Question

Explain how to distinguish between the members of each pair of constitutional isomers based on the number of signals in the proton-decoupled \({ }^{13} \mathrm{C}\)-NMR spectrum of each member.

Short answer

In order to distinguish between constitutional isomers based on their proton-decoupled \({ }^{13}\mathrm{C}\)-NMR spectrum, one must compare the number of signals that correspond to unique carbon environments in the isomers. If the number of signals differs, it suggests that the isomers have different carbon environments and therefore are distinct constitutional isomers. If the number of signals is the same, further spectroscopic methods may be required to differentiate between them.

Step-by-step solution

Understanding proton-decoupled \({ }^{13}\mathrm{C}\)-NMR

In proton-decoupled \({ }^{13}\mathrm{C}\)-NMR (Nuclear Magnetic Resonance) spectroscopy, we analyze the carbon-13 nuclei in a molecule, which allows us to obtain information about the carbon skeleton and functional groups of the molecule. The term "proton-decoupled" means that the effects of protons (hydrogen atoms) on the carbon-13 nucleus are suppressed, making it easier to analyze the carbon signals.

Understanding the concept of signals in the NMR spectrum

In an NMR spectrum, each peak or signal corresponds to a specific type of chemical environment of the nuclei being analyzed. In the case of proton-decoupled \({ }^{13}\mathrm{C}\)-NMR, each signal corresponds to a unique carbon atom's chemical environment. If there are identical or equivalent environments due to symmetry, they will give rise to a single signal.

Comparing signals to determine constitutional isomers

To distinguish constitutional isomers based on proton-decoupled \({ }^{13}\mathrm{C}\)-NMR spectra, we must compare the number of signals in the spectra of the isomers. If the number of signals in the NMR spectra differs, it indicates that the isomers have different carbon environments, and thus they are different constitutional isomers. On the other hand, if the number of signals is the same, other spectroscopic methods may be required to distinguish the isomers.

Example application (optional)

For instance, let's say we have two constitutional isomers of C4H10: n-butane (CH3-CH2-CH2-CH3) and isobutane ((CH3)3CH). In n-butane, there are two unique carbon environments: terminal (CH3) and internal (CH2) carbons. Hence, we expect two signals in its \({ }^{13}\mathrm{C}\)-NMR spectrum. In isobutane, there are two unique carbon environments as well: central (C surrounded by three CH3) and terminal (CH3). Again, we expect two signals in its \({ }^{13}\mathrm{C}\)-NMR spectrum. In this case, we cannot distinguish between n-butane and isobutane based solely on the number of signals in the NMR spectrum.