Q8(c). Equivalent protons and number of 1H NMR signals

Reading of the question: “p-ethylbenzene” has no para partner; it is read as p-diethylbenzene (1,4-diethylbenzene). p-Ethyltoluene, another possible reading, is noted in point 3.

Introduction. Protons that are interchanged by a symmetry operation of the molecule (or by fast rotation) are chemically equivalent and give one signal. Count the sets of equivalent protons; each set is labelled with a letter.

Scheme: Letters mark one proton of each equivalent set.

1. Mesitylene (1,3,5-trimethylbenzene) has threefold symmetry: all three methyls are equivalent and all three ring H are equivalent: two singlets in the ratio 9: 3 (3: 1). No coupling between them.
2. p-Diethylbenzene: a mirror plane and twofold axes make both ethyl groups equivalent and all four ring H equivalent: three signals, CH₃ triplet, CH₂ quartet, ArH singlet (6: 4: 4).
3. If the compound is p-ethyltoluene, there are five sets: CH₃ of ethyl (t), CH₂ (q), Ar–CH₃ (s), and two kinds of ring H (an AA'BB' pair of doublets).
4. Isopropylbenzene (cumene): the two methyls are equivalent (a, doublet, 6H) and couple to the methine H (b, septet, 1H). The ring has three kinds of H (ortho c, meta d, para e) in the ratio 2: 2: 1, so strictly five sets; at ordinary field their shifts nearly coincide and the ring appears as one 5H multiplet, giving three observed signals (6: 1: 5).

Conclusion. (i) 2 signals; (ii) 3 signals (as p-diethylbenzene); (iii) 5 sets of equivalent H, seen as 3 signals (doublet, septet, aromatic multiplet) at routine field.

Application. Counting signals and their integrals distinguishes isomeric aromatic hydrocarbons (for example the three trimethylbenzenes or the xylenes) in petroleum fractions without chromatography.