Question

In NMR if a chemical shift(δ) is 173.6 ppm from the tetramethylsilane (TMS) standard and the spectrometer frequency is 285 MHz, how many Hz from TMS is the signal at? Give at least three significant figures.

Answer 1

The expression of chemical shift in Hz unit which are too lengthy, would have been inconvenient for NMR data. And that is why a dimension less ppm unit has been adopted. The peak appears at a down field position from TMS proportionally to the strength of an operating magnetic field.

The relationship for N MHz spectrometer, if the chemical shift is m Hz then,

m Hz/N MHz = m Hz/(Nx10⁶) = (m/N)x10^-6 = m/N ppm

For the peak at 173.6 ppm on a 285 MHz NMR spectrometer: m Hz / (285 x 10⁶ Hz) = (m/285) x 10^-6 = m/285 ppm = 173.6 ppm

Therefore, m=285*173.6 = 49476.00 Hz

In other way, 1 ppm on a 285 MHz NMR spectrometer corresponds to: 1 x 10^-6 x 285 x 10⁶ Hz = 285 Hz

Therefore, 173.6 ppm = 285*173.6 H = 49476.00 Hz.