12-15
12.13 We are asked to calculate the theoretical density of NiO. This density may be computed using
Equation (12.1) as
ρ =
(
n' ANi + AO
)
VC N A
Since the crystal structure is rock salt, n' = 4 formula units per unit cell. Using the ionic radii for Ni2+ and O2- from
Table 12.3, the unit cell volume is computed as follows:
⎛
⎞3
VC = a 3 = ⎜2r 2+ + 2r 2- ⎟ = [2 (0.069 nm) + 2 (0.140 nm)]3
⎝ Ni
O ⎠
= 0.0730
cm 3
nm3
= 7.30 x 10-23
unit cell
unit cell
Thus,
ρ =
(4 formula units/unit cell)(58.69 g/mol + 16.00 g/mol)
7.30 x 10-23 cm3/unit cell 6.023 x 1023 formula units/mol
(
)(
)
= 6.79 g/cm3
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