a. List the symmetry elements of the following molecules and name the point groups to which they belong: (a) NO2, (b) N2O, (c) CHCl3, (d) CH2=CH2, (e) cis-CHBr=CHBr, (f) trans-CHCl=CHCl.
b. List the symmetry elements of the following molecules and name the point groups to which they belong: (a) naphthalene, (b) anthracene, (c) the three dichlorobenzenes.
The Correct Answer and Explanation is :
a. Symmetry Elements and Point Groups:
- NO2 (Nitrogen Dioxide)
- Symmetry elements: No mirror plane (σ), no inversion center (i), and only a C₂ axis of symmetry (rotation about the bond axis).
- Point group: C₂v
- Explanation: NO2 has a C₂ axis (rotation by 180° around the N-O axis) and vertical mirror planes (σv) passing through the N and O atoms. It does not possess inversion symmetry.
- N2O (Nitrous Oxide)
- Symmetry elements: C∞ axis, inversion center (i).
- Point group: D∞h
- Explanation: N2O has an infinite axis of symmetry (C∞), meaning it can rotate indefinitely with the same symmetry. Additionally, it possesses an inversion center at the nitrogen atom.
- CHCl3 (Chloroform)
- Symmetry elements: C₃ axis, σv mirror planes.
- Point group: C₃v
- Explanation: Chloroform has a C₃ axis of symmetry (rotation by 120° around the C-H axis) and three vertical mirror planes passing through the C atom and one of the Cl atoms.
- CH2=CH2 (Ethene)
- Symmetry elements: C₂ axis, σh mirror plane.
- Point group: D₂h
- Explanation: Ethene has a C₂ axis (rotation by 180° around the central C=C bond) and horizontal mirror planes (σh), which is typical for planar molecules with a double bond.
- cis-CHBr=CHBr (Cis-1,2-Dibromoethene)
- Symmetry elements: C₂ axis, σv mirror plane, no inversion center.
- Point group: C₂v
- Explanation: In the cis form, the Br atoms are in the same plane, and the molecule possesses a C₂ axis (rotation around the C=C bond) and a vertical mirror plane passing through the central bond.
- trans-CHCl=CHCl (Trans-1,2-Dichloroethene)
- Symmetry elements: C₂ axis, σh mirror plane.
- Point group: D₂h
- Explanation: The trans-configuration of dichloroethene has a C₂ axis (rotation by 180° around the C=C bond) and horizontal mirror planes (σh), which makes it a D₂h molecule.
b. Symmetry Elements and Point Groups:
- Naphthalene
- Symmetry elements: C₂ axis, σh, i (inversion center).
- Point group: D₂h
- Explanation: Naphthalene has multiple symmetry elements, including a C₂ axis perpendicular to the molecular plane and an inversion center. It belongs to the D₂h point group, characterized by a high degree of symmetry.
- Anthracene
- Symmetry elements: C₂ axis, σh, i (inversion center).
- Point group: D₂h
- Explanation: Like naphthalene, anthracene has similar symmetry elements, including a C₂ axis and an inversion center. It is a larger aromatic molecule but retains the D₂h symmetry.
- Three Dichlorobenzenes (1,2-Dichlorobenzene, 1,3-Dichlorobenzene, and 1,4-Dichlorobenzene)
- 1,2-Dichlorobenzene: Point group C₂v
- 1,3-Dichlorobenzene: Point group C₂v
- 1,4-Dichlorobenzene: Point group D₂h
- Symmetry elements:
- 1,2-Dichlorobenzene and 1,3-Dichlorobenzene: C₂ axis, σv mirror planes (vertical through Cl atoms).
- 1,4-Dichlorobenzene: C₂ axis, σv mirror planes, inversion center.
- Explanation: The point group classifications for dichlorobenzenes depend on the relative positions of the chlorine atoms. The 1,2- and 1,3- configurations (both C₂v) have mirror planes through the C-Cl bonds and a C₂ axis, while 1,4-dichlorobenzene (D₂h) has additional symmetry due to its linear, symmetrical arrangement of Cl atoms.