A substance forms f.c.c. crystal structure. Its density is $1.984 \mathrm{gm} {\mathrm{cm}}^{-3}$ and the length of the edge of the unit cell is $630 \mathrm{pm}$. Calculate the molar mass.

Mathematically, the formula of density can be represented using the equation:

$\mathrm{d}=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3}$

Rearranging the formula and substituting the given values we get:

$\mathrm{M}=\frac{\mathrm{d}\times {\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3}{\mathrm{Z}}$

$\mathrm{M}=\frac{1.984\times 6.023\times {10}^{23}\times {\left(630\times {10}^{-10}\right)}^3}{4}$

$\mathrm{M}\simeq 74.7 \text{amu}$