Question

When the \({ }^{1} \mathrm{H}\) NMR spectrum of acetone, \(\mathrm{CH}_{3} \mathrm{COCH}_{3}\), is recorded on an instrument operating at \(200 \mathrm{MHz}\), a single sharp resonance at \(2.1 \delta\) is seen. (a) How many hertz downfield from TMS does the acetone resonance correspond to? (b) If the \({ }^{1} \mathrm{H}\) NMR spectrum of acetone were recorded at \(500 \mathrm{MHz}\), what would the position of the absorption be in \(\delta\) units? (c) How many hertz downfield from TMS does this \(500 \mathrm{MHz}\) resonance correspond to?

Short answer

(a) 420 Hz, (b) 2.1 \(\delta\), (c) 1050 Hz

Step-by-step solution

Understanding Shifts in NMR

A chemical shift in NMR is given in dimensionless units called delta (\(\delta\)), which are parts per million (ppm). This number represents how far, in ppm, a given proton resonates from a reference compound, usually tetramethylsilane (TMS). The chemical shift does not depend on the strength of the spectrometer in MHz.

Calculate Hertz Downfield at 200 MHz

In a 200 MHz \(^{1}H\) NMR spectrum, the shift in Hertz can be found by multiplying the shift in ppm (\(2.1 \, \delta\) for acetone) by the operating frequency of the instrument (200 MHz):\[\text{Frequency shift in Hz} = \delta \times \text{Spectrometer Frequency (MHz)} = 2.1 \, \delta \times 200 \, \text{MHz}\]\[\Rightarrow \text{Frequency shift in Hz} = 420 \, \text{Hz}\]

Position at 500 MHz

To find the position of absorption in \(\delta\) units when using a 500 MHz spectrometer, recognize that \(\delta\) values are constant across different spectrometer frequencies since they are in ppm units. Thus, the position will remain 2.1 \(\delta\) at 500 MHz.

Calculate Hertz Downfield at 500 MHz

With the chemical shift of acetone remaining at \(2.1 \, \delta\), the new frequency shift in Hertz when recorded at 500 MHz is calculated as follows:\[\text{Frequency shift in Hz} = \delta \times \text{Spectrometer Frequency (MHz)} = 2.1 \, \delta \times 500 \, \text{MHz}\]\[\Rightarrow \text{Frequency shift in Hz} = 1050 \, \text{Hz}\]

Key concepts

Chemical Shift

Chemical shift is a crucial concept in NMR (Nuclear Magnetic Resonance) Spectroscopy. It quantifies the resonance position of nuclei in a molecule relative to a standard compound. This measurement is often expressed in parts per million (ppm) using the symbol delta (\(\delta\)). The standard reference compound usually used is tetramethylsilane (TMS). Chemical shifts are vital as they can provide insights into the electronic environment around the nucleus.

• The chemical shift does not change with different spectrometer frequencies. This means a shift of 2.1 \(\delta\) on a 200 MHz spectrometer will be the same on a 500 MHz one.
• This constancy makes it easier for chemists to compare spectra from different instruments.

Understanding the concept of chemical shifts is essential as it helps in determining the structure and environment of the chemical compounds being analyzed.

Acetone

Acetone, with the chemical formula \(\mathrm{CH_{3}COCH_{3}}\), is a simple and well-known solvent. In NMR Spectroscopy, it provides a clear representation of how chemical shifts work. In the NMR spectrum, acetone shows a single sharp peak, attributed to the equivalent protons of its two \(\mathrm{CH_3}\) groups.

• For a 200 MHz instrument, the NMR spectrum of acetone shows a peak at 2.1 \(\delta\).
• This single chemical environment for the protons leads to a clear and sharp resonance.

Acetone's simple structure makes it a straightforward example to study the effect of chemical shifts in spectroscopy.

Tetramethylsilane (TMS)

Tetramethylsilane, abbreviated as TMS, is a standard reference compound used in NMR Spectroscopy. TMS is often chosen because its protons generate a signal that is further upfield than most organic compounds due to its high degree of symmetry and relatively low electron density.

• TMS is set as the zero point in the \(\delta\) scale for chemical shifts, simplifying the comparison of different spectra.
• It provides a \'benchmark\' resonance peak, allowing the relative position of other peaks to be easily determined.

Thanks to its simplicity and stable reference point, TMS is an invaluable component in NMR analyses.

Spectrometer Frequency

The frequency of an NMR spectrometer, expressed in MHz, is a crucial factor that can affect the interpretation of spectra. However, the chemical shift value in \(\delta\) remains constant regardless of the spectrometer frequency used, due to its ppm unit representation.

• On a 200 MHz spectrometer, an acetone resonance marked at 2.1 \(\delta\) corresponds to a 420 Hz frequency shift downstream from TMS.
• In contrast, on a 500 MHz spectrometer, the same 2.1 \(\delta\) shift results in a 1050 Hz frequency shift.

Thus, while frequency changes affect Hz values, the accompanying \(\delta\) shifts remain unchanged, facilitating the comparison between spectra obtained on different devices.