Download Problem Set IX Crystalline Solids

Chem 115 Problem set IX - 1
Problem Set IX
Crystalline Solids
1. The unit cell for nickel arsenide is shown below. What is the formula for this compound?
2. Titanium has an atomic radius of 142 pm and crystallizes with a body centred cubic unit cell. What is the
density of solid titanium?
3. Cesium chloride crystallises with Cs+ cation at the centre of the unit cell and a Cl- anion at each of the
corners (a bcc arrangement). The density of CsCl is 3.99 g/cm3. Calculate the distance radius of a Cs cation.
The radius of a chloride anion is 180 pm.
4. Below 1000°C Fe crystallizes in a body-centred cubic unit cell with an edge length of 0.28664 nm.
Determine the mass and volume of the unit cell and hence the density of Fe.
Above 1000°C Fe forms a face-centred cubic cell with an edge length of 0.363 nm. Determine the density of
Fe under these conditions.
5. A metallic solid with atoms in body centered cubic unit cell with an edge length of 328 pm has a density of
4.50g/cm3. Calculate the atomic mass and the atomic radius of the metal. 1 mole = 6.022 x 1022 entities.
6.
A solid contains the elements Ba, Cu, and O and the crystal structure shows the unit cell to be as
drawn below. What is the molecular formula of the solid?
7a) Given the densities for lithium fluoride (2.640 g.cm-3), sodium fluoride (2.780 g.cm-3), and potassium
fluoride (2.481g.cm-3), and assuming all three solids have a unit cell where fluoride is in a face centred cubic
arrangement with the metal cation in all the octahedral holes, calculate the distance between the nuclei of the
fluoride anion and the metal cation (when they are nearest neighbours).
Then compare your results with those calculated from the ionic radii given in the table below.
Ion
Radii (pm)
F−
136
Ionic Radii
Li+
68
Na+
97
K+
133
7b) Now assuming the fluoride is packed in a face centred cubic arrangement, calculate the radii of the
fluoride anion for each of the three solids from the unit cell edge length calculated above. Explain the
discrepancies between your calculated value and that given in the table above for fluoride.
7c) How does the radius ratios of these three solids calculated from the given ionic radii, compare with the
expected radius ratios given in the preamble to this problem set (Notes on Crystal structures)?
Chem 115 Problem set IX - 2
8. C60 is a molecule shaped like a soccer ball, and a newly discovered allotropic form of carbon. It has been
named Buckministerfullerene after the architect who designed the geodesic dome. The C60 molecules closepack into a face centred cubic crystal lattice with a cell edge of 1410.0 pm and a C60 molecule at each lattice
point.
a) What is the distance between the centres of nearest neighbour C60 molecules?
b) What is the density of the C60 crystal in g.cm-3 ?
c) Calculate the volume and percent of dead space (unoccupied space) in the unit cell.
9. Molybdenum, density 10.2 g/mL crystallizes with a body-centred cubic structure. If the atomic radius of
molybdenum is 136.2 pm, estimate the percentage of free space in the unit cell of molybdenum metal.