5.03 In-Class Exam 2
Christopher C. Cummins
March 12, 2010
Instructions
Clearly write your name at the top of this front page, but otherwise do not write on this front page
as it will be used for scoring. This exam is closed-book and no calculators or electronic devices
may be employed. There are five sections so please read over the exam before you begin and expect
to take on average ten minutes per section. Read all questions carefully before writing down any
answers. Enjoy the material!
1
1
Boron and Polyhedral Boranes
The following questions are worth 4 points each.
1. How many skeletal bonding electrons are present for [B6 H6 ]2− ?
2. The skeletal bonding electrons in [B6 H6 ]2− break down according to a1 + t2u + t2g . Of these,
the t2g set is of the pure tangential variety. On the set of line drawings below, sketch out the
t2g set of MOs, making sure to indicate clearly the nodal character of each MO.
3. What is the chemical formula of the nido structure that corresponds to [B6 H6 ]2− ?
2
4. Sketch a line drawing of the nido structure that corresponds to [B6 H6 ]2− ? Use small circles
to clearly indicate the position of all hydrogens.
5. What is the structural motif that is found in crystalline elemental boron?
3
2
Phosphorus Allotropes
The following questions are worth 4 points each.
1. How many stable molecular allotropes exist for the element phosphorus?
2. With reference to the 2(N + 1)2 spherical aromaticity criterion, the P4 molecule has a single
filled π molecular orbital (N = 0 for the π system). Sketch out the appearance of this orbital
on the tetrahedron below, indicating clearly which atomic orbitals are overlapping to produce
this MO.
3. Which allotrope of phosphorus can be understood in terms of two-dimensional sheets?
4. This question makes reference to the photoelectron spectrum of P4 shown below:
4
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12
11
10
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Ionization Energy (eV)
In this energy range, three bands are seen as marked A, B, and C (the splitting of bands
A and B into additional peaks is due to the lowering of the symmetry of the P4 molecule
upon ionization). All three of the bands in this energy range arise from MOs having mainly
phosphorus 3p atomic orbital character, as the MOs arising from phosphorus 3s atomic orbitals
are much lower in energy and not seen in this energy window. Which band in this spectrum
corresponds to ionization of the P4 HOMO?
5. Explain why band C has substantial vibrational fine structure, and determine which MO it
corresponds to.
5
3
Nitrogen Fixation
The following questions are worth 4 points each.
1. In the nitrogenase crystal structure the iron-molybdenum cofactor Fe7 MoS9 X cluster is bound
to the protein by two points of attachment. Sketch out the cluster structure and indicate (a)
to which atom a protein cysteine residue attaches, and (b) to which residue a protein histidine
residue binds.
2. What is known about the identity of the atom X at the center of the Fe7 MoS9 X cluster?
3. Shown below are two crystal planes for the packing in an iron single crystal. Which of these
two crystal planes gives greater activity (a greater reaction rate) for the dissociative adsorption
of N2 ?
( 1 1 1 )c Body centered cubic (bcc)
( 1 1 0 )c Body centered cubic (bcc)
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4. In no more than one short sentence, explain your answer to the foregoing question.
5. Sketch the HOMO of the N2 molecule and label the sketch with the symmetry (Mulliken
symbol) for this orbital.
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4
Oxygen
The following questions are worth 5 points each.
1. Molecular oxygen has a ground configuration bearing two electrons in a doubly degenerate
πg molecular orbital. Figuring out how many wave functions from this ground configuration
amounts to finding out how many different ways there are to put two electrons into the four
boxes shown here:
Now, show that there are six different wave functions by writing the letter e twice, six different
ways, in the set of boxes below:
2. The electronic states of O2 that arise from the ground configuration are summarized by their
1
1 +
term symbols: 3 Σ−
g , ∆g , and Σg , here written in order of increasing energy. For each of
these states, give the total (spin + orbital) degeneracy. Give also the sum of the degeneracies
of these three states.
3. Would it be correct to say that the active oxygen species responsible for killing cells in photodynamic therapy has its two highest-lying electrons paired up in a single πg molecular orbital?
Explain your answer briefly.
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4. Determine the symmetries (Mulliken symbols) for the three energetically lowest-lying valence
molecular orbitals of ozone, O3 . Show your work.
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5
Sulfur
The questions on this page are worth 5 points each.
1. Write down a balanced equation for the synthesis of S7 .
2. Draw the structure of the molecule of which commercially available elemental sulfur mainly
consists, and assign it to its proper point group.
3. On the drawing of S4 N4 below, draw two lines to indicate S· · ·S bonds of approximate order
0.3.
4.
• What is the point group of S4 N4 ?
• Is the enthalpy of formation of S4 N4 positive or is it negative?
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11
12
13
C v
Yes
6C5
Yes
Yes
Ih
No
I
Yes
Oh
No
O
i
No
No
3C4
Yes
i
No
3S4
Td
Yes
No
Yes
Th
No
T
i
Normal
symmetry
Yes
C2 Cn
Yes
Dnh
Yes
No
No
Yes
Yes
Dnd
No
Dn
Cnh
No
Yes
v
Cnv
No
S2n
Yes
S 2n
No
Cn
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High Symmetry
Elements
Sure? More than one
Cn axis of C3
or higher?
Normal Symmetry
Elements (most common)
C1
octahedral
No
Tetrahedral
Ci
Dihedral
Yes
Yes
i
Single Axis
Cs
Yes
icosahedral
Special Group
Elements
Yes
No
highly symmetric
(octahedral,
tetrahedral,
icosahedral)
No
i
single element
Linear or
low symmetry
D h
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linear
Yes
linear
Yes
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Structure