The Foundations of Chemistry

EXAMPLE 13-10 Density, Cell Volume, and Avogadro’s Number

Titanium crystallizes in a body-centered cubic unit cell with an edge length of 3.306 Å. The
density of titanium is 4.401 g/cm^3. Use these data to calculate Avogadro’s number.

Plan
We relate the density and the volume of the unit cell to find the total mass contained in one
unit cell. Knowing the number of atoms per unit cell, we can then find the mass of one atom.
Comparing this to the known atomic weight, which is the mass of one mole (Avogadro’s number)
of atoms, we can evaluate Avogadro’s number.

Solution

We first determine the volume of the unit cell.

Vcell(3.306 Å)^3 36.13 Å^3

We now convert Å^3 to cm^3.

_?_cm^3 36.13 Å^3 

3

3.613 10 ^23 cm^3

The mass of the unit cell is its volume times the observed density.

Mass of unit cell3.613 10 ^23 cm^3 1.590 10 ^22 g

The bcc unit cell contains 8(^18 )
1 2 Ti atoms, so this represents the mass of two Ti atoms.
The mass of a single Ti atom is

Mass of atom7.950 10 ^23 g/atom

From the known atomic weight of Ti (47.88), we know that the mass of one mole of Ti is
47.88 g/mol. Avogadro’s number represents the number of atoms per mole, and can be calcu-
lated as

NAv6.023^1023 atoms/mol

You should now work Exercise 96.

Ionic Solids

Most salts crystallize as ionic solids with ions occupying the unit cell. Sodium chloride (Figure
13-28) is an example. Many other salts crystallize in the sodium chloride (face-centered cubic)
arrangement. Examples are the halides of Li
, K
, and Rb
, and M^2
X^2 oxides and sulfides
such as MgO, CaO, CaS, and MnO. Two other common ionic structures are those of cesium
chloride, CsCl (simple cubic lattice), and zincblende, ZnS (face-centered cubic lattice), shown
in Figure 13-29. Salts that are isomorphous with the CsCl structure include CsBr, CsI, NH 4 Cl,
TlCl, TlBr, and TlI. The sulfides of Be^2
, Cd^2
, and Hg^2
, together with CuBr, CuI, AgI,
and ZnO, are isomorphous with the zincblende structure (Figure 13-29c).
The ions in an ionic solid can vibrate only about their fixed positions, so ionic solids are
poor electrical and thermal conductors. Liquid (molten) ionic compounds are excellent conduc-
tors, however, because their ions are freely mobile.

1 atom



7.950 10 ^23 g

47.88 g



mol

1.590 10 ^22 g



2 atoms

4.401 g



cm^3

10 ^8 cm



Å

13-16 Bonding in Solids 523

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 13.13, Solid Structures (2): Ionic

Solids.