Using a 60-MHz spectrometer, a chemist observes the following absorption: doublet, J = 7 Hz, at d 4.00 (a) What would the chemical shift (d) be in the 300-MHz spectrum? (b) What would the splitting value J be in the 300-MHz spectrum? (c) How many hertz from the TMS peak is this absorption in the 60-MHz spectrum? In the 300-MHz spectrum?

Verified step by step guidance

1. Identify the relationship between the chemical shift ($\delta$) and the spectrometer frequency. The chemical shift is expressed in parts per million (ppm) and is independent of the spectrometer frequency.
2. For part (a), recognize that the chemical shift ($\delta$) remains the same regardless of the spectrometer frequency. Therefore, $\delta =4.00$ ppm in both the 60-MHz and 300-MHz spectra.
3. For part (b), understand that the coupling constant (J) is measured in hertz (Hz) and is also independent of the spectrometer frequency. Thus, $J=7$ Hz in both the 60-MHz and 300-MHz spectra.
4. For part (c), calculate the frequency in hertz from the TMS peak for the 60-MHz spectrum using the formula: $\text{Frequency (Hz)}=\delta \times \text{Spectrometer Frequency (MHz)}$. Substitute $\delta =4.00$ ppm and $\text{Spectrometer Frequency}=60$ MHz.
5. For the 300-MHz spectrum, use the same formula: $\text{Frequency (Hz)}=\delta \times \text{Spectrometer Frequency (MHz)}$. Substitute $\delta =4.00$ ppm and $\text{Spectrometer Frequency}=300$ MHz.

Key Concepts

Chemical Shift

Chemical shift refers to the resonant frequency of a nucleus relative to a standard reference, typically tetramethylsilane (TMS) in NMR spectroscopy. It is measured in parts per million (ppm) and provides insight into the electronic environment surrounding the nuclei. The chemical shift can change with the frequency of the spectrometer, but the relative positions remain consistent across different frequencies.

J-Coupling (Spin-Spin Splitting)

J-coupling, or spin-spin splitting, occurs when nuclei interact with each other through chemical bonds, leading to the splitting of NMR signals into multiple peaks. The value of J, measured in hertz (Hz), indicates the strength of this interaction and remains constant regardless of the spectrometer frequency. Understanding J-coupling is essential for interpreting the multiplicity of signals in NMR spectra.

Frequency Dependence in NMR

In NMR spectroscopy, the frequency of the spectrometer affects the resolution and sensitivity of the measurements. While chemical shifts are expressed in ppm and remain consistent across different frequencies, the absolute frequency of the signals will change. This means that when transitioning from a 60-MHz to a 300-MHz spectrometer, the observed chemical shifts will be recalibrated, but the J-coupling values will remain unchanged.