Question

What is the distance between Na+ and Cl- in a NaCl crystal if its density is 2.165 g cm^-3? NaCl crystallizes in fcc lattice.

Answer 1

M is the molecular mass of NaCl crystal. And N is the Avogadro's number of atoms.
Since there are 2N ions in one gram molecule,
The mass associated with each ion = M/2N
pd³ = M/2N
d = [M/2N x p]^1/3
Here M = 58.5 g = 58.5 X10^-3 kg
N = 6.023x10²³
p= 2.165 g/cm³ = 2.165x10^-3 kg.m^-3
d = [58.5 X10^-3/6.023x10²³ x 2.165x10^-3]^1/3
d = 2.814 x10^-10 m

Distance d = 281.4 pm