Question

A H NMR signal is observed at 198.0 Hz (downfield of TMS) on a 135-MHz Instrument. a) What is the observed chemical shift in parts per million (ppm)? Number ppm b) What is the chemical shift, in parts per million (ppm), if the sample is analyzed with a 200.0-MHz instrument? Number ppm c) Where will the proton signal appear, in hertz, if the sample is analyzed with a 200.0-MHz instrument? Number Hz

Answer 1

chemical shift(ppm)= chemical shift (Hz) / frequency of instrument (MHz)

The origin of this formula is as follows:

Chemical shift (ppm)= [10⁶ X Chemical Shift (Hz)]/ [(Frequency of instrument(Hz) X 10⁶) (Hz)]

MHz has been converted into Hz by multiplying with 10⁶ in the denominator.

10⁶ in numerator is to convert in parts per million (ppm)

Thus 10⁶ cancels out and we are left with the formula given on top.

a) chemical shift (ppm)= 198/135 = 1.467 ppm

b) important note : chemical shift in ppm is independent of instrument used, so it comes out to be same for a sample; no matter if different machines are used. This is because on using different machine chemical shift in Hz changes and hence when we divide chemical shift in Hz by instrument frequency, the ratio comes out to be same for different machines.

Thus chemical shift in ppm when 200 MHz machine is used is 1.467 ppm (same as in part (a))

c) chemical shift in ppm= chemical shift in Hz/ instrument frequency (MHZ)

therefore, chemical shift in Hz= Chemical shift in ppm X instrument frequency (MHz)

-> chemical shift in Hz= 1.467 X 200= 293.4 Hz