Question

The following \({ }^{1} \mathrm{H}\) 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) \(\mathrm{CH}_{3} \mathrm{OH} ; 693 \mathrm{~Hz}\) (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2} ; 1060 \mathrm{~Hz}\)

Short answer

(a) 7.27 ppm, (b) 3.05 ppm, (c) 3.47 ppm, (d) 5.30 ppm.

Step-by-step solution

Understanding the Formula

To convert frequency into chemical shift (\( \delta \) units, ppm), use the formula: \( \delta (\text{ppm}) = \frac{\text{Frequency (Hz)}}{\text{Spectrometer Frequency (MHz)}} \). This provides the shift in parts per million relative to the spectrometer frequency.

Convert CHCl₃ Frequency

For \( \text{CHCl}_3 \), substitute the values into the formula: \( \delta = \frac{1454 \text{ Hz}}{200 \text{ MHz}} = 7.27 \text{ ppm} \).

Convert CH₃Cl Frequency

For \( \text{CH}_3\text{Cl} \), use the formula: \( \delta = \frac{610 \text{ Hz}}{200 \text{ MHz}} = 3.05 \text{ ppm} \).

Convert CH₃OH Frequency

For \( \text{CH}_3\text{OH} \), apply the formula: \( \delta = \frac{693 \text{ Hz}}{200 \text{ MHz}} = 3.47 \text{ ppm} \).

Convert CH₂Cl₂ Frequency

For \( \text{CH}_2\text{Cl}_2 \), compute: \( \delta = \frac{1060 \text{ Hz}}{200 \text{ MHz}} = 5.30 \text{ ppm} \).

Key concepts

Chemical Shift

The chemical shift in NMR spectroscopy is a critical concept that helps scientists and chemists understand the environment of nuclei within a molecule. It refers to the resonant frequency of a nucleus relative to a standard reference. This shift can provide valuable information about the electronic environment surrounding the nucleus.
In practical terms, the chemical shift means how much upfield or downfield (lower or higher frequency) an observed signal is compared to a reference compound.

• The chemical shift is expressed in parts per million (ppm).
• It is denoted by the symbol \( \delta \).
• It is essential for identifying different types of hydrogen atoms in organic molecules.

By examining the chemical shift, you can determine what types of nearby atoms or functional groups might be influencing the nucleus being observed.

Spectrometer Frequency

Spectrometer frequency is an essential feature of NMR instruments. It is the frequency at which the spectrometer operates, usually reported in megahertz (MHz).
The spectrometer frequency is directly related to the strength of the magnetic field and the type of nucleus being detected. In general, higher magnetic field strengths correspond to higher spectrometer frequencies.

• The typical spectrometer frequency used for \( ^1H \) NMR ranges from 60 MHz to 900 MHz.
• In the provided exercise, the spectrometer operates at 200 MHz.
• Spectrometer frequency is a critical variable in calculating the chemical shift, as we see in the formula used to convert Hz to ppm.

This frequency is significant because the chemical shift, in ppm, is calculated using the spectrometer frequency as part of the conversion process. Therefore, it ensures that chemical shifts are consistent across different spectrometer settings.

PPM Conversion

PPM conversion is a method used to convert the measured frequency shifts in hertz (Hz) to chemical shift values in parts per million (ppm).
This conversion is crucial because it standardizes the measurement of chemical shifts, making them independent of the spectrometer frequency.

• The formula used for this conversion is \( \delta (\text{ppm}) = \frac{\text{Frequency (Hz)}}{\text{Spectrometer Frequency (MHz)}} \).
• This formula helps express the chemical environment experienced by nuclei in a molecule.

By using ppm, chemists can compare chemical shifts obtained from different devices or conditions. This conversion provides a universal way of expressing the data, ensuring that the shifts reflect intrinsic chemical properties rather than variations in the equipment used.