1. Write the electron configurations for the following (use the rare gas notation for closed shells): a) Sc+; b) N3–; c) Zn2+; d) Cu+; e) Au3+; f) Gd3+; g) Ce3+.
2. Write the electron configurations for the following (use the rare gas notation for closed shells): a) Gd3+; b) Rh3+; c) Os3+; d) Tl3+; e) Bi3+.
3. Find the electron configuration for the following: Cr3+; Eu3+; S–; Ca+; Ni4+.
4. Find the electron configuration for the following species: S, S2–, W, W+, Ni2+, Ce3+, Os, Eu.
5. Determine the electron configurations for the following gas phase ions: Mn+, Sm3+, Pt2+, Pb2+, Pb4+.
6. Find all the Russell-Saunders terms for the f2 configuration. Energy order them. For the ground state, find all the J values and energy order these states.
7. Find all of the Russell-Saunders terms for the s1d1 electron configuration. Predict the energetic ordering of the different states.
8. Find all of the Russell-Saunders and J terms for the f1 electron configuration. Predict the energetic ordering of the different states.
9. Find all of the term symbols for the s1p1 electron configuration, including J values. Energy order these states.
10. Use Slater's rules to calculate Z* for Ru, Rh, Pd, Os, Ir, and Pt. What are the periodic trends? Compare the trends in the first ionization potential, the electron affinity, the metallic radius, the Pauling electronegativity, and the density for these six elements. Does Z*, as calculated by Slater's Rules, adequately explain the trends in each of these properties? Why or why not?
11. Plot electron affinity and Z* (calculated using Slater's rules) as a function of atomic number for the atoms from Li to Ne. In general, does Z* account for the variation in electron affinity? Why or why not? Are there any specific anomalies in the trend? If so, give an explanation.
12. Calculate Z* for the highest energy electron in the following ions: K+, Ca+, Sc+, Ti+, V+. Does Z* account for the observed values of the second ionization potential of these elements? Why or why not? Some have argued that Ca+ should be considered a transition metal. Give an argument to support this contention.
13. Calculate Z* according to Slater's rules for the first row transition elements, Sc to Zn. Compare these to the Clementi-Raimondi Z* values. Which values compare favorably and which values compare poorly? In those cases where the comparison is poor, suggest a reason.
14. Consider the melting point data for the natural forms of the second row elements. Calculate Z* using Slater's rules for the outermost electron for each of these elements. Does Z* give a reasonable accounting of the trend in the melting point? Why or why not? Should melting point be considered a periodic property of atoms? Why or why not?
Melting Point (°C)
Na 98 Mg 650 Al 660 Si 1414 P 44 S 115 Cl –101.5 Ar –189
15. For each of the following species write the lowest energy Lewis structure, indicate the formal charge and oxidation number of each atom, show the geometric structure and estimate the bond angles, indicate the σ hybridization about the central atom, and give the point group. a) XeO3, b) XeOF2, c) XeO64–, d) KrF2, e) SeF4.
16. Consider the following two compounds: CF2C(F)CN (having a C-C-C backbone) and CF2C(F)NC (having a C-C-N backbone). Write the lowest energy Lewis structures for each, give the formal charge and oxidation number for each atom, estimate the bond lengths for each bond and bond angles for each atom along the backbone, and indicate the likely hybridization at each atom along the backbone.
17. For the following chemical species, write the Lewis dot structure that minimizes formal charge, give the formal charge and oxidation number on each atom, show the structure including estimates of all bond angles accurate to ±2°, give the likely hybrid on the central atom, and give the point group: NH2Cl; SF3+; SOF4.
18. Write the Lewis dot structures for the following species, including all low energy resonance structures: SO2, TeCl4, BrCl3, HClO2. Give the formal charge and the oxidation number of each atom.
19. Find the Lewis Dot structures for the following species: a) ClO4–; b) S2O32–; c) CO; d) AlF3. In each case, write a Lewis stucture with minimum formal charge and one that obeys the octet rule, if possible. Find the formal charge and oxidation number for each atom for each Lewis structure.
20. Estimate the order of the boiling points for XeO3, XeOF2, KrF2, and SeF4. Explain your reasoning.
21. Find the point group for each of the following compounds: a) SO2; b) TeCl4; c) BrCl3; d) HClO2; e) PF5; f) PF3; g) XeF2; h) XeF4; i) CH2Cl2; j) trans-C2H2Cl2; k) cis-C2H2Cl2.
22. Find the point groups for the following molecules or ions: a) CCl4; b) CHCl3; c) CH2Cl2; d) PF6–; e) PF5; f) SF4.
23. The characters for the total representation of the C-H bonds in CH4 are given below. Find the irreducible representations for this total representation.
24. The total representation for some set of objects in the D6 point group is given below. Find the irreducible representations for this set of objects.
E 2C6 2C3 C2 3C2' 3C2"
6 –2 0 –2 0 0
25. Derive the irreducible representations for the s, p, and d orbitals for SF4. Show your work. Confirm that your answers match those given in the character table.
26. Label the following orbitals as bonding or antibonding, σ, π, or δ.
27. Find the irreducible representations for the σ bonds in NH3.
28. Construct a molecular orbital energy diagram for Cr2 using only the 3d orbitals as the basis set. Label each orbital as nb, σ, π, δ, σ*, π*, or δ*. Show that the bond order is equal to 4. How many unpaired spins are there? Sketch the shapes and phase relationships of each of the bonding orbitals; if there are degenerate orbitals, only sketch one orbital of that energy. Hint: although the 4s orbital in Cr is not used in the basis set, the electrons from the 4s orbitals are used in the MO diagram.
29. Find the irreducible representations of the C π orbitals in . Draw sketches of each of the orbitals and energy order them. Show the electron occupation of the orbitals.
30. Use group theoretical techniques to construct an MO energy diagram for the pi orbitals in pyridine. What is the pi bond order?
31. Sodium chloride is typically thought of as an ionic compound, but one can draw a molecular orbital diagram for NaCl, as well. Use the provided MO diagram and answer the following questions: a) label the orbitals as σ, σ*, π, π*, or nb; b) show the electron occupation in the molecular orbitals; c) sketch the highest energy orbital, showing both shape and phase; d) is this MO diagram consistent with NaCl being ionic? Why or why not?
32. Estimate the lattice energy for calcium fluoride using both the Born-Landé equation and a Born-Haber cycle. Compare the two results.
33. Read the paper: Gold Is Smaller than Silver. Crystal Structures of [Bis(trimesitylphosphine)gold(I)] and [Bis(trimesitylphosphine)silver(I)] Tetrafluoroborate by A. Bayler, A. Schier, G. A. Bowmaker, and H. Schmidbaur (J. Am. Chem. Soc., 1996, 118, 7006-7007). Explain how the authors determined the radii of Ag(I) and Au(I), why they had to go to some effort to accomplish this, and why they believe gold is smaller than silver. How do the radii proposed by the authors for Ag(I) and Au(I) compare to literature values?
34. Calculate the lattice energy for Al2O3. Estimate the Born exponent based on the electron configurations of the ions.
35. Find the experimental lattice energy of aluminum oxide using a Born-Haber cycle. In addition to data available in your textbook, the following thermodynamic values will be of use: the second electron affinity for oxygen is –779.6 kJ/mol, the sublimation energy for Al is 330.0 kJ/mol, and the heat of formation of aluminum oxide is –1675.7 kJ/mol. Compare the experimental value to the calculated value from problem 34.
36. Show that the zinc blende structure shown in Figure 5.6 matches the stoichiometry.
37. Magnesium has the filled s2 electron configuration yet is still a metal. Give an explanation for this in terms of a metallic bonding description.
38. Plot the densities of the second row transition metals (Y to Cd) as a function of Z. Explain the trend in terms of metallic bonding.
39. GaN is being considered for use as a semiconductor in certain applications. GaN is an intrinsic semiconductor. Draw Lewis dot structures for GaN and p-doped GaN (your choice of dopant).
40. Read the paper entitled Synthesis and Properties of Low-Bandgap Zwitterionic and Planar Conjugated Pyrrole-Derived Polymeric Sensors. Reversible Optical Absorption Maxima from the UV to the Near-IR by T. W. Brockmann and J. M. Tour (J. Am. Chem. Soc., 1995, 117, 4437-4447). Give an explanation about why polypyrrole is a semiconductor. Why does zwitterion formation have such an important effect on the semiconducting properties?