Chapter 4: Problem 1

Assign the symmetry point group to the following molecules: (a) Benzene (b) \(\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (d) Acetylene

Short Answer

Expert verified

The point groups for the given molecules are: (a) Benzene - D6h, (b) Water - C2, (c) Ethene - D2h, and (d) Acetylene - D∞h.

Step by step solution

Assigning Point Group for Benzene

Benzene has a six-fold rotation axis along the axis perpendicular to the plane of the molecule, and also has a plane of symmetry in the plane of the molecule. These characterstics make it belong to the D6h point group.

Assigning Point Group for \(\mathrm{H}_{2} \mathrm{O}\)

Water (\(\mathrm{H}_{2} \mathrm{O}\)) is a bent molecule without any symmetry with respect to a plane or inversion center. However, it has a C2 rotation axis. Therefore, it belongs to the C2 point group.

Assigning Point Group for \(\mathrm{C}_{2} \mathrm{H}_{4}\)

Ethene (\(\mathrm{C}_{2} \mathrm{H}_{4}\)) has a plane of symmetry in the plane of the molecule and also has a C2 rotation axis. Therefore, it belongs to the D2h point group.

Assigning Point Group for Acetylene

Acetylene has a linear geometry with a C∞v rotation axis and an infinite number of planes of symmetry. Therefore, it belongs to the D∞h symmetry point group.

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Assign the symmetry point group to the following molecules: (a) Benzene (b) \(\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (d) Acetylene

Short Answer

Step by step solution

Assigning Point Group for Benzene

Assigning Point Group for \(\mathrm{H}_{2} \mathrm{O}\)

Assigning Point Group for \(\mathrm{C}_{2} \mathrm{H}_{4}\)

Assigning Point Group for Acetylene

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