24. The total number of multiplet peaks in the 1H NMR spectrum of 1,3,5-tri-isopropylbenzene in CDCl3 is .
Total Number of Multiplet Peaks in the ¹H NMR Spectrum of 1,3,5-Tri-isopropylbenzene
Understanding the Structure of 1,3,5-Tri-isopropylbenzene
To determine the total number of multiplet peaks in the ¹H NMR spectrum of 1,3,5-tri-isopropylbenzene, the first step is to examine the molecular structure carefully. The molecule contains a benzene ring substituted with three identical isopropyl groups at positions 1, 3, and 5.
An isopropyl group has the general structure:
–CH(CH₃)₂
Therefore, each isopropyl substituent contains one methine proton, represented by –CH–, and six methyl protons distributed between two equivalent CH₃ groups.
The 1,3,5-substitution pattern gives the molecule a high degree of symmetry. Because the three substituents are identical and symmetrically arranged around the benzene ring, many apparently different protons become chemically equivalent. This molecular symmetry is the key to solving the question correctly.
Role of Molecular Symmetry in the ¹H NMR Spectrum
In 1,3,5-tri-isopropylbenzene, the three aromatic hydrogen atoms occupy positions 2, 4, and 6 of the benzene ring. Due to the threefold symmetry of the molecule, all three aromatic protons are chemically equivalent.
Similarly, the three methine protons of the three isopropyl groups are chemically equivalent to one another. The eighteen methyl protons are also equivalent because the isopropyl groups are identical and symmetrically positioned, while the two methyl groups within each isopropyl unit are equivalent under ordinary achiral NMR conditions.
As a result, the molecule contains only three major types of proton environments: the aromatic protons, the isopropyl methine protons, and the isopropyl methyl protons.
However, the question does not ask for the total number of proton environments or the total number of NMR signals. It specifically asks for the total number of multiplet peaks. Therefore, the individual lines produced by spin-spin splitting must be counted.
Splitting of the Aromatic Protons
The three aromatic protons at positions 2, 4, and 6 are chemically equivalent because of molecular symmetry. Chemically equivalent protons do not normally split one another.
Consequently, the three aromatic protons appear as a single resonance and are treated as a singlet for this question.
Since a singlet is not a split multiplet, this aromatic signal is not included when calculating the total number of multiplet peaks requested in the question.
Therefore, the aromatic proton contribution to the number of multiplet peaks is not counted.
Splitting of the Isopropyl Methine Protons
Each isopropyl group contains one methine proton with the structural environment:
–CH(CH₃)₂
The methine proton is adjacent to two equivalent methyl groups. Together, these two methyl groups contain a total of six equivalent neighboring protons.
According to the n + 1 rule of proton NMR spectroscopy, a proton with n equivalent neighboring protons is split into:
Number of peaks = n + 1
For the methine proton:
n = 6
Therefore:
Number of peaks = 6 + 1 = 7
The methine proton signal is consequently split into a septet, which contains seven individual peaks.
Because all three methine protons in the molecule are chemically equivalent, they produce one septet rather than three separate septets.
Thus, the methine protons contribute:
7 multiplet peaks
Why the Methine Signal Appears as a Septet
The septet is a characteristic feature of an isopropyl group in a ¹H NMR spectrum. The single methine proton interacts with the six equivalent protons of the two neighboring methyl groups.
The six equivalent neighboring protons can adopt different combinations of spin orientations relative to the observed methine proton. These combinations produce seven distinct energy environments, resulting in seven spectral lines.
The relative intensities of an ideal first-order septet follow the binomial distribution:
1 : 6 : 15 : 20 : 15 : 6 : 1
Therefore, the methine resonance is not merely one peak. It is one NMR signal composed of seven individual peaks.
This distinction between an NMR signal and the individual peaks within a multiplet is essential for answering the question.
Splitting of the Isopropyl Methyl Protons
Each methyl group in an isopropyl unit is adjacent to one methine proton. Therefore, the methyl protons experience spin-spin coupling with one neighboring proton.
Using the n + 1 rule:
n = 1
Therefore:
Number of peaks = 1 + 1 = 2
The methyl proton signal consequently appears as a doublet, containing two individual peaks.
Because of the symmetry of 1,3,5-tri-isopropylbenzene, all eighteen methyl protons are chemically equivalent and produce one doublet.
Thus, the methyl protons contribute:
2 multiplet peaks
Why All Eighteen Methyl Protons Produce Only One Doublet
The molecule contains six methyl groups in total because each of the three isopropyl substituents contains two methyl groups.
At first glance, it may appear that these six methyl groups should generate several different NMR signals. However, the high symmetry of 1,3,5-tri-isopropylbenzene makes the corresponding methyl groups chemically equivalent.
Furthermore, within each ordinary isopropyl group, the two methyl groups are equivalent in an achiral environment such as CDCl₃. Consequently, all eighteen methyl protons contribute to a single resonance.
This resonance is split by the adjacent methine proton into a doublet containing two individual peaks.
The large integration value of eighteen protons affects the area under the signal, but it does not increase the number of splitting lines.
Calculation of the Total Number of Multiplet Peaks
The methine proton signal appears as a septet and therefore contains:
7 peaks
The methyl proton signal appears as a doublet and therefore contains:
2 peaks
Therefore:
Total number of multiplet peaks = 7 + 2
Total number of multiplet peaks = 9
Hence, the required answer is:
9
Complete ¹H NMR Pattern of 1,3,5-Tri-isopropylbenzene
The ¹H NMR spectrum of 1,3,5-tri-isopropylbenzene is expected to contain three main proton environments.
The three aromatic protons produce one singlet. The three methine protons produce one septet because each methine proton is coupled to six equivalent methyl protons. The eighteen methyl protons produce one doublet because each methyl group is coupled to one neighboring methine proton.
Thus, the expected pattern can be summarized as:
Aromatic protons: 3H → singlet
Methine protons: 3H → septet → 7 peaks
Methyl protons: 18H → doublet → 2 peaks
The total number of multiplet peaks is therefore:
7 + 2 = 9
Difference Between Number of Signals and Number of Multiplet Peaks
An important concept in this question is the difference between the number of chemically distinct signals and the number of individual peaks created by spin-spin splitting.
1,3,5-Tri-isopropylbenzene has three major chemically distinct proton environments and therefore gives three main ¹H NMR signals: one aromatic signal, one methine signal, and one methyl signal.
However, the question asks for the total number of multiplet peaks, not the total number of signals. The methine signal is divided into seven peaks, while the methyl signal is divided into two peaks.
Therefore, the answer is not 2 or 3. The required number is obtained by adding the individual peaks of the split multiplets.
Effect of CDCl₃ on the Spectrum
CDCl₃, or deuterated chloroform, is one of the most commonly used solvents in proton NMR spectroscopy. It is used because ordinary chloroform contains hydrogen and would produce a very intense proton signal that could interfere with the spectrum of the sample.
Deuterium has different NMR properties from ordinary hydrogen and therefore does not produce a major signal in a conventional ¹H NMR spectrum. A small residual CHCl₃ signal may still appear, but it does not affect the splitting calculation for 1,3,5-tri-isopropylbenzene.
Therefore, the use of CDCl₃ does not change the required number of multiplet peaks in this problem.
Final Answer
The methine protons of 1,3,5-tri-isopropylbenzene are split by six equivalent neighboring methyl protons and produce a septet containing 7 peaks. The methyl protons are split by one neighboring methine proton and produce a doublet containing 2 peaks.
Therefore:
Total number of multiplet peaks = 7 + 2 = 9
Correct Answer: 9
