Question

Question: The following¹H NMR absorptions were obtained on a spectrometer

operating at 200 MHz and are given in hertz downfield from the TMS

standard. Convert the absorptions to$\delta$units.

(a)436 Hz(b)956 Hz(c)1504 Hz

Short answer

(a) 2.18$\delta$

(b) 4.78$\delta$

(c) 2.52$\delta$

Step-by-step solution

NMR spectroscopy

NMR stands for Nuclear Magnetic Resonance Spectroscopy. This is the technique used for determining the structure of the organic compounds. It is a non-destructive technique. It is of two types¹H NMR and¹³C NMR.

• ·It exploits the magnetic properties of certain atomic nuclei to determine physical and chemical properties of molecules in which they are contained.
• ·Any proton or nucleus with odd mass number spin on its axis.
• ·The nucleus or the proton behaves as a tiny spinning bar magnet due to both electric charge and mechanical spinning.

Chemical Shift

In 1951, Packward observed three different precessional frequencies of proton in EtOH. Since the shift in frequency was due the chemical environment, it was named as chemical shift. The shift in the position of PMR signals resulting through shielding and deshielding by circulation of electron in chemical bonds is called the Chemical shift.

The relative position of the signal along the frequency axis in the delta scale is a reflection of the extent of electron density around the different type of protons.

Chemical shift is expressed in the following two scales:

The tau $\left(\tau \right)$scale,$\tau =\left(10-\delta \right)$

The delta$\left(\delta \right)$scale

role="math" localid="1663237142507" $\delta =\frac{\left(ObservedshiftfromTMSinhertz\right)\times {10}^6}{\left(operatingfrequencyoftheinstrumentinhertz\right)}$

Convert the absorptions to δ units

In order to calculate delta value we need to divide chemical shift in hertz by the spectrometer frequency in MHz

(a) The absorption in delta unit can be converted as:

$$\begin{gathered} \delta =\frac{\left(ObservedshiftfromTMSinhertz\right)\times {10}^6}{\left(200MHz\right)} \\ \delta =\frac{\left(436\right)\times {10}^6}{\left(200\times {10}^{6}Hz\right)} \\ \delta =2.18ppm \end{gathered}$$

(b) The absorption in delta unit can be converted as:

$$\begin{gathered} \frac{\left(ObservedshiftfromTMSinhertz\right)\times {10}^6}{\left(200MHz\right)} \\ \delta =\frac{\left(956\right)\times {10}^6}{\left(200\times {10}^{6}Hz\right)} \\ \delta =4.78ppm \end{gathered}$$

(c) The absorption in delta unit can be converted as:

$$\begin{gathered} \frac{\left(ObservedshiftfromTMSinhertz\right)\times {10}^6}{\left(200MHz\right)} \\ \delta =\frac{\left(1504\right)\times {10}^6}{\left(200\times {10}^{6}Hz\right)} \\ \delta =7.52ppm \end{gathered}$$