HW 4 Inorganic Materials
Chemistry
Name:
Points: C7780 Date due: Dec. 12, 2013
Max. 100 points Fall 2013 A
1. (50 pts) Use the ligand field theory to explain why Mn3O4 is a normal spinel while Fe3O4 is an
inverse spinel. Hint: draw diagrams of energy levels of d-electrons for ions in tetrahedral and
octahedral sites, use approximation ΔT = 4/9 ΔO, consider all MO4 and MO6 moieties as high
spin complexes, calculate ligand field stabilization energy in terms of ΔO for both normal and
inverse arrangement of ions, compare them and find which is more stable.
2. (50 pts) Although hexagonal wurzite (W) and cubic sphalerite (S, also called zincblende)
structures are often very close in energy and many compounds that exhibit one structure also
exhibit the other, the wurzite structure is often preferred by compounds having appropriate radius
ratios and high ionicities. For example, the wurzite structure is strongly preferred for ZnO. Could
the preference for the wurzite structure in such cases be merely due to the slightly higher value
of the wurzite Madelung constant (AW = 1.6413 vs. AS = 1.6381)? Please assume that wurzite
and sphalerite structures of ZnO are in equilibrium with one another at room temperature:
Equilibrium: ZnO (wurtzite) ZnO (sphalerite) Keq
Calculate the value of the equilibrium constant (Keq) assuming that ΔG0
= ΔL = LS  LW. Recall
that ΔG0
= RT ln Keq. Use ionic radii of 0.74 Å and 1.26 Å for Zn2+
and O2–
, respectively. What
is the ratio of moles of wurzite ZnO crystals to moles of sphalerite ZnO crystals at equilibrium?
NA = Avogadro constant, d = interionic distance, L = lattice enthalpy, n = Born exponent (use
value of 8).
Use Born–Lande equation for the lattice enthalpy L:
40 = 1.11 10-10
C2
J-1
m-1 






nd
eZZ
ANL BA
A
1
1
4 0
2
