CHE 332:  Chapter 4 Problems
 

2.  a)  3 mutually perpendicular C2 axes, mirror plane perpendicular to each one.    D2h
     b)  mirror plane in the plane of the molecule.    Cs
     c)  1,1-dichloroethene has a C2 axis along the C-C bond and two mirror planes containing this axis (vertical planes).    C2v
         cis-1,2-dichloroethene has a C2 axis perpendicular to the C-C bond and in the plane of the molecule, plus two mirror planes containing this axis (vertical planes).    C2v
          trans-1,2-dichloroethene has a C2 axis perpendicular to the C-C bond and perpendicular to the plane of the molecule, plus a mirror plane perpendicular to this axis (in the plane of the molecule, horizontal plane).     C2h
 

4.  a)  naphthalene has 3 mutually perpendicular C2 axes and mirror planes perpendicular to each axis (horizontal).    D2h
     b)  the 2,2'-dichloronaphthalene has a C2 axis along the C-C bond where the two rings are fused, and a mirror plane containing this axis (vertical).     C2v
     c)  2,4'-dichloronaphthalene has a C2 axis perpendicular to the plane of the molecule.  The plane of the molecule is a horizontal mirror plane.     C2h
     d)  2,3-dichloronaphthalene has a mirror plane in the plane of the molecule.    Cs
 

5.  a)  There is a C2 axis through the Fe atom, parallel to the cyclopentadienyl rings and perpendicular to a plane passing through both Cl atoms.  This plane is also a horizontal mirror plane.     C2h
     b)  Dibenzenechromium has a six-fold rotation axis passing through the centers of the two benzene rings, six two-fold rotation axes passing through the Cr atom and parallel to the planes of the benzene rings, and a horizontal mirror plane through the Cr atom (as well as six dihedral mirror planes).    D6h
     c)  The phenyl-substituted dibenzenechromium has a mirror plane running along the long axis of the two connected rings (in the plane of the paper).    Cs
     d)  Hydronium ion is a trigonal pyramidal species with a three-fold rotation axis and three vertical mirror planes.     C3v
     e)  Difluoroperoxide has only a two-fold rotation axis.    C2
     f)  Formaldehyde has a two-fold rotation axis along the C=O bond and two vertical mirror planes.     C2v
     g)  Cyclooctasulfur is a puckered ring in which alternating S atoms are up or down.  There is a four-fold rotation axis, four two-fold axes, and four dihedral planes.     D4d
     h)  Borazine has a three-fold rotation axis, three two-fold axes at right angles to it, and a horizontal mirror plane.     D3h
     i)  Trisoxalatochromate(3-) looks like a 3-bladed propellor with a twist to the blades.  There is a three-fold rotation axis and three two-fold axes perpendicular to it.     D3
     j)  A tennis ball or the allene molecule has three mutually perpendicular C2 axes and two dihedral mirror planes.     D2d
 

10.  a)  The px orbital has an infinite-order rotation axis along its length and an infinite number of vertical mirror planes containing this axis.    Coov
       b)  The dxy orbital has two-fold axes along each pair of opposing lobes and also perpendicular to the principal plane of the orbital.  There is also a horizontal mirror plane.     D2h
       c)  The dx2-y2 orbital has 3 mutually perpendicular two-fold rotation axes and a horizontal plane.     D2h
       d)  The dz2 orbital has an infinite-order rotation axis, an infinite number of two-fold rotation axes all perpendicular to this one, and a horizontal mirror plane.     Dooh