Question

Question: Rank each group of protons in order of increasing chemical shift.

a.

b.

Short answer

a. \({{\rm{H}}_{\rm{c}}}\;\langle \;{{\rm{H}}_{\rm{a}}}\;\langle \;{{\rm{H}}_{\rm{b}}}\)

b.\({{\rm{H}}_{\rm{c}}}\;\langle \;{{\rm{H}}_{\rm{a}}}\;\langle \;{{\rm{H}}_{\rm{b}}}\)

Step-by-step solution

Chemical shift

The difference in the absorption position of a particular proton due to variation in its chemical environment from that of an isolated proton is the chemical shift of that proton.It is usually represented by\(\delta \)-scale and \(\tau \)-scale.

Equation for chemical shift

A chemical shift in terms of frequency can be represented by the equation:

\(\delta = \frac{{{\nu _{sample}} - {\nu _{reference}}}}{{{\nu _{sample}}}} \times {10^6}\)

Ranking each group of protons in order of increasing chemical shift

Representation of different protons in a.

Since \({{\rm{H}}_{\rm{c}}}\)is bonded to the \({\rm{s}}{{\rm{p}}^{\rm{3}}}\;{\rm{C}}\)\({{\rm{H}}_{\rm{c}}}\), the protons are highly shielded, and this gives them the lowest chemical shift value. \({{\rm{H}}_{\rm{a}}}\;\)is bonded to an \({\rm{sp}}\;{\rm{C}}\), so they are shielded, giving them a chemical shift value higher than that of \({{\rm{H}}_{\rm{c}}}\). And the \({{\rm{H}}_{\rm{b}}}\)protons are deshielded as they are bonded to the \({\rm{s}}{{\rm{p}}^{\rm{2}}}\;{\rm{C}}\), which gives them a higher chemical shift value. So, the order of increasing chemical shift value is, \({{\rm{H}}_{\rm{c}}}\;\langle \;{{\rm{H}}_{\rm{a}}}\;\langle \;{{\rm{H}}_{\rm{b}}}\).

Representation of different protons in b.

Since \({{\rm{H}}_{\rm{c}}}\)is bonded to the \({\rm{s}}{{\rm{p}}^{\rm{3}}}\;{\rm{C}}\)\({{\rm{H}}_{\rm{c}}}\) , the protons are highly shielded and this gives them the lowest chemical shift value. \({{\rm{H}}_{\rm{a}}}\;\)is slightly deshielded as the \({\rm{C}}{{\rm{H}}_3}\) group is bonded to a C=O, and this gives them a chemical shift value higher than that of \({{\rm{H}}_{\rm{c}}}\). And the \({{\rm{H}}_{\rm{b}}}\)protons are deshielded as the \({\rm{C}}{{\rm{H}}_2}\)group is bonded to an O atom, which gives them a higher chemical shift value. So, the order of increasing chemical shift value is,\({{\rm{H}}_{\rm{c}}}\;\langle \;{{\rm{H}}_{\rm{a}}}\;\langle \;{{\rm{H}}_{\rm{b}}}\).