Question

In sodium chloride, the distance between the center of the sodium ion and the center of an adjacent chloride ion is 2.819Å (1Å = 10-10m). Calculate the density in g/cm3 of an ideal NaCl crystal from this information and the data from the model you collected.

Model Data:

4 Na+ Ions per unit cell

4 Cl- ions per unit cell

Simplest formula NaCl

Coordination # for Na+ is 6

Coordination # for Cl- is 12

Answer 1

p(rho) = (Z X M)/(a^3 X No)

where p(rho) is density of crystal in g/cm^3
Z = number of particles present per unit cell ,,for fcc it is = 4
M = mass of NaCl = 23 + 35.5 = 58.5 g/mole
No is Avogadro's number = 6.022 X 10^23
a = edge of unit cell..
as distance between Na+ and Cl- is given as 2.819Å = 281 pm
so edge length a will = 281 X 2 = 562 pm = 562 X 10^-12 metre or 562 X 10^-10 cm

putting the values...
p(rho) = (4 X 58.5)/ [ (562 X 10^-10)^3 X 6.022 X 10^23 ]
= 2.189 g/cm^3 ---------------------------answer