Advanced Inorganic Chemistry

Final Exam

Name:  ________________________                                                                           May 2, 2008

Total:  152 points.

Spectrochemical series:  I- < Br- < S2- < SCN- < Cl- < NO2- < N3- < F- < OH- < C2O42- < H2O < NCS- < CH3CN < py < NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO

1.   (6 pts)  Fill in the blank in the following nuclear reaction, which have been used to synthesize lawrencium:

                   

2.   (18 pts)  Calculate the binding energy per nucleon of lithium-7, 7Li, in MeV.  The mass of Li-7 is 7.01600 u (u is atomic mass units).

particle

mass /u

 

neutron

1.008665

 

proton

1.007277

 

electron

0.000548

 

 

 

 

u ® kg

1.66 ´ 10-27

 kg/u

c

3.00 ´ 10+8

 m/s

J ® eV

1.60 ´ 10-19

 J/eV

The mass of 4 neutrons, 3 protons, and 3 electrons is 7.058135 u. 

The difference is 0.04213 u. 

Converting to kg gives 7.00 ´ 10-29 kJ. 

Using E = mc2 gives 6.26 ´ 10-12 J. 

Converting to MeV gives a binding energy of 39.25 Mev. 

And, dividing by 7 gives the binding energy per nucleon, -5.607 MeV.  (The negative sign isn’t necessary.)       -2 pts if not divide by 7

3.   (4 pts)  Sketch the dxy orbital.  Include the sign of the wavefunction (+ & –).

     - 2 pts if drew dx2 – y2

This page:  28 pts

 

4.   (2 pts)  Which orbitals are responsible for the lanthanide contraction?

The lanthanide contraction is caused by the filling of f-orbitals.

5.   (3 pts)  How many radial nodes does a 5f orbital have?  ____   1

6.   (8 pts)  a)  Draw the Lewis structure of SO3.  Include resonance structures.

(Other resonance forms are possible, which would have lower formal charges.)

 (2 pts)  b)  What is the name of the shape of SO3?                  Trigonal planar

Must be consistent with Lewis structure

S197.   (6 pts)  Construct a molecular orbital diagram for [He2]+. 

 

 

 

Here it is for He2.  He2+ would have one less electron:  2 bonding electrons and one antibonding electron.  The result would be a bond order of ½. 

 

 

 

 

 

8.   (3 pts)  What is the bond order of [He2]+, according to your diagram?  Show your calculation.

b. o. = ½(bonding – antibonding) = ½(2 – 1) = ½.

9.   (1 pts)  According to your MO diagram, is [He2]+ paramagnetic or diamagnetic?

Paramagnetic

This page:  25 pts

 

10. (9 pts)  To what point groups do the following belong?  (No flowchart is provided; you will have to try to do this one without it.)

a) CoCl4I23-

 

                   D4h 5 pts

- 3 pts for Oh

b) O=C=O

D∞h 4 pts

-2 pts for C∞v

11. a) (4 pts)  The NO2- ion, , has 2p orbitals on the oxygens that can overlap with orbitals on the nitrogen. From the two p orbitals on oxygen shown, sketch the ligand group orbitals that can be constructed from these two orbitals.

One is shown; the other looks like this: 

a)       (8 pts) Which symmetry types do these fragment orbitals belong to in C2v?  (The character table is provided below.)

C2v

E

C2

sv(xz)

sd(yz)

 

 

  A1

1

1

1

1

  z

  x2, y2, z2

  A2

1

1

-1

-1

  Rz

  xy

  B1

1

-1

1

-1

  x, Ry

  xz

  B2

1

-1

-1

1

  y, Rx

  yz

Symmetric:   1           1           1           -1    } this is symmetry type A1

Asymmetric: 1           -1          1           -1    } this is symmetry type B1

b)       (10 pts)       Which orbitals on the nitrogen have the same symmetry as your fragment orbitals?  Include any relevant d orbitals.

Symmetric ligand group orbital:  s, pz, and dz2 (and, dx2-y2) orbitals have this symmetry.

Asymmetric ligand group orbital:  px and dxy orbitals have this symmetry.

This page:  31 pts

 

12. (12 pts)      Use the following data to construct a Born-Haber cycle.  Show a graph of the cycle, and calculate the enthalpy change for the reaction Ba(s) + I2(s) ® BaI2(s).

Ba(s) à Ba(g)

DH°sublimation

147.12 kJ/mol

1st ionization energy of Ba

 

502.9 kJ/mol

2nd ionization energy of Ba

 

965.3 kJ/mol

I2(s) ® I2(g)

DH°sublimation

57.32 kJ/mol

I2(g) ® 2I(g)

DH°dissociation

151.088 kJ/mol

e– + I(g) ® I–(g)

DH°electron gain

-295.2 kJ/mol

BaI2(s) ® Ba2+(g) + 2I–(g)

DH°lattice

1694.3 kJ/mol

Here are my calculations, from a spreadsheet.

Ba(s) à Ba(g)

DH°sublimation

147.12

 

---

DH°dissociation

---

 

Ba(g) à Ba+2(g) + 2e–

DH°ionization

1468.16

 

I2(s) à I2(g)

DH°sublimation

57.32

 

I2(g) à 2I(g)

DH°dissociation

151.088

 

2e– + 2I(g) à 2I–(g)

DH°electron gain

-590.304

2 × EA = 2 × -295.152

Ba2+(g) + 2I–(g) à BaI2(s)

-DH°lattice

-1694.3

 

Ba(s) + I2(s) à BaI2(s)

DHformation

-460.9

kJ/mol

And here’s the graph of the data (a little fancier than necessary).   3 pts for graph

 

This page:  12 pts

 

13. (8 pts)  Describe the rock salt (NaCl)  lattice in terms of a closest packed array of one ion with the other ion in holes.

Either ion can be described as a cubic closest packed (or face-centered cubic) array, with the other ion in octahedral holes.

14. (6 pts)  Use the radius ratio and the data below to predict the crystal structure of MnS.

 

 

C.N.

Spin

Ionic Radii, pm

Mn2+

4

high

66

 

5

high

75

 

6

low

67

 

6

high

83

 

7

high

90

 

 

 

 

S2-

4

 

168(approximately)

 

6

 

184

 

Madelung Constant, A

 

 

 

radius ratio

 

A

C. N.

min

max

Sphalerite (ZnS)

1.638

(4, 4)

0.225

0.414

Rock Salt (NaCl)

1.748

(6, 6)

0.414

0.73

Cesium Chloride (CsCl)

1.763

(8, 8)

0.73

--

Let’s assume to start with that the ions both have a coordination number of 6 in the crystal.  The S2- radius would then be 184 pm.  For Mn2+,  the size also depends on the spin state of the Mn2+.  From the previous problem, this is a high-spin compound, so the Mn2+ radius would be 83 pm.  This gives a radius ratio of 83/184 = 0.451, which corresponds to the rock salt crystal structure.

The rock salt structure also fit the data.  (Grumble, grumble.)

15. (5 pts)  Using the data in the previous problem, calculate the lattice enthalpy of MnS.

Here are the formulas, from the first page:

; ; d* = 34.5 pm

z+ = +2; z– = -2.  d is the sum of radii, which is 83 + 184 = 267 pm.  The Madelung constant to use is 1.748.  Putting all these values into the equation gives V = -3167 kJ/mol

(or -3317 kJ/mol for sphalerite structure)

This page:  19 pts

16. The complex [MnS6]10- doesn’t exist in solution, but can be considered to be part of the crystal structure of MnS(s).  Determine the following: 

a)      (6 pts) What is the electron configuration of the metal(in the form t2gmegn)?

Because S2- is a weak field ligand, the configuration is t2g3eg2

 -2 for t2g5eg0

6 pts:  2 pts for d5, 2 pts for a strong field configuration, 2 for correct configuration

b)      (1 pt) Is this a high-spin or low-spin complex?

High-spin    1 pt:  must be consistent with part a).

c)      (5 pts) Calculate its ligand-field stabilization energy as a multiple of ΔO.

LFSE = 3 × 0.4 ΔO - 2 × 0.6 ΔO = 0 ΔO

(or, for low-spin case, 0.4 ΔO × 5 - 0.6 ΔO × 0 = 2.0 ΔO) Must be consistent with part a).

17. (8 pts)  The position of CO in the spectrochemical series is explained by ligand field theory in terms of π-bonding.  Sketch a molecular orbital diagram illustrating how π-bonding increases ΔO when CO is coordinated to an octahedral metal.

fig0723c

18. (3 pts)  Which isomer of triamminotrichlorocobalt(III) is shown below?

fac-triamminotrichlorocobalt(III)

This page:  23 pts

 

19. Sketch the d orbital splitting pattern of the following octahedral complexes; include the correct number of electrons in the diagrams.  Assume that water is a weak-field ligand.

a)      (4 pts)  [W(OH2)6]3+. 

 

       

 

 

b)       (3 pts) Would a Jahn-Teller distortion be expected in [W(OH2)6]3+?  Give a reason.

Compound is d3, which is not degenerate, so no Jahn-Teller distortion is expected.

c)      (4 pts)  [Ti(OH2)6]3+

 

       

 

 

d)      (3 pts)  Would a Jahn-Teller distortion be expected in [Ti(OH2)6]3+?  Give a reason.

Compound is d1, which is degenerate, so a Jahn-Teller distortion is expected.

This page:  14 pts