Question

Assuming the molecular formula of 9 is established as \(\mathrm{C}_{40} \mathrm{H}_{60} \mathrm{~N}_{6} \mathrm{Zr}_{2}\), explain how the proposed structure is consistent with \({ }^{15}\) N NMR spectra as follows. Made with \({ }^{15} \mathrm{~N} \equiv{ }^{14} \mathrm{~N}, 9\) shows three widely separated resonance lines of equal intensity. However, when 9 is made with \({ }^{15} \mathrm{~N} \equiv{ }^{15} \mathrm{~N}\), two of the peaks become doublets with a spacing of \(6 \mathrm{~Hz}\).

Short answer

Three symmetric nitrogen environments exist; two nitrates couple showing doublets.

Step-by-step solution

Understanding the Isotopes and NMR

In NMR spectroscopy, uclear spins create resonances that reflect the chemical environment of the isotope. Here, when compounds have atom connectivity that changes based on isotopic substitution (\( ^{15} ext{N} \) replaces \( ^{14} ext{N} \)), their NMR signals provide structural clues. Given that molecule 9 has the formula \(\text{C}_{40}\text{H}_{60}\text{N}_{6}\text{Zr}_{2}\), focus on the six nitrogen atoms since NMR focuses on isotopically labeled \( \text{N}\).

Analyzing the Three Resonance Lines

The compound shows three resonance lines of equal intensity in \(^{15}\he N\) NMR: this suggests symmetry among the nitrogen atoms such that they fall into equivalent categories. Three distinct environments exist because nitrogen atoms are arranged symmetrically, likely as groups of two where each group shares the same environment considering symmetry in molecular structure.

Doublets in Updated Compound

When 9 uses \(^{15}\text{N} \), it introduces splitting not seen with \(^{14} ext{N} \). This splitting occurs due to coupling of N atoms with identical isotopic substitution. In this case, we observe two peaks turning into doublets, indicting that nearby \(^{15} ext{N} \) atoms influence each other's magnetic fields, splitting signals by about \(6 ext{Hz}\).

Consistent Structure Hypothesis

There are two resonant nitrogens in identical environments, experiencing a coupling interaction seen as doublets. This implies the other nitrogen atoms might have symmetric configurations, showing no splitting. Consequently, three unique symmetric environments exist: suggesting groups possibly in pairs due to symmetry, seen in models that fit such isotropic growth. This solidifies that nitrogen atoms show three distinct environments due to the symmetric surroundings, where certain pairs couple to split into observed doublets.

Key concepts

Isotopic Labeling

Isotopic labeling is a powerful technique used to study molecular structures and interactions. By replacing certain atoms within a molecule with their isotopic versions, scientists can observe changes in physical or chemical behavior. For example:

• In this exercise, nitrogen atoms are substituted with their isotopic form, extsuperscript{15}N. This substitution allows us to examine specific interactions within the molecule that would otherwise be invisible.

When isotopic labeling is applied, it helps to highlight distinct parts of the molecule. This can lead to a better understanding of the arrangement and interactions of atoms within complex structures, making it an essential tool in structural chemistry.

Nuclear Magnetic Resonance

Nuclear Magnetic Resonance (NMR) is a sophisticated analytical technique that relies on the magnetic properties of certain atomic nuclei. When a sample is placed in a magnetic field:

• Nuclei with a magnetic moment, such as extsuperscript{15}N, align with or against the field.

Each nucleus absorbs and re-emits electromagnetic radiation at a specific frequency, known as its resonance frequency.

The resonance frequencies offer cues about the electronic environment surrounding the nuclei. This provides insights into:

• The molecular structure
• Dynamics
• Chemical environment

NMR is particularly valuable in determining the number and type of chemical environments. The number and position of resonance lines can indicate potential symmetries or equivalent environments within a molecule. The sharpness and splitting of these lines can reveal interactions between different atoms, such as the coupling observed in isotopically labeled compounds.

Chemical Environment

In chemistry, the term "chemical environment" refers to the surrounding atoms and the spatial arrangement around a particular atom within a molecule. This environment influences an atom's electronic characteristics and behavior during spectroscopic analyses like NMR.

For instance, in a compound:

• Atoms in similar surroundings may exhibit the same resonance signals, reflecting their equivalent chemical environments.

In the given molecular formula, extsuperscript{15}N NMR reveals three distinct resonance lines. This indicates the existence of three unique chemical environments for the nitrogen atoms, possibly due to symmetrical arrangements.

Analyzing chemical environments helps scientists predict reactivity, stability, and potential interactions with other molecules. It serves as a cornerstone for designing experiments and interpreting spectroscopic data to verify molecular structures.

Isotopic Substitution

Isotopic substitution involves replacing one isotope in a molecule with another. This has a subtle yet profound impact on spectroscopic results and molecular interactions within the compound. In the context of NMR spectroscopy, isotopic substitution can reveal detailed information about atomic interactions.

In this exercise:

• The substitution of extsuperscript{14}N with extsuperscript{15}N causes noticeable changes in the NMR spectrum.

The appearance of doublets in certain resonance peaks arises from the magnetic coupling between isotopes, demonstrating internal interactions that were previously invisible.

Such changes provide crucial evidence for verifying or hypothesizing the molecular structure and understanding atom-to-atom couplings. Analyzing these shifts allows researchers to probe deeper into the physical and magnetic properties of the molecule, unlocking a greater understanding of its structural dynamics.