The density of crystalline $\mathrm{NaCl}$ is $2.165 g\mathrm{m} {\mathrm{cm}}^{-3}$. What would be the volume of the cube containing one mole of $\mathrm{NaCl}$ ?

Mathematically, the relation between molar mass, molar volume and density is

$\text{ Molar volume }=\frac{\text{ Molar mass }}{\text{ Density }}$

We know that the molar mass of $NaCl$ is $58.5 \mathrm{gm} {\mathrm{mol}}^{-1}$ and molar volume is nothing but a cube of the edge length.

Substituting provided and known values in the equation and solving we get,

$a^3=\frac{58.5}{2.165}$

$a^3\simeq 27.0 {\mathrm{cm}}^3$

Hence, the volume of the cube containing one mole of $\mathrm{NaCl}$ is $27{ \mathrm{cm}}^3$.