Question

The number of signals observed in the $^1H NMR$ spectrum of the compound

is _________.

Answer 1

Correct Answer: 3

The number of signals observed in the ${}^{1}\text{H NMR}$ spectrum of a compound is equal to the number of sets of chemically non-equivalent protons.

The given compound is a substituted biphenyl derivative, specifically $2,2',4,4',6,6'$-hexamethylbiphenyl.

$\text{Analysis of Molecular Symmetry}$

Rotation about the $1-1'$ bond: The two phenyl rings are not necessarily coplanar due to the steric hindrance of the $\text{ortho}$ methyl groups. Because the substituents on each ring are identical ($\text{Me}$ at $2, 4, 6$ and $\text{Me}$ at $2', 4', 6'$), and the $\text{ortho}$ positions have bulky methyl groups, there is restricted rotation around the single bond connecting the two rings. The molecule exists as a mixture of conformers, but for high-resolution NMR, the molecule is often considered to have a certain time-averaged symmetry or, if the barrier to rotation is very high, to be conformationally stable.

Symmetry in Hexamethylbiphenyl: Due to the identical substitution pattern on both rings, the molecule possesses an axis of symmetry passing through the center of the $\text{C}1-\text{C}1'$ bond and perpendicular to it, which equates the two phenyl rings. This is a $C_{2}$ axis of rotation that passes through the midpoint of the $\text{C}1-\text{C}1'$ bond and relates one ring to the other.

$\text{Identification of Non-equivalent Protons}$

Based on the symmetry of the molecule, we can identify the sets of equivalent protons.

$\text{1. Aromatic Protons}$

Each phenyl ring has one $\text{para}$ position ($\text{C}4$ and $\text{C}4'$) and two $\text{ortho}$ positions ($\text{C}2, \text{C}6$ and $\text{C}2', \text{C}6'$) substituted with methyl groups.

The only remaining unsubstituted positions on the ring are the $\text{meta}$ positions, $\text{C}3, \text{C}5$ and $\text{C}3', \text{C}5'$.

Because the two rings are chemically and magnetically equivalent due to the $C_{2}$ symmetry, the protons at:

$\text{C}3$ and $\text{C}3'$ are equivalent.

$\text{C}5$ and $\text{C}5'$ are equivalent.

Furthermore, due to the internal symmetry of each ring (or the $C_{2}$ axis relating the positions $3 \to 5$ and $3' \to 5'$ after rotation of the molecule), the $\text{H}$ atoms at the $\text{C}3, \text{C}5, \text{C}3', \text{C}5'$ positions are all chemically equivalent.

Signal 1 ($\delta_{\text{Ar}}$): $\text{Four}$ aromatic protons ($\text{H}$ at $\text{C}3, \text{C}5, \text{C}3', \text{C}5'$) give one signal.

$\text{2. Methyl Protons}$

The compound has six methyl ($\text{Me}$) groups:

Two $\text{ortho}$ methyl groups: $\text{Me}$ at $\text{C}2$ and $\text{Me}$ at $\text{C}2'$.

Two $\text{para}$ methyl groups: $\text{Me}$ at $\text{C}4$ and $\text{Me}$ at $\text{C}4'$.

Two $\text{ortho}$ methyl groups: $\text{Me}$ at $\text{C}6$ and $\text{Me}$ at $\text{C}6'$.

Due to the $C_{2}$ axis of symmetry:

The $\text{para}$ methyl groups ($\text{C}4-\text{Me}$ and $\text{C}4'-\text{Me}$) are equivalent.

Signal 2 ($\delta_{\text{p-Me}}$): $\text{Six}$ protons of the $\text{para}$ methyl groups give one signal.

The $\text{ortho}$ methyl groups ($\text{C}2-\text{Me}, \text{C}6-\text{Me}, \text{C}2'-\text{Me}, \text{C}6'-\text{Me}$) are equivalent.

Signal 3 ($\delta_{\text{o-Me}}$): $\text{Twelve}$ protons of the $\text{ortho}$ methyl groups give one signal.

$\text{Conclusion}$

The molecule contains three sets of chemically non-equivalent protons:

Aromatic protons ($\text{H}$ at $\text{C}3, \text{C}5, \text{C}3', \text{C}5'$).

$\text{para}$ methyl protons ($\text{Me}$ at $\text{C}4, \text{C}4'$).

$\text{ortho}$ methyl protons ($\text{Me}$ at $\text{C}2, \text{C}6, \text{C}2', \text{C}6'$).

The number of signals observed in the ${}^{1}\text{H NMR}$ spectrum is $\mathbf{3}$.

$$\text{The number of signals observed in the } {}^{1}\text{H NMR } \text{spectrum of the compound is } \mathbf{3}$$