Callister - An introduction - 8th edition

12.2 Crystal Structures • 463
EXAMPLE PROBLEM 12.3
Theoretical Density Calculation for Sodium Chloride
On the basis of crystal structure, compute the theoretical density for sodium
chloride. How does this compare with its measured density?
Solution
The theoretical density may be determined using Equation 12.1 where n, the
number of NaCl units per unit cell, is 4 because both sodium and chloride ions
form FCC lattices. Furthermore,
2(r Na + + r Cl –)
A C A Na 22.99 g/mol
A A A Cl 35.45 g/mol
Because the unit cell is cubic, V C a 3 , a being the unit cell edge length. For
the face of the cubic unit cell shown in the accompanying figure,
a 2r Na
2r Cl
r Na
and r Cl
being the sodium and chlorine ionic radii, given in Table 12.3 as
0.102 and 0.181 nm, respectively.
r Cl –
r Na +
a
Na + Cl –
Thus,
And, finally,
r n¿1A Na A Cl 2
12r Na
2r Cl
2 3 N A
4122.99 35.452
3210.102 10 7 2 210.181 10 7 24 3 16.022 10 23 2
2.14 g/cm 3
V C a 3 12r Na
2r Cl
2 3
This result compares very favorably with the experimental value of 2.16 g/cm 3 .