Question

Draw a splitting diagram for H_bwere

a.J_ba= 12 Hz andJ_bc= 6Hz b.J_ba= 12 Hz andJ_bc= 12Hz

Short answer

The splitting of the H_b proton is shown below.

a.

b.

Step-by-step solution

Step-by-Step SolutionStep 1: Splitting of diagram (a) with different coupling constant values

Splitting diagram (a)

The signal for the H_b proton of the above diagram is a doublet of a doublet. The H_bsignal split into a doublet by H_a proton, and these resulted peaks split into a doublet by H_c proton. In the given diagram, the two sets H_a and H_b are non-equivalent protons and have different coupling constant values. Thus, multiplicity of signal can be determined using (N_a+1) (N_b+1) rule, i.e., (1+1) (1+1) = 4.

Thus, two non-equivalent protons split into two doublets, resulting in a doublet of doublet signal for the H_a proton.

Splitting of diagram (b) with same coupling constant values

The signal for the H_b proton of the above diagram is a triplet. The diagram shows that the two sets, H_a and H_b, are non-equivalent protons and have the same coupling constant values. Thus, the two different H_a and H_b split a signal Ha the multiplicity can be calculated using the (N+1) rule, i.e., (2+1) = 3.

Thus, two non-equivalent protons split into triplets because of the same coupling constant values.

Splitting diagram (b)