Question

The following "H NMR peaks were recorded on a spectrometer operating at \(200 \mathrm{MHz}\). Convert each into \(\delta\) units. (a) \(\mathrm{CHCl}_{3} ; 1454 \mathrm{~Hz}\) (b) \(\mathrm{CH}_{3} \mathrm{Cl} ; 610 \mathrm{~Hz}\) (c) \(\mathrm{CH}_{2} \mathrm{OH}\) : \(693 \mathrm{H}\) (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}: 1060 \mathrm{H}_{7}\)

Short answer

(a) 7.27 ppm, (b) 3.05 ppm, (c) 3.465 ppm, (d) 5.30 ppm.

Step-by-step solution

Understand the problem

We need to convert the proton NMR (nuclear magnetic resonance) peaks given in Hertz (Hz) for a 200 MHz spectrometer into chemical shift units (δ), which are measured in parts per million (ppm). The chemical shift δ is calculated using the formula: \( \delta = \frac{\text{frequency in Hz}}{\text{spectrometer frequency in MHz}} \).

Calculate δ for CHCl₃

For \( \mathrm{CHCl}_{3} \), we have a frequency of 1454 Hz. Using the formula, we calculate: \(\delta = \frac{1454\, \mathrm{Hz}}{200\, \mathrm{MHz}} = 7.27 \).Thus, the chemical shift \( \delta \) for \( \mathrm{CHCl}_{3} \) is 7.27 ppm.

Calculate δ for CH₃Cl

For \( \mathrm{CH}_{3} \mathrm{Cl} \), the frequency is 610 Hz. We calculate:\[\delta = \frac{610\, \mathrm{Hz}}{200\, \mathrm{MHz}} = 3.05\]So, the chemical shift \( \delta \) for \( \mathrm{CH}_{3} \mathrm{Cl} \) is 3.05 ppm.

Calculate δ for CH₂OH

For \( \mathrm{CH}_{2} \mathrm{OH} \), the frequency given is 693 Hz. Using the formula, we find:\[\delta = \frac{693\, \mathrm{Hz}}{200\, \mathrm{MHz}} = 3.465\]Therefore, the chemical shift \( \delta \) for \( \mathrm{CH}_{2} \mathrm{OH} \) is 3.465 ppm.

Calculate δ for CH₂Cl₂

For \( \mathrm{CH}_{2} \mathrm{Cl}_{2} \), the frequency is 1060 Hz. Calculating gives:\[\delta = \frac{1060\, \mathrm{Hz}}{200\, \mathrm{MHz}} = 5.30\]Thus, the chemical shift \( \delta \) for \( \mathrm{CH}_{2} \mathrm{Cl}_{2} \) is 5.30 ppm.

Key concepts

Chemical Shift

The concept of chemical shift is fundamental in nuclear magnetic resonance (NMR) spectroscopy, particularly in H NMR (proton NMR). It measures how much a nucleus's nuclear magnetic resonance frequency differs from a standard reference frequency. This is crucial because it allows chemists to determine the electronic environment surrounding a specific proton in a molecule, which provides insights into the molecular structure and dynamics.
In practice, we express chemical shifts in parts per million (ppm) relative to the reference compound, usually tetramethylsilane (TMS) for protons. The chemical shift is crucial because it tells us:

• The chemical environment of protons, identifying whether they're in high or low electron density areas.
• Information about connectivity and proximity to electronegative atoms or pi bonds.

The formula to convert frequency (from Hz) to chemical shift (\(\delta\) in ppm) is:
\[ \delta = \frac{\text{frequency in Hz}}{\text{spectrometer frequency in MHz}} \]
This conversion allows us to compare NMR data from different instruments since it normalizes the outcomes to a standard frequency unit.

H NMR

H NMR, or proton NMR, specifically targets hydrogen nuclei, the most common being the proton. It's a sensitive method for identifying and quantifying the number of hydrogen atoms in specific environments within a molecule. Proton NMR works by placing the sample in a magnetic field, causing the hydrogen nuclei to align with or against the field. When a radiofrequency pulse is applied, these nuclei absorb energy and shift alignment, generating a signal.
Key features of H NMR include:

• Peak multiplicity: This tells us about neighboring nuclei using the n+1 rule, where n is the number of nearby hydrogens.
• Integration: This provides the relative number of hydrogens contributing to each peak.
• Chemical Shift (\(\delta\)): As covered in the previous section, the actual position on the spectrum indicative of the proton's electronic environment.

This method is indispensable in confirming molecular structures, analyzing impurities, and understanding reaction mechanisms.

Nuclear Magnetic Resonance

Nuclear Magnetic Resonance (NMR) is a powerful analytical technique utilized to determine the structure of organic compounds. It relies on the magnetic properties of certain nuclei. When placed in an external magnetic field, these nuclei resonate at specific frequencies when exposed to a matching frequency. This resonance is detectable and forms the basis of NMR spectroscopy.
The significance of NMR in chemistry lies in its ability to:

• Identify molecular structures by elucidating functional groups.
• Provide details about molecular dynamics and confirm molecular symmetry.
• Offer non-destructive analysis, meaning samples are preserved post-examination.

NMR spectrometers operate at a specified frequency—like the 200 MHz in our exercise—, which determines the precision of the measurements. The higher the MHz, the better the resolution of the data.
*NMR is a versatile method, providing exceptional detail that is unmatched by other forms of spectroscopy.*