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Chapter 13: Problem 1

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.

Short Answer

Expert verified
Short Answer: The ketone with the molecular formula \(C_{7}H_{14}O\) has two signals in its \(^{1}\text{H-NMR}\) spectrum, corresponding respectively to 11 and 3 hydrogens, based on the given line of integration (62 and 10 chart divisions). The proposed structural formula for this ketone is \(CH_3CH_2CH_2C(=O)CH_2CH(CH_3)_2\), which contains a carbonyl group, an alkyl group with 11 hydrogens, and an isopropyl group with 3 hydrogens.

Step by step solution

01

Analyze the given information

First, we need to evaluate the given information in the problem. We know that the \({ }^{1}\text{H-NMR}\) spectrum of the ketone has two signals. The line of integration of these signals rises 62 and 10 chart divisions, respectively.
02

Calculate the total number of hydrogens

According to the molecular formula \(C_7H_{14}O\), the ketone contains a total of 14 hydrogens.
03

Find the ratio of hydrogens giving rise to each signal

To calculate the number of hydrogens giving rise to each signal, we need to find the ratio of the rises in chart divisions. The ratio is 62:10, which simplifies to 31:5 after dividing both numbers by their greatest common divisor (2).
04

Distribute the hydrogens according to the ratio

Now that we know the ratio is 31:5, we can distribute the total number of hydrogens accordingly. Since there are 14 hydrogens, let's find the fractions corresponding to each part of the ratio: For the first signal, the fraction of hydrogens is \(\frac{31}{31+5}\). For the second signal, the fraction of hydrogens is \(\frac{5}{31+5}\). Now let's find the number of hydrogens corresponding to each signal: First signal: \(\frac{31}{31+5} \times 14 \approx 11\) hydrogens. Second signal: \(\frac{5}{31+5} \times 14 \approx 3\) hydrogens. So, the first signal corresponds to 11 hydrogens, and the second signal corresponds to 3 hydrogens.
05

Propose a structural formula for the ketone

We know the molecular formula is \(C_{7}H_{14}O\). The ketone functional group is characterized by having a carbonyl group (C=O) flanked by two carbon groups. Following this structure, we propose the following structural formula, which accounts for the number of hydrogens in each signal: \(CH_3CH_2CH_2C(=O)CH_2CH(CH_3)_2\) This ketone structure has a carbonyl group in the middle, with 11 hydrogens on the left side (an alkyl group) and three hydrogens on the right side (an isopropyl group). This proposal is consistent with the spectral information provided, as well as the molecular formula.

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Most popular questions from this chapter

The \({ }^{13} \mathrm{C}\) NMR spectrum of s-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.

\- The key relationship for NMR is that the difference in energy between the \(+\frac{1}{2}\) and \(-\frac{1}{2}\) nuclear spin states is proportional to the strength of the magnetic field experienced by a given nucleus.

Propose a structural formula for compound \(\mathrm{J}\), molecular formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\), consistent with the following \({ }^{1}\) H-NMR spectrum.

The natural abundance of \({ }^{19} \mathrm{C}\) is only \(1.1 \%\). Furthermore, its sensitivity in NMR specroscopy (a measure of the energy difference between a spin aligned with or against an applied magnetic field) is only \(1.6 \%\) that of \({ }^{1} \mathrm{H}\). What are the relative signal intensiies expected for the \({ }^{1} \mathrm{H}-\mathrm{NMR}\) and \({ }^{13} \mathrm{C}-\mathrm{NMR}\) spectra of the same sample of \(\mathrm{Si}\left(\mathrm{CH}_{5}\right)_{4}\) ?

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, \(\mathrm{C}_{8} \mathrm{H}_{11} \mathrm{NO}_{2}\)
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