In: Chemistry
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
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 Cn 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 Sn which involves
rotation of the molecule by a Cn 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 Td 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 C3v. It has E, 2
C3 axes and 3
planes and so its symmetry number is 6.