Identify Compound [X] using Spectral Data

The problem asks us to identify compound [X], a monobromo ketone with molecular formula C$_5$H$_9$BrO, based on its $^1$H and $^{13}$C NMR data.

Structure Elucidation using NMR Data

Analyze the given spectral data for compound [X]:

• Molecular Formula: C$_5$H$_9$BrO. This indicates one degree of unsaturation (likely the C=O group).
• $^{13}$C NMR: $\delta$ 17, 37, 39, 210.
  • The signal at $\delta$ 210 ppm is characteristic of a ketone carbonyl carbon (C=O).
  • The signal at $\delta$ 17 ppm suggests methyl carbons (CH$_3$).
  • Signals at $\delta$ 37 and 39 ppm suggest aliphatic carbons (CH or CH$_2$).
  • The presence of 4 signals suggests some symmetry or overlap.
• $^1$H NMR:
  • $\delta$ 1.17 (d, 6H): Indicates two equivalent methyl groups attached to a CH group, forming an isopropyl fragment ((CH$_3$)$_2$CH-).
  • $\delta$ 3.02 (m, 1H): Corresponds to the CH proton of the isopropyl group, adjacent to the carbonyl group.
  • $\delta$ 4.10 (s, 2H): Indicates two equivalent protons on a CH$_2$ group, adjacent to an electronegative atom (like Br) and/or the carbonyl group, and not adjacent to any other protons (hence the singlet).

Proposing the Structure of [X]

Combining the NMR data and the molecular formula:

• The presence of (CH$_3$)$_2$CH- (3H + 1H = 4H) and a C=O group accounts for C$_3$H$_7$O.
• The singlet at $\delta$ 4.10 (2H) suggests a -CH$_2$- group.
• The formula requires C$_5$H$_9$BrO. We have accounted for C$_4$H$_9$O. We need one more carbon and one bromine.
• The structure must be BrCH$_2$-CO-CH(CH$_3$)$_2$. Let's verify this structure.
  • Formula: C$_5$H$_9$BrO. Correct.
  • $^{13}$C NMR: C=O (210 ppm), CH$_3$ (17 ppm, two equivalent carbons), CH (37-39 ppm), CH$_2$Br (37-39 ppm). Fits the observed 4 signals (CH and CH$_2$Br likely overlap or are very close).
  • $^1$H NMR:
    • (CH$_3$)$_2$CH-: Doublet (6H) at 1.17 ppm, Multiplet (1H) at 3.02 ppm. Matches.
    • BrCH$_2$-CO-: Singlet (2H) at 4.10 ppm. Matches.
• This structure corresponds to option 4.

Conclusion

The spectral data perfectly matches the structure 1-bromo-3-methylbutan-2-one (BrCH$_2$-CO-CH(CH$_3$)$_2$), which is represented by option 4.