Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 19

When a hydrogen nucleus is coupled to more than one set of adjacent hydrogen nuclei, the couplings combine. \- In the general case, if a hydrogen nucleus is coupled to a set of \(n\) hydrogen nuclei on one side and a set of \(m\) hydrogen nuclei on the other, the signal will be split into a maximum of \((n+1)(m+1)\) peaks. \- In molecules that are rigid, for example alkenes or cyclic molecules, all the \((n+1)(m+1)\) peaks can often be seen. \- However, because coupling constants can be similar, especially in flexible molecules, this splitting can simplify to a number of observed peaks that is equal to the number of adjacent H atoms \(A 1\), regardless of patterns of equivalence.

Short Answer

Expert verified
Question: Explain how the number of peaks in the coupling pattern of a hydrogen nucleus coupled to n hydrogen nuclei on one side and m hydrogen nuclei on the other side can be influenced by molecule rigidity, coupling constants, and patterns of equivalence. Answer: The number of peaks in the coupling pattern can be up to (n+1)(m+1), but it is influenced by molecule rigidity, coupling constants, and patterns of equivalence. In rigid molecules, all (n+1)(m+1) peaks are typically observed, while in flexible molecules with similar coupling constants, the observed peaks might simplify to just the number of adjacent hydrogen atoms (A 1).

Step by step solution

01

Understand Coupling Combinations in Hydrogen Nuclei

In general, when a hydrogen nucleus is coupled to \(n\) hydrogen nuclei on one side and \(m\) hydrogen nuclei on the other side, the signal will be split into a maximum of \((n+1)(m+1)\) peaks, due to the interactions between the different hydrogen nuclei and their magnetic environment.
02

Determine the Influence of Rigidity

Molecule rigidity plays a significant role in the observed splitting pattern. In rigid molecules, such as alkenes or cyclic molecules, it is common to observe all \((n+1)(m+1)\) possible peaks in the splitting pattern due to the restricted flexibilities and limited range of spatial orientations that the molecule can adopt.
03

Consider the Effect of Coupling Constants

Coupling constants can affect the observed splitting patterns, especially in flexible molecules. When the coupling constants are similar, the splitting pattern might be simplified and might not show all the possible \((n+1)(m+1)\) peaks. In such cases, the number of observed peaks might be equal to the number of adjacent hydrogen atoms (\(A 1\)), regardless of patterns of equivalence.
04

Summarize the Key Points

In conclusion, the number of peaks in the coupling pattern of a hydrogen nucleus coupled to \(n\) hydrogen nuclei on one side and \(m\) hydrogen nuclei on the other side can be influenced by the molecule rigidity, similarity in coupling constants, and patterns of equivalence. In general, the number of peaks can be up to \((n+1)(m+1)\), while in some cases, depending on the molecular properties and interactions, it can simplify to just the number of adjacent hydrogen atoms (\(A 1\)).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The percent scharacter of carbon participating in a \(\mathrm{C}-\mathrm{H}\) bond can be established by measuring the \({ }^{13} \mathrm{C}-{ }^{1} \mathrm{H}\) coupling constant and using the relationship $$ \text { Percent scharacter }=0.2 \mathrm{~J}\left({ }^{13} \mathrm{C}-{ }^{1} \mathrm{H}\right) $$ The \({ }^{15} \mathrm{C}-{ }^{1} \mathrm{H}\) coupling constant observed for methane, for example, is \(125 \mathrm{~Hz}\), which gives \(25 \%\) scharacter, the value expected for an \(s p^{3}\) hybridized carbon atom. (a) Calculate the expected \({ }^{13} \mathrm{C}-{ }^{1} \mathrm{H}\) coupling constant in ethylene and acetylene. (b) In cyclopropane, the \({ }^{19} \mathrm{C}-{ }^{1} \mathrm{H}\) coupling constant is \(160 \mathrm{~Hz}\). What is the hybridization of carbon in cyclopropane?

The line of integration of the two signals in the \({ }^{1} \mathrm{H}-\mathrm{NMR}\) spectrum of a ketone with the molecular formula \(\mathrm{C}_{7} \mathrm{H}_{14} \mathrm{O}\) rises 62 and 10 chart divisions, respectively. Calculate the number of hydrogens giving rise to each signal, and propose a structural formula for this ketone.

Calculate the index of hydrogen deficiency of these compounds. (a) Aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) (b) Ascorbic acid (vitamin \(\mathrm{C}\) ), \(\mathrm{C}_{6} \mathrm{H}_{g} \mathrm{O}_{6}\) (c) Pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\) (d) Urea, \(\mathrm{CH}_{4} \mathrm{~N}_{2} \mathrm{O}\) (e) Cholesterol, \(\mathrm{C}_{2} \mathrm{H}_{45} \mathrm{O}\) (f) Dopamine, \(\mathrm{C}_{8} \mathrm{H}_{11} \mathrm{NO}_{2}\)

\({ }^{13} \mathbf{C}-\mathrm{NMR}\) is like \({ }^{1} \mathrm{H}-\mathrm{NMR}\), except the nuclear spins of \({ }^{13} \mathrm{C}\) nuclei are being analyzed. \- \({ }^{13}\) C-NMR spectra are commonly recorded in a hydrogen-decoupled instrumental mode. In this mode, all \({ }^{13} \mathrm{C}\) signals appear as singlets. \- The number of different signals in a \({ }^{13} \mathrm{C}-\mathrm{NMR}\) spectrum tell you how many nonequivalent carbon atoms are in a molecule. \- \({ }^{13}\) CNMR chemical shifts tell you what kind of carbon atoms are present.

The \({ }^{1} \mathrm{H}-\mathrm{NMR}\) of compound \(\mathrm{R}, \mathrm{C}_{6 i} \mathrm{H}_{14} \mathrm{O}\), consists of two signals: \(\delta 1.1\) (doublet) and \(\delta 3.6\) (septet) in the ratio \(6: 1\). Propose a structural formula for compound \(R\) consistent with this information.
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free