Solutions 7

Q1:

Below are molecules of similar symmetry and the required symmetry elements.

a).

b).

c).

d).

Q2:

Symmetry elements

s orbital: inversion center, infinite planes of reflection, infinite axes of proper and improper rotations

p orbital: inversion center, 1 vertical plane of reflection, infinite horizontal planes of reflection, infinite  $$C_2$$ and $$S_2)\ axes, 1 \(C_\infty$$ and $$S_\infty$$  axis of rotation, inversion center

$$d_{z^2}$$ : same as p orbital

Q4:

a). $$C_1$$

b).  $$T_d$$

c). $$C_\infty$$

d). $$C_1$$

e). $$C_{2v}$$

f). $$C_2$$

Q5:

a). An inversion center will prevent a molecule from being polar. Molecules (a), (c), (e), and (f) are all polar.

b). Planes of reflection exclude chirality. Molecule (d) is chiral.