Question

The following 1H NMR absorptions were obtained on a spectrometer

operating at 300 MHz. Convert the chemical shifts from $\delta$units to hertz

downfield from TMS.

(a)2.1(b)3.45(c)6.30(d)7.70$\delta$

Short answer

(a) 2.1 $\mathrm{\delta }$

$$\begin{gathered} 2.1\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 630\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

(b) 3.45$\mathrm{\delta }$

$$\begin{gathered} 3.45\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 1035\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

(c) 6.30$\mathrm{\delta }$

$$\begin{gathered} 6.30\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 1890\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

(d) 7.70$\mathrm{\delta }$

$$\begin{gathered} 7.70\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 2130\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

Step-by-step solution

NMR spectroscopy

Spectroscopy is the branch of science which deals with interaction of matter with electromagnetic radiations. NMR stands for Nuclear Magnetic Resonance spectroscopy. This is the technique for determining the structure of organic molecules.

• 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 proto 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($\mathrm{\tau }$) scale, $\tau =(10-\delta )$

The delta $\mathrm{\delta }$scale =$\mathrm{\delta }=\frac{(\mathrm{Observed}\mathrm{shift}\mathrm{from}\mathrm{TMS}\mathrm{in}\mathrm{Hertz})\times {10}^6}{(\mathrm{operating}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{instrument}\mathrm{in}\mathrm{hertz})}$

Convert chemical shifts from δ units to hertz downfield from TMS

We know that,

In order to determine the delta shift of these peaks, we need to divide chemical shift in Hz by the spectrometer frequency in MHz

$\mathrm{\delta }=\frac{(\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\mathrm{Hertz})}{(\mathrm{operating}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{instrument}\mathrm{in}\mathrm{hertz})}$

As spectrometer is operating at frequency 300 MHz given, this gives

$\mathrm{\delta }\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\mathrm{Hz}$

So, therefore

(a) 2.1

$$\begin{gathered} 2.1\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 630\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

(b) 3.45

$$\begin{gathered} 3.45\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 1035\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

(c) 6.30

$$\begin{gathered} 6.30\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 1890\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$

(d) 7.70

$$\begin{gathered} 7.70\times 300\mathrm{MHz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \\ 2130\mathrm{Hz}=\mathrm{Observed}\mathrm{chemical}\mathrm{shift}\mathrm{in}\left(\mathrm{Hz}\right) \end{gathered}$$