Calculate the edge length (in pm) of the unit cell of sodium chloride given density of $\mathrm{NaCl}$ is $2.17\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and molecular weight $58.5 \mathrm{x} {10}^{-3}$ $\mathrm{kg} {\mathrm{mol}}^{-1}$

$\begin{array}{l}\mathrm{NaCl} \mathrm{is} \mathrm{FCC}, \mathrm{so} \mathrm{Z}=4.\\ \mathrm{\rho }=2.17\times {10}^6\mathrm{g} {\mathrm{m}}^{-3}\\ \mathrm{M}=58.5\times {10}^{-3}\times {10}^3\mathrm{g}/\mathrm{mol}=58.5\mathrm{g}/\mathrm{mol}\\ {\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}{\mathrm{mol}}^{-1}\end{array}$

$$\begin{gathered} \begin{array}{l}\mathrm{\rho }=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3} \\ {\mathrm{a}}^3=\frac{58.5\times 4}{6.023\times {10}^{23}\times 2.17\times {10}^6}\\ {\mathrm{a}}^3=1.79\times {10}^{-28} {\mathrm{m}}^3\\ \mathrm{a}=5.64\times {10}^{-10} \mathrm{m}=564 \mathrm{pm}\end{array} \end{gathered}$$