Inorganic ChemistryI. How many planes of symmetry does benzene have? Locate them in a drawing.
II. Draw the ammonia molecule, find the symmetry elements, and list all symmetry
operations.
III. The rotations of ammonia form a subgroup of order 3. Write out the multiplication table.
IV. Assign point groups to the following molecules and ions.
P
P P
P P
Cr
Br
Br
Cl
Cl
Cl
Cl
Cr
Br
Br
Cl
Cl
4
V. Assume cyclobutadiene is a square-planar molecule. Find the locations of all C2 axes and planes of symmetry consistent with the characters assigned below for thefour carbon-carbon bonds.
D4h
E
2C4
C2
2C2
2C2
i
2S4
sh
2 sv
2 sd
GCC
4
0
0
0
2
0
0
4
0
2
VI. The complex Ru(PPh3)3(CO)2 (1) shows a single band in the C=O stretching region of the IR spectrum. On the other hand, the related complex Ru(PPh3)2(CO)2L (2)incorporates a different phosphine L and exhibits two relatively intense C=O stretching bands. If both complexes are effectively trigonal bipyramidal, deduce likelystructures for each compound. Use group theoretical methods to support your answer.
Compound
?(CO), cm-1
1
1905
2
1888, 1941
VII. Consider the three p orbitals px, py, and pz, which are degenerate for an isolated atom M. If M is surrounded by several X atoms, the latter impose anelectrostatic field that can lift the degeneracy of the p orbitals. According to character tables, how do the p orbitals split in each of the following structures?
a) MX3, pyramidal
b) MX4, tetrahedral