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 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 MHz resonance correspond to?

Short answer

(a) 420 Hz (b) 2.1 δ (c) 1050 Hz

Step-by-step solution

Understanding Chemical Shift

The chemical shift (\( \delta \) ) is given in parts per million (ppm) and is a relative measurement describing how far a proton's resonance frequency is from the reference compound TMS (Tetramethylsilane). At a given frequency, the shift in Hertz can be calculated by multiplying \( \delta \) by the spectrometer frequency in MHz.

Calculating Hertz Downfield at 200 MHz

Given that the chemical shift of acetone is \( 2.1 \ \delta \) ppm, and it's recorded at \( 200 \ \text{MHz} \), the shift in Hertz is calculated as \( 2.1 \times 200 = 420 \ \text{Hz} \). This means the acetone resonance is 420 Hz downfield from TMS.

Determining Absorption Position at 500 MHz

The chemical shift in \( \delta \) units remains the same regardless of the instrument's operating frequency. Thus, if recorded with a \( 500 \ \text{MHz} \) spectrometer, the absorption of acetone still appears at \( 2.1 \ \delta \).

Calculating Hertz Downfield at 500 MHz

At \( 500 \ \text{MHz} \), the shift in Hertz is \( 2.1 \times 500 = 1050 \ \text{Hz} \). Therefore, the acetone resonance at 500 MHz is 1050 Hz downfield from TMS.

Key concepts

Chemical Shift

In NMR spectroscopy, the concept of chemical shift is central to interpreting spectra. Chemical shifts are expressed in parts per million (ppm) and signify how the resonance frequency of a nucleus differs from a standard reference. This difference is relative, making it independent of the spectrometer's operational frequency.
For example, in the NMR spectrum of acetone, a chemical shift of 2.1 ppm indicates the position of the hydrogen resonance concerning the reference compound. This means the protons in acetone resonate at a position shifted downfield compared to the reference, which is commonly Tetramethylsilane (TMS).

Key Points to Remember:

• It's a relative measure, not an absolute frequency.
• Expressed in ppm, allowing comparisons across different spectrometers.
• Used to identify functional groups and molecular structure.

Tetramethylsilane (TMS)

Tetramethylsilane, commonly abbreviated as TMS, plays a vital role in NMR spectroscopy as a reference point for chemical shifts. TMS is chosen because it has

Characteristics of TMS

• One of the most shielded compounds, leading to a low-frequency resonance.
• TMS signals appear at what is defined as 0 ppm.
• The singlet peak ensures clarity and ease of identification.

When you record an NMR spectrum, the chemical shifts of all sample signals are measured relative to this TMS signal. It serves as a universal standard, which means you can easily interpret spectra from different studies or instruments.
TMS is chemically inert and mixes well with most organic solvents, making it an ideal reference for a wide range of compounds.

Spectrometer Frequency

The frequency of a spectrometer, usually given in megahertz (MHz), is crucial in NMR spectroscopy because it dictates the energy levels at which nuclear resonance occurs. Spectrometers come in different frequencies such as 200 MHz or 500 MHz, impacting the resolution and detail of the spectra.

Importance of Spectrometer Frequency

• Higher frequency spectrometers offer better sensitivity and resolution.
• Frequencies must be adjusted to match the energy difference between nuclear spin states in a magnetic field.
• Spectrometer frequency particularly affects the conversion of chemical shifts from ppm to Hertz.

For instance, the 2.1 ppm shift in acetone will correspond to different Hertz values depending on the instrument's frequency. At 200 MHz, it translates to 420 Hz, whereas at 500 MHz, it is 1050 Hz. This highlights the spectrometer's role in scaling the ppm values to practical measurements that can be used for analysis.