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Solutions to Problems 209 50. The NMR of the product closely resembles that of the tertiary alcohol 2-methyl-2-butanol (Problem 47, spectrum C), but the signal for the OH group is missing, and the molecular formula has a Br instead of an OH. The product is 2-bromo-2-methylbutane, and the signals in the spectrum are assigned similarly. How does it form? Rearrangements! CH₃ CH₃ H CHCH₂CH₂OH CH₃ CH₃ CH₃ H CH₃ + CH₃ CH₃ CH₃ Br CH₃ 51. At 60 MHz, only the CH₂ next to CI (δ = 3.5) is clearly resolved. The very distorted CH₃ triplet is barely separated (δ = 0.9) from the other three CH₂'s, which overlap from δ = 1.0-2.0. At 500 MHz, the separation of signals in hertz is so much greater that the entire spectrum consists of nearly first-order signals: δ = 0.92 (triplet, CH₃), 1.36 (sextet, C4 CH₂), 1.42 (quintet, C3 CH₂), 1.79 (quintet, C2 CH₂), 3.53 (triplet, CH₂). Notice how the multiplets appear so much narrower at 500 MHz. In reality, the coupling constants are unchanged. However, recall that, at 60 MHz, the distance between δ = 0 and δ = 4 is only 240 Hz, whereas, at 500 MHz, the same 4-ppm spectrum width corresponds to 2000 Hz! So the 6- to 8-Hz splittings appear to spread out over a much larger chemical-shift range at 60 MHz than they do at 500 MHz. 52. Neighboring nonequivalent hydrogens split one another. When a hydrogen is split by two or more hydrogens that are themselves not equivalent, the coupling constants of those splittings may be different in magnitude, as illustrated by the spectrum of (Figures 10-25 and 26). (a) triplet of triplets, from large splitting by the two cis neighbors (Hc) and smaller splitting by the two trans neighbors quartet, from geminal splitting to the Hc on the same carbon and trans splittings to Hₐ and the Hc one carbon over, all of which are approximately the same in magnitude; doublet of triplets, the doublet splitting with the (cis) Hₐ being larger than the triplet splitting to the two Hb (one geminal and one trans). Br Hₐ vicinal (trans) Hb Hb geminal Hc Hc vicinal (cis) (b) No splitting. (c) quartet, from geminal splitting to and trans splittings to the two doublet of triplets, the doublet geminal splitting with Hₐ being smaller than the triplet splitting to the two cis Hc; doublet of doublets, the doublet splitting with the (cis) Hb being larger than that to the (trans) Hₐ Hc Br Br

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