Arsenic pentachloride, AsCl5 is a trigonal bipyramidal molecule. To what point group does it belong? a. D3v b. D3h c. C3h d. C3v
The Correct Answer and Explanation is:
The correct answer is b. D3h.
To determine the point group of a molecule, we analyze its symmetry elements. Arsenic pentachloride (AsCl5) is specified as having a trigonal bipyramidal geometry. This structure features a central arsenic (As) atom, with three chlorine (Cl) atoms in a triangular plane (equatorial positions) and two Cl atoms along an axis perpendicular to this plane, one above and one below (axial positions).
Let’s identify the symmetry elements present in AsCl5:
- Identity (E): Every object has an identity element, which corresponds to doing nothing.
- Principal Axis of Rotation (Cn): There is a rotational axis passing through the two axial Cl atoms and the central As atom. Rotating the molecule by 120 degrees (360°/3) around this axis leaves it indistinguishable because it swaps the three equatorial Cl atoms. Therefore, this is a C3 principal axis.
- Perpendicular C2 Axes: There are three C2 (180-degree) rotational axes that are perpendicular to the main C3 axis. Each of these C2 axes passes through the central As atom and one of the equatorial Cl atoms. A 180-degree rotation around one of these axes will exchange the other two equatorial Cl atoms and also exchange the two axial Cl atoms. The presence of a Cn axis and n perpendicular C2 axes means the molecule belongs to a D point group. Since n=3, the molecule is in the D3 family.
- Horizontal Mirror Plane (σh): The molecule has a horizontal mirror plane that lies perpendicular to the C3 principal axis. This plane is the same one that contains the central arsenic atom and the three equatorial chlorine atoms. Reflection across this plane swaps the top axial Cl atom with the bottom axial Cl atom, leaving the equatorial atoms unchanged.
The combination of a C3 axis, three perpendicular C2 axes, and a horizontal mirror plane (σh) uniquely defines the D3h point group. The other options are incorrect: C3v and C3h lack the three perpendicular C2 axes, and D3v lacks the crucial horizontal mirror plane.
