Question

An amine of unknown structure contains one nitrogen and nine carbon atoms. The \({ }^{13} \mathrm{C}\) NMR spectrum shows only five signals, all between 20 and 60 ppm. Three cycles of Hofmann elimination sequence [(1) \(\mathrm{CH}_{3} \mathrm{I} ;(2) \mathrm{Ag}_{2} \mathrm{O}, \mathrm{H}_{3} \mathrm{O}\); (3) heat] give trimethylamine and \(1,4,8\)-nonatriene. Propose a structural formula for the amine.

Short answer

Answer: The structural formula of the given amine is N(CH3)3-(CH2)6-CH=CH-CH=CH-CH=CH2, also known as N,N,N-trimethyl-1,4,8-nonatrienamine.

Step-by-step solution

Analyzing the given information about the amine.

The amine contains one nitrogen atom and nine carbon atoms. The \({ }^{13} \mathrm{C}\) NMR spectrum shows only five signals between 20 and 60 ppm, indicating that there are five different types of carbon atoms present in the molecule.

Understanding Hofmann elimination.

Hofmann elimination is a three-step process used to convert amines to olefins. The three steps involved are: (1) Alkylation with an alkyl halide (e.g., CH3I), (2) Oxidation with silver oxide (Ag2O) and water (H3O), and (3) Heating.

Analyzing the given information about Hofmann elimination.

After three cycles of Hofmann elimination, trimethylamine and 1,4,8-nonatriene are given as products. This information helps us deduce the structure of the initial amine.

Propose the initial amine structure.

Since the amine has nine carbon atoms and the product 1,4,8-nonatriene has nine carbon atoms, no carbon atoms are lost during the Hofmann elimination. This suggests that the initial amine has \(3\) methyl groups attached to the nitrogen, which are then removed as trimethylamine. Thus, the structure of the amine is N(CH3)3 bound to a nine-carbon chain having the following double bond placements:

Drawing the structural formula.

We will now draw the molecular structure of the amine based on our conclusions:  The structural formula for the amine is: \(N(CH_3)_3-(CH_2)_6-CH=CH-CH=CH-CH=CH_2\) So the given amine is N,N,N-trimethyl-1,4,8-nonatrienamine.

Key concepts

13C NMR Spectroscopy

Understanding 13C NMR spectroscopy is crucial for chemists when they aim to elucidate the structure of organic molecules. It's a type of nuclear magnetic resonance (NMR) spectroscopy that is specific to the carbon-13 isotope, which provides information about the carbon framework of a compound.

Each signal in a 13C NMR spectrum corresponds to a unique carbon environment. In the problem presented, the spectrum shows five distinct signals, which means there are five different carbon environments within the molecule. Seeing signals between 20 and 60 ppm typically suggests the presence of aliphatic carbons, which are part of chains or non-aromatic rings. These signals help to map out the molecule's carbon skeleton, providing a starting point for further structural elucidation.

Detailed interpretation of a 13C NMR spectrum can reveal further information such as the symmetry within the molecule, the degree of saturation, and the presence of substituents. An understanding of coupling patterns and chemical shifts is paramount in piecing together the molecular puzzle.

Amine Structure Elucidation

Elucidation of an amine's structure often involves a combination of spectroscopic methods, with 13C NMR being one part of the puzzle. Amines are organic compounds that contain a nitrogen atom with a lone pair of electrons. The exercise provided hints at a complex amine structure deduced through analytical techniques and chemical reactions like Hofmann elimination.

The number of signals in the 13C NMR spectrum indicates the number of unique carbon environments, which combined with the nitrogen count, provides insights into the amine's framework. By taking into account the products formed after Hofmann elimination, it's possible to backtrack and infer the pre-elimination structure of the amine. In this case, the elimination produces trimethylamine, indicating that the original amine had three methyl groups attached to its nitrogen atom.

Additional evidence from the elimination process, such as the type of alkene formed, can be combined with NMR data to deduce the placement of double bonds and the overall structure of the amine. This process showcases the detective work involved in organic chemistry, where reactions and spectroscopy work hand-in-hand.

Organic Synthesis

The field of organic synthesis is about constructing organic molecules through a series of chemical reactions. Hofmann elimination, as mentioned in the exercise, is one of the classical reactions in an organic chemist's toolkit. It transforms amines into olefins, or alkenes, through a series of well-orchestrated steps.

Firstly, alkylation introduces an alkyl group to the amine. Subsequent oxidation and elimination steps lead to the formation of an alkene and the simplified amine, trimethylamine. This transformation is indicative of the molecule's structure before the reaction occurred.

Understanding the synthesis pathway is not just about knowing the reactions involved but also about predicting and analyzing the outcomes based on the structure of the starting materials. In education and real-world applications, an organic synthesis problem often doubles as a structural elucidation exercise, challenging students and professionals to think backwards from products to reactants—a method known as retrosynthetic analysis. This example clearly demonstrates how reactions can be used to infer not only the functional groups present in a molecule but also the connectivity and positional isomerism of those groups.