Determine the point group for the ideal molecular geometry of each of the following: PCl4+, PCl6, PCIs, COS, 1,4-dichlorobenzene, 1,3-dichlorobenzene, and a tennis ball (ignoring printing, just the seams)
The Correct Answer and Explanation is:
Here are the point groups for each molecule/object followed by an explanation:
- PCl₄⁺ → T_d
- PCl₆ (assumed to be PCl₆⁻) → O_h
- PCl₅ → D₃h
- COS → C_∞v
- 1,4-dichlorobenzene → D₂h
- 1,3-dichlorobenzene → C₂v
- Tennis ball (ignoring print, just the seam) → D₂d
Explanation:
PCl₄⁺: This ion has a tetrahedral geometry similar to CH₄, where phosphorus forms four bonds in a symmetric 3D shape. Tetrahedral structures belong to the T_d point group, which has high symmetry with multiple C₃ and C₂ axes and mirror planes.
PCl₆⁻: Assuming the negative ion form (PCl₆⁻), it adopts an octahedral geometry where phosphorus is surrounded by six chlorine atoms. Octahedral molecules belong to the O_h point group, the highest order point group for non-linear molecules, with several symmetry elements including inversion, multiple rotational axes, and mirror planes.
PCl₅: This molecule has a trigonal bipyramidal geometry. It has a C₃ axis along with three vertical mirror planes, classifying it under the D₃h point group.
COS: This linear molecule (Carbonyl Sulfide) is analogous to CO₂ in shape and symmetry. Linear molecules with different terminal atoms and a center of mass at one point belong to the C_∞v point group, which includes infinite rotation symmetry and an infinite number of mirror planes.
1,4-dichlorobenzene: The para-disubstituted benzene has a center of symmetry and multiple perpendicular mirror planes, fitting the D₂h point group.
1,3-dichlorobenzene: The meta isomer has less symmetry than the para form. It retains a single C₂ axis and vertical mirror planes, placing it in the C₂v point group.
Tennis ball: Ignoring print and focusing only on the seam, the tennis ball has D₂d symmetry — it has two perpendicular C₂ axes, a C₂ axis perpendicular to them, and diagonal mirror planes, matching the twisted D₂d group, often used to describe symmetric but chiral-like objects.
