Question

A 250 MHz \(^{1}\) H spectrum of a compound shows two peaks. The frequency of one peak is 510 Hz higher than that of the reference compound (tetramethylsilane) and the second peak is at a frequency 170 Hz lower than that of the reference compound. What chemical shift should be assigned to these two peaks?

Short answer

The chemical shifts for the two peaks in the \(^1\)H NMR spectrum are calculated using the formula: Chemical shift (in ppm) = (difference in frequency / spectrometer frequency) × 10^6. For Peak 1, with a frequency difference of +510 Hz, the chemical shift is 2.04 ppm. For Peak 2, with a frequency difference of -170 Hz, the chemical shift is -0.68 ppm.

Step-by-step solution

Identify given frequencies and the spectrometer frequency

Spectrometer frequency (ν) = 250 MHz Frequency difference for Peak 1 relative to TMS = +510 Hz Frequency difference for Peak 2 relative to TMS = -170 Hz

Calculate the chemical shift for Peak 1

We will use this formula to calculate the chemical shift for Peak 1: Chemical shift (in ppm) = (difference in frequency / spectrometer frequency) × 10^6 For Peak 1, Chemical shift = (510 Hz / 250 MHz) × 10^6 ppm = (510 / 250 × 10^6) × 10^6 ppm

Calculate the chemical shift for Peak 2

We will use the same formula to calculate the chemical shift for Peak 2: For Peak 2, Chemical shift = (-170 Hz / 250 MHz) × 10^6 ppm = (-170 / 250 × 10^6) × 10^6 ppm

Simplify and report the results

For Peak 1, Chemical shift = (510 / 250 × 10^6) × 10^6 ppm = 2.04 ppm For Peak 2, Chemical shift = (-170 / 250 × 10^6) × 10^6 ppm = -0.68 ppm The chemical shifts for these two peaks are 2.04 ppm and -0.68 ppm, respectively.

Key concepts

Chemical Shift

Chemical shift is a key concept in Nuclear Magnetic Resonance (NMR) spectroscopy. It helps researchers and chemists identify different nuclei within a molecule based on its environment. The chemical shift is expressed in parts per million (ppm) and gives us information about the electronic environment around the nuclei.

Whenever a nucleus experiences a shift in the magnetic field due to the shielding or deshielding effects caused by surrounding electrons, a unique signal is produced in the NMR spectrum. This shift is defined in terms of its frequency difference from a standard reference, typically tetramethylsilane (TMS).

To calculate the chemical shift, we use the formula:

• \( \text{Chemical shift (ppm)} = \left( \frac{\text{Frequency difference in Hz}}{\text{Spectrometer frequency in MHz}} \right) \times 10^6 \)

By measuring from the TMS reference, we can determine the position of each peak relative to it for clear analysis.

Tetramethylsilane (TMS)

Tetramethylsilane (TMS) is the standard reference compound used in NMR spectroscopy. It establishes a zero-point for chemical shift measurements. TMS is chosen for several reasons. Firstly, it provides a single strong signal at a near-zero ppm, making it easily distinguishable from other signals.

Moreover, TMS is chemically inert and does not interact with the sample, ensuring that it doesn't interfere with the compound being analyzed. Its low boiling point also makes it easy to remove from the sample, if needed, after the measurement.

The use of TMS helps ensure that the measurements are consistent and reproducible across different experiments and spectrometers. This reliability makes it an ideal reference, forming the basis for comparing chemical environments in diverse samples.

Spectrometer Frequency

The spectrometer frequency is the frequency at which the NMR spectrometer operates, typically denoted in megahertz (MHz). It is a crucial factor when calculating the chemical shift because it sets the scale for frequency measurements.

Higher spectrometer frequencies offer greater resolution and sensitivity, allowing for a more detailed analysis of the sample. This can be especially helpful for complex molecules with many similar environments that need to be distinguished.

In the given exercise, the spectrometer frequency is 250 MHz. To find the chemical shift, you divide the frequency difference of the peaks by the spectrometer frequency and then multiply by one million to convert the result into ppm. This method standardizes the chemical shifts, making them independent of the absolute field strength, and easily comparable irrespective of the spectrometer used.