Question

The density of crystalline sodium chloride is $2.165gc{m}^{-3}$. What is the edge length of the unit cell. What would be the dimensions of cube containing one mole of $NaCl$?

Answer 1

We know that,
$\rho =\frac{N}{a^3}\left(\frac{M}{N_A}\right)$
where, $\rho =density=2.165gc{m}^{-3}$
$M=molarmass=58.5$
$N_A=Avogadr{o}^{\prime }snumber=6.023\times {10}^{23}$
$N=$ number of formula unit per unit cell
$=4$ (for fcc)
$a^3=\frac{N}{\rho }\left(\frac{M}{N_A}\right)=\frac{4}{2.165}\left[\frac{58.5}{6.023\times {10}^{23}}\right]$
$-1.794\times {10}^{-22}$
$a=5.64\times {10}^{-8}cm$
Molar volume $=\frac{molarmass}{Density}=\frac{58.5}{2.165}$
Edge length $\left(a\right)={\left[\frac{58.5}{2.165}\right]}^{1/3}=3cm$.