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Chapter 13: Problem 17

According to the \((n+1)\) rule, if a hydrogen has \(n\) hydrogens nonequivalent to it but equivalent among themselves on the same or adjacent atom(s), its \({ }^{1} \mathrm{H}-\mathrm{NMR}\) signal will be split into \((n+1)\) peaks. \- Splitting patterns are commonly referred to as singlets (s), doublets (d), triplets \((t)\), quartets \((q)\), quintets, and multiplets ( \(m\) ). \- The relative intensities of peaks in a multiplet can be predicted from an analysis of spin combinations for adjacent hydrogens or from the mnemonic device called Pascal's triangle. \- A coupling constant \((J)\) is the distance between adjacent peaks in a multiplet and is reported in hertz \((\mathrm{Hz})\). The value of \(J\) depends only on internal fields within a molecule and is independent of the spectrometer field.

Short Answer

Expert verified
Short Answer: In proton NMR spectroscopy, the (n+1) rule, splitting patterns, relative intensities, and coupling constants offer valuable information about molecular structure. The (n+1) rule predicts the splitting pattern of a hydrogen signal, while splitting patterns indicate the number of peaks and are named accordingly (e.g., singlet, doublet, etc.). Relative intensities, given by Pascal's Triangle, help determine peak intensities in a multiplet, and coupling constants (J), reported in hertz (Hz), express the distance between adjacent peaks in a multiplet.

Step by step solution

01

Understanding the \((n+1)\) Rule

The \((n+1)\) rule helps predict the splitting pattern of a hydrogen (proton) signal in an NMR spectrum. If a hydrogen atom has \(n\) non-equivalent but equivalent among themselves hydrogens on the same or adjacent atoms, its \({}^{1} \mathrm{H} - \mathrm{NMR}\) signal will be split into \((n+1)\) peaks.
02

Splitting Patterns and Terminology

Different terminology is used to describe the splitting pattern, depending on the number of peaks: 1. Singlet (s) - 1 peak 2. Doublet (d) - 2 peaks 3. Triplet (t) - 3 peaks 4. Quartet (q) - 4 peaks 5. Quintet - 5 peaks 6. Multiplet (m) - more than 5 peaks
03

Relative Intensities and Pascal's Triangle

The relative intensities of peaks in a multiplet can be predicted using either an analysis of spin combinations for adjacent hydrogens or Pascal's Triangle - a triangular array of numbers. Each number is the sum of the two numbers directly above it, with the outer edges of the triangle filled with 1's. The intensity ratios of the peaks of a multiplet can be obtained from the rows in Pascal's Triangle. For example, the intensity ratio for a quartet would be 1:3:3:1 (from the 4th row of Pascal's Triangle).
04

Coupling Constant (J)

The coupling constant, denoted by \(J\), is the distance between adjacent peaks in a multiplet. It is reported in hertz \((\mathrm{Hz})\). \(J\) depends only on the internal fields within a molecule and is independent of the spectrometer field. Now you have learned about the \((n+1)\) rule, splitting patterns, relative intensities, and coupling constants. You can apply these concepts to analyze and understand \({}^{1} \mathrm{H} - \mathrm{NMR}\) spectra in the future.

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Most popular questions from this chapter

The experimental conditions required to cause nuclei to resonate are affected by the local chemical and magnetic environments. \- Electrons around a hydrogen or carbon create local magnetic fields that shield the nuclei of these atoms from the applied field. \- Any factor that increases the exposure of nuclei to an applied field is said to deshield them and shifts their signal downfield to a larger \(\delta\) value. \- Conversely, any factor that decreases the exposure of nuclei to an applied field is said to shield them and shifts their signal upfield to a smaller \(\delta\) value.

The C-NMR spectrum of 3-methyl-2-butanol shows signals at \(\delta 17.88\left(\mathrm{CH}_{3}\right), 18.16\) \(\left(\mathrm{CH}_{3}\right), 20.01\left(\mathrm{CH}_{3}\right), 35.04\) (carbon-3), and \(72.75\) (carbon-2). Account for the fact that each methyl group in this molecule gives a different signal.

Compound \(\mathrm{K}\), molecular formula \(\mathrm{C}_{8} \mathrm{H}_{14} \mathrm{O}\), readily undergoes acid-catalyzed dehydration when warmed with phosphoric acid to give compound L, molecular formula \(\mathrm{C}_{6} \mathrm{H}_{12}\), as the major organic product. The \({ }^{1} \mathrm{H}\)-NMR spectrum of compound \(\mathrm{K}\) shows signals at \(\delta 0.90(\mathrm{t}, 6 \mathrm{H}), 1.12(\mathrm{~s}, 3 \mathrm{H}), 1.38(\mathrm{~s}, 1 \mathrm{H})\), and \(1.48(\mathrm{q}, 4 \mathrm{H})\). The \({ }^{19} \mathrm{C}-\mathrm{NMR}\) spectrum of compound \(\mathrm{K}\) shows signals at \(\delta 72.98,33.72,25.85\), and 8.16. Deduce the structural formulas of compounds \(\mathrm{K}\) and \(\mathrm{L}\).

The area of a \({ }^{1} \mathrm{H}-\mathrm{NMR}\) signal is proportional to the number of equivalent hydrogens giving rise to that signal.

Compound M, molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}\), readily decolorizes \(\mathrm{Br}_{2}\) in \(\mathrm{CCl}_{4}\) and is converted by \(\mathrm{H}_{2} / \mathrm{Ni}\) into compound \(\mathrm{N}\), molecular formula \(\mathrm{C}_{3} \mathrm{H}_{12} \mathrm{O}\). Following is the \({ }^{1} \mathrm{H}-\mathrm{NMR}\) spectrum of compound \(\mathrm{M}\). The \({ }^{19} \mathrm{C}-\mathrm{NMR}\) spectrum of compound \(\mathrm{M}\) shows signals at \(\delta 146.12,110.75,71.05\), and \(29.88\). Deduce the structural formulas of compounds \(M\) and N.
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