CHAPTER CONTENTS - 13.2 The Nature of NMR Absorptions

From the description thus far, you might expect all ${ }^{1} \mathrm{H}$ nuclei in a molecule to absorb energy at the same frequency and all ${ }^{13} \mathrm{C}$ nuclei to absorb at the same frequency. If so, we would observe only a single NMR absorption signal in the ${ }^{1} \mathrm{H}$ or ${ }^{13} \mathrm{C}$ spectrum of a molecule, a situation that would be of little use. In fact, the absorption frequency is not the same for all ${ }^{1} \mathrm{H}$ or all ${ }^{13} \mathrm{C}$ nuclei.


All nuclei in molecules are surrounded by electrons. When an external magnetic field is applied to a molecule, the electrons moving around nuclei set up tiny local magnetic fields of their own. These local magnetic fields act in opposition to the applied field so that the effective field actually felt by the nucleus is a bit weaker than the applied field.


$$
B_{\text {effective }}=B_{\text {applied }}=B_{\text {local }}
$$


In describing this effect of local fields, we say that nuclei experience shielding from the full effect of the applied field by the surrounding electrons. Because each chemically distinct nucleus in a molecule is in a slightly different electronic environment, each nucleus is shielded to a slightly different extent and the effective magnetic field felt by each is slightly different. These tiny differences in the effective magnetic fields experienced by different nuclei can be detected, and we thus see a distinct NMR signal for each chemically distinct ${ }^{13} \mathrm{C}$ or ${ }^{1} \mathrm{H}$ nucleus in a molecule. As a result, an NMR spectrum effectively maps the carbon-hydrogen framework of an organic molecule. With practice, it's possible to read this map and derive structural information.


FIGURE 13.4 shows both the ${ }^{1} \mathrm{H}$ and the ${ }^{13} \mathrm{C}$ NMR spectra of methyl acetate, $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{CH}_{3}$. The horizontal axis shows the effective field strength felt by the nuclei, and the vertical axis indicates the intensity of absorption of rf energy. Each peak in the NMR spectrum corresponds to a chemically distinct ${ }^{1} \mathrm{H}$ or ${ }^{13} \mathrm{C}$ nucleus in the molecule. Note that NMR spectra are formatted with the zero absorption line at the bottom, whereas IR spectra are formatted with the zero absorption line at the top; Section 12.5 . Note also that ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ spectra can't be observed simultaneously on the same spectrometer because different amounts of energy are required to spinflip the different kinds of nuclei. The two spectra must be recorded separately.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0411.jpg?height=1085&width=1429&top_left_y=1406&top_left_x=348)

FIGURE 13.4 (a) The ${ }^{\mathbf{1}} \mathrm{H}$ NMR spectrum and (b) the proton-decoupled ${ }^{13} \mathrm{C}$ NMR spectrum of methyl acetate, $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{CH}_{3}$. The small peak
labeled "TMS" at the far right of each spectrum is a calibration peak, as explained in the next section.
The ${ }^{13}$ C NMR spectrum of methyl acetate in FIGURE 13.4b shows three peaks, one for each of the three chemically distinct carbon atoms in the molecule. The ${ }^{1} \mathrm{H}$ NMR spectrum in FIGURE 13.4a shows only two peaks, however, even though methyl acetate has six hydrogens. One peak is due to the $\mathrm{CH}_{3} \mathrm{C}=\mathrm{O}$ hydrogens, and the other to the $-\mathrm{OCH}_{3}$ hydrogens. Because the three hydrogens in each methyl group have the same electronic environment, they are shielded to the same extent and are said to be equivalent. Chemically equivalent nuclei always show the same absorption. The two methyl groups themselves, however, are not equivalent, so the two sets of hydrogens absorb at different positions.


The operation of a basic NMR spectrometer is illustrated in FIGURE 13.5. An organic sample is dissolved in a suitable solvent (usually deuteriochloroform, $\mathrm{CDCl}_{3}$, which has no hydrogens) and placed in a thin glass tube between the poles of a magnet. The strong magnetic field causes the ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ nuclei in the molecule to align in one of the two possible orientations, and the sample is irradiated with rf energy. If the frequency of the rf irradiation is held constant and the strength of the applied magnetic field is varied, each nucleus comes into resonance at a slightly different field strength. A sensitive detector monitors the absorption of rf energy, and its electronic signal is then amplified and displayed as a peak.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0412.jpg?height=657&width=1237&top_left_y=948&top_left_x=433)

FIGURE 13.5 Schematic operation of a basic NMR spectrometer. A thin glass tube containing the sample solution is placed between the poles of a strong magnet and irradiated with rf energy.


NMR spectroscopy differs from IR spectroscopy (Section 12.6-Section 12.8) in that the timescales of the two techniques are quite different. The absorption of infrared energy by a molecule giving rise to a change in vibrational amplitude is an essentially instantaneous process (about $10^{-13} \mathrm{~s}$ ), but the NMR process is much slower (about $10^{-3} \mathrm{~s}$ ). This difference in timescales between IR and NMR spectroscopy is analogous to the difference between cameras operating at very fast and very slow shutter speeds. The fast camera (IR) takes an instantaneous picture and freezes the action. If two rapidly interconverting species are present, IR spectroscopy records the spectrum of both. The slow camera (NMR), however, takes a blurred, time-averaged picture. If two species interconverting faster than $10^{3}$ times per second are present in a sample, NMR records only a single, averaged spectrum, rather than separate spectra of the two discrete species.


Because of this blurring effect, NMR spectroscopy can be used to measure the rates and activation energies of very fast chemical processes. In cyclohexane, for example, a ring-flip (Section 4.6) occurs so rapidly at room temperature that axial and equatorial hydrogens can't be distinguished by NMR; only a single, averaged ${ }^{1} \mathrm{H}$ NMR absorption is seen for cyclohexane at $25^{\circ} \mathrm{C}$. At $-90^{\circ} \mathrm{C}$, however, the ring-flip is slowed down enough that two absorption peaks are visible, one for the six axial hydrogens and one for the six equatorial hydrogens. Knowing the temperature and the rate at which signal blurring begins to occur, it's possible to calculate that the activation energy for the cyclohexane ring-flip is $45 \mathrm{~kJ} / \mathrm{mol}(10.8 \mathrm{kcal} / \mathrm{mol})$.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0413.jpg?height=294&width=887&top_left_y=189&top_left_x=616)


PROBLEM 2-Chloropropene shows signals for three kinds of protons in its ${ }^{1}$ H NMR spectrum. Explain. 13-3


CHAPTER CONTENTS - 13.3 Chemical Shifts

NMR spectra are displayed on charts that show the applied field strength increasing from left to right (FIGURE 13.6). Thus, the left part of the chart is the low-field, or downfield, side, and the right part is the high-field, or upfield, side. Nuclei that absorb on the downfield side of the chart require a lower field strength for resonance, implying that they have less shielding. Nuclei that absorb on the upfield side require a higher field strength for resonance, implying that they have more shielding.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0413.jpg?height=510&width=1397&top_left_y=897&top_left_x=359)

FIGURE 13.6 The NMR chart. The downfield, deshielded side is on the left, and the upfield, shielded side is on the right. The tetramethylsilane (TMS) absorption is used as reference point.


CHAPTER CONTENTS - 13.3 Chemical Shifts

To define the position of an absorption, the NMR chart is calibrated and a reference point is used. In practice, a small amount of tetramethylsilane $\left[\mathrm{TMS} ;\left(\mathrm{CH}_{3}\right)_{4} \mathrm{Si}\right]$ is added to the sample so that a reference absorption peak is produced when the spectrum is run. TMS is used as reference for both ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ measurements because in both cases it produces a single peak that occurs upfield of other absorptions normally found in organic compounds. The ${ }^{1} \mathrm{H}$ and ${ }^{13} \mathrm{C}$ spectra of methyl acetate in FIGURE 13.4 have the TMS reference peak indicated.


CHAPTER CONTENTS - 13.3 Chemical Shifts

The position on the chart at which a nucleus absorbs is called its chemical shift. The chemical shift of TMS is set as the zero point, and other absorptions normally occur downfield, to the left on the chart. NMR charts are calibrated using an arbitrary scale called the delta ( $\boldsymbol{\delta}$ ) scale, where $1 \delta$ equals 1 part-per-million ( 1 ppm ) of the spectrometer operating frequency. For example, if we were measuring the ${ }^{1} \mathrm{H}$ NMR spectrum of a sample using an instrument operating at $200 \mathrm{MHz}, 1 \delta$ would be 1 part per million of $200,000,000 \mathrm{~Hz}$, or 200 Hz . If we were measuring the spectrum using a 500 MHz instrument, $1 \delta=500 \mathrm{~Hz}$. The following equation can be used for any absorption:


CHAPTER CONTENTS - 13.3 Chemical Shifts

$$
\delta=\frac{\text { Observed chemical shift (number of Hz away from TMS) }}{\text { Spectrometer frequency in } \mathrm{MHz}}
$$


CHAPTER CONTENTS - 13.3 Chemical Shifts

Although this method of calibrating NMR charts may seem complex, there's a good reason for it. As we saw earlier, the rf frequency required to bring a given nucleus into resonance depends on the spectrometer's magnetic field strength. But because there are many different kinds of spectrometers with many different magnetic field strengths available, chemical shifts given in frequency units ( Hz ) vary from one instrument to another. Thus, a resonance that occurs at 120 Hz downfield from TMS on one spectrometer might occur at 600 Hz downfield from TMS on another spectrometer with a more powerful magnet.


CHAPTER CONTENTS - 13.3 Chemical Shifts

By using a system of measurement in which NMR absorptions are expressed in relative terms (parts per million relative to spectrometer frequency) rather than absolute terms (Hz), it's possible to compare spectra obtained
on different instruments. The chemical shift of an NMR absorption in $\delta$ units is constant, regardless of the operating frequency of the spectrometer. A ${ }^{1} \mathrm{H}$ nucleus that absorbs at $2.0 \delta$ on a 200 MHz instrument also absorbs at $2.0 \delta$ on a 500 MHz instrument.


CHAPTER CONTENTS - 13.3 Chemical Shifts

The range in which most NMR absorptions occur is quite narrow. Almost all ${ }^{1} \mathrm{H}$ NMR absorptions occur from 0 to $10 \delta$ downfield from the proton absorption of TMS, and almost all ${ }^{13} \mathrm{C}$ absorptions occur from 1 to $220 \delta$ downfield from the carbon absorption of TMS. Thus, there is a likelihood that accidental overlap of nonequivalent signals will occur. The advantage of using an instrument with higher field strength (say, 500 $\mathrm{MHz})$ rather than lower field strength $(200 \mathrm{MHz})$ is that different NMR absorptions are more widely separated at the higher field strength. The chances that two signals will accidentally overlap are therefore lessened, and interpretation of spectra becomes easier. For example, two signals that are only 20 Hz apart at $200 \mathrm{MHz}(0.1$ ppm) are 50 Hz apart at 500 MHz (still 0.1 ppm ).
PROBLEM The following ${ }^{1} \mathrm{H}$ NMR peaks were recorded on a spectrometer operating at 200 MHz . Convert each 13-4 into $\delta$ units.
(a) $\mathrm{CHCl}_{3} ; 1454 \mathrm{~Hz}$
(b) $\mathrm{CH}_{3} \mathrm{Cl} ; 610 \mathrm{~Hz}$
(c) $\mathrm{CH}_{3} \mathrm{OH} ; 693 \mathrm{~Hz}$
(d) $\mathrm{CH}_{2} \mathrm{Cl}_{2} ; 1060 \mathrm{~Hz}$

PROBLEM When the ${ }^{1} \mathrm{H}$ NMR spectrum of acetone, $\mathrm{CH}_{3} \mathrm{COCH}_{3}$, is recorded on an instrument operating at 200 13-5 MHz, a single sharp resonance at $2.1 \delta$ is seen.
(a) How many hertz downfield from TMS does the acetone resonance correspond to?
(b) If the ${ }^{1} \mathrm{H}$ NMR spectrum of acetone is recorded at 500 MHz , what would the position of the absorption be in $\delta$ units?
(c) How many hertz downfield from TMS does this 500 MHz resonance correspond to?


CHAPTER CONTENTS - 13.4 Chemical Shifts in ${ }^{1} \mathrm{H}$ NMR Spectroscopy

As mentioned previously, differences in chemical shifts are caused by the small local magnetic field of electrons surrounding different nuclei. Nuclei that are more strongly shielded by electrons require a higher applied field to bring them into resonance so they absorb on the right side of the NMR chart. Nuclei that are less strongly shielded need a lower applied field for resonance so they absorb on the left of the NMR chart.


Most ${ }^{1} \mathrm{H}$ chemical shifts fall within the range 0 to $10 \delta$, which can be divided into the five regions shown in TABLE 13.2. By remembering the positions of these regions, it's often possible to tell at a glance what kinds of protons a molecule contains.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0414.jpg?height=586&width=1345&top_left_y=1561&top_left_x=382)


TABLE 13.3 shows the correlation of ${ }^{1} \mathrm{H}$ chemical shift with electronic environment in more detail. In general, protons bonded to saturated, $s p^{3}$-hybridized carbons absorb at higher fields, whereas protons bonded to $s p^{2}$-hybridized carbons absorb at lower fields. Protons on carbons that are bonded to electronegative atoms, such as N, O, or halogen, also absorb at lower fields.


| Type of hydrogen |  | Chemical shift ( $\mathbf{8}$ ) |
| :---: | :---: | :---: |
| Reference | $\mathrm{Si}\left(\mathrm{CH}_{3}\right)_{4}$ | 0 |
| Alkyl (primary) | $-\mathrm{CH}_{3}$ | 0.7-1.3 |
| Alkyl (secondary) | $-\mathrm{CH}_{2}-$ | 1.2-1.6 |
| Alkyl (tertiary) | <smiles>CC(C)C</smiles> | 1.4-1.8 |
| Allylic | <smiles>C=CC(C)C</smiles> | 1.6-2.2 |
| Methyl ketone | <smiles>CC(C)=O</smiles> | 2.0-2.4 |
| Aromatic methyl | $\mathrm{Ar}-\mathrm{CH}_{3}$ | 2.4-2.7 |
| Alkynyl | $-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}$ | 2.5-3.0 |
| Alkyl halide | <smiles>CCC(C)C</smiles> | 2.5-4.0 |
| Alcohol | <smiles>CC(C)(C)O</smiles> | 2.5-5.0 |
| Alcohol, ether | <smiles>COC(C)C</smiles> | 3.3-4.5 |
| Vinylic | <smiles>CC=C(C)C</smiles> | 4.5-6.5 |
| Aryl | Ar-H | 6.5-8.0 |
| Aldehyde | <smiles>CC=O</smiles> | $9.7-10.0$ |
| Carboxylic acid | <smiles>CC(=O)O</smiles> | 11.0-12.0 |


WORKED EXAMPLE 13.1 -


Predicting Chemical Shifts in ${ }^{1}$ H NMR Spectra -

Methyl 2,2-dimethylpropanoate $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CCO}_{2} \mathrm{CH}_{3}$ has two peaks in its ${ }^{1} \mathrm{H}$ NMR spectrum. What are their approximate chemical shifts?


Strategy -

Identify the types of hydrogens in the molecule, and note whether each is alkyl, vinylic, or next to an electronegative atom. Then predict where each absorbs, using TABLE 13.3 if necessary.


Solution -

The $-\mathrm{OCH}_{3}$ protons absorb around 3.5 to $4.0 \delta$ because they are on carbon bonded to oxygen. The $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-$ protons absorb near $1.0 \delta$ because they are typical alkane-like protons.


Solution -


Solution - 13.5 Integration of ${ }^{1} \mathrm{H}$ NMR Absorptions: Proton Counting

Look at the ${ }^{1} \mathrm{H}$ NMR spectrum of methyl 2,2-dimethylpropanoate in FIGURE 13.7. There are two peaks, corresponding to the two kinds of protons, but the peaks aren't the same size. The peak at $1.2 \delta$, due to the $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}$ - protons, is larger than the peak at $3.7 \mathrm{\delta}$, due to the $-\mathrm{OCH}_{3}$ protons.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0416.jpg?height=492&width=1391&top_left_y=1738&top_left_x=367)

FIGURE 13.7 The ${ }^{\mathbf{1}} \mathbf{H}$ NMR spectrum of methyl 2,2-dimethylpropanoate. Integrating the peaks in a stair-step manner shows that they have a $1: 3$ ratio, corresponding to the ratio of the numbers of protons $(3: 9)$ responsible for each peak. Modern instruments give a direct digital readout of relative peak areas.


The area under each peak is proportional to the number of protons causing that peak. By electronically measuring, or integrating, the area under each peak, it's possible to measure the relative numbers of the different kinds of protons in a molecule.

Modern NMR instruments provide a digital readout of relative peak areas, but an older, more visual method displays the integrated peak areas as a stair-step line, with the height of each step proportional to the area under the peak, and therefore proportional to the relative number of protons causing the peak. For example, the two steps for the peaks in methyl 2,2-dimethylpropanoate have a $1: 3$ (or $3: 9$ ) height ratio when integrated-exactly what we expect because the three $-\mathrm{OCH}_{3}$ protons are equivalent and the nine $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}$ - protons are equivalent.


PROBLEM How many peaks would you expect in the ${ }^{1} \mathrm{H}$ NMR spectrum of 1,4-dimethylbenzene (para-xylene,
13-8 or $p$-xylene)? What ratio of peak areas would you expect on integration of the spectrum? Refer to Table 13.3 for approximate chemical shifts, and sketch what the spectrum would look like. (Remember from Section 2.4 that aromatic rings have two resonance forms.)
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$p$-Xylene


Solution - 13.6 Spin-Spin Splitting in ${ }^{1}$ H NMR Spectra

In the ${ }^{1} H$ NMR spectra we've seen thus far, each different kind of proton in a molecule has given rise to a single peak. It often happens, though, that the absorption of a proton splits into multiple peaks, called a multiplet. For example, in the ${ }^{1} \mathrm{H}$ NMR spectrum of bromoethane shown in FIGURE 13.8, the $-\mathrm{CH}_{2} \mathrm{Br}$ protons appear as four peaks (a quartet) centered at $3.42 \delta$ and the $-\mathrm{CH}_{3}$ protons appear as three peaks (a triplet) centered at $1.68 \delta$.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0417.jpg?height=494&width=1394&top_left_y=1076&top_left_x=363)

FIGURE 13.8 The ${ }^{\mathbf{1}} \mathbf{H}$ NMR spectrum of bromoethane, $\mathbf{C H}_{\mathbf{3}} \mathbf{C H}_{\mathbf{2}} \mathbf{B r}$. The $-\mathrm{CH}_{2} \mathrm{Br}$ protons appear as a quartet at $3.42 \delta$, and the $-\mathrm{CH}_{3}$ protons appear as a triplet at $1.68 \delta$.


Called spin-spin splitting, multiple absorptions of a nucleus are caused by the interaction, or coupling, of the spins of nearby nuclei. In other words, the tiny magnetic field produced by one nucleus affects the magnetic field felt by a neighboring nucleus. Look at the $-\mathrm{CH}_{3}$ protons in bromoethane, for example. The three equivalent $-\mathrm{CH}_{3}$ protons are neighbored by two other magnetic nuclei-the two protons on the adjacent $-\mathrm{CH}_{2} \mathrm{Br}$ group. Each of the neighboring $-\mathrm{CH}_{2} \mathrm{Br}$ protons has its own nuclear spin, which can align either with or against the applied field, producing a tiny effect that is felt by the $-\mathrm{CH}_{3}$ protons.

There are three ways in which the spins of the two $-\mathrm{CH}_{2} \mathrm{Br}$ protons can align, as shown in FIGURE 13.9. If both proton spins align with the applied field, the total effective field felt by the neighboring $-\mathrm{CH}_{3}$ protons is slightly larger than it would be otherwise. Consequently, the applied field necessary to cause resonance is slightly reduced. Alternatively, if one of the $-\mathrm{CH}_{2} \mathrm{Br}$ proton spins aligns with the field and one aligns against the field, there is no effect on the neighboring $-\mathrm{CH}_{3}$ protons. (This arrangement can occur in two ways, depending on which of the two proton spins aligns which way.) Finally, if both $-\mathrm{CH}_{2} \mathrm{Br}$ proton spins align against the applied field, the effective field felt by the $-\mathrm{CH}_{3}$ protons is slightly smaller than it would be otherwise, and the applied field needed for resonance is slightly increased.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0418.jpg?height=684&width=1180&top_left_y=178&top_left_x=470)


FIGURE 13.9 The origin of spin-spin splitting in bromoethane. The nuclear spins of neighboring protons, indicated by horizontal arrows, align either with or against the applied field, causing the splitting of absorptions into multiplets.


Any given molecule has only one of the three possible alignments of $-\mathrm{CH}_{2} \mathrm{Br}$ spins, but in a large collection of molecules, all three spin states are represented in a 1:2:1 statistical ratio. We therefore find that the neighboring $-\mathrm{CH}_{3}$ protons come into resonance at three slightly different values of the applied field, and we see a 1:2:1 triplet in the NMR spectrum. One resonance is a little above where it would be without coupling, one is at the same place it would be without coupling, and the third resonance is a little below where it would be without coupling.

In the same way that the $-\mathrm{CH}_{3}$ absorption of bromoethane is split into a triplet, the $-\mathrm{CH}_{2} \mathrm{Br}$ absorption is split into a quartet. The three spins of the neighboring $-\mathrm{CH}_{3}$ protons can align in four possible combinations: all three with the applied field, two with and one against (three ways), one with and two against (three ways), or all three against. Thus, four peaks are produced for the $-\mathrm{CH}_{2} \mathrm{Br}$ protons in a 1:3:3:1 ratio.


As a general rule, called the $\boldsymbol{n}+1$ rule, protons that have $n$ equivalent neighboring protons show $n+1$ peaks in their NMR spectrum. For example, the spectrum of 2-bromopropane in FIGURE 13.10 shows a doublet at 1.71 $\delta$ and a seven-line multiplet, or septet, at $4.28 \delta$. The septet is caused by splitting of the $-\mathrm{CHBr}-$ proton signal by six equivalent neighboring protons on the two methyl groups ( $n=6$ leads to $6+1=7$ peaks). The doublet is due to signal splitting of the six equivalent methyl protons by the single $-\mathrm{CHBr}-$ proton ( $n=1$ leads to 2 peaks). Integration confirms the expected $6: 1$ ratio.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0418.jpg?height=494&width=1405&top_left_y=1713&top_left_x=355)

FIGURE 13.10 The ${ }^{\mathbf{1}} \mathbf{H}$ NMR spectrum of 2-bromopropane. The $-\mathrm{CH}_{3}$ proton signal at $1.71 \delta$ is split into a doublet, and the $-\mathrm{CHBr}-\mathrm{proton}$ signal at $4.28 \delta$ is split into a septet. Note that the distance between peaks is the same in both multiplets. Note also that the two outer peaks of the septet are small enough to be nearly missed.


The distance between peaks in a multiplet is called the coupling constant and is denoted J. Coupling constants are measured in hertz and generally fall in the range 0 to 18 Hz . The exact value of the coupling constant between two neighboring protons depends on the geometry of the molecule, but a typical value for an openchain alkane is $J=6$ to 8 Hz . The same coupling constant is shared by both groups of hydrogens whose spins are coupled and is independent of spectrometer field strength. In bromoethane, for instance, the $-\mathrm{CH}_{2} \mathrm{Br}$ protons
are coupled to the $-\mathrm{CH}_{3}$ protons and appear as a quartet with $J=7 \mathrm{~Hz}$. The $-\mathrm{CH}_{3}$ protons appear as a triplet with the same $J=7 \mathrm{~Hz}$ coupling constant.


Because coupling is a reciprocal interaction between two adjacent groups of protons, it's sometimes possible to tell which multiplets in a complex NMR spectrum are related to each other. If two multiplets have the same coupling constant, they are probably related, and the protons causing those multiplets are therefore adjacent in the molecule.


The most commonly observed coupling patterns and the relative intensities of lines in their multiplets are listed in TABLE 13.4. Note that it's not possible for a given proton to have five equivalent neighboring protons. (Why not?) A six-line multiplet, or sextet, is therefore found only when a proton has five nonequivalent neighboring protons that coincidentally happen to be coupled with an identical coupling constant $J$.


TABLE 13.4 Some Common Spin Multiplicities


| Number of equivalent adjacent protons | Multiplet | Ratio of intensities |
| :---: | :--- | :---: |
| 0 | Singlet | 1 |
| 1 | Doublet | $1: 1$ |
| 2 | Triplet | $1: 2: 1$ |
| 3 | Quartet | $1: 3: 3: 1$ |
| 4 | Quintet | $1: 4: 6: 4: 1$ |
| 6 | Septet | $1: 6: 15: 20: 15: 6: 1$ |


Spin-spin splitting in ${ }^{1} \mathrm{H}$ NMR can be summarized by three rules.


RULE 1 -


RULE 1 -

Three C-H protons are chemically equivalent; no splitting occurs.

Four C-H protons are chemically equivalent; no splitting occurs.


RULE 1 -

RULE 2
The signal of a proton with $n$ equivalent neighboring protons is split into a multiplet of $n+1$ peaks with coupling constant $\boldsymbol{J}$. Protons that are farther than two carbon atoms apart don't usually couple, although they sometimes show weak coupling when they are separated by a $\pi$ bond.
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Splitting observed
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RULE 1 -

Splitting not usually observed


RULE 1 -

RULE 3
Two groups of protons coupled to each other have the same coupling constant, $J$.
The spectrum of para-methoxypropiophenone in FIGURE 13.11 further illustrates these three rules. The downfield absorptions at 6.91 and $7.93 \delta$ are due to the four aromatic-ring protons. There are two kinds of aromatic protons, each of which gives a signal that is split into a doublet by its neighbor. The $-\mathrm{OCH}_{3}$ signal is
unsplit and appears as a sharp singlet at $3.84 \delta$. The $-\mathrm{CH}_{2}$ - protons next to the carbonyl group appear at $2.93 \delta$ in the region expected for protons on carbon next to an unsaturated center, and their signal is split into a quartet by coupling with the protons of the neighboring methyl group. The methyl protons appear as a triplet at $1.20 \delta$ in the usual upfield region.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0420.jpg?height=503&width=1392&top_left_y=388&top_left_x=364)


RULE 1 -

FIGURE 13.11 The ${ }^{\mathbf{1}} \mathbf{H}$ NMR spectrum of para-methoxypropiophenone.


WORKED EXAMPLE 13.2 -


Assigning a Chemical Structure from a ${ }^{1} \mathrm{H}$ NMR Spectrum -

Propose a structure for a compound, $\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}$, that fits the following ${ }^{1} \mathrm{H}$ NMR data: $0.92 \delta(3 \mathrm{H}$, triplet, $J=7 \mathrm{~Hz}$ ), $1.20 \delta(6 \mathrm{H}$, singlet), $1.50 \delta(2 \mathrm{H}$, quartet, $J=7 \mathrm{~Hz}$, $1.64 \delta(1 \mathrm{H}$, broad singlet).


Strategy -

It's best to begin solving structural problems by calculating a molecule's degree of unsaturation (we'll see this again in Worked Example 13.4). In the present instance, a formula of $\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}$ corresponds to a saturated, openchain molecule, either an alcohol or an ether.


Strategy -

To interpret the NMR information, let's look at each absorption individually. The three-proton absorption at $0.92 \delta$ is due to a methyl group in an alkane-like environment, and the triplet-splitting pattern implies that the $\mathrm{CH}_{3}$ is next to a $\mathrm{CH}_{2}$. Thus, our molecule contains an ethyl group, $\mathrm{CH}_{3} \mathrm{CH}_{2}-$. The six-proton singlet at $1.20 \delta$ is due to two equivalent alkane-like methyl groups attached to a carbon with no hydrogens, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}$, and the twoproton quartet at $1.50 \delta$ is due to the $\mathrm{CH}_{2}$ of the ethyl group. All 5 carbons and 11 of the 12 hydrogens in the molecule are now accounted for. The remaining hydrogen, which appears as a broad one-proton singlet at 1.64 $\delta$, is probably due to an OH group, since there is no other way to account for it. Putting the pieces together gives the structure: 2-methyl-2-butanol.


Solution -


Solution -

PROBLEM Draw structures for compounds that meet the following descriptions:
13-10
(a) $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}$; one singlet
(b) $\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{Cl}$; one doublet and one septet
(c) $\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{Cl}_{2} \mathrm{O}$; two triplets
(d) $\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}$; one singlet, one triplet, and one quartet


Solution -

PROBLEM The integrated ${ }^{1} \mathrm{H}$ NMR spectrum of a compound of formula $\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}$ is shown in Figure 13.12.
13-11 Propose a structure.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0421.jpg?height=502&width=1400&top_left_y=454&top_left_x=449)


Solution -

FIGURE 13.12 An integrated ${ }^{1} \mathrm{H}$ NMR spectrum for Problem 11.


13.7 ${ }^{1} \mathrm{H}$ NMR Spectroscopy and Proton Equivalence -

Because each electronically distinct hydrogen in a molecule has its own unique absorption, one use of ${ }^{1} \mathrm{H}$ NMR is to find out how many kinds of electronically nonequivalent hydrogens are present. In the ${ }^{1} \mathrm{H}$ NMR spectrum of methyl acetate shown previously in FIGURE 13.4a, for instance, there are two signals, corresponding to the two kinds of nonequivalent protons present, $\mathrm{CH}_{3} \mathrm{C}=\mathrm{O}$ protons and $-\mathrm{OCH}_{3}$ protons.


For relatively small molecules, a quick look at the structure is often enough to decide how many kinds of protons are present and thus how many NMR absorptions might appear. If in doubt, though, the equivalence or nonequivalence of two protons can be determined by comparing the structures that would be formed if each hydrogen were replaced by an X group. There are four possibilities.


- One possibility is that the protons are chemically unrelated and thus nonequivalent. If so, the products formed on substitution of H by X would be different constitutional isomers. In butane, for instance, the $-\mathrm{CH}_{3}$ protons are different from the $-\mathrm{CH}_{2}$ - protons. They therefore give different products on substitution by X than the $-\mathrm{CH}_{2}$ protons and would likely show different NMR absorptions.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0421.jpg?height=172&width=492&top_left_y=1773&top_left_x=708)
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The $-\mathrm{CH}_{2}$ - and $-\mathrm{CH}_{3}$ hydrogens are unrelated and have different NMR absorptions.
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The two substitution products are constitutional isomers.