Question 1 of 13: Structure Elucidation from IR/ 13 C NMR (C 4 H 6 O 2 )

Question 1: Structure Elucidation from IR/¹³C NMR (C₄H₆O₂)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Framing constraint. Every part shares the same formula, so the degree of unsaturation is fixed before any spectrum is read: $$\mathrm{DoU=\dfrac{2(4)+2-6}{2}=2}$$ Two degrees of unsaturation must be distributed, in each part, among rings, C=C, C≡C and C=O — the IR carbonyl region and the ¹³C shift ranges then say exactly how.

1. (a) A strained-ring ketone bearing a symmetric β-hydroxyl — 3-hydroxycyclobutan-1-one. 214 ppm is deep in the ketone ¹³C window (acyclic/6-ring ketones sit near 205–212; four-membered-ring ketones are pushed further downfield by ring strain), and 1745 cm^-1 is likewise elevated relative to the ~1715 cm^-1 of an unstrained ketone — both point at a small-ring ketone, not an ester (esters/lactones sit at 165–178 ppm, nowhere near 214). That uses one DoU and one oxygen; the second oxygen must be a non-carbonyl –OH (no second carbonyl signal is reported), and the second DoU must be the ring that carries it. Only three ¹³C signals are reported for four carbons — a direct symmetry clue: 3-hydroxycyclobutan-1-one has a mirror plane through C1 and C3, making the two α-CH₂ carbons (C2, C4) equivalent by symmetry. That gives exactly three unique carbons: the ring carbonyl (214), the CHOH (58), and the equivalent pair of α-CH₂'s (41).
   3-hydroxycyclobutan-1-one — C1 carbonyl and C3 mirror plane make C2≡C4
2. (b) A symmetric internal alkyne diol — but-2-yne-1,4-diol. No carbonyl band is reported at all — only a broad O–H stretch at 3300 cm^-1 — and neither ¹³C shift (62, 79) falls in the alkene (100–145) or carbonyl (165–220) windows, so both degrees of unsaturation must be a single C≡C (a triple bond alone accounts for DoU=2 with no ring needed). Alkyne sp-carbons resonate in exactly the 65–90 ppm range, matching 79 ppm, while propargylic CH₂OH carbons match 62 ppm. Only two signals for four carbons again signals molecular symmetry: HOCH₂–C≡C–CH₂OH has a C₂ axis relating C1/C4 and C2/C3. Why no C≡C stretch is mentioned: a symmetric, internally-substituted alkyne has (near) zero change in dipole moment along the stretch, making the C≡C IR band weak-to-absent — a classic diagnostic absence, not an omission.
   but-2-yne-1,4-diol — C2-symmetric, alkyne sp-carbons ≈79 ppm
3. (c) A five-membered ring lactone — γ-butyrolactone (oxolan-2-one). 178 ppm sits squarely in the ester/lactone carbonyl window (165–180), not the ketone window used in (a); combined with the ring (DoU=2 total = one ring + one C=O), and no second, separate oxygen signal needed (the lactone's second oxygen is the ring C–O–C(=O), already inside the same functional group), the four-carbon, two-oxygen budget is exactly satisfied by an unsubstituted γ-lactone: O=C–CH₂–CH₂–CH₂–O (ring closed). The remaining three ¹³C shifts (86, 40, 27) are the ring CH₂'s — the one attached directly to the ring oxygen is the most deshielded of the three (an O–CH₂ adjacent to an ester oxygen), the one α to the carbonyl and the middle CH₂ fill the remaining upfield values. 770 cm^-1 is a ring/C–O–C skeletal deformation in the fingerprint region — secondary evidence, with the carbonyl shift and the DoU/formula budget carrying the actual assignment.
   γ-butyrolactone — carbonyl 178 ppm, ring O–C=O supplies both oxygens
4. (d) A conjugated (α,β-unsaturated) ester — methyl acrylate. Two IR bands in the carbonyl/alkene region (1720 and 1650 cm^-1, both strong) is the signature of an enone/enoate: conjugation lowers the C=O stretch from the ~1740 cm^-1 of a saturated ester down to ~1720, and simultaneously raises the intensity (and lowers the frequency somewhat) of the conjugated C=C stretch into the 1620–1660 range. The ¹³C data confirm it directly: 165 ppm (conjugated ester carbonyl, slightly upfield of a saturated ester's ~170 due to conjugative donation from the alkene), 131 and 133 ppm (the two vinyl carbons, both sp², of CH₂=CH–), and 54 ppm (the OCH₃). DoU=2 is exactly C=C + C=O, no ring. Structure: CH₂=CH–CO₂CH₃ (methyl prop-2-enoate).
   methyl acrylate — conjugated ester, two IR bands (1720, 1650 cm⁻¹)