5.03 In-Class Exam 2

Transcription

1 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

2 1 Boron and Polyhedral Boranes The following questions are worth 4 points each. 1. How many skeletal bonding electrons are present for [B 6 H 6 ] 2? 2. The skeletal bonding electrons in [B 6 H 6 ] 2 break down according to a 1 + t 2u + t 2g. Of these, the t 2g set is of the pure tangential variety. On the set of line drawings below, sketch out the t 2g 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 [B 6 H 6 ] 2? 2

3 4. Sketch a line drawing of the nido structure that corresponds to [B 6 H 6 ] 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

4 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 P 4 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 P 4 shown below: 4

5 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 P 4 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 P 4 HOMO? 5. Explain why band C has substantial vibrational fine structure, and determine which MO it corresponds to. 5

6 3 Nitrogen Fixation The following questions are worth 4 points each. 1. In the nitrogenase crystal structure the iron-molybdenum cofactor Fe 7 MoS 9 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 Fe 7 MoS 9 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 N 2? ( )c Body centered cubic (bcc) ( )c Body centered cubic (bcc) 6

7 4. In no more than one short sentence, explain your answer to the foregoing question. 5. Sketch the HOMO of the N 2 molecule and label the sketch with the symmetry (Mulliken symbol) for this orbital. 7

8 4 Oxygen The following questions are worth 5 points each. 1. Molecular oxygen has a ground configuration bearing two electrons in a doubly degenerate π g 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: w, 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 O 2 that arise from the ground configuration are summarized by their term symbols: 3 Σ g, 1 g, and 1 Σ + g, 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 π g molecular orbital? Explain your answer briefly. 8

9 4. Determine the symmetries (Mulliken symbols) for the three energetically lowest-lying valence molecular orbitals of ozone, O 3. Show your work. 9

10 5 Sulfur The questions on this page are worth 5 points each. 1. Write down a balanced equation for the synthesis of S 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 S 4 N 4 below, draw two lines to indicate S S bonds of approximate order What is the point group of S 4 N 4? Is the enthalpy of formation of S 4 N 4 positive or is it negative? 10

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12 E g T 1g (R x, R y, R z ) T 2g A 1u A 2u E u T 1u (x, y, z) T 2u Character table for D h point group E 2C... σ v i 2S... C' 2 linear functio rotations A 1g =Σ + g A 2g =Σ - g R z E 1g =Π g 2 2cos(φ) cos(φ)... 0 (R x, R y ) E 2g =Δ g 2 2cos(2φ) cos(2φ)... 0 E 3g =Φ g 2 2cos(3φ) cos(3φ) A 1u =Σ + u z A 2u =Σ - u E 1u =Π u 2 2cos(φ) cos(φ)... 0 (x, y) E 2u =Δ u 2 2cos(2φ) cos(2φ)... 0 E 3u =Φ u 2 2cos(3φ) cos(3φ)

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14 Structure Linear or low symmetry linear i i D h 8 C v 8 Cs Ci C1 single element linear Special Group Elements highly symmetric (octahedral, tetrahedral, icosahedral) Sure? More than one Cn axis of C3 or higher? 6C 5 3C 4 3S 4 i i i Ih I Oh O T d Th T icosahedral octahedral Tetrahedral High Symmetry Elements rmal symmetry C C 2 n v S 2n D nh D nd D n C nh C nv S 2n C n Dihedral S i n g l e A x i s rmal Symmetry Elements (most common) 14