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 pageas it will be used for scoring. This exam is closed-book and no calculators or electronic devicesmay be employed. There are five sections so please read over the exam before you begin and expectto take on average ten minutes per section. Read all questions carefully before writing down anyanswers. Enjoy the material!

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1 Boron and Polyhedral Boranes

The following questions are worth 4 points each.

1. How many skeletal bonding electrons are present for [B6H6]2−?

2. The skeletal bonding electrons in [B6H6]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 thet2g 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 [B6H6]2−?

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4. Sketch a line drawing of the nido structure that corresponds to [B6H6]2−? Use small circlesto clearly indicate the position of all hydrogens.

5. What is the structural motif that is found in crystalline elemental boron?

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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 singlefilled π molecular orbital (N = 0 for the π system). Sketch out the appearance of this orbitalon the tetrahedron below, indicating clearly which atomic orbitals are overlapping to producethis 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:

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13 12 11 10 9

Ionization Energy (eV)

In this energy range, three bands are seen as marked A, B, and C (the splitting of bandsA and B into additional peaks is due to the lowering of the symmetry of the P4 moleculeupon ionization). All three of the bands in this energy range arise from MOs having mainlyphosphorus 3p atomic orbital character, as the MOs arising from phosphorus 3s atomic orbitalsare much lower in energy and not seen in this energy window. Which band in this spectrumcorresponds to ionization of the P4 HOMO?

5. Explain why band C has substantial vibrational fine structure, and determine which MO itcorresponds to.

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3 Nitrogen Fixation

The following questions are worth 4 points each.

1. In the nitrogenase crystal structure the iron-molybdenum cofactor Fe7MoS9X cluster is boundto 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 histidineresidue binds.

2. What is known about the identity of the atom X at the center of the Fe7MoS9X cluster?

3. Shown below are two crystal planes for the packing in an iron single crystal. Which of thesetwo crystal planes gives greater activity (a greater reaction rate) for the dissociative adsorptionof N2?

( 1 1 0 )c Body centered cubic (bcc) ( 1 1 1 )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 (Mullikensymbol) 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 degenerateπg molecular orbital. Figuring out how many wave functions from this ground configurationamounts to finding out how many different ways there are to put two electrons into the fourboxes shown here:

Now, show that there are six different wave functions by writing the letter e twice, six differentways, in the set of boxes below:

2. The electronic states of O2 that arise from the ground configuration are summarized by theirterm symbols: 3Σ−g , 1∆g, and 1Σ+

g , here written in order of increasing energy. For each ofthese states, give the total (spin + orbital) degeneracy. Give also the sum of the degeneraciesof these three states.

3. Would it be correct to say that the active oxygen species responsible for killing cells in photo-dynamic 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 valencemolecular 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 mainlyconsists, and assign it to its proper point group.

3. On the drawing of S4N4 below, draw two lines to indicate S· · ·S bonds of approximate order0.3.

4. • What is the point group of S4N4?

• Is the enthalpy of formation of S4N4 positive or is it negative?

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Structure

Linear orlow symmetry

highly symmetric(octahedral,tetrahedral,icosahedral)

Normalsymmetry

Sure? More than oneCn axis of C3

or higher?

linear i

i

D

C

C

C

C

8h

8v

s

i

1

6C5

3C4

3S4

i

I

I

h

i

O

O

h

i

T

T

h

Td

C C2 nDnh

Dnd

Dn

S

v

2n

Cnh

Cnv

S2n

Cn

Yes

Yes

Yes

Yes

Yes

YesYes Yes

Yes

YesYes

Yes

Yes

Yes Yes Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No

No

No

No

NoNo

No

No

Spe

cial

G

roup

Ele

men

ts

Hig

h S

ymm

etry

Ele

men

ts

Nor

mal

Sym

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(m

ost

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linea

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ngle

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icos

ahed

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octa

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S i

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s

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