Question

The following \({ }^{1} \mathrm{H}\) NMR absorptions were obtained on a spectrometer operating at \(200 \mathrm{MHz}\) and are given in hertz downfield from the TMS standard. Convert the absorptions to \(\delta\) units. (a) \(436 \mathrm{~Hz}\) (b) \(956 \mathrm{~Hz}\) (c) \(1504 \mathrm{~Hz}\)

Short answer

(a) 2.18 ppm; (b) 4.78 ppm; (c) 7.52 ppm.

Step-by-step solution

Understand the concept of Chemical Shift

Chemical shift ( \(\delta\) units) in \(\(\textit{NMR spectroscopy}\) \) is a way to express the difference in the resonance frequency of nuclei, relative to a reference compound, usually TMS (Tetramethylsilane). It is defined in parts per million (ppm) and allows for comparison between different operating frequencies of spectrometers.

Formula for Conversion

To convert an absorption in hertz to \(\delta\) units, we use the formula: \[ \delta(\text{ppm}) = \frac{\text{frequency in Hz}}{\text{operating frequency of the spectrometer in MHz}} \] This formula adjusts the raw Hertz reading by the spectrometer's operating frequency, converting it to ppm.

Calculate \(\delta\) for 436 Hz

Using the formula: \( \delta = \frac{436 \text{ Hz}}{200 \text{ MHz}} \). Perform the division: \[ \delta = \frac{436}{200} = 2.18 \text{ ppm} \]

Calculate \(\delta\) for 956 Hz

Using the same formula: \( \delta = \frac{956 \text{ Hz}}{200 \text{ MHz}} \). Perform the division: \[ \delta = \frac{956}{200} = 4.78 \text{ ppm} \]

Calculate \(\delta\) for 1504 Hz

Use the formula again: \( \delta = \frac{1504 \text{ Hz}}{200 \text{ MHz}} \). Perform the division: \[ \delta = \frac{1504}{200} = 7.52 \text{ ppm} \]

Key concepts

Chemical Shift

Chemical shift is a pivotal concept in nuclear magnetic resonance ( NMR ) spectroscopy. It indicates how nuclear spins of atoms in a molecule resonate at different frequencies, depending on their environment. This resonance difference is measured relative to a reference compound, primarily Tetramethylsilane (TMS).

The chemical shift is expressed in parts per million ( ppm ), which allows scientists to easily compare shifts across different spectrometers and their settings. Understanding chemical shifts enables a deeper insight into molecular structure, helping identify different functional groups and their surroundings in molecules.

Tetramethylsilane (TMS)

Tetramethylsilane ( TMS ) is the most commonly used reference compound in NMR spectroscopy. TMS is chosen because its inert nature and the fact that it has a single proton environment, resulting in a sharp, distinct signal.

Here’s why TMS is ideal as a reference standard: - **Clean Signal**: Produces a clear single peak separate from most organic compounds. - **Non-reactive**: The silicon-carbon bonds in TMS are generally inert, preventing interference with the sample. - **Volatile**: It can easily be removed from samples, reducing contamination risk.

By comparing all sample readings to TMS, researchers can determine actual shifts that occur in the sample relative to this constant baseline.

Parts per Million (ppm)

The unit parts per million ( ppm ) is crucial in the context of NMR spectroscopy because it standardizes the chemical shifts across different operating frequencies. NMR systems operate at varied frequencies, so using hertz wouldn't allow data comparison.

With ppm , shifts are expressed as a ratio of the frequency differences, scaled by a million. This turns large frequency values into small, manageable numbers.

When you see a chemical shift in ppm , it suggests how much a particular nuclei's environment causes its resonance frequency to deviate from the reference (TMS). This standardized measurement enables chemists to predict molecular structure through comparison across different substances and equipment.

Operating Frequency

Operating frequency in NMR spectroscopy refers to the frequency at which the spectrometer is set to observe the resonances of interest. It is typically denoted in megahertz (MHz). The NMR machines have different operating frequencies, which require standardizing signal measurements using ppm to allow comparison.

The formula \( \delta(\text{ppm}) = \frac{\text{frequency in Hz}}{\text{operating frequency of the spectrometer in MHz}} \) leverages this concept to enable conversion. This helps translate the absorption signals, which can range in hertz, into a uniform ppm scale.

Operating frequencies can vary widely, such as 200 MHz or even higher, impacting the sensitivity and resolution of the NMR analysis. Understanding these frequencies, and thus the conversion formula, is key for interpreting the NMR spectra meaningfully.