Number of Peaks in the ¹³C NMR Spectrum of CDCl₃

The correct answer is 3 peaks.

The number of peaks observed for CDCl₃ in a ¹³C NMR spectrum is a frequently tested concept because it combines the basic principles of nuclear spin with spin–spin coupling. Although CDCl₃ contains only one carbon atom and therefore has only one chemically distinct carbon environment, its carbon resonance does not appear as a single unsplit peak. Instead, the carbon signal is split by the directly attached deuterium atom.

As a result, CDCl₃ appears as a triplet consisting of three peaks with an intensity ratio of approximately 1:1:1 in the ¹³C NMR spectrum.

Understanding the Structure of CDCl₃

CDCl₃ is deuterated chloroform, commonly known as chloroform-d. Its structure contains one carbon atom bonded to three chlorine atoms and one deuterium atom.

CDCl₃

The carbon atom is directly bonded to one deuterium nucleus. This direct carbon–deuterium bond is the key to understanding why three peaks are observed.

If we considered only the number of chemically different carbon atoms, we might expect CDCl₃ to produce only one ¹³C NMR signal because the molecule contains only one carbon atom. However, the observed multiplicity of a signal also depends on coupling with nearby NMR-active nuclei.

Why CDCl₃ Gives Three Peaks in ¹³C NMR

Deuterium, represented by D or ²H, is an isotope of hydrogen. Unlike ordinary protium, ¹H, which has a nuclear spin quantum number of 1/2, deuterium has a nuclear spin quantum number:

I = 1

The carbon atom in CDCl₃ is directly bonded to one deuterium nucleus. Therefore, the ¹³C resonance undergoes ¹³C–²H spin–spin coupling.

The number of peaks produced by coupling with nuclei having a spin quantum number greater than 1/2 is calculated using the general splitting equation:

Number of peaks = 2nI + 1

Here, n is the number of equivalent neighboring nuclei and I is the nuclear spin quantum number of the coupling nucleus.

Applying the 2nI + 1 Rule to CDCl₃

For CDCl₃, the carbon atom is coupled with one deuterium nucleus. Therefore:

n = 1

The nuclear spin quantum number of deuterium is:

I = 1

Substituting these values into the equation:

Number of peaks = 2nI + 1

Number of peaks = 2(1)(1) + 1

Number of peaks = 3

Therefore, the carbon resonance of CDCl₃ is split into three peaks.

Why the Signal Appears as a 1:1:1 Triplet

The three peaks arise from the three possible magnetic spin states of the deuterium nucleus. Since deuterium has a nuclear spin quantum number of I = 1, it can adopt three possible magnetic quantum numbers:

m_I = +1, 0 and −1

The ¹³C nucleus experiences three possible magnetic environments because of these three spin states of the attached deuterium nucleus. Consequently, the original carbon resonance is split into three components.

These three components have approximately equal intensities. Therefore, the CDCl₃ solvent signal appears as a:

1:1:1 triplet

This is different from the familiar 1:2:1 triplet produced by coupling with two equivalent spin-1/2 protons.

Why the Simple n + 1 Rule Is Not Used

The familiar n + 1 rule is mainly used when a nucleus is coupled with equivalent neighboring nuclei having a spin quantum number of I = 1/2, such as ordinary ¹H nuclei.

If the n + 1 rule were incorrectly applied to the one attached deuterium atom in CDCl₃, the predicted multiplicity would be:

1 + 1 = 2 peaks

This would give a doublet, which is incorrect.

Deuterium has I = 1 rather than I = 1/2. Therefore, the more general equation must be used:

2nI + 1

This gives the correct result of three peaks.

Why the Answer Is Not One Peak

One peak might initially appear reasonable because CDCl₃ contains only one carbon atom. It is true that the molecule has only one chemically distinct carbon environment, so it has only one carbon resonance position.

However, this resonance is split by the attached deuterium nucleus. Therefore, one carbon environment does not necessarily mean one individual spectral line.

The single carbon resonance is divided into three lines by carbon–deuterium coupling. Hence, the observed number of peaks is three, not one.

Why the Answer Is Not Two Peaks

Two peaks would correspond to a doublet. A doublet is expected when coupling occurs with one nucleus having I = 1/2.

For example, coupling with one ordinary proton can split a signal into:

2(1)(1/2) + 1 = 2 peaks

However, the attached nucleus in CDCl₃ is deuterium, not ordinary hydrogen. Since deuterium has I = 1, the carbon signal is split into three peaks rather than two.

Therefore, a doublet is not the correct multiplicity for the ¹³C signal of CDCl₃.

Why the Answer Is Not Four Peaks

Four peaks represent a quartet. A quartet may arise under appropriate coupling conditions, such as coupling with three equivalent spin-1/2 nuclei.

CDCl₃ contains only one deuterium atom attached to the carbon. The number of lines is determined by the spin of this single deuterium nucleus:

2(1)(1) + 1 = 3

Therefore, four peaks are not expected.

Difference Between Number of Signals and Number of Peaks

This question highlights an important distinction between the terms signal and peak.

CDCl₃ contains only one chemically distinct carbon atom. Therefore, it has one carbon environment and one fundamental ¹³C resonance. However, because this resonance is split through coupling with deuterium, it appears as three individual peaks.

Thus:

Number of chemically distinct carbon environments = 1

Number of observed peaks after ¹³C–²H coupling = 3

This distinction is essential when solving NMR spectroscopy problems.

CDCl₃ as a Common Solvent in ¹³C NMR Spectroscopy

CDCl₃ is one of the most widely used deuterated solvents in NMR spectroscopy. In a typical ¹³C NMR spectrum recorded in CDCl₃, the solvent resonance is commonly observed near 77 ppm.

Instead of appearing as a single sharp line, this solvent resonance is generally seen as three closely spaced peaks because of coupling between ¹³C and the directly bonded deuterium nucleus.

Recognizing this characteristic solvent triplet is useful when interpreting experimental ¹³C NMR spectra because it prevents the solvent peaks from being mistaken for peaks belonging to the sample.

Step-by-Step Calculation for CDCl₃

The directly attached coupling nucleus is deuterium, whose nuclear spin is:

I = 1

The number of equivalent deuterium nuclei attached to carbon is:

n = 1

Using the general splitting equation:

Number of peaks = 2nI + 1

Therefore:

Number of peaks = 2 × 1 × 1 + 1 = 3

Hence, the ¹³C resonance of CDCl₃ appears as a triplet with a 1:1:1 intensity ratio.

Key Concept Behind the Answer

The most important point is that deuterium is a spin-1 nucleus. A ¹³C nucleus directly coupled to one spin-1 deuterium nucleus is split into three lines. Therefore, the characteristic CDCl₃ solvent resonance in a ¹³C NMR spectrum is a triplet.

Final Answer

CDCl₃ contains one carbon atom directly bonded to one deuterium atom. Since deuterium has a nuclear spin quantum number of I = 1, the carbon signal is split according to:

Number of peaks = 2nI + 1

= 2(1)(1) + 1

= 3 peaks

Therefore, the number of peaks in the ¹³C NMR spectrum of CDCl₃ is:

3 peaks

Correct Answer: 3