Question

Question: The \(^{\bf{1}}{\bf{H}}\) NMR spectrum of \({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{OH}}\) recorded on a 500 MHz NMR spectrometer consists of two signals, one due to the \({\bf{C}}{{\bf{H}}_{\bf{3}}}\) protons at 1715 Hz and one due to the OH proton at 1830 Hz, both measured downfield from TMS. (a) Calculate the chemical shift of each absorption. (b) Do the \({\bf{C}}{{\bf{H}}_{\bf{3}}}\) protons absorb upfield or downfield from the OH proton?

Short answer

(a) The chemical shifts for \({\rm{C}}{{\rm{H}}_3}\) and OH protons are 3.43 ppm and 3.66 ppm, respectively.

(b) The \({\rm{C}}{{\rm{H}}_3}\) protons absorb upfield to the OH protons as the chemical shift of \({\rm{C}}{{\rm{H}}_3}\) is less than the chemical shift of OH protons.

Step-by-step solution

Formula of chemical shift

The chemical shift is given by the formula:

\({\bf{Chemical}}\;{\bf{shift}}\left( {\bf{\delta }} \right){\bf{ = }}\frac{{{\bf{Observed}}\;{\bf{\delta }}\;{\bf{downfiled}}\;{\bf{from}}\;{\bf{TMS}}\left( {{\bf{Hz}}} \right)}}{{{\bf{Frequency}}\;{\bf{of}}\;{\bf{the}}\;{\bf{NMR}}\left( {{\bf{MHz}}} \right)}}\)

Calculation of chemical shift in a

(a)The frequency of the NMR spectrometer is 500 MHz.

For \({\rm{C}}{{\rm{H}}_{\rm{3}}}\) protons, the observed chemical shift is 1715 Hz. Substitute the values in the above formula.

\(\begin{array}{c}{\rm{Chemical}}\;{\rm{shift}}\;{\rm{for}}\;{\rm{C}}{{\rm{H}}_3}{\rm{ = }}\frac{{{\rm{1715}}\;{\rm{Hz}}}}{{{\rm{500}}\;{\rm{MHz}}}}\\{\rm{\delta }} = 3.43\;{\rm{ppm}}\end{array}\)

For OH protons, the observed chemical shift is 1830 Hz. Substitute the values in the above formula.

\(\begin{array}{c}{\rm{Chemical}}\;{\rm{shift}}\;{\rm{for}}\;{\rm{OH = }}\frac{{{\rm{1830}}\;{\rm{Hz}}}}{{{\rm{500}}\;{\rm{MHz}}}}\\{\rm{\delta }} = 3.66\;{\rm{ppm}}\end{array}\)

Thus, the chemical shifts for \({\rm{C}}{{\rm{H}}_3}\) and OH protons are 3.43 ppm and 3.66 ppm, respectively.

Explanation for b

(b)The chemical shifts of\({\rm{C}}{{\rm{H}}_3}\)and OH protons are 3.43 ppm and 3.66 ppm, respectively.The chemical shift of\({\rm{C}}{{\rm{H}}_3}\)is less than that of OH protons.

The downfield value of chemical shift increases from right to left. Thus, the \({\rm{C}}{{\rm{H}}_3}\) protons absorb upfield to the OH protons.