Question

Give the symmetry number for each of the following molecules
a)Co b)O2 c)H2S d)SiH4 and e)CHCl3.  

Also explain please and include diagram if possible

Answer 1

The symmetry number of an object gives the number of indistinguishable orientations of the object in space, after various symmetry operations, which in essence is the order of the point group the object belongs to.

For molecules, the symmetry operations considered are rotational axes denoted by C_n where n gives the angle 360/n the molecule should be rotated about to be indistinguishable after the operation; mirror planes denoted by with the subscript v for vertical, h for horizontal and d for diagonal; point of inversion i and element S_n which involves rotation of the molecule by a C_n axis followed by a reflection perpendicular to the axis apart from the identity element E that exists in all molecules.

a) Co is a single atom and in symmetry and group theory in chemistry, all atoms are considered to be spheres. The sphere has infinite rotational axes, mirror planes, an inversion point and infinite S elements, giving its order to be infinite. Similarly, carbon monoxide with has infinite rotational axes, the inherent E and infinite mirror planes giving CO also an infinite symmetry number.

b) The oxygen molecule is another moiety of high symmetry. With both ends to the linear molecule possessing similar atoms, the symmetry element i is also possible and the presence of i and infinite rotational axes makes the existence of also possible, giving this moiety's symmetry number to also be infinite.

c) Hydrogen sulfide is of the point group due to the bent shape from two lone pairs on S. It has E, C₂ and two vertical mirror planes and giving the molecule's symmetry number to be 4.

d) Silane belongs to the point group T_d since it is perfectly tetrahedral. It has E, 8 C₃ axes, 3 C₂ axes, 6 S₄ axes and 6 . So its symmetry number is 24.

e) Chloroform's point group is C_3v. It has E, 2 C₃ axes and 3 planes and so its symmetry number is 6.