yield fewer peaks in a spectrum. This simplification often assists chemists in identifying unknown compounds based on their NMR data.

Organic Structures

Organic structures form the foundation of molecules encountered in NMR studies. Understanding the organization of carbon and hydrogen atoms within these frameworks is essential. Organic molecules are composed of carbon-based structures, often with varying degrees of saturation and functional groups.

Alkanes, cycloalkanes, and esters are just a few types of organic structures that can affect NMR results. In our exercise, we analyzed:

• Neopentane (\(\mathrm{C}-(\mathrm{CH}_3)_4\)) - a highly symmetrical alkane, forming a single peak in NMR.
• Cyclopentane (\(\mathrm{C}_5 \mathrm{H}_{10}\)) - a cycloalkane with equivalent hydrogen environments, thus displaying one peak.
• Tert-butyl formate (\(\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}_2\)) - an ester where the tert-butyl group stabilizes equivalent hydrogen positions.

These structures are cleverly designed to show only one peak in their \(^1 \mathrm{H}\) NMR, simplifying their spectrum analysis.

Hydrogen Environments

In NMR spectroscopy, understanding hydrogen environments is crucial to interpreting spectra. The environment of each hydrogen atom in a molecule determines its specific resonance frequency. Molecules that display a single peak in their NMR spectra typically have hydrogen atoms in identical environments.

The term "hydrogen environment" refers to the unique electronic and spatial context surrounding a hydrogen atom. This encompasses factors such as:

• Proximity to electronegative atoms or groups
• Position within a cyclic or linear structure
• Bonding partners (other atoms connected to the same carbon atom)

In our exercise, each compound was chosen for its ability to house all hydrogens in a single environment. For instance, in cyclopentane, each hydrogen is positioned identically relative to the ring structure, causing them all to exhibit the same NMR behavior. This consistent alignment exemplifies the power of symmetrical geometries in simplifying hydrogen environments.